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Bob Glenn
08-27-2018, 11:07 AM
When was the last time you used algebra? I got C's and D's in algebra but aced geometry which I use all the time while wood working. The grandson has a five year degree from Purdue in food science and had to take endless algebra, trig, and calculus classes. He holds several patents. I asked him when was the last time he used algebra. He just gave me a blank look. Told me he had several thousand dollars wrapped up in books and classes in those subjects.

So, we mostly did away with shop class and home economics and now a lot of people can't change a light bulb or car tire, but we still retain algebra classes in high school. Maybe it just one of those hoops you have to jump through to qualify for the next higher level.

Stephen Tashiro
08-27-2018, 12:14 PM
I got C's and D's in algebra but aced geometry which I use all the time while wood working.

Debates about "Is ...such and such...useful" involve the question of whether so-and-so knows ways to use them. We tend to use things we are good at using. You could also ask the general population "When was the last time you had to use a table saw?".



When was the last time you used algebra?

It was the last time I had to figure out something involving geometry - because I don't figure out geometric things by making scale drawings. I draw sketches and use algebra and trigonmetry to figure out the unknowns.

Dave Anderson NH
08-27-2018, 12:28 PM
I use algebraic formulae every single day at work. It makes life simpler. Now the 4 semesters of calculus and one of differential equations are a different story. I haven't used those since I graduated engineering school.

glenn bradley
08-27-2018, 12:29 PM
Many of us use algebra without even realizing it. Any time you work out something like "I wonder how tall a bookshelf needs to be to hold three shelves of 12" tall books." you are using algebra. Fundamentally the arm of mathematics that uses symbols for values and the methods of using those symbols. You know you need 3 shelves and that each shelf must hold a 12" tall book; "how tall" is the symbol you are solving for. I too was a solid D student in algebra but, graduated early and was well into college before my classmates donned their gowns. Obviously algebra didn't help me with that. I would have gladly swapped it for shop class :D

Jim Koepke
08-27-2018, 12:34 PM
For me the question might be how many times has my puttering in the shop made me wish trigonometry and calculus had been part of my high school classes.

Though my math skills are decent it often occurs that if they were pushed a little harder in my youth it would have come in handy at times.

Just last week planning a project had me pulling out my trig tables and later a slide rule just for the heck of it. My plan is to make a purpose, specific shooting board for making what is called a 'stripped' deck of cards. The deck has a taper of ~0.005". This facilitates numerous card tricks. The last set of mine, made with a rigged up holder for shooting, was given to one of my grandsons.

jtk

Mike Cutler
08-27-2018, 12:38 PM
Most days at work I use it. Whether to decay the effective source strengths of radioisotopes, determine radiation detector linearity and efficiency, or compensate for reactor fuel burn. My case is somewhat unique

Last time I used differential calculus was to determine the erosion penalty for earthen dams in CT.

Glen is correct though, you're using algebra everyday, you just don't realize it.

William Adams
08-27-2018, 12:41 PM
Algebra teaches one that there are efficient and elegant tools and approaches for solving problems --- understanding that, and better, being able to act on that knowledge is a big part of making one's life better.

Chuck Wintle
08-27-2018, 12:47 PM
When was the last time you used algebra? I got C's and D's in algebra but aced geometry which I use all the time while wood working. The grandson has a five year degree from Purdue in food science and had to take endless algebra, trig, and calculus classes. He holds several patents. I asked him when was the last time he used algebra. He just gave me a blank look. Told me he had several thousand dollars wrapped up in books and classes in those subjects.

So, we mostly did away with shop class and home economics and now a lot of people can't change a light bulb or car tire, but we still retain algebra classes in high school. Maybe it just one of those hoops you have to jump through to qualify for the next higher level.
It is good for those who wish to have a useful tool to solve problems. Its just a question of practice practice to become at ease with it. And it help to exercise the mind in a direction it is not accustomed. :D

Dan Friedrichs
08-27-2018, 1:00 PM
I use algebra (and calculus, and differential equations) on a daily basis.

Asking 5th graders if they anticipate needing to know algebra for their future career plans seems foolish. Better that some have skills they don't use, than to have some lack skills they need.

John K Jordan
08-27-2018, 1:12 PM
The grandson has a five year degree from Purdue in food science and had to take endless algebra, trig, and calculus classes. He holds several patents. I asked him when was the last time he used algebra. He just gave me a blank look.

At first I thought this was a joke!

I use algebra and trig often now, 12 years after I retired. When working I used those and other math constantly, both when designing and developing software and when creating technical graphics. (Yes, I aced the math and science courses and hold several patents too.) There is no WAY could I have worked effectively in the careers I made for myself without the math. (Try writing machine vision and control software without the math or even function in an optics lab.)

I understand a huge percentage of our adult population couldn't derive, solve, or even formulate the problem to be solved (many can't even use ratios to solve everyday problems) but that doesn't mean it shouldn't be taught to everyone. What jr-high/high-school student knows exactly what they will do with their lives and what math understanding they will need?

The death of shop and even art and music education in public schools is a terrible shame, but dropping math would be even more short-sighted and only contribute to our downward spiraling of the quality of education in the US. We, on the average, are already close to illiterate in mathematics and science compared to many in the world. It's especially sad when the ignorant in high places have a part in making the decisions on education.

If it is a vote I vote to keep the algebra, trig, linear algebra, statistics, and calculus in high school.

JKJ

Tom Stenzel
08-27-2018, 1:20 PM
When I worked I used algebra on an almost daily basis. Plus the days I didn't use it were probably the days I helped the apprentices with their algebra homework.

When Dennis Archer became Mayor of Detroit he was appalled by the communication, writing and math skills of the supervisors and management staff. He instituted both English and math sections to the tests for promotion. Want a promotion? Better know your diction and math. With algebra. Several times after a round of testing there wouldn't be anyone that passed and the position would remain empty.

I remember when I would turn in my daily paperwork a supervisor would catch me so I could type a memo for them. My 45 WPM seemed blistering fast to them(!). Plus I had to turn the intentions into readable sentences. On overtime!

-Tom

Steve Peterson
08-27-2018, 1:50 PM
Algebra is the foundation for geometry and trigonometry. I use it all the time, mostly while solving geometry calculations and occasionally trigonometry.

Steve Peterson
08-27-2018, 1:53 PM
Asking 5th graders if they anticipate needing to know algebra for their future career plans seems foolish. Better that some have skills they don't use, than to have some lack skills they need.

Good point.

Jim Becker
08-27-2018, 2:01 PM
Algebra is basic math and the precursor to other things. While it's true that very few folks use these skills manually today, that doesn't take away the value of understanding them which in turn helps folks to understand how they apply. That said, what's really lacking in many educational programs that's "math related" is practical applications like budgeting, simple accounting such as what's needed to balance a checking account, etc. These are necessary "life skills" and are best taught early, right along side of things like how to cook, clean and maintain a home...

Ken Fitzgerald
08-27-2018, 2:21 PM
Before I retired, I used algebra and other high level forms of math daily. I actually worked with some image reconstruction circuitry which performed algebraic equations and based on the incorrect answer the circuitry gave to the diagnostic software which allowed you to enter your own variables, you could troubleshoot the circuitry to the failing integrated circuit in the days when we troubleshot to the IC level and replaced same as they were socketed.

Kev Williams
08-27-2018, 2:24 PM
I hated algebra in high school, so if I'm using it now, I don't know it ;) But any faith I had in algebra was shattered one day many years ago while watching a local college professor on public TV running thru a series of equations on a whiteboard, and when he was done, he stood back and said "... so the answer is zero..." then paused, looked at the board a sec, then said ".. or minus two"...

I swear, that's what he said. That doesn't work for me...

Dan Friedrichs
08-27-2018, 2:30 PM
That said, what's really lacking in many educational programs that's "math related" is practical applications like budgeting, simple accounting such as what's needed to balance a checking account, etc. These are necessary "life skills" and are best taught early, right along side of things like how to cook, clean and maintain a home...

A budgeting example of using algebra, though: What percentage of my salary should be put in a pre-tax retirement account to result in saving $5k/yr if my employer contributes a base $500/yr plus a 50% match up to 6%?

Tom M King
08-27-2018, 2:43 PM
The biggest hurdle for education to get over is getting the uneducated to understand real value in education. Algebra is just one step on the way. Even if one is not going to directly use algebra for whatever they end up doing, the more different things that are mastered along the way, the easier the next step is, regardless of what it is.

Personally, I use Geometry almost every day, and that doesn't work without algebra. I can't imagine stopping Math education pre-algebra.

Mike Cutler
08-27-2018, 3:34 PM
I hated algebra in high school, so if I'm using it now, I don't know it ;) But any faith I had in algebra was shattered one day many years ago while watching a local college professor on public TV running thru a series of equations on a whiteboard, and when he was done, he stood back and said "... so the answer is zero..." then paused, looked at the board a sec, then said ".. or minus two"...

I swear, that's what he said. That doesn't work for me...

I love it. That's funny!:p

About 20 years ago I was in a digital electronics course for an automated machine loading sequencer. The instructor started off the course by stating. "Any 1 into a NANd gate is effectively a 1 out". Two weeks later when the machine didn't start, on paper, we had to point out that two 1's into a NANd gate was a 0 out. :eek: I rode him about that until he retired.

Mike Cutler
08-27-2018, 3:41 PM
The biggest hurdle for education to get over is getting the uneducated to understand real value in education. Algebra is just one step on the way. Even if one is not going to directly use algebra for whatever they end up doing, the more different things that are mastered along the way, the easier the next step is, regardless of what it is.

Personally, I use Geometry almost every day, and that doesn't work without algebra. I can't imagine stopping Math education pre-algebra.

Maybe their trying to figure out to make "Common Core" work with an algebra equation. I'm not seeing it happen.

John M Wilson
08-27-2018, 4:40 PM
Algebra teaches one that there are efficient and elegant tools and approaches for solving problems.

This gets to the heart of the matter: is your education about "training" (mastering specific skills that you can employ in your daily life) or "learning" (figuring out basic principles that can be applied in many, often unsuspected or unrelated ways)?

Long story: The college where I earned my undergraduate degree in Mechanical Engineering was 100% co-op. We went to school for half a semester, then went to work alongside engineers for half a semester. This cycle repeated for the entire 5 year program.

When I was a junior, I had a couple of years of working with engineers, and often asked them "When was the last time you used multivariate calculus?" and got the expected responses. This did not help my motivation in class, and my grades were terrible. One day the professor noticed the look of absolute disinterest on my face, and called me out in front of the whole class. He wanted to know why I wasn't doing my homework, wasn't paying attention, and appeared to be doing the bare minimum. Feeling bold, I told him of my investigations into the worthlessness of multivariate calculus to my future job, and its complete lack of practical application. He replied, quite forcefully, "Mr. Wilson... I am not trying to teach you your JOB, I am trying to teach you HOW TO THINK!"

This stuck with me. When I retired after 33 years of doing MY JOB, I got a masters in teaching, and began to teach High School science (mostly Physics). I stressed to my students early and often that most of them would not be expected to regurgitate Newton's Laws ever again, but that applying his principles to everyday life (like the proper way to smack a ketchup bottle to release the ketchup) would be very handy. I told them the ability to apply critical thinking to things as diverse as Multi-Level Marketing claims, Facebook "facts", or political promises was just icing on the cake.

TLDR: it's not about memorizing and later recalling arcane facts, it's about exposing your mind to logical problem solving and learning thinking skills that can be applied in a multitude of ways.

Rod Sheridan
08-27-2018, 5:00 PM
Daily...............Regards, Rod.

Mike Kreinhop
08-27-2018, 5:25 PM
I hated algebra in high school, so if I'm using it now, I don't know it ;) But any faith I had in algebra was shattered one day many years ago while watching a local college professor on public TV running thru a series of equations on a whiteboard, and when he was done, he stood back and said "... so the answer is zero..." then paused, looked at the board a sec, then said ".. or minus two"...

I swear, that's what he said. That doesn't work for me...

Depending on the lesson being taught and the equations on the board, those answers are perfectly fine if the resulting equations reduced down to the quadratic equation x^2 +2x = 0. The two solutions for x in this case are zero and -2.

Julie Moriarty
08-27-2018, 5:29 PM
If you take away algebra and calculus, my GPA won't look so hot.

Chris Padilla
08-27-2018, 5:38 PM
Simple answer: It is fundamental like reading and writing.

John Stankus
08-27-2018, 5:42 PM
When was the last time you used algebra? I got C's and D's in algebra but aced geometry which I use all the time while wood working. The grandson has a five year degree from Purdue in food science and had to take endless algebra, trig, and calculus classes. He holds several patents. I asked him when was the last time he used algebra. He just gave me a blank look. Told me he had several thousand dollars wrapped up in books and classes in those subjects.

So, we mostly did away with shop class and home economics and now a lot of people can't change a light bulb or car tire, but we still retain algebra classes in high school. Maybe it just one of those hoops you have to jump through to qualify for the next higher level.

I have debated how to respond, but I use algebra and calculus all the time, but I am a chemistry professor now. Actually, I apply more calculus than my friends up in the math department use.
In my prior life in the technology industries (semiconductor and telecom) I used algebra and calculus as part of my job very frequently. (I have 11 patent by the way).

Honestly, if you want students to get algebra, geometry and calculus better, schools should bring back shop classes (and music). Studies have shown a connection in learning these abstract concepts with the hands on application.

John

Jim Koepke
08-27-2018, 6:13 PM
many can't even use ratios to solve everyday problems

If people were asked which is larger, 3/4 or 75% we might be amazed at the number of people who didn't know or couldn't figure it out.

jtk

Roy Petersen
08-27-2018, 6:31 PM
...giving up on this place...

Edwin Santos
08-27-2018, 8:31 PM
This gets to the heart of the matter: is your education about "training" (mastering specific skills that you can employ in your daily life) or "learning" (figuring out basic principles that can be applied in many, often unsuspected or unrelated ways)?

Long story: The college where I earned my undergraduate degree in Mechanical Engineering was 100% co-op. We went to school for half a semester, then went to work alongside engineers for half a semester. This cycle repeated for the entire 5 year program.

When I was a junior, I had a couple of years of working with engineers, and often asked them "When was the last time you used multivariate calculus?" and got the expected responses. This did not help my motivation in class, and my grades were terrible. One day the professor noticed the look of absolute disinterest on my face, and called me out in front of the whole class. He wanted to know why I wasn't doing my homework, wasn't paying attention, and appeared to be doing the bare minimum. Feeling bold, I told him of my investigations into the worthlessness of multivariate calculus to my future job, and its complete lack of practical application. He replied, quite forcefully, "Mr. Wilson... I am not trying to teach you your JOB, I am trying to teach you HOW TO THINK!"

This stuck with me. When I retired after 33 years of doing MY JOB, I got a masters in teaching, and began to teach High School science (mostly Physics). I stressed to my students early and often that most of them would not be expected to regurgitate Newton's Laws ever again, but that applying his principles to everyday life (like the proper way to smack a ketchup bottle to release the ketchup) would be very handy. I told them the ability to apply critical thinking to things as diverse as Multi-Level Marketing claims, Facebook "facts", or political promises was just icing on the cake.

TLDR: it's not about memorizing and later recalling arcane facts, it's about exposing your mind to logical problem solving and learning thinking skills that can be applied in a multitude of ways.

John,
Good story, thanks for sharing it and for drawing the distinction between literal equations and daily application of the underlying concepts. I'm sure the original question was rhetorical.
Could you imagine if the post was titled "Why are we still teaching problem solving"?
Edwin

Edwin Santos
08-27-2018, 8:34 PM
I hated algebra in high school, so if I'm using it now, I don't know it ;) But any faith I had in algebra was shattered one day many years ago while watching a local college professor on public TV running thru a series of equations on a whiteboard, and when he was done, he stood back and said "... so the answer is zero..." then paused, looked at the board a sec, then said ".. or minus two"...

I swear, that's what he said. That doesn't work for me...


I love it. That's funny!:p




Depending on the lesson being taught and the equations on the board, those answers are perfectly fine if the resulting equations reduced down to the quadratic equation x^2 +2x = 0. The two solutions for x in this case are zero and -2.

Thanks to Mike K. the story just became way funnier. Edwin

Ronald Blue
08-27-2018, 8:37 PM
One thing I learned later in life is the teacher can be the difference between having a firm grasp of algebra or whatever math segment you choose and struggling with it. That of course applies to virtually every subject. Only after I took some math classes at the local community college did I learn how pathetic my high school math teacher was. Just because they've held the position for years doesn't mean they are good at teaching it. As for whether it should still be taught my answer is a definite yes.

Bill McNiel
08-27-2018, 8:51 PM
This question unfortunately provides one of the answers to the riddle of how did education in the USA sink to such an international low. We have fostered the concept of "it is hard to understand so I will declare it worthless", instead of attacking a challenge we chose to demean it.

My response is not directed at the OP or any other poster, I am just dismayed at the national disregard for a well rounded education and the future it holds

BTW - the answer to the OP's question is, IMHO, because algebra is an essential problem solving tool.

Bruce Wrenn
08-27-2018, 9:47 PM
Use algebra everyday. But can't remember the last time anyone asked me about Shakespear. I think it was my senior year in high school (1966.)

julian abram
08-27-2018, 9:53 PM
Remember sitting in algebra classes thinking this is a waste of time, will never use it. Years later I used the old Pythagorean Theorem a2+b2=c2 many times to layout square house foundations. This was before laser transits.

Bill Dufour
08-27-2018, 10:16 PM
What bothers me is that my district has no math below algebra. They have no classes that teach how to run a budget or fill out a check. They do interest rate stuff but that is it. Students who do not pass algebra are doomed to repeat it until they do or age out.
My uncle, the rocket scientist, said he never used more then algebra other then one time. They had to run a round fuel pipe through a round fuel tank at an angle. What shape to cut the hole. There is math for that. I am sure now a CAD program will solve it for you.
He explained you wanted the hole as close to needed size as possible so there was as little extra weight of weld bead as possible. Both for weight saving and overall balance.
Bill D

andrew whicker
08-27-2018, 10:42 PM
Math should probably be taught along side the thing you are interested in. It will be more interesting that way. In engineering school we took math classes and engineering classes. Math classes tended to be very boring. You took them because they were a pre-requisite for other engineering classes. When you took the engineering class you would have an ah ha moment (especially with regard to diff eq and calculus). But by that time, you couldn't go backwards and re pay attention to the math class. It's a shame.

Math is a tool and you need it to do anything cool. Building furniture uses math. Figuring out how things work requires math. Machining requires math. Everything cool in the design / engineering / building world requires math.

Music uses math, painting can use math, architecture uses math.

Rick McQuay
08-28-2018, 2:46 AM
I worked in retail management for 12 years and used algebra a lot more than you would think. Comes in pretty handy.

Rick Potter
08-28-2018, 3:18 AM
I had to laugh when reading the title of this thread.

Sitting right in front of me is my soda in a can cozy that states: "Yet another day has passed without me using algebra once".

It is a replacement for one I had that disappeared, which said: "If a man says he will do something, he will. No need to remind him every 6 months". I think my wife made it go away.:rolleyes:

John K Jordan
08-28-2018, 7:48 AM
Math should probably be taught along side the thing you are interested in. It will be more interesting that way. ...

I agree. However, there is something to be said for teaching a broad and perhaps somewhat simplified math spectrum when younger. (Same with physics, etc.) Even if not completely understood, this way the basic concepts are not new when buckling down in college. For example, calculus was the only math course I took in high school which didn't "click" with me entirely, although I learned the why and how. But when I got to college, calculus it was so easy - everything made sense. Without the background in high school, who knows, I might have struggled.

JKJ

roger wiegand
08-28-2018, 9:20 AM
How can you get through a day without using algebra? ie, i have a board 8 ft long and I need a one 49" and one 18", can I get them out of my 8 ft board? Answering that question by calculation is algebra, whether you like it or recognize it or not. Yes you could use a story stick and get a geometric solution, but I'll bet most of you take the calculated (algebraic) approach when staring at your wood pile. I use algebra 100 times a day, whether it is calculating angles, figuring how long a piece needs to be, or deciding if I will have enough money left in my pocket for a hot dog if I buy a beer.

Just think of the endless discussions on this site of how big a pipe or wire one needs to serve multiple air tools or power tools. The answer is almost always simple algebra. Algebra is basically the study of equations, so whenever you say x=y you are asserting a hypothesis that is subject to proof, so 2+2 =x represents a very simple, yet useful, algebraic equation, 2+x=4 a slightly more interesting one. Ability to use a symbol for a number (x in this case) opens up a whole world of possibilities for doing calculation as well as describing general solutions to frequently encountered problems, like area=pi*radius squared for a circle. Isn't it nice to have algebra so that you can either know the radius and find the area or know the area you want and calculate the radius?

Matt Day
08-28-2018, 9:41 AM
I highly doubt your grandson is taking algebra in college. I took calc 3 & 4 and differential equations in engineering school, and given that Purdue is an engineering school, that’s probably more along the lines of what he’s taking.

I bet he has thousands of dollars wrapped up in books, but math, physics, fluid dynamics, etc.

Prashun Patel
08-28-2018, 9:56 AM
Algebra is the basis for computer science. If you want to write a computer program, you need algebra.

If you ever had to figure out the length of a table apron given leg thickness and overhang, you used algebra.

Robert Hazelwood
08-28-2018, 11:44 AM
I conceive of algebra as the underlying language of mathematics, without which math would be fairly useless except for party tricks like being able to recite your multiplication tables. To actually get any work done with math, you need to define relationships between things until you can solve for an unknown- algebra is simply the formal method for doing this. But a lot of people seem to view algebra as some arcane pursuit, of interest only to eggheads, without realizing that they almost certainly use algebraic concepts on a regular basis.

I think this is because algebra is taught mostly from a purely theoretical, jargon-heavy standpoint, as if all students will go on to be mathematicians. While this abstract, analytical approach is ultimately necessary to do math at the high levels required for much STEM work, it is also alienating to most people, who are not comfortable with that level of abstraction. I think it can be understood much more intuitively than the modern textbook approaches it- I have often tutored friends and family and I can usually get them to understand concepts, create equations and solve problems, if I use real world examples. Then they look back at the textbook and get totally confused again.

I actually think you could teach algebra in the context of a shop class and have much more success. Make the students design their own objects, and plan out dimensions. Make them define the relationship between the parts- if part A is supposed to be twice as long as part B, then A=2B. If A is 12 inches long, how long is part B? Etc. Gradually increase the complexity of the design, adding angles and so forth. Of course, then they actually make the parts and assemble their design. So the intuitive people (your future tradesmen, machinists, mechanics, etc.) get introduced to algebra in a way they can relate to, and thereby gain the ability to solve more complex problems than they would have been able to previously. The analytical types (future engineers, physicists, computer programmers etc.) would gain a real world understanding, and some much needed mechanical knowledge to boot (like how to turn a wrench, .etc)

Stan Calow
08-28-2018, 12:49 PM
Its one of those things that if you don't learn it yourself, you'll be paying people to know it for you, whether you realize it or not.

Jim Becker
08-28-2018, 2:24 PM
Honestly, I don't think that Algebra is "the problem" in school math programs. Where current things fall down, in my humble opinion having had both daughters go through elementary school math in a relatively recent time frame, is the whackadoodle math methodologies that are being taught that eschew the simple and straight forward way that most of us learned addition/subtraction/multiplication/division for all kinds of creative methods that might offer interesting thought processes, but don't really get to the answer any better or faster for most normal humans. And those programs are nearly impossible for parents to understand, too, meaning the students don't have quite the support system they would have if math was taught in the more traditional way. The program used in our local district is called "Everyday Math" and it's an abomination...again, IMHO. Jumping to Algebra from there is a bigger leap than it was from "normal" math because suddenly, folks have to "do normal math" to do the Algebra. But what do I know... ;)

Kev Williams
08-28-2018, 2:44 PM
Here's why I failed algebra... below is a screenshot of a 'kids introduction to algebra'..,

================================================== ==
http://www.engraver1.com/erase2/ALG.jpg
================================================== ======

In what universe should I find it necessary to cancel out a +5 with a -5 and 'have a go at subtracting 5 from both sides', to end up with a 9 character equation to get to another 5 character equation-- I mean, what does +5 and -5 equaling 0 have anything at all to do with "what plus 5 equals 12"? The SIMPLE equation change is x=12-5 ...! THAT I can understand!

Jim Becker
08-28-2018, 3:37 PM
That's an example of what I mean about how math is being taught these days...useless operations. And it's not about algebra...it's about the strange thought processes they are teaching that make things more complicated in my mind. The fact that this is labeled as an algebra problem and the initial equation looks like one masks the reality that this "problem" is part of the "new-new-new math" methodology being taught in elementary schools in recent times.

Prashun Patel
08-28-2018, 3:55 PM
I totally agree with you, Jim. My kids just finished middleschool algebra, and the "explain your thought process" really made them doubt their intuition.

Rod Sheridan
08-28-2018, 4:17 PM
Here's why I failed algebra... below is a screenshot of a 'kids introduction to algebra'..,

================================================== ==
http://www.engraver1.com/erase2/ALG.jpg
================================================== ======

In what universe should I find it necessary to cancel out a +5 with a -5 and 'have a go at subtracting 5 from both sides', to end up with a 9 character equation to get to another 5 character equation-- I mean, what does +5 and -5 equaling 0 have anything at all to do with "what plus 5 equals 12"? The SIMPLE equation change is x=12-5 ...! THAT I can understand!

Kev, you can't simply move the 5 to the other side of the equation.

You can do the same thing to both sides of the equation, and keep the validity of the equation.

In other words you can add -5 to both sides of the equation, or subtract +5 from both sides. Obviously that's the same result, a different "visualization" is all.

It's pretty obvious to you because you've mastered the skill and don't have to write it down, however what you are really doing is adding -5 to both sides of the equation............Rod.

Perry Hilbert Jr
08-28-2018, 4:33 PM
It isn't so much the math operation as being able to use reason to figure out the answer to a problem. I have seen some incredibly complex property line descriptions for the arc of a curved property line. There is a simple configuration of target rifling that was used by a famous gunsmith Marksman, But trying to explain it to laymen just gets blank stares and itchy scalps. The concept is simple, but the result seems incredibly complex. The round bottom rifling is shaped like an arc from a circle that is twice the diameter of the bore. The result is that the grooves are deeper along the lands (sides of the groove) than they are in the middle of the groove. Folks have a terrible time accepting that unless they were good in math. Harry Pope was the gunsmith/marksman who developed it and his guns are still worth over 5 figures today. Almost 40 years ago, I went to a custom barrel maker and asked him to make a target barrel for me based on Popes method. When I told him what I wanted, he had enough machinist back round to understand right off. He suggested some slight changes and I gave him the go ahead. He made my barrel and five others just like it. His partner won several regional championships with the design we came up with. Algebra teaches people to think, it teaches logic and reasoning. more than any other math. While it may seem like it is full of abstract concepts it is hardly abstract. If you want abstract, try to solve one of David Hilbert's 23 problems, or just read about his take on the theory of transfinite numbers. (I once kept a copy of one of his books on my bookshelf just to make people wonder)

Matthew Curtis
08-28-2018, 5:27 PM
That's an example of what I mean about how math is being taught these days...useless operations. And it's not about algebra...it's about the strange thought processes they are teaching that make things more complicated in my mind.


That's the thing. It is strange in your mind but not others. That is how we ended up with "common core". It made sense to someone and they had the ability to change how we do things. It is a better way of learning for some and not for others.

Jim Becker
08-28-2018, 5:31 PM
That's the thing. It is strange in your mind but not others. That is how we ended up with "common core". It made sense to someone and they had the ability to change how we do things. It is a better way of learning for some and not for others.
Most of the parents we interacted with during those elementary school days were equally flummoxed and most of their kids also struggled with having as many as a half-dozen different and strange ways presented to solve a problem other than the most basic ways we all learned. School board meetings got pretty heated over it, too... And then as soon as they hit 7th grade, math subjects were "back to normal" and the kids were confused by that because they didn't learn that way...go figure.

Robert Hazelwood
08-28-2018, 5:35 PM
Ha, I thought that screenshot was a pretty good example, honestly. It's important to remember the rules like always doing the same operation to both sides (which makes intuitive sense, because both sides of the equation have to remain the same value, which is why its called an equation). You can do simple problems like that in your head without thinking about the rules, but when you get to more complex problems that you can't just solve in your head, the rules and processes are important.

This weekend I was designing a bi-fold door for an entertainment center. The doors will be plank and batten construction with 12 planks across the width of the opening (3 for each half-door), so I had to figure out the plank widths. That would normally be an example of an algebra problem you could do in your head, or at least with a calculator. You could even just use dividers. But then I realized that the inner half-doors would need to be 1" shorter than the outer doors in order for the inner door to clear the Euro hinges that mount the outer doors to the case, so that the two half-doors can fold together tightly before retracting into the case (pocket doors). I didn't want the unequal doors to look weird, so I thought maybe I could disguise it by making the planks progressively narrower as they get towards the middle. I had to figure out by what amount I needed to reduce each plank width by, and what the width of the outermost plank would be, such that all of the planks together add up to the correct width while making the sum of the widths of first three planks be 1" greater than the sum of the next 3, all while having the plank widths step down in equal increments.

I don't know about you but I couldn't do that in my head :). But after thinking for a few minutes I was able to define the problem with a series of three equations. They were complex enough that I needed to do a bit of simplifying in order to solve by substituting variables from one equation into the others. I don't often have to do that level of algebra for woodworking (or use 'formal' algebra at all, really) but I think it shows the power of knowing the process.

andrew whicker
08-28-2018, 6:22 PM
Good example. When I build furniture, I inevitably come to a decision like you described and I'm too much of a perfectionist on the design side to let it go. (Wish I was more of a perfectionist on the build side).

The Golden Ratio is a great example of math in design. I use it or at least try it out when I'm going thru the design phase to see if it works.

Charlie Velasquez
08-28-2018, 8:46 PM
Kev, you can't simply move the 5 to the other side of the equation.

You can do the same thing to both sides of the equation, and keep the validity of the equation.

In other words you can add -5 to both sides of the equation, or subtract +5 from both sides. Obviously that's the same result, a different "visualization" is all.

It's pretty obvious to you because you've mastered the skill and don't have to write it down, however what you are really doing is adding -5 to both sides of the equation............Rod.

+1.

That is why we do the common core stuff. Unknowingly, you did the 5-5 in your head, without realizing it. But we want the students to realize it... so when they have more complex problems they will recall that they were able to isolate variables by performing identical functions on each side of the equation and still have an equality.

Jason Roehl
08-29-2018, 6:47 AM
I highly doubt your grandson is taking algebra in college. I took calc 3 & 4 and differential equations in engineering school, and given that Purdue is an engineering school, that’s probably more along the lines of what he’s taking.

I bet he has thousands of dollars wrapped up in books, but math, physics, fluid dynamics, etc.

Purdue is a 'university' WITH engineering schools. They are well-known for said engineering schools, but they are also fairly well known for other schools as well, such as their vet program, ag science and econ, management, hospitality management, and food science, to name a few. Of course, they have a regular litany of degrees available from the School of Liberal Arts, too, but those are not as well touted.

roger wiegand
08-29-2018, 8:18 AM
The example is quite good, I think because it illustrates a fundamental principle in a very simple way, to wit if you can do the same thing to both sides fo the equation the equation remains true. It is, by the way, exactly how I was taught to do algebra some 55 years ago, so not exactly "new math". To my eye it contains exactly the necessary and sufficient steps to solve the problem correctly in a general way. Sure you can jump over a couple of the steps in your head in this simple example, but you will quickly be in a world of hurt dong that in a complex calculation involving functions that aren't simple arithmetic and numbers that aren't simple integers. The fun starts when the things you add or subtract to each side don't look like each other but can be proven to be equivalent.

I've dealt with decades of lab techs who were so intent on "the answer" that they had no clue what they were doing or why, so had no intuition whatsoever about easier ways to solve problems, and worse no clue whether the number their calculatior or spreadsheet was off by three orders of magnitude.

I really liked they way my kids were taught math in the public schools, spending a lot of time and effort on process and estimation. As a result they can look at a number and say "hey, that's not right" without recalculating the whole problem-- of course when you have that reaction you eventually need to be able to calculate a correct answer. They seem quite functional out in the world without having wasted years in elementary school memorizing times tables and doing long division the way I did.

Calculus is a whole 'nother beast. I did a lot of calculus, through differential equations and I have to say that in 40+ years as a working scientist I never once needed to use calculus to get my work done. I very much appreciate understanding the underlying concepts as they relate to force and acceleration and rate of change, it has made my reading of science fiction much easier. But I had that in the first half of High School calc-- the following four years worth of study was wasted agony. That time in my case would have been much more profitably spent studying statistics, which I do use all the time. Living in a country where "all the children are above average" it seems that the concepts are widely missing.

Prashun Patel
08-29-2018, 8:38 AM
Having watched my son struggle through this methodology, I am of the mind that the common-core (while well-intentioned) is highly imperfect and ironically prevents certain minds from learning material.

We'll need to figure out how to make an 'uncommon core' education in the next century. It's already happening. I look at the cost of expensive, big box colleges and private schools, and all the problems with public schools, and then I look at what is happening on the Internet (Khan Academy, Code Academy, Duolingo). If it weren't for that rubber stamp we all seek when validating each other in job interviews, I'd push my kids to on-line learning in a heartbeat.

Bill Berklich
08-29-2018, 8:54 AM
I use algebraic formulae every single day at work. It makes life simpler. Now the 4 semesters of calculus and one of differential equations are a different story. I haven't used those since I graduated engineering school.

ROFLMAO!!! True then add in Tensor math and LaPlace and I really do understand why Cast Iron is used for table saw and how it damps vibrations because of the crystal structure...

Ron Citerone
08-29-2018, 9:07 AM
Having watched my son struggle through this methodology, I am of the mind that the common-core (while well-intentioned) is highly imperfect and ironically prevents certain minds from learning material.

We'll need to figure out how to make an 'uncommon core' education in the next century. It's already happening. I look at the cost of expensive, big box colleges and private schools, and all the problems with public schools, and then I look at what is happening on the Internet (Khan Academy, Code Academy, Duolingo). If it weren't for that rubber stamp we all seek when validating each other in job interviews, I'd push my kids to on-line learning in a heartbeat.

"This Methodology" was around way before common core. I don't believe it "Prevents certain minds from learning material" because an experienced teacher includes multiple approaches to content regardless of the Curriculum, which is only a guide. If a student can't either show the steps. or explain their logic, I think the chance of long term retention is in jeopardy. Experienced teachers understand their are different learning styles and incorporate variations in their lessons to accommodate them...........especially when a class or student is not grasping a concept.

Dan Friedrichs
08-29-2018, 9:39 AM
The aversion to "common core"-type instruction confuses me. Do people think this was pulled out of thin air? Of course not. Experts in pedagogy developed these approaches, tested them in real students, assessed what worked best, and it was adopted by those who saw the value of the results. It's not some bureaucrats making things hard for fun - these techniques come from experts in teaching and learning who have evidence to show this works. If it didn't work, why would it have gotten so much traction?

Aside from that, in a highly-innumerate country (like the US), it's difficult to understand the logic of staying with the status quo...

Prashun Patel
08-29-2018, 9:40 AM
I just don't believe that the ability to explain logic is not for everyone a prerequisite for understanding, using, and extrapolating logic. In theory a good teacher guides, but in practicality, good teachers are not always present. Even in my relatively well-heeled district, the good teachers are hit and miss.

I'm not demeaning the centuries of development that got us to this kind of education. I am saying it's time for it to evolve. I'm not an education scientist, but I do have 2 bright kids that have bumped into obstacles with common core in the past 3 years. So, believe what you want, I think some flexibility and evolution is due.

William Adams
08-29-2018, 10:38 AM
The problem is, education bumps into legal problems in terms of access and so forth --- what else can one make of the school system which I attended for 3rd and 4th grade (which allowed me to take 8th grade English, math, and science classes, and would have released the 4 year cap if I'd stayed there until 8th grade so that I could've started on college classes --- all the teachers in the High School were dual-accredited w/ a local college) because it provided unfair advantages to the disciplined and gifted students, while unfairly singling out the lazy and average to seemingly be held behind, or at least that was my interpretation of the Mississippi State Supreme Court case which ruled the system illegal.

Still waiting for someone to work out what the best public domain textbooks were, put them up somewhere that everyone can have access to them, and just be done with it.

Edwin Santos
08-29-2018, 5:41 PM
That's an example of what I mean about how math is being taught these days...useless operations. And it's not about algebra...it's about the strange thought processes they are teaching that make things more complicated in my mind. The fact that this is labeled as an algebra problem and the initial equation looks like one masks the reality that this "problem" is part of the "new-new-new math" methodology being taught in elementary schools in recent times.

Jim,
Would it help to think about Math in the same terms as thinking about teaching English? Math is a language of expression and to call the steps illustrated useless operations and strange thought processes would be like turning to English and objecting to synonyms and metaphors on the basis that we don't need multiple ways to say the same thing (some of which might be unfamiliar and hence strange).

I can completely see where these steps come across as questionable in a simple equation example, but like others have pointed out, the idea is for the student to understand the building blocks of the language so that when the equation becomes more complicated (and it quickly will), these rules and steps will guide the way when things aren't simply intuitive.

Can you imagine someone suggesting doing away with teaching students about verbs, nouns, modifiers and the other technical building blocks of language because we don't really think about them in daily practice, we just intuitively talk? Understanding these technical building blocks allows the educated student to express themselves in different and subtle ways that makes greater use of the breadth of language, and will open doors for them throughout life. The more complex life becomes, the more valuable this ability will be. Math fluency works in much the same way with regard to problem solving.

Not trying to change your mind or say you're wrong, just offering a alternate point of view of why there might be method to what you're perceiving as madness.
Edwin



EDIT - Education is subjective and ultimately I think it's a parent's right to form their own opinions. A parent can delegate to the local school district, or if they are motivated enough, pursue other options like home schooling, charter schools, private schools, online supplementation other hybrid approaches. There are certainly many more options available than there were in the past.

Jim Becker
08-29-2018, 10:21 PM
Edwin, the example in this thread is really, really mild compared to a lot of the "stuff" that's being taught in the common core type curriculums. (there are multiple versions...my local district used/uses "Everyday Math" developed, I believe, out of the University of Chicago which happens to be Professor Dr. SWMBO's undergraduate alma mater) My experience with my kids echos Prashun's experience with his kids. My younger is a math wiz (like able to do mental math at an almost savant level sometimes) and still struggled with the very obtuse and multiple methodologies she was subjected to for developing solutions to math problems in elementary school. And as I mentioned, neither I nor my spouse could be of much help...and The Professor does calculus and heavy statistics nearly daily. So many other parents expressed the same concerns. The district has backed down a little and started also teaching the more traditional ways, which the teachers also appreciate. They get frustrated when the kids can't do their homework even with whatever help parents can lend!

Lee DeRaud
08-29-2018, 10:36 PM
Asking 5th graders if they anticipate needing to know algebra for their future career plans seems foolish.The very concept of "the future career plans of 5th graders" seems foolish.

Lee DeRaud
08-29-2018, 10:42 PM
I can't imagine stopping Math education pre-algebra.Yup. That would just be arithmetic, at which point you might as well just have a class titled "How to install a calculator app on your phone".

Mike Kreinhop
08-30-2018, 4:11 AM
The very concept of "the future career plans of 5th graders" seems foolish.

The German school system does exactly that. All children attend Grundschule through the fourth grade. At the fifth grade, the school system branches out to Hauptschule (grades 5-9), Realschule (grades 5-10), and Gymnasium (grades 5-12). Hauptschule and Realschule are a mix of classroom and vocational training that lead to apprenticeship and employment in the career path chosen at the start. Gymnasium (pronounced gim-na'-zee-um) is the academic path for university.

I certainly didn't know what I wanted to do with my life at the start of the fifth grade, but this decision is routinely made here. Once a career path or trade skill is chosen for the child, it seldom changes. However, high performers in Realshule sometimes have the opportunity to change to Gymnasium and go on to college.

Tom Bender
08-30-2018, 7:18 AM
So in engineering school We solved engineering problems using calculus. That absorbed HALF my energy. Then I worked in engineering for 40 years. Never met an engineer who used calculus for anything. Yes there are a few I did not meet who do but to force every engineer to burn so much energy on something almost arcane is inappropriate. What would have helped more would have been courses in;

Accounting

Languages

Politics

Planning

Law

Patents

Ethics

etc.

Engineering is not so much about math as about getting things done.

And hiring expertise in narrow fields is the way things get done.

John K Jordan
08-30-2018, 9:30 AM
...That time in my case would have been much more profitably spent studying statistics, which I do use all the time. Living in a country where "all the children are above average" it seems that the concepts are widely missing.

That's probably true! As are our national delusions.

Another valuable math skill, depending on your interests, is linear algebra. Learning matrix math was key in developing software to process and then display vector graphics on bitmap screens and other output devices (e.g., a good exercise is write your own flight simulator software). My second bitmap display hardware (in the '70s) was capable of 512x512 b/w or a 256 pixel square in several shades of grey - geek nirvana! Color then: a dream.

John K Jordan
08-30-2018, 9:43 AM
The German school system does exactly that. All children attend Grundschule through the fourth grade. At the fifth grade, the school system branches out to Hauptschule (grades 5-9), Realschule (grades 5-10), and Gymnasium (grades 5-12). Hauptschule and Realschule are a mix of classroom and vocational training that lead to apprenticeship and employment in the career path chosen at the start. Gymnasium (pronounced gim-na'-zee-um) is the academic path for university.

I certainly didn't know what I wanted to do with my life at the start of the fifth grade, but this decision is routinely made here. Once a career path or trade skill is chosen for the child, it seldom changes. However, high performers in Realshule sometimes have the opportunity to change to Gymnasium and go on to college.

Our friends in Italy tell me their educational system is similar. In what I think we would call "junior high" they have to decide on which "high school" they want to attend, each with the same core education but with a different focus. Two of our young friends chose art school; one chose language school. (There are others.) The girl who chose language school now speaks seven languages and spent the summer in France and Russia honing her skills. Our art-student Italian house guest came this summer to work on her English and visit art museums. From what she told us the course of study seems far more extensive than what we have in the US. She said in graduating from any of the schools the student has enough of the basic education to go into law school, medicine, anything. It sounded to me that by they time went to university they might already had the equivalent of an undergraduate degree here. I'd like to learn more about the educational systems in other European countries.

JKJ

Dan Friedrichs
08-30-2018, 11:08 AM
So in engineering school We solved engineering problems using calculus. That absorbed HALF my energy. Then I worked in engineering for 40 years. Never met an engineer who used calculus for anything. Yes there are a few I did not meet who do but to force every engineer to burn so much energy on something almost arcane is inappropriate. What would have helped more would have been courses in;

Accounting

Languages

Politics

Planning

Law

Patents

Ethics

etc.

Engineering is not so much about math as about getting things done.

And hiring expertise in narrow fields is the way things get done.

As an engineer, I am horrified at this statement...

To me, your list of topics is heavily weighted towards practical skills. A university education is training to teach yourself those practical skills.

I had often wanted for more practical statistics education, as while I took calculus-based statistics in engineering school, I didn't immediately understand how to apply it in practical situations. I later realized that I had the tools at my disposal to teach myself how to apply it, and more importantly, understand it. Had I taken an introductory statistics course, I might have been able to practically apply it, but I would have just been "turning the crank" on a machine that someone else built for me, rather than understanding it.

Lee DeRaud
08-30-2018, 11:46 AM
Engineering is not so much about math as about getting things done.

And hiring expertise in narrow fields is the way things get done.On a personal level, I am truly glad some people think that way. I started with an MS in math, and spent a 30+ year career in aerospace coming up with out-of-the-box solutions to the problems that arose when those "narrowly-focused experts" dug deep holes and lacked the imagination to get out.

Rod Sheridan
08-30-2018, 1:53 PM
When I was in high school in the seventies, we had a 3 stream system that took you to University, college or trades and I'm not sure what the lower stream was meant for....Rod.

Andrew Pitonyak
08-31-2018, 2:26 PM
use it all the time.... For example, which box of cereal gives me the most for my money with this coupon? Pretty easy to do...

I wanted the Internal Rate of Return for my investments based on irregular intervals, deposits and withdrawals.... My spreadsheet did not have a built-in function to do it, so, I derived it then implemented it using a macro. OK, that was more than simple algebra because there was not a closed form solution easily available.

I showed a girl how to calculate simple interest rates and she figured out that when she borrowed money from a friend that her friend had charged her 100% interest on a three month loan. She had no idea how much her friend had charged her. Then again, her friend may not have had a clue either.

Why do doctors learn calculus and similar? So that they can calculate dosage. Reality, they do not calculate dosage, they look at a chart created by someone else who knows calculus. OK, the resesarchers probably do it themselves.

John K Jordan
08-31-2018, 5:12 PM
...
Why do doctors learn calculus and similar? So that they can calculate dosage. Reality, they do not calculate dosage, they look at a chart created by someone else who knows calculus. OK, the resesarchers probably do it themselves.

Try giving medicine to llamas - there's no chart. Although it's basically a simple ratio calculation, since there are no meds dosed by the mfgrs specifically for llamas they are all "off label"and it gets tricky. In using meds labeled for sheep or horses you have to convert from the label dose in milligrams or the number of "clicks" for gun dispensers for the weight of the other livestock, then take into consideration the guidelines on a llama's physiology needs compared to the other livestock, then calculate the dose based on the weight. It can get SO confusing unless each step is written down and combined into one equation to give the # of clicks or milligrams to give for the llamas weight. Someone without math skills has to call the vet and ask. Then how can they possibly check the vet's advice for accuracy??

I've mentioned this thread to several people. They all had the same response: it would be irresponsible to drop or reduce math instruction; what's desperately needed is MORE math in public schools.

JKJ

Tom Bender
08-31-2018, 7:02 PM
"It would be irresponsible to drop or reduce math instruction; what's desperately needed is MORE math in public schools."

Agree completely, but let's stick to useful math. An engineer must be fearless when it comes to math and many other subjects. But is is not practical to teach every subject in extreme depth. Most engineers must be jacks of all trades so we can get things done. Specialties (including arcane math) should be developed in advanced degree programs, personal passions or as the job requires.

Julie Moriarty
08-31-2018, 8:24 PM
When was the last time you used algebra?
You know, I happen to be very good with algebra. So stop picking on one of the few things I've mastered. I'm getting a complex. ;)

Van Huskey
09-01-2018, 4:12 PM
Now the 4 semesters of calculus and one of differential equations are a different story. I haven't used those since I graduated engineering school.

I use algebraic principles all the time and I expect many do without even knowing it. However, I have not used Diffy Qs since my exam on them, I think I mave have used calculus a couple of times but it is extremely rare.

Jim Koepke
09-01-2018, 7:02 PM
Why do doctors learn calculus and similar? So that they can calculate dosage. Reality, they do not calculate dosage, they look at a chart created by someone else who knows calculus. OK, the resesarchers probably do it themselves.

The knowledge math could likely set off an alarm in a doctor's mind if a chart had a misprint or typo.

As was mentioned earlier it helps students to learn how to use their brain as much as it teaches a useful tool.


But is is not practical to teach every subject in extreme depth.

True, should we let bureaucrats decide when to direct students away from the path of higher learning to a path of low on the ladder wage slave for the rest of their lives?

Math skills come in handy in everything from shopping for groceries and planning meals to paying bills and home maintenance.

Reading, writing and arithmetic are the foundation of all education. With a meager beginning of engaging the human mind with the "three Rs" all else can be explored, learned and put to use.

jtk

John K Jordan
09-01-2018, 8:32 PM
Math skills come in handy in everything from shopping for groceries and planning meals to paying bills and home maintenance.


And making life decisions based on more than hope. Math came in handy when I was trying to decide when to retire - for a given expected lifetime, for a given retirement age what is the break-even age considering a reduced income and the trade-off between reduced work-related expenses vs estimated increased avocational expenses, also considering the private insurance and Medicare numbers. After careful calculations I decided to retire at age 56. Best decision I ever made (besides the choice of life partner!)

JKJ

Steve Demuth
09-01-2018, 9:32 PM
That's an example of what I mean about how math is being taught these days...useless operations. And it's not about algebra...it's about the strange thought processes they are teaching that make things more complicated in my mind. The fact that this is labeled as an algebra problem and the initial equation looks like one masks the reality that this "problem" is part of the "new-new-new math" methodology being taught in elementary schools in recent times.

Nothing "new math" about that. The foundation of algebraic solving is that you simplify equations by performing identical operations to both of two equal things (the opposite sides of the equation) until you have a simple form that answers your question. That's what was being demonstrated there, with a very simple example. The real value comes when the equation starts more complex, but you start with simple to learn the techniques.

Kev Williams
09-01-2018, 9:34 PM
Here's why I failed algebra... below is a screenshot of a 'kids introduction to algebra'..,

================================================== ==
http://www.engraver1.com/erase2/ALG.jpg
================================================== ======

In what universe should I find it necessary to cancel out a +5 with a -5 and 'have a go at subtracting 5 from both sides', to end up with a 9 character equation to get to another 5 character equation-- I mean, what does +5 and -5 equaling 0 have anything at all to do with "what plus 5 equals 12"? The SIMPLE equation change is x=12-5 ...! THAT I can understand!


Kev, you can't simply move the 5 to the other side of the equation.

You can do the same thing to both sides of the equation, and keep the validity of the equation.

In other words you can add -5 to both sides of the equation, or subtract +5 from both sides. Obviously that's the same result, a different "visualization" is all.

It's pretty obvious to you because you've mastered the skill and don't have to write it down, however what you are really doing is adding -5 to both sides of the equation............Rod.

To begin, I didn't say anything about moving the 5 to the other side, the puzzle said that!

Second, my calculation to get at the answer uses simple SUBTRACTION! Which for some reason doesn't get drilled into kids heads in school like addition and multiplication... example, off the top of your head, who here doesn't know what 7x9=, 6x8=, 3x5= --- or 2+2 or 5+8, etc... but how many of us have to THINK was 8-5 is, or 9-3, or 7-4? Easy enough, but me, I don't have subtraction memorized like addition or multiplication, simply because I was taught my basic addition, and then came the times-tables until they were second nature (and still are!) But while they taught us how to subtract, we were never taught to memorize any 'minus tables', at least not in my time ('72 grad)...

My whole point here, is that I think a kid would likely find it much easier to understand that figuring out what X is involves nothing more than subtracting 5 from 12, and ESPECIALLY if kids had basic subtraction memorized. Maybe kids know subtraction better these days, I don't know, but what I do know is x=12-5 \ =7 makes perfect sense, but x= x+5-5=12-5 \ x+0=7 \ x=7 is complete nonsense!

Steve Demuth
09-01-2018, 9:42 PM
I use algebra all the time in my work, and not infrequently outside work. Calculus less often, but still shows up in both. Ditto statistics.

But to answer the original question, we still teach algebra because many people WILL need and use it. We taught both our children algebra and higher math (they were home schooled). One is now a history professor, and probably uses any of it rarely if at all. One is a research scientist who uses higher math literally every working day. He wouldn't have had that opportunity had he not learned algebra first.

Mike Kreinhop
09-02-2018, 8:25 AM
Maybe kids know subtraction better these days, I don't know, but what I do know is x=12-5 \ =7 makes perfect sense, but x= x+5-5=12-5 \ x+0=7 \ x=7 is complete nonsense!

This might be nonsense to you, but my experience in teaching algebra to students of all ages indicates it is not nonsense. When I start with a simple equation, such as X + 5 = 12, and tell the students the process starts by isolating the x term, I usually have blank stares because they don't have any idea where to start. What you find obvious is not obvious to all. From a mathematical point of view, there is no such thing as moving a term or value from one side of an equation to the other. The "moving" is accomplished by performing identical operations to both sides of the equation in order to eliminate the unwanted variable or value.

In the case of the equation above, isolating x starts with subtracting 5 from both sides. In my experience with students new to algebra, this has to be shown in detail, with every step clearly defined, so the student can understand the process and build on it as the equations become more complex. Crawl, walk, run. In time everyone understands the process, and some steps in isolating terms can combined as you described.

To further complicate the teaching, some students don't understand the order of precedence in arithmetic operations, which can produce incorrect results in solving equations. In these cases, a few steps backwards for the class, or extra help for the individual, is required.

Bob Glenn
09-02-2018, 11:18 AM
How can you get through a day without using algebra? ie, i have a board 8 ft long and I need a one 49" and one 18", can I get them out of my 8 ft board? Answering that question by calculation is algebra, whether you like it or recognize it or not. Yes you could use a story stick and get a geometric solution, but I'll bet most of you take the calculated (algebraic) approach when staring at your wood pile. I use algebra 100 times a day, whether it is calculating angles, figuring how long a piece needs to be, or deciding if I will have enough money left in my pocket for a hot dog if I buy a beer.

Just think of the endless discussions on this site of how big a pipe or wire one needs to serve multiple air tools or power tools. The answer is almost always simple algebra. Algebra is basically the study of equations, so whenever you say x=y you are asserting a hypothesis that is subject to proof, so 2+2 =x represents a very simple, yet useful, algebraic equation, 2+x=4 a slightly more interesting one. Ability to use a symbol for a number (x in this case) opens up a whole world of possibilities for doing calculation as well as describing general solutions to frequently encountered problems, like area=pi*radius squared for a circle. Isn't it nice to have algebra so that you can either know the radius and find the area or know the area you want and calculate the radius?

I don't consider 2 plus 2 as algebra. 2 plus 2 is basic math as are most "daily calculations". Anyone can make something complicated, it takes some thought to make things simple. You don't need an algebraic equation to figure out if you have enough money in your pocket to buy something or if your board is long enough to cut two pieces pieces to length. That, sir is simple math.

William Adams
09-02-2018, 11:43 AM
Yes, but you do need Algebra to determine which package of crackers is the best buy at the grocery store w/ without coupon.

If folks want to be ignorant, that's their choice --- certainly society still has lots of ways to punish such willful ignorance --- you get charged more at the grocery store for not finding the best buy, folks waste money on lottery tickets because they don't understand probability and odds, folks don't properly save for and invest in retirement, or they choose the wrong time and interest rate to refinance their house.

But as a society, we have an obligation to offer future citizens the best opportunities which we can, and that includes an education which will make it possible to learn anything which they might wish. I've experienced both the best and the worst of what U.S. school systems can offer, and any school system which does not offer all possible subjects at all possible levels matched to each student's ability is a dis-service to those students, and society because the students with greater potential, who are not offered such opportunities will not get the best education which they can.

We've got legislators who want to know why NASA has to launch weather satellites, when all one has to do to get the forecast is check the TV forecast --- we need better education which includes mathematics which is the fundamental language of science.

This pretty much sums it up:

http://matt.might.net/articles/phd-school-in-pictures/

John K Jordan
09-02-2018, 1:33 PM
This pretty much sums it up:
http://matt.might.net/articles/phd-school-in-pictures/

What an interesting way to illustrate!

JKJ

Jim Koepke
09-02-2018, 3:13 PM
This pretty much sums it up:

http://matt.might.net/articles/phd-school-in-pictures/

That is better than how a PhD was explained to me as something being Piled higher and Deeper.

jtk

Steve Demuth
09-02-2018, 4:22 PM
Second, my calculation to get at the answer uses simple SUBTRACTION!

How do you know what to subtract from what? You know because you have an intuitive grasp of algebra. Teaching algebra creates that grasp, and puts it on a firm foundation so you can do more complicated computations for which the answer isn't immediately obvious. How many sheets of OSB and how many bundles of shingles at 4 bundles per square do I need to reroof my semi gable-roofed house with attached lean-to roof, and how does the cost of that compare to the cost of a steel roof? There is a bunch of basic algebra to get the answer, even though you may never actually write an equation with an "x =" in when doing the calculation.

Aubrey Blalock
09-03-2018, 3:37 PM
Whether it is used is certainly an advantage.

Its another example of just teaching people to think and reason for themselves.

Pat Barry
09-03-2018, 6:16 PM
To begin, I didn't say anything about moving the 5 to the other side, the puzzle said that!

Second, my calculation to get at the answer uses simple SUBTRACTION! Which for some reason doesn't get drilled into kids heads in school like addition and multiplication... example, off the top of your head, who here doesn't know what 7x9=, 6x8=, 3x5= --- or 2+2 or 5+8, etc... but how many of us have to THINK was 8-5 is, or 9-3, or 7-4? Easy enough, but me, I don't have subtraction memorized like addition or multiplication, simply because I was taught my basic addition, and then came the times-tables until they were second nature (and still are!) But while they taught us how to subtract, we were never taught to memorize any 'minus tables', at least not in my time ('72 grad)...

My whole point here, is that I think a kid would likely find it much easier to understand that figuring out what X is involves nothing more than subtracting 5 from 12, and ESPECIALLY if kids had basic subtraction memorized. Maybe kids know subtraction better these days, I don't know, but what I do know is x=12-5 \ =7 makes perfect sense, but x= x+5-5=12-5 \ x+0=7 \ x=7 is complete nonsense!

Its called an EQUATION. Both sides are equal. To keep this true, whatever is done to one side of the equation needs to be done to the other or you have an inequality. Thus, you must subtracr 5 from BOTH sides of that equation. You, and most everyone, forgets that, and skips proper accounting.

Jay Radke
09-03-2018, 8:30 PM
I have used algebra all my life as a scientist. Lots of solving for x in making many different solutions and other routine things.

Wade Lippman
09-03-2018, 9:30 PM
I use algebraic formulae every single day at work. It makes life simpler. Now the 4 semesters of calculus and one of differential equations are a different story. I haven't used those since I graduated engineering school.

I use calculus occasionally, but haven't even looked at a differential equation in 45 years. I sometimes wonder if I could get it back with a little effort.

Stan Calow
09-04-2018, 9:27 AM
Wade, I am convinced that the most one can hope for is to understand differential equations temporarily. I did, one summer, long ago, now its gone forever.

Prashun Patel
09-04-2018, 9:37 AM
Differential equations are SOOO derivative.

I have heard that the rate of understanding of differential equations diminishes exponentially with time, but I can't remember the exact equation.

Lee Schierer
09-04-2018, 2:26 PM
It wasn't until I took college physics and engineering courses that differential equations actually started making some sense and could actually be used.

Edwin Santos
09-04-2018, 7:11 PM
Differential equations are SOOO derivative.

I have heard that the rate of understanding of differential equations diminishes exponentially with time, but I can't remember the exact equation.

Maybe it's just integral to the aging process that the rate of comprehension will approach zero.

Art Mann
09-05-2018, 10:07 AM
As an engineer, I have used algebra my entire career. To me, that question is the same as asking why we still teach people to read.

John K Jordan
09-05-2018, 10:35 AM
As an engineer, I have used algebra my entire career. To me, that question is the same as asking why we still teach people to read.


That's a great point.

Rather than dump any kind of instruction perhaps things could be taught in entirely different ways. A story in yesterday's paper was about a program that uses music to get kids excited about math. They found it worked better than they expected, changing kids who said they hated math, the school programs were dumb, and they didn't want to go to collage. Several weeks later some of the same kids are saying they love math (pre-algebra), it's their favorite subject. They plan to use these concepts to improve methods of learning and help kids to realize their potential. So many just give up.

Matt Day
09-05-2018, 10:38 PM
I still don’t understand why the OP seems to hate math so much. And why his grandson who is in college is taking algebra.

I vote we buy him this hat.

Bill Dufour
09-05-2018, 11:05 PM
A professor from the mid west was held at the airport while carrying a protractor and compass...weapons of math instruction.
A new terrorist cell is having problems recruiting in America. Loyal Americans tremble at it's name, Al Ge Bra.

Steve Demuth
09-05-2018, 11:05 PM
I still don’t understand why the OP seems to hate math so much. And why his grandson who is in college is taking algebra.

I vote we buy him this hat.

I'm in. Where do we send our $?

Although in my case, I use algebra, I love calculus.

Rick Potter
09-06-2018, 2:50 AM
I suspect the OP is overwhelmed by how seriously his post was taken. It struck me as simply wry humor.

Lee DeRaud
09-06-2018, 11:44 AM
To me, that question is the same as asking why we still teach people to read.I've been meaning to ask you about that... :)

Prashun Patel
09-06-2018, 12:05 PM
X-cuse me for asking, but Y are we still debating this?

Mike Kreinhop
09-06-2018, 12:27 PM
X-cuse me for asking, but Y are we still debating this?

OMG! R U 4 real?

Jim Becker
09-06-2018, 12:43 PM
X-cuse me for asking, but Y are we still debating this?

You haz Z gumption to ask? :D

John K Jordan
09-06-2018, 3:22 PM
X-cuse me for asking, but Y are we still debating this?

I for 1 luv C-ing how many creekerz use z X n Y.

Ron Bontz
09-07-2018, 2:40 PM
Short story: Once upon a time in a dynamics class the question was asked of the instructor, who was an older (pre computer) engineer, why we have to go through all the calculous, diffy Q, etc. when the computer does so much of it. His answer was simple. "So we recognize bad numbers when we see them and the dam doesn't fail.". Garbage in = garbage out, basically. I did not finish my last year of engineering, but have never regretted all that math, etc. Even something as simple as flow rates of fire hose involve algebra. So that's my story and I am sticking with it.:)

Jim Koepke
09-07-2018, 6:27 PM
"So we recognize bad numbers when we see them and the dam doesn't fail."

That is likely one of the best reasons to stay sharp at things mathematical.

Today while shopping the cans of tomato sauce were priced in a way that looked strange to me. In other words it looked like the larger cans were more expensive than the smaller cans. The only problem for the average shopper is the shelf tag for one was broken down to cost per ounce and the other was price per pound. This kind of bugs me when the people doing the programming can't keep these breakdowns in the units.

One of the strangest times was when milk was at 99¢ for a half gallon and the gallons were priced at $2.59. When this was mentioned to someone who was buying a few gallon containers of milk, his reply was his kids drink it faster if he buys it in the half gallon jugs.

Wouldn't that be good for the kids?

jtk

Lee DeRaud
09-07-2018, 8:04 PM
"So we recognize bad numbers when we see them..."In 1971/72, HP used our engineering school for a mass beta-test of one of their early hand-held scientific calculators. (Can't recall the model number offhand...I just remember I couldn't deal with their RP input scheme and switched to TI at the first opportunity.) The professor in an advanced physics class I was taking forbid their use, insisting that everyone use slide rules or do the computations by hand. When asked why, he said, "Your answer will still be wrong no matter how many decimal places you compute it to."

Jason Roehl
09-08-2018, 6:36 AM
Today while shopping the cans of tomato sauce were priced in a way that looked strange to me. In other words it looked like the larger cans were more expensive than the smaller cans. The only problem for the average shopper is the shelf tag for one was broken down to cost per ounce and the other was price per pound. This kind of bugs me when the people doing the programming can't keep these breakdowns in the units.


I don't think that was a mistake. If the price per unit were consistent across the different size container, you could more easily choose the most economical and least profitable option. They're counting on the likelihood that you can't do the math (or won't). Of course, even though I tend to be pretty cheap, I've gotten to where I value my time more, so I don't fret a few bucks here and there. I buy what I want/need, and go by whether or not I'm willing to spend the amount of the listed price. The larger the price, the more willing I am to comparison shop for a better deal.

Art Mann
09-08-2018, 9:29 AM
Astute observation, Jason. The stores are taking advantage of the general mathematical illiteracy of the population. The OP may think it is a good idea to dumb down high school mathematics but I don't and this is a good example of why.

John K Jordan
09-08-2018, 1:21 PM
...The stores are taking advantage of the general mathematical illiteracy of the population.

How about things priced at $3.99 or $89.95? To me this is incredibly idiotic. This is a careful scheme to trick the educationally deprived and cognitively challenged into buying something because they think it's cheaper.

https://www.livescience.com/33045-why-do-most-prices-end-in-99-cents-.html

It also makes it more difficult for people to estimate how much they are spending as they put things in the shopping cart. I'm not the only one who does this, right? (I love the dollar store. The "everything's a euro" store across the pond is even better since the tax is included in the posted price - it says 2 euros, you hand the clerk 2 euros.)

When a clerk or phone rep tells me something is $49.99 I say, ok, 50 bucks. Sometimes this confuses them for a moment.

If I were King I would decree that using the digit 9 to deceive be punishable by a week in the dungeon. While I'm at it, the .9 cents added to each gallon of fuel will also be banished.

JKJ

Mel Fulks
09-08-2018, 1:52 PM
I see it as a nonsensical custom. Doesn't take much of a scientist to come up with an evil reason for it. Or to see that $1.99 takes a big bite out of a two dollar bill. Did you know that sports fans are often hypnotized to do the "wave" to cool the air and that it can make change fall out of a shirt pocket?

Jim Koepke
09-08-2018, 2:07 PM
I've gotten to where I value my time more

The person who puts money in my pocket for not spending a few seconds to do an easy calculation has never shown their face in my presence.

The less than a minute calculation saved me more than a half a dollar on my purchase of quite a few cans of tomato sauce.

Another quick calculation makes it quite clear that even if it took a whole minute the return would be better than $30 bucks an hour.

My feeling is it is time well spent for savings like that all day long.

Besides, it is a way of making my brain exercise.

jtk

Pat Barry
09-08-2018, 6:54 PM
$19.99 is less expensive than $20.00. Everyone knows that and has a huge jar of penny's to prove it.

Jim Koepke
09-08-2018, 7:40 PM
$19.99 is less expensive than $20.00. Everyone knows that and has a huge jar of penny's to prove it.

You must live in one of the five states without sales tax.

jtk

Jason Roehl
09-09-2018, 9:00 AM
I should mention, that if there's a painfully obvious price advantage across package sizes, I'll take the better deal. All too often, I'll see something that's $1.99 for 8 oz. and $3.99 for 16 oz. Ummm...

Bill Dufour
09-11-2018, 11:26 PM
I was in OSH today a couple in their 50's asked me if I was good at percentages. Is said yes and they asked me how much $9.99 tub would be with the 15% close out price discount. They both had calculators on their phones and were not sure. I though a few seconds .85 cents on the dollar so $8.50 plus tax so a little over $9.00 after tax.
Not sure if that is algebra or just simple percent,but still math they could not do with a calculator.
I notice many stores sell items for like .99 or two shrink wrapped together for 1.99. I always save my pennies.
Bill D

Robert Hazelwood
09-12-2018, 11:08 AM
I would consider that informal algebra. You had to understand the relationship between all of the numbers in order to knew what steps to take, which is fundamental to actually using math. Their calculator was perfectly capable of crunching the numbers but they didn't know what to punch in.

Discount Price = (1-Discount Rate)*Original Price

You did the (1-Discount Rate) in your head to get "85 cents on the dollar". The fact that the original price was $10 made it easy to solve.

Brett Luna
09-12-2018, 2:36 PM
I've used a lot of algebra in the 40 years since high school, in both vocation and avocations. I've also used geometry (both vanilla and analytical), trigonometry, and even boolean algebra. But then, I maintained USAF avionic sensors for many years and I was an electronics/computer hobbyist and a model rocketeer. I also learned drafting/mechanical drawing in high school, the old fashioned way: with a t-square, triangles, and a slide rule. Yeah. Nerd.

I actually got a D in algebra the first time I took it, so I opted to take it again and also talked the counselor into letting me take physics the same year. That's when it clicked...with the application. It went from being a pain to putting another tool in my bag.

In all this time I've learned a couple of things.


2 + 2 = 5, where quantities of two are sufficiently large

and

There are 10 kinds of people in this world: those who understand binary and those who don't.

Pete Staehling
09-12-2018, 7:13 PM
As an engineer, I have used algebra my entire career. To me, that question is the same as asking why we still teach people to read.
My thoughts ran along the same lines. I was kind of shocked to read the original post and found it hard to imagine anyone that managed to attain any level of mastery of algebra didn't find it useful in their daily life.

Larry Frank
09-12-2018, 8:26 PM
There was an article this week about a study done by Bankrate and listed the best and worse college majors. The answer to the question about algebra is in the article and has to do with income and employment rates.

This is a great article for parents to discuss with their kids when discussing college choices.

I want to also say that college is certainly not the right choice for everyone. However, many of the non-college career paths are helped greatly by understanding algebra.

Bill Dufour
09-12-2018, 11:29 PM
When I worked at the lab I used to get bank notices offering to loan me money to go to graduate school. They would offer loans for many years all the way to advanced medical degrees. But they spelled out not for philosophy or sociology majors.
Bill D.

Jacob Reverb
09-13-2018, 6:00 AM
Golly, I use algebra all the time.

If you're not going to teach algebra, then why teach addition, subtraction, multiplication or division, either? Because it's almost as common, and just as indispensable. [Shaking head]

Seriously, who doesn't use algebra on a weekly basis at least?

Bob Glenn
09-13-2018, 11:03 AM
With all the algebraic equations floating around in this thread, I guess if you have minus two apples, then I give you two apples, then you end up with no apples even though I just gave you two.

You can complicate this all you want, your choice. I choose to keep things simple. Good thing I don't have to calculate the decay rate of radioactive isotopes in a non linear situation.

Brett Luna
09-13-2018, 2:08 PM
You can complicate this all you want, your choice. I choose to keep things simple. Good thing I don't have to calculate the decay rate of radioactive isotopes in a non linear situation.

A favorite 'quote' of mine, often attributed Albert Einstein: "Everything should be made as simple as possible, but not simpler."

Basic algebra is not that complicated and it's a useful tool to have for so many things...and not just college. I'm glad that it's taught because high school should be a challenge. If our young folks can't rise to that challenge, I think maybe we're doing something wrong.

Roger Feeley
09-13-2018, 2:22 PM
I taught High School for eight years and my answer to kids griping about never needing this or that was the same:

When are you ever going to use push-ups? No one is ever going to hire you to be a push-up specialist. You do push-ups to build strength in a part of your body so you can then do something else. It's the same with Algebra, Chemistry, Foreign Language or any subject. These subjects will build up strengths and skills in parts of your brain.

You are in High School now and parts of your brain, if not exercised, are already starting to atrophy. Brain science tells us that if you don't assimilate a second language by puberty, it's very hard for you to learn a foreign language later in life. Look at immigrant families where the young children pick up English with ease and older parents struggle all their lives. Conversely, my son-in-law was born in Moscow and emigrated to Canada when he was four. He learned English in Toronto and now speaks six languages fluently.

So, yes, you may never have a use for Algebra but that part of your brain will always be available to you and your reasoning abilities will be stronger. Just like doing push-ups makes it easier for you to play Basketball or Tennis or a million other things.

It always seemed to satisfy them.

John K Jordan
09-13-2018, 2:28 PM
Good thing I don't have to calculate the decay rate of radioactive isotopes in a non linear situation.

It's not that hard. But it's usually no problem - even 45 years ago I didn't need any math when I needed to know the radioactive strength of a source (in my case of iridium-192 and cobalt-60). Everyone used tables. (Maybe they have an app these days.) The person who made the tables was the one who had to be literate.

Phillip Gregory
09-13-2018, 10:09 PM
When was the last time you used algebra? I got C's and D's in algebra but aced geometry which I use all the time while wood working. The grandson has a five year degree from Purdue in food science and had to take endless algebra, trig, and calculus classes. He holds several patents. I asked him when was the last time he used algebra. He just gave me a blank look. Told me he had several thousand dollars wrapped up in books and classes in those subjects.

So, we mostly did away with shop class and home economics and now a lot of people can't change a light bulb or car tire, but we still retain algebra classes in high school. Maybe it just one of those hoops you have to jump through to qualify for the next higher level.

I last used algebra the last time a few minutes before I left work. I work in healthcare, which is a field notorious for the Barbie sentiment of "Math is haaaaard!" You have somebody using 3 of something per day and you need a month's worth. x quantity/month = 30 days/month * 3 ea/day. Hmm, solve for x, that is algebra! Just because it isn't polynomials or factoring doesn't mean it's not algebra.

Doing away with shop class and home economics is equally stupid as doing away with algebra. I can't say that I've used my college classes on differential equations very much since graduating, but simpler math such as algebra, and for woodworkers, trig, gets used a lot. Shoot, calculus even gets some use if you have to figure out any sort of statics/strengths or fluids problems- which is pretty common in the skilled trades, but many don't really realize that is really what they are doing (they are using the derived formulas and constants to do the calculations, or using lookup tables.)

There are many things that schools concentrate on today that are actually worthless, but algebra is not one of them.

Steve H Graham
09-14-2018, 11:35 AM
The other day, I read that Bill Nye (non-scientist with bachelor's degree in mechanical engineering) had said something really stupid about the New England Patriots "Deflategate" scandal. I sat down and used algebra and the ideal gas law to prove he was wrong.

His screwup was major. It was like an ENT giving a patient birth control pills instead of antibiotics for strep throat. Total incompetence. I kind of wonder what kind of program he attended, where they didn't get around to the ideal gas law.

When I was in junior high and high school, I hated math classes because I didn't do any homework. Without practice, exams are hard. I got a D in Algebra II, and I believe I got an F in something called Math Analysis, which was a higher-level course.

When I was about 30, I went back to college after a rather long hiatus, and I decided to become a veterinarian. I had forgotten all about my earlier problems with math. In order to get through calculus and physics, I had to learn algebra at the same time.

I ended up getting a physics degree with a math minor, and then I went to graduate school.

I have used my skills in hobbies and elsewhere. I took up building tube amplifiers for guitars, and my background helped.

The moral of the story is that you shouldn't assume the math courses you take in school are useless. When you're a teenager, you're just too stupid to make calls like that.

I thought math was horrible. I was a little idiot.

In contrast, many trendy liberal arts course ARE useless or even harmful, and when it comes to college, they are certainly expensive.

Bob Glenn
09-17-2018, 2:01 PM
I last used algebra the last time a few minutes before I left work. I work in healthcare, which is a field notorious for the Barbie sentiment of "Math is haaaaard!" You have somebody using 3 of something per day and you need a month's worth. x quantity/month = 30 days/month * 3 ea/day. Hmm, solve for x, that is algebra! Just because it isn't polynomials or factoring doesn't mean it's not algebra.

Doing away with shop class and home economics is equally stupid as doing away with algebra. I can't say that I've used my college classes on differential equations very much since graduating, but simpler math such as algebra, and for woodworkers, trig, gets used a lot. Shoot, calculus even gets some use if you have to figure out any sort of statics/strengths or fluids problems- which is pretty common in the skilled trades, but many don't really realize that is really what they are doing (they are using the derived formulas and constants to do the calculations, or using lookup tables.)

There are many things that schools concentrate on today that are actually worthless, but algebra is not one of them.

Ahhhhhhh. 3 times 30 is algebra? Anyone can over complicate things as we are seeing. Just sayin.......

Jim Koepke
09-17-2018, 3:53 PM
Everyone used tables. (Maybe they have an app these days.) The person who made the tables was the one who had to be literate.

A trig table is kept in the shop. The only calculator out there is of the slip stick variety. The trig tables are used to calculate as needed.

Just have to remember things like Chief Soh Cah Toa, Eli the Ice man and the eye (I) seeing the eagle (E) over the rabbit (R) I=E/R.

jtk

Lee DeRaud
09-17-2018, 3:59 PM
A trig table is kept in the shop. The only calculator out there is of the slip stick variety. The trig tables are used to calculate as needed.You have a sliderule without trig functions?!? What kind of backwoods do you live in? :)

Jim Koepke
09-17-2018, 6:19 PM
You have a sliderule without trig functions?!? What kind of backwoods do you live in? :)

In the backwoods of barely knowing the basics of multiplying and division on a slide rule. They were on their way out during my high school years.

It's not the slide rule, it is the user.

jtk

Charlie Velasquez
09-17-2018, 6:58 PM
..... Anyone can over complicate things as we are seeing. Just sayin.......

I would have said just the opposite, a good understanding of algebra and math simplifies things. My experience as a fifth grade teacher, primarily math & science.

Solving math problems is a state of mind. Once the kids are in the right frame of mind they pretty much can do just about anything.
Probably two of the most difficult operations for fifth graders is subtraction of mixed numbers with regrouping, and division of mixed numbers. Most text books don't even broach division of mixed numbers in fifth grade. My kids didn't even know these operations were supposed to be difficult, they just did it - without me showing them how.

Our district had hired a new curriculum director. The first thing she did was visit classrooms to see what we were doing. When she got around to me she looked at my lesson plan book, then sat in the back and watched. We started the lesson by repeating rule #1: "If you're adding elephants you should . . . add elephants." She looked confused.
My kids smiled, "Oh, yes, that's the most important rule in arithmetic."

First problem we did was something like 4hrs 17 minutes minus 1hr 25 minutes, we talked about borrowing from the hours and adding to the minutes. The kids worked through that. Then 7 weeks 2 days minus 2 wks 4 days. We did a few more like that. Gave the kids some to do at their desk as I walked around. The director came up to me and whispered, "Your plan says you were supposed to be introducing subtraction of mixed numbers with unlike denomnators and regrouping, why did you change?"
I looked at her and replied, "I didn't. The kids can do it now, they just don't know they can do it.
...I wasn't going to do this till tomorrow, but, ok..."

So, I told each row to choose one person to go to the board. "Alright, here's the deal, if the person you selected gets this problem right, your whole row gets candy (yeah, I used candy a lot). Ready, 5ft 2in minus 3ft 5in," (chose ft and in on purpose)...... And everyone at the board got it right. Director wasn't impressed
"Must have been too easy. Alright, try this one... it will look a little different, so if you people at the board want, you can talk it over with the people in your row. And people in the the rows, you need to watch your person, if you think they are doing it wrong, you can tell them to stop and have a row conference.... and there is more candy involved!
5 2/12 minus 1 5/12. "

Within a minute you could see the light bulbs click on. Kids at their seats were calling for conferences, the ones at the board were exasperated, "I don't need a conference I know what to do!" But the rules called for the conference if requested. Then all were talking about how to do the problem.
Pretty soon every person at the board had the right answer, and most of the people at their seats could explain how they got it.

I went to the board, erased the 2/12 and changed it to 1/6, and asked, "And now?"
They replied, "No problem, just change it to 12ths so they are the same again." Left it on the board as we did a couple of similar problems.
Erased the 1/6 and changed it to 1/4. "Same way you did it before. It's the same problem as before, just with different numbers," they said.

BINGO! Once they realized that all those problems were the same thing, including the days/hrs and similar, but only looked different, with different numbers, they had it beat. That's what teaching algebra, Common Core, and similar is all about. It teaches a way of thinking, a way of attacking a problem. It is a very convenient vehicle for learning to organize a problem and finding a solution.

John K Jordan
09-17-2018, 7:04 PM
A trig table is kept in the shop. The only calculator out there is of the slip stick variety. The trig tables are used to calculate as needed.

Just have to remember things like Chief Soh Cah Toa, Eli the Ice man and the eye (I) seeing the eagle (E) over the rabbit (R) I=E/R.

jtk

Same here. I used the slide rule for multiplication/division, logs and square root but used tables for trig - more precise and quicker.

For remembering simple trig/geometry we were taught Oscar Had A Heap Of Apples.

The slide rule we used for the pilot's license was a special circular rule, also did wind vectors and such. A friend of mine preferred a circular slide rule over a stick - he said this let him operate it with one hand while he did the math with a pencil in the other hand. Better man than I.

Remember when all the math/science classrooms had a giant slide rule on the wall above the blackboard?

JKJ

Pat Barry
09-17-2018, 7:47 PM
Same here. I used the slide rule for multiplication/division, logs and square root but used tables for trig - more precise and quicker.

For remembering simple trig/geometry we were taught Oscar Had A Heap Of Apples.

The slide rule we used for the pilot's license was a special circular rule, also did wind vectors and such. A friend of mine preferred a circular slide rule over a stick - he said this let him operate it with one hand while he did the math with a pencil in the other hand. Better man than I.

Remember when all the math/science classrooms had a giant slide rule on the wall above the blackboard?

JKJ
I forgot there is/was such a thing as a trig table.

Lee DeRaud
09-17-2018, 9:12 PM
The slide rule we used for the pilot's license was a special circular rule, also did wind vectors and such. A friend of mine preferred a circular slide rule over a stick - he said this let him operate it with one hand while he did the math with a pencil in the other hand. Better man than I.You mean a Jeppsen calculator? I used to have my dad's from his Air Force days...one of many treasures that got lost during the multitude of moves we made over the years.

John M Wilson
09-17-2018, 9:17 PM
Solving math problems is a state of mind. Once the kids are in the right frame of mind they pretty much can do just about anything.
That's what teaching algebra, Common Core, and similar is all about. It teaches a way of thinking, a way of attacking a problem. It is a very convenient vehicle for learning to organize a problem and finding a solution.

As a retired high school Physics teacher, this warms my heart. I used to tell my students that the actual subject that they were learning was problem solving. We were just using the physics as a framework to find some good, practical problems to solve.

Carl Beckett
09-18-2018, 2:24 PM
I have a slightly different question, but along the same theme:

What is the goal of Elementary school?
What is the goal of grade school?
What is the goal of high school?
What is the goal of College?

These questions are surprisingly difficult to answer.

As for math and its purpose, the same question could be asked about social sciences? Civics? Literature? Philosophy?

Philosophy is especially intriguing to me, since many of the historically great scientists were also philosophers. I find that the older I get, the more my problem solving starts out on a philosophical level (as in, what is the goal of school to begin with? What are you hoping to achieve by going? What is its purpose? Likely it fits into some higher level 'what is the goal in life' type of question. Unless you can answer these questions, you cant narrow down into a subject matter and how it fits into the higher overall purpose).

And the thing is, every person is a unique case and has their own philosophical view.

So that is my (philosophical) answer.

Travis Porter
09-18-2018, 11:04 PM
My answer to the original poster is to make parents lives hell.

Too many nights I am up with my daughter helping her with her Algebra and searching khan academy and other sites for examples of how to do stuff I have long forgotten. The most recent example was solving and graphing linear inequalities. No matter how I figure out how to do it, it is never the way the teacher showed them how to do it.

Dont get me wrong, I fully support teaching it and the need for teaching it. I just thought I was done with some of the twists that I haven’t used in sooooooo long. I was so wrong.:(

Carl Beckett
09-19-2018, 8:39 AM
My answer to the original poster is to make parents lives hell.

Too many nights I am up with my daughter helping her with her Algebra and searching khan academy and other sites for examples of how to do stuff I have long forgotten. The most recent example was solving and graphing linear inequalities. No matter how I figure out how to do it, it is never the way the teacher showed them how to do it.

Dont get me wrong, I fully support teaching it and the need for teaching it. I just thought I was done with some of the twists that I haven’t used in sooooooo long. I was so wrong.:(

Yes, this. But I learn another way, and ultimately part of learning how to 'do school' is learning that it isnt about getting the 'right' answer as much as it is about 'giving the teacher the answer they wanted', which often means a particular 'method' or way of doing the problem.

Certainly extra effort to come in with no context and figure out 'how' the teacher wants them to do a particular problem. And most times my son prefers to just figure it out on his own, and keep me out of it (in a way that is mission accomplished right there! - his math is very good).

But after a few years of helping with math homework, my own knowledge has increased.... :)

Bob Glenn
09-19-2018, 10:22 AM
We were always told, to get credit, you must not only have the right answer but also show your work.

Wade Lippman
09-19-2018, 2:35 PM
Oh, algebra has to be taught!

I go on Medicare next month and went into an agent to make sure I had everything right.

She tells me I should get a "G" supplement rather than a "F" supplement because the G only $180/mth compared to the F at $205, but only has $185/term in extra expenses. I say sure, but we are only talking about 3 months, so the F is cheaper. She assures me it isn't.
I point out that the extra $75 for the F is much less than the extra $185 expense for the G.
She gets out her calculator and multiplies 205x3 and subtracts 180x3. She stares at it for 30 seconds and agrees I am right.

It was a very very long session.

Bob Glenn
09-19-2018, 3:57 PM
Okay, okay......But if you're going 80 MPH how long will it take to travel 80 miles?

Jim Koepke
09-19-2018, 4:17 PM
Okay, okay......But if you're going 80 MPH how long will it take to travel 80 miles?

Is part of the equation how long it takes each speeding ticket to be issued?

jtk

Brett Luna
09-19-2018, 7:46 PM
Okay, okay......But if you're going 80 MPH how long will it take to travel 80 miles?

t = d/v

Just because you don't show your work doesn't mean it isn't algebra.

Charlie Velasquez
09-19-2018, 8:55 PM
t = d/v

Just because you don't show your work doesn't mean it isn't algebra.

Yes! Another example of algebra simplifying a problem! Done by a fifth grader...

The problem was the classic fly on the trains.

There is a train on a track in Muscatine, IA, going west at 2mph. There is another train on the same track in Des Moines, IA, going east at 3 mph. There is a fly on the front of the train in Muscatine, it flies at 7 mph straight to the Des Moines train then immediately turns around, flies back to the Muscatine train, then back to the Des Moines train, and so on.. till the trains collide!
The fly begins its journey when the trains are at speed and 150 miles apart.
How far does the fly fly?

Most of my class struggled with this. Then one student answered correctly.
Me: "Outstanding! how did you get this answer?"
Lori: "Well, you said we don't do hard problems, so I changed it to a simple problem.
If I was driving 10 mph and I wanted to know how far I have gone I need to know how long I was driving, then multiply. So if I wanted to know how far the fly went I need to know how long it was flying. So the real problem is how long before they crashed. Then you just multiply"


She came up with a general formula, inputted the data specific to this problem, then it was just arithmetic. The essence of teaching math.

Charlie Velasquez
09-19-2018, 9:05 PM
We were always told, to get credit, you must not only have the right answer but also show your work.

You would probably not have liked some of my tests. Sometimes they already had all the answers on them. They only got credit if they showed how to get it. And just to make it more fun, sometimes I put the wrong answer on 2 or 3 problems and they had to find them.

Matt Mattingley
09-19-2018, 10:29 PM
I personally use algebra all the time. Algebra is just a way of thinking through a word problem. Usually a alphabetical symbol or symbols can be used. a² x b² =c² Sure you could use trig.

Here’s one I give my students. I actually get them to work through it. Solve for X. They already have the training in other areas of math. They need to give me an algebraic equation that will always solve for X. There could be more or less sides or angles but always one angle is missing. How do you solve for X?

Algebra is usually used when trying to solve an unknown with enough known. I’ll leave this one with you guys for fun. 393549

Bill Boehme
09-20-2018, 1:48 AM
Knowing and using higher math on a daily basis saved me from a career of asking "would you like fries with that"? :D

Tom Stenzel
09-20-2018, 9:12 AM
Knowing and using higher math on a daily basis saved me from a career of asking "would you like fries with that"? :D

Algebra is easy.
Board-feet is hard.

By the way Bill, you DID ask for fries. I remember that when I took your order... ;)

-Tom

Bob Glenn
09-20-2018, 1:29 PM
Charlie, that was great, I don't think I could have sorted that one out on my own. Maybe you can help me out with this classic puzzle:

Three guys go into a hotel to spend the night, but there is only one room left, so they decided to share the last room. The hotel manager said that will be thirty dollars for the room, so each man paid ten dollars to make up the thirty and they went up to the room. Soon after, the hotel manager realized that he had charged the men five dollars too much, so he had the bell boy refund the five dollars. However, the bell boy didn't know how to split the five dollars three ways, so he just gave each man a one dollar refund and kept the two dollars left over as a tip.

So now, each man paid ten dollars then got a dollar back, so now each man paid nine dollars. So the total the men paid was twenty seven, plus the two dollars the bell boy kept, make it twenty nine dollars. What happened to the other dollar?

Brett Luna
09-20-2018, 2:02 PM
Charlie, that was great, I don't think I could have sorted that one out on my own. Maybe you can help me out with this classic puzzle:

Three guys go into a hotel to spend the night, but there is only one room left, so they decided to share the last room. The hotel manager said that will be thirty dollars for the room, so each man paid ten dollars to make up the thirty and they went up to the room. Soon after, the hotel manager realized that he had charged the men five dollars too much, so he had the bell boy refund the five dollars. However, the bell boy didn't know how to split the five dollars three ways, so he just gave each man a one dollar refund and kept the two dollars left over as a tip.

So now, each man paid ten dollars then got a dollar back, so now each man paid nine dollars. So the total the men paid was twenty seven, plus the two dollars the bell boy kept, make it twenty nine dollars. What happened to the other dollar?

The 'other dollar' is a red herring. You don't add the two dollars, you subtract it.

The math should be: Actual room cost ($25) = amount paid ($30) – partial refund for overcharge ($3) – amount kept by bellboy ($2)

Matt Mattingley
09-20-2018, 2:27 PM
This is why the saying BEDMAS needs to be applied. Brackets Exponents Division Multiplication Addition subtraction. This is called order of operations. 10x3=1+1+1+2+25=25+3+2= (25÷3)(1x3)+2



The three men are out $28. 28÷3=$9.33 they each gave $.66 tip to the bellboy. $.66x3=$2.00

Charlie Velasquez
09-20-2018, 2:43 PM
The 'other dollar' is a red herring. You don't add the two dollars, you subtract it.

The math should be: Actual room cost ($25) = amount paid ($30) – partial refund for overcharge ($3) – amount kept by bellboy ($2)


Yes, But I will use your equation to form the equation I would have used to explain it.... by using the process Kev Williams used in post #46 to get the $30 by itself on one side.

Actual room cost ($25) = amount paid ($30) – partial refund for overcharge ($3) – amount kept by bellboy ($2)
First move the Bellboy'"tip" to the other side by adding the same to each side to zero it on the right.
Actual room cost ($25) + amount kept by bellboy ($2) = amount paid ($30) – partial refund for overcharge ($3) – amount kept by bellboy ($2) + amount kept by bellboy ($2) =>
Actual room cost ($25) + amount kept by bellboy ($2) = amount paid ($30) – partial refund for overcharge ($3) – 0


Next move the amount paid to the left by adding the partial refund for overcharge ($3) to both sides
Actual room cost ($25)+amount kept by bellboy($2)+partial refund for overcharge($3)=amount paid ($30)–partial refund for overcharge($3)+partial refund for overcharge($3) –0 =>
Actual room cost ($25)+amount kept by bellboy($2)+partial refund for overcharge($3)=amount paid ($30) -0 -0 = $30

But to address the apparent anomaly,
The two dollars is the red herring as Brett said.
The $27 dollars that the men paid included the $25 charge AND the the two dollars the bellboy kept, so you don't add that again. You only add the $3 change they got back to get the $30. You can see in the last equation that you already added that $2, so you know you don't do it again.

Bob Glenn
09-20-2018, 3:32 PM
This is why the saying BEDMAS needs to be applied. Brackets Exponents Division Multiplication Addition subtraction. This is called order of operations. 10x3=1+1+1+2+25=25+3+2= (25÷3)(1x3)+2

Matt, I always heard, Pretty Please my dear aunt Sally. Parenthese, Powers, Multiplication, Division, Addition, Subtraction.

Bob Glenn
09-20-2018, 3:35 PM
Ding, Ding, Ding, Ding.........Exactly! You guys are too smart! Good on ya. Bob

Brett Luna
09-20-2018, 3:41 PM
Just to illustrate it another way, since I'm a Government budget professional:




Guest Room
$ 30.00


Room Rate Adjustment
$ (5.00)


Bellhop service charge
$ 2.00


Subtotal
$ 27.00


CASH PAID
$ (27.00)


AMOUNT DUE
$ 0.00

Ben Rivel
09-20-2018, 5:42 PM
lol "BEDMAS"! Or in the US we learn "PEMDAS" to remember the order of operations (LINK (https://en.wikipedia.org/wiki/Order_of_operations)), see Mnemonics section.

Pat Barry
09-20-2018, 6:08 PM
OMG - This example is just sleight of hand, not algebra.

Matt Mattingley
09-20-2018, 10:42 PM
lol "BEDMAS"! Or in the US we learn "PEMDAS" to remember the order of operations (LINK (https://en.wikipedia.org/wiki/Order_of_operations)), see Mnemonics section.

They’re both right. Which one seems easier to remember???

Matt Mattingley
09-20-2018, 11:00 PM
Billy works in an automotive shop and he changes oil. He gets paid .3 of an hour (on piecework). He is saving for a trip that will cost a total of $3000. He only works five days a week but his daily expenses are $35. He will be gone for a week so he needs to cover those expenses as well. This is Monday at the start of his shift. He leaves in 6 weeks to the day. How many oil changes does he need to do if he makes $30/piecework hour in the next six weeks? And how many will he need to do per day?

Bob Glenn
09-21-2018, 10:15 AM
You would probably not have liked some of my tests. Sometimes they already had all the answers on them. They only got credit if they showed how to get it. And just to make it more fun, sometimes I put the wrong answer on 2 or 3 problems and they had to find them.

Charlie, I wish I would have a teacher like you. I probably would have done better in school. We need more like you! Bob Glenn

Pat Barry
09-21-2018, 10:20 AM
Billy works in an automotive shop and he changes oil. He gets paid .3 of an hour (on piecework). He is saving for a trip that will cost a total of $3000. He only works five days a week but his daily expenses are $35. He will be gone for a week so he needs to cover those expenses as well. This is Monday at the start of his shift. He leaves in 6 weeks to the day. How many oil changes does he need to do if he makes $30/piecework hour in the next six weeks? And how many will he need to do per day?
Lets make it real. Billy will charge the trip on his Chase Visa card and pay it off over time with minimum required monthly payment, and he will likely miss a payment every now and then
Now you figure out the real cost of that trip assuming a 19.8% interest rate and $30 penalty charge for missing a few payments over the next 4 years.

Matt Mattingley
09-21-2018, 10:47 AM
Lets make it real. Billy will charge the trip on his Chase Visa card and pay it off over time with minimum required monthly payment, and he will likely miss a payment every now and then
Now you figure out the real cost of that trip assuming a 19.8% interest rate and $30 penalty charge for missing a few payments over the next 4 years.
Lol don’t forget Billy is 33 years old and still lives in his parents basement. His mom which is 65 years still cook his meals, packs his lunch, does his laundry, cleans up after him and makes his bed.

Charlie Velasquez
09-21-2018, 1:50 PM
Lol don’t forget Billy is 33 years old and still lives in his parents basement. His mom which is 65 years still cook his meals, packs his lunch, does his laundry, cleans up after him and makes his bed.

All because he didn't pay attention in class when he took algebra in high school! See how important it was?

Charlie Velasquez
09-21-2018, 1:59 PM
Charlie, I wish I would have a teacher like you. I probably would have done better in school. We need more like you! Bob Glenn

Thanks. I was lucky, every morning I would get ready for school and say to myself, "Today I get to be a teacher!" Not everyone finds a job that makes him/her happy to wake up.

Even after I retired from the classroom, my wife let me teach her math and science lessons. I still get to teach as I work with at-risk kids in an after-school program.

Bill Boehme
09-21-2018, 5:39 PM
Charlie, that was great, I don't think I could have sorted that one out on my own. Maybe you can help me out with this classic puzzle:

Three guys go into a hotel to spend the night, but there is only one room left, so they decided to share the last room. The hotel manager said that will be thirty dollars for the room, so each man paid ten dollars to make up the thirty and they went up to the room. Soon after, the hotel manager realized that he had charged the men five dollars too much, so he had the bell boy refund the five dollars. However, the bell boy didn't know how to split the five dollars three ways, so he just gave each man a one dollar refund and kept the two dollars left over as a tip.

So now, each man paid ten dollars then got a dollar back, so now each man paid nine dollars. So the total the men paid was twenty seven, plus the two dollars the bell boy kept, make it twenty nine dollars. What happened to the other dollar?

It's $30 - $3 - $2 tip = $25. Don't forget that I wanted fries and a Big Gulp with my double bacon cheeseburger.

Tyler A Anderson
09-21-2018, 6:59 PM
Why Algebra?

Because its the foundation of advanced math and science. Want to do physics? yep, need algebra. Chemistry, engineering, computer science, medicine, yep those all require algebra as well.

The real question is why do we wait so long to introduce it to kids, it should start in elementary school

Charlie Velasquez
09-21-2018, 8:30 PM
Why Algebra? Because its the foundation of advanced math and science. Want to do physics? yep, need algebra. Chemistry, engineering, computer science, medicine, yep those all require algebra as well. The real question is why do we wait so long to introduce it to kids, it should start in elementary school

The NCTM have had the basics of algebra as standards starting in 3rd or 4th grade for a long time.... decades. But change in education comes slowly.

Regardless of standards, many teachers tend to teach the way they were taught.
They see some students struggle as they introduce a new focus of instruction (the relationship between numbers instead of the computation of numbers), so they revert to what "worked" for them when they were growing up.

Or, maybe the teacher doesn't understand or embrace the new focus him/her self.
Alas, my experience is a lot of elementary teachers fell in love with teaching because they loved to read, not because they loved math (many of those ended up as math teachers in middle and high school). So, their focus is often on teaching the kids to find a specific answer to a specific problem, not understanding the how or why.

Common Core standards incorporated much of the NCTM work, and you can read about the backlash in the news on a regular basis. Change comes slowly.....

Matt Mattingley
09-21-2018, 11:45 PM
All because he didn't pay attention in class when he took algebra in high school! See how important it was?
Charlie I appreciate everything you have said in this thread. It touches home with a grand slam. In grade school I was in the top 5% for math. When I hit high school my math teachers turn me the other way. In grade 11 I found a physics teacher. Who took the time to really hone my skills. He used to say to me I think you stay after class for about half hour. In 3 to 4 weeks he fixed and caught me up. I kept pushing for the extra help. (I took its course because I was on his track team and had a good feeling how he would treat me). I took his gr12 & pre-university course gr13. And never advanced on the training. I never went to university. I went to a pretty decent college as I liked working with my hands. I took automotive and machine shop. I became a fixture maker comet tool and die maker and partially a millwright. This one teacher had the desire to teach. He provided me with the steppingstones and the desire. I partially finished a automotive apprenticeship. Built 6 houses from the ground up. And worked for 25 years carving metal.

I Somewhat retired three years ago. Now I teach in a college. I push my kids hard, but I like to stop for second and remember where I once was, and try to give back. So three days a week I now stay for half hour on my own time for those who wish to get extra help.

I usually have 3 to 4 students staying. One of them is a mature student. The mature student is the top kid in my class, but he’s trying to find out the little extra tricks to remembering, and takes advantage of the free time.

Charlie you seem like a teacher that I would’ve respected as a student or now a coworker!

Charlie Velasquez
09-22-2018, 2:48 AM
Charlie I appreciate everything you have said in this thread. . . .

Charlie you seem like a teacher that I would’ve respected as a student or now a coworker!

Thanks. Every life has its high and lows. Teaching, especially math and science, always got me through the lows. In fact, one of those lows was when my wife asked me if I loved teaching more than her . . . and I hesitated... ;)

Phillip Gregory
09-22-2018, 7:46 AM
Lol don’t forget Billy is 33 years old and still lives in his parents basement. His mom which is 65 years still cook his meals, packs his lunch, does his laundry, cleans up after him and makes his bed.

A Billy that works as a mechanic doing $30/piecework hour would not be likely to be still living in his parent's basement. The Billy living in his parents' basement at 33 would need to figure out how much income-based repayment of his $150,000 student loan debt for his underwater basket weaving degree slows down paying off his credit card. Bonus points if he figures out how much he'd actually have to pay on that student loan debt and *if* he'd ever pay it off.

The mechanic Billy's calculations would need to calculate how much he actually gets to take home after paying $600/month for health insurance to heavily subsidize his 65 year old parents' Medicare and how much he has to pay in income and payroll taxes for their Social Security.

Bob Glenn
09-22-2018, 10:09 AM
I was a shop teacher after graduating from college. I only lasted a couple years and moved on to something else after realizing teaching wasn't for me. You are a special breed.

Prashun Patel
09-22-2018, 11:14 AM
I heard algebra is taught in middle school because the ability to conceive abstractly about unknowns develops in the mind during puberty.

Not sure how much fact there is to that.

Charlie Velasquez
09-22-2018, 3:16 PM
I heard algebra is taught in middle school because the ability to conceive abstractly about unknowns develops in the mind during puberty.

Not sure how much fact there is to that.

Pretty accurate according to many educational psychologists. Formal operations (abstract thinking) starts about 10-12 years for most kids according to Piagetian theorists (a leading educational psychologist in the 50's-80's). But there have been cases of kids reaching that stage much, much earlier. But that is for completely abstract reasoning. Basic concepts can be introduced earlier, but needs a lot of concrete manipulation and/or visual representation.

So, at about 5th grade you can see kids start to handle a little more abstract thinking. Research suggests that by and large you can't do a lot to speed up that cognitive development but if you have a kid on the threshold of formal and concrete operations, you can give him/her a nudge with adequate novel experiences.

John K Jordan
09-22-2018, 3:42 PM
...Formal operations (abstract thinking) starts about 10-12 years for most kids according to Piagetian theorists (a leading educational psychologist in the 50's-80's). But there have been cases of kids reaching that stage much, much earlier. ...


It would be a shame to start some types of education to fit the average and fail to identify and challenge those who might benefit earlier.

An example - a friend here started at the U of TN Animal Science when she was 13 and graduated number 1 in her class, in Vet school now. Fortunately, she had strong family support.

I've known some without such support and challenge - they seemed to always be bored and frustrated, some labeled trouble makers in public schools. Maybe there is better screening in public schools these days and special help for those on the far end of the spectrum.

Charlie Velasquez
09-23-2018, 9:17 AM
It would be a shame to start some types of education to fit the average and fail to identify and challenge those who might benefit earlier.

An example - a friend here started at the U of TN Animal Science when she was 13 and graduated number 1 in her class, in Vet school now. Fortunately, she had strong family support.

I've known some without such support and challenge - they seemed to always be bored and frustrated, some labeled trouble makers in public schools. Maybe there is better screening in public schools these days and special help for those on the far end of the spectrum.

Actually, the last couple of decades I saw just the opposite.
With the advent of the No Child Left Behind legislation federal money was tied to student achievement. Achievement was measured in several ways including the number of students passing minimum grade level competency tests, the disparity between the scores of the whole group and various sub-groups of your student population, and having a minimum percentage of students taking the test so as to not inflate the scores by having low kids just not test. A district did not get points for how high students scored, only how many passed minimum competency (in Iowa that was at the 40th petcentile on the Iowa Test of Basiic Skills /Educational Development as measured on the 2001 tests).

Not only was federal money dependent on the scores, but state busing money and other ancillary expenses were affected. Newspapers published these scores and resultant labels (watch lists, schools or district in need of assistance). Realtors listed these when selling houses.

One can see immediately a school can improve their chances of staying off the bad lists by focusing their efforts on the students who were the bottom 40% or on the bottom of the at-risk populations (low social economic, English Limited Learners, special education). So that is what many districts did. District money and teacher inservices focused on these students. Schools' curriculum was modified to emphasize the types of problems the "bubble kids" were likely to have on the ITBS.

The first place money could be found to pay for this shift was from the budget of the talented and gifted as those students would hit the minimum level regardless. So, many did. In some districts there was immediate backlash. In Seattle parents of T&G students threatened to pull their kids from state tests if the T&G budget was not restored. This would reduce the number of kids passing, thereby increasing the percentage of kids not passing, and possibly reduce the participation number below the critical threshold.

Other districts handled it more discreetly; more stringent requirements to qualify for the T&G program or making the program a push-in rather than a pull-out (so the T&G teachers could also work with the other students in the class, freeing up the classroom teacher for a time to do remedial work with the lower 40%).

This new focus was successful. As a nation we did improve instruction for the lower 40%, and the spotlight on achievement gap of various sub-groups helped to identify where we were failing. But, there were casualties. Subjects not on the state assessments were left to hang in the wind. In our district penmanship, spelling, and social studies were de-emphasized. And, I suspect, the T&G and the near T&G kids got less indvidual attention.

William Adams
09-23-2018, 11:06 AM
And that's it in a nutshell.

Education would be best if it enabled each student to reach their maximum potential and be the best possible citizen, and it's a disservice to society to fail to give any student the best education which they are suited for.

Getting back to the original topic, the game "Dragonbox" is essentially an Algebra tutorial --- highly recommended.

Jim Koepke
09-23-2018, 12:04 PM
In Seattle parents of T&G students threatened to pull their kids from state tests if the T&G budget was not restored.

Even with my rusty algebra skills it wasn't difficult to solve for T&G.

Why are some students called Tongue & Groove?

Is this a special class in high schools now? Isn't it just part of wood shop?

jtk

Dave Zellers
09-23-2018, 10:49 PM
Yes! Solve for T&G and show your work.

Now I understand why this thread became so long. :D

Both machine and hand tool answers will be accepted.

Pat Barry
09-24-2018, 7:46 AM
Actually, the last couple of decades I saw just the opposite.
With the advent of the No Child Left Behind legislation federal money was tied to student achievement. Achievement was measured in several ways including the number of students passing minimum grade level competency tests, the disparity between the scores of the whole group and various sub-groups of your student population, and having a minimum percentage of students taking the test so as to not inflate the scores by having low kids just not test. A district did not get points for how high students scored, only how many passed minimum competency (in Iowa that was at the 40th petcentile on the Iowa Test of Basiic Skills /Educational Development as measured on the 2001 tests).

Not only was federal money dependent on the scores, but state busing money and other ancillary expenses were affected. Newspapers published these scores and resultant labels (watch lists, schools or district in need of assistance). Realtors listed these when selling houses.

One can see immediately a school can improve their chances of staying off the bad lists by focusing their efforts on the students who were the bottom 40% or on the bottom of the at-risk populations (low social economic, English Limited Learners, special education). So that is what many districts did. District money and teacher inservices focused on these students. Schools' curriculum was modified to emphasize the types of problems the "bubble kids" were likely to have on the ITBS.

The first place money could be found to pay for this shift was from the budget of the talented and gifted as those students would hit the minimum level regardless. So, many did. In some districts there was immediate backlash. In Seattle parents of T&G students threatened to pull their kids from state tests if the T&G budget was not restored. This would reduce the number of kids passing, thereby increasing the percentage of kids not passing, and possibly reduce the participation number below the critical threshold.

Other districts handled it more discreetly; more stringent requirements to qualify for the T&G program or making the program a push-in rather than a pull-out (so the T&G teachers could also work with the other students in the class, freeing up the classroom teacher for a time to do remedial work with the lower 40%).

This new focus was successful. As a nation we did improve instruction for the lower 40%, and the spotlight on achievement gap of various sub-groups helped to identify where we were failing. But, there were casualties. Subjects not on the state assessments were left to hang in the wind. In our district penmanship, spelling, and social studies were de-emphasized. And, I suspect, the T&G and the near T&G kids got less indvidual attention.
T&G kids don't deserve more public funding than those with special needs or your typical, run if the mill, average students, do they? On the other hand, brining up the average by teaching the less than T&G makes the most sense. Not to say that the T&G should be neglected, but, lets face it, they are already ahead, so maybe they should be moved up a grade.

Jim Becker
09-24-2018, 8:50 AM
Pat, the issue with "moving T&G students up a grade" is that it often puts them in with students that are at a different development level emotionally and socially and that can be a a real problem for many. By providing more challenging and stimulating material in their normal grade for age, they get what they need to develop intellectually without compromising them being normal, growing kids otherwise. The programs also benefit the more average students in that they (and their teachers) are not distracted by having time taken for more advanced studies in the mainstream classroom. The purpose of education is to help each and every student be the best they can be...poor funding aside.

Pat Barry
09-24-2018, 9:34 AM
Pat, the issue with "moving T&G students up a grade" is that it often puts them in with students that are at a different development level emotionally and socially and that can be a a real problem for many. By providing more challenging and stimulating material in their normal grade for age, they get what they need to develop intellectually without compromising them being normal, growing kids otherwise. The programs also benefit the more average students in that they (and their teachers) are not distracted by having time taken for more advanced studies in the mainstream classroom. The purpose of education is to help each and every student be the best they can be...poor funding aside.
No good answer for sure, and I'm not convinced algebra can solve the problem. Probably involves calculus.

Charlie Velasquez
09-24-2018, 9:39 AM
Pat, the issue with "moving T&G students up a grade" is that it often puts them in with students that are at a different development level emotionally and socially and that can be a a real problem for many. .....

This was the case for one of my students, similar to John's friend, a prodigy. Entered our school as a 5-year old kindergartener, a month later they put him in 1st grade with extra instruction. Skipped 2nd grade. Third grade with extra instruction. Fourth grade he came to my class for 5th grade math and science. Semester he was moved to my fifth grade class full time. We flip-flopped specials (art, music p.e.), he went with the other 5th grade section while my class had math. When my class had specials he stayed for one-on-one math.

His family moved to Moline, IL during the summer. I saw his dad the following October and asked how Chad liked middle school.
Dad replied, "He's not in middle school. We had him repeat fifth grade. As we got ready to register we told him of all the advanced things he would learn. He started crying. He told us all he wanted was to be able to play kickball with his classmates."

My class had always included him in recess games and things, but the kid was smart. He knew he was the worst kickball player, the slowest in races; he knew he was different. He had always had emotional support from our staff, his parents, and his classmates; but he still knew. Saw his mom many years later. Chad was married and was working for Qualcom (are they still around?). Said holding him back was the best decision they ever made.

Jim Becker
09-24-2018, 11:36 AM
Your story about Chad doesn't surprise me...and it just reinforces my feeling that adapting the learning for more gifted students while letting them still have the opportunity to be kids with their age peers is a good thing. And thank you for being a teacher...the most important occupation in the world bar none.

Jim Andrew
10-02-2018, 10:55 PM
I was that PITA kid who always could show the teacher a simpler way to solve a problem. In spite of my public school education, I found math skills very helpful in the construction business. Especially before I bought a calculator. I would have loved to be allowed to graduate a year or four early.

Ole Anderson
10-03-2018, 9:51 AM
Algebra is basically the intro course to more complex math. How are you going to know math is your stuff if you don't try it out? My question is why Latin?

William Adams
10-03-2018, 10:37 AM
Latin helps one to understand the well-springs of our language, and is an excellent foundation for the arts and sciences, all of which are helped by knowing it.

For the story about Chad --- that's why the school system which I attended for 3rd and 4th grade limited working ahead of one's grade level to academic courses only --- one still did recess and so forth with one's peers. It was a great system until the state Supreme Court ruled it illegal.

Bob Glenn
10-03-2018, 11:40 AM
My school didn't offer Latin. I sure could have used it more than algebra. I agree, algebra is an intro to higher math, which most people don't use. A lot of the examples cited in the previous posts are simple arithmetic problems, nothing more. (is your six foot long board long enough if you need a 30 inch piece and an 18 inch piece? Really?) Please look to wikipedia for a description of algebra.

Brett Luna
10-03-2018, 3:17 PM
A lot of the examples cited in the previous posts are simple arithmetic problems, nothing more. (is your six foot long board long enough if you need a 30 inch piece and an 18 inch piece? Really?) Please look to wikipedia for a description of algebra.

Wikipedia (https://en.wikipedia.org/wiki/Elementary_algebra) may not support your assertion as much as you think: "Whereas arithmetic deals with specified numbers,[1] algebra introduces quantities without fixed values, known as variables.[2]"

Yes, the problem as you presented it is arithmetic because it is the special case where the quantities are specified numbers...with the added wrinkle of asking if the stock board is long enough, yes or no. But another way of looking at it is: I have several boards on hand in various lengths. What's the shortest board I can use to cut a given number of shorter boards? In algebraic form you can express it as:

TLmin = L1 + L2 [... + Ln]

Where:

TLmin = total minimum length of stock board

L1 = length of board 1

L2 = length of board 2

Ln = lengths of additional boards



This is a generalized representation that can be applied to specific problems. It is both algebra and simple...so simple, most of us substitute for L1 and L2 then solve for TLmin on the fly, in our heads, without really giving it a second thought...or showing our work.

Lee DeRaud
10-03-2018, 3:34 PM
My school didn't offer Latin. I sure could have used it more than algebra. I agree, algebra is an intro to higher math, which most people don't use.Most people don't use Latin either. And for a large percentage of the people who do, it's mostly as a way to make their jobs look harder (i.e. more valuable) to outside observers.

The real value of algebra is that it is a vaccine against chronic innumeracy. Part of the higher math it introduces is probability/statistics, which is almost as good as Latin for sliding nonsense past people who don't understand it.

Charlie Velasquez
10-03-2018, 4:27 PM
My school didn't offer Latin. I sure could have used it more than algebra. I agree, algebra is an intro to higher math, which most people don't use. A lot of the examples cited in the previous posts are simple arithmetic problems, nothing more.....

And that is math (algebra, calculus, trig, et al,) in a nutshell... to reduce a problem to nothing more than an arithmetic solution.

Charlie Velasquez
10-03-2018, 4:29 PM
Most people don't use Latin either. And for a large percentage of the people who do, it's mostly as a way to make their jobs look harder (i.e. more valuable) to outside observers.

The real value of algebra is that it is a vaccine against chronic innumeracy. Part of the higher math it introduces is probability/statistics, which is almost as good as Latin for sliding nonsense past people who don't understand it.

Hey!, I resemble that remark! My degree is in educational statistics & measurement...

Lee DeRaud
10-03-2018, 6:43 PM
Hey!, I resemble that remark! My degree is in educational statistics & measurement...Just because it's good doesn't mean it can't be misused. :)
(I have a MS in math, BTW)

John K Jordan
10-03-2018, 6:55 PM
Most people don't use Latin either. And for a large percentage of the people who do, ...


Hmm.. "a large percentage"? Sounds like statistics. :)

I don't use latin, but I know several who do, one reason is to read things written in Latin. (None, AFAIK, converse in Latin.) Then there are others I know - one friend (age 17) can converse in seven languages, one speaks AND reads nine, one four - languages must be as easy to them as "Veni, vidi, vici"!

It's refreshing to know there are brilliant people everywhere. One good friend started university at age 13 and graduated number one in her class. An older friend holds 14 patents. A young nephew raised thousands for travel by performing piano concerts while in high school.

Funny thing, those I know with minds like that never seem to feel the need to impress anyone.

JKJ

Steve Demuth
10-03-2018, 7:34 PM
Funny thing, those I know with minds like that never seem to feel the need to impress anyone.

JKJ

I'd go with rarely, rather than never. I work every day with top-drawer scientists and physicians. Most of them (19 of 20, I would guess) don't feel the need to impress anyone. I suspect that's for two reasons: one, the more you know, and the more you are able to understand and manipulate the world through symbolic tools, the more you will generally be aware of the limitations of your knowledge and those tools; two, they know people respect their knowledge and skills because the world comes to them every day for their help.

But there is the odd one who can't help but beat the world over the head with their mastery. Not surprisingly, most of that lot are surgeons. Surgery seems not to breed humility.

Bob Glenn
10-03-2018, 9:18 PM
Sorry, Brett, all due respect, but I'm not buying it.

Phillip Gregory
10-03-2018, 9:58 PM
I'd go with rarely, rather than never. I work every day with top-drawer scientists and physicians. Most of them (19 of 20, I would guess) don't feel the need to impress anyone. I suspect that's for two reasons: one, the more you know, and the more you are able to understand and manipulate the world through symbolic tools, the more you will generally be aware of the limitations of your knowledge and those tools; two, they know people respect their knowledge and skills because the world comes to them every day for their help.

Also, people who are experts in a field such as medicine know that there is a lot that is not yet known and that there are very few certainties in the field. Knowing that even though you are an expert, you can and will be wrong with some regularity, tends to be humbling enough to prevent a lot of arrogance.


But there is the odd one who can't help but beat the world over the head with their mastery. Not surprisingly, most of that lot are surgeons. Surgery seems not to breed humility.

Surgeons have much less uncertainty in their practice than do physicians who practice in primarily cognitive fields. A risk-stratified patient with known cholelithiasis on ultrasound going to a surgeon to laparoscopically remove their stone-filled gallbladder is a very straightforward case and one can perform that very well-defined mechanical task with a high degree of success. The CMS RVRBS also heavily reimburses physicians who touch patients with sharp objects and pays those who do not very little, so the surgeons feel both mastery of their task and reward for doing their work and get arrogant. Contrast that to internists, family physicians, and others in "cognitive specialties" who mainly bill off of E&M codes and not procedure codes and get paid a small fraction of what surgeons make, try to diagnose new patients with vague, ill-defined symptoms, and their MBA employers are largely replacing them with midlevels who do much of their extremely limited training online. That breeds demoralization, not arrogance.

Also, medical training leads to a lot of self-selection. People who are repulsed by arrogance stay away from surgery, and those who enjoy the one-upsmanship gladly go into surgery.

John K Jordan
10-04-2018, 2:31 AM
But there is the odd one who can't help but beat the world over the head with their mastery. Not surprisingly, most of that lot are surgeons. Surgery seems not to breed humility.

Like you, I detect a calm confidence instead in the sciences and technical fields. During my 30 years at a national research lab I worked and associated with many dozens if not hundreds of highly educated and intellegent people. It was rare to meet someone obviously trying to impress.

Just once, that I can remember - I met a young neighbor's dad who said he also worked at the lab. When I asked him about his area of interest he answered "I'm a PHD scientist." From that I suspected he felt under-appreciated, disliked his field, or was missing something in his life.

JKJ

Brett Luna
10-04-2018, 3:02 PM
Sorry, Brett, all due respect, but I'm not buying it.

I suppose that can't be helped, then. The great thing about beating your head against a wall: it feels so much better when you stop.

John K Jordan
10-04-2018, 5:33 PM
. But another way of looking at it is: I have several boards on hand in various lengths. What's the shortest board I can use to cut a given number of shorter boards? In algebraic form ...

Beautiful formatting Brett! Hand-coded HTML or WYSIWYG editor?

Your example reminded me of software I wrote long ago to pack a number of arbitrary shapes into other arbitrary shapes, e.g. for wood interest consider inputting a cut list and fitting it efficiently into either sheets goods or arbitrary sized boards, maintaining a specified grain orientation, working around defects, and maintaining kerf widths and allowing for surfacing waste. It's been a long time so I forget the details but you can bet your bippy I used a bit o' algebra. Good clean fun!

For those unfamiliar, when developing software the use of constants for anything is rare. The math (simple algebra, matrix algebra, calculus, etc.) is the easy part, normally done on paper first - the computer does nothing but dumb arithmetic. The logic and "bookkeeping" usually need far more thought than the math.

JKJ

Bob Glenn
10-04-2018, 5:40 PM
I know what you mean. Lots of beating going on here. I don't remember a thread this long. Must be a sensitive subject. (pun intended)

Lee DeRaud
10-04-2018, 7:20 PM
I don't remember a thread this long.You need to get out more. :)
https://sawmillcreek.org/showthread.php?238771-Glowforge-release has 1768 posts, but I'm not even sure that's the record here.

Mark Rainey
10-04-2018, 7:24 PM
I enjoyed math in school and excelled in algebra thru calculus. I discovered my daughter had little aptitude in math, and just could not grasp algebra. She was very talented in literature and communication skills, but much less in math. She had multiple tutors and just could not grasp the concepts. The problem for many is that algebra is used in high school as prerequisite to head to college, and if you don't have the ability and you want to go to college, you suffer. Knowledge is a wonderful thing. Algebra can be fun and useful for some. For others it is useless and/or painful, or worse, a roadblock in life. Schools must understand the diverse nature of human intelligence ( athletic, social, musical, verbal, artistic, mathematical, etc ) and support students in pursuing their goals and working through or around obstacles.

Jim Becker
10-04-2018, 7:26 PM
My younger daughter grasps math through calculus very well...except for geometry for some reason. And maps...geography. Go figure... :) :D

Brett Luna
10-05-2018, 2:44 PM
Beautiful formatting Brett! Hand-coded HTML or WYSIWYG editor?

Your example reminded me of software I wrote long ago to pack a number of arbitrary shapes into other arbitrary shapes, e.g. for wood interest consider inputting a cut list and fitting it efficiently into either sheets goods or arbitrary sized boards, maintaining a specified grain orientation, working around defects, and maintaining kerf widths and allowing for surfacing waste. It's been a long time so I forget the details but you can bet your bippy I used a bit o' algebra. Good clean fun!

For those unfamiliar, when developing software the use of constants for anything is rare. The math (simple algebra, matrix algebra, calculus, etc.) is the easy part, normally done on paper first - the computer does nothing but dumb arithmetic. The logic and "bookkeeping" usually need far more thought than the math.

JKJ

Thanks, John but it's simple stuff, really. Done with a combination of WYSIWYG and manual* BB Code entry, using the [FONT], [SIZE], [SUB], and a few other formatting tags. If only the board had a LaTeX plugin, we could have some real fun. I need to install a TeX extension for Chrome one of these days.

*because WYSIWYG's code result is often...um...inelegant.

William Adams
10-05-2018, 3:10 PM
The nicely formatted equation was a nice thing to see.

I've always thought it unfortunate that markup languages didn't learn more from LaTeX, though MathML has been an interesting development.

For the nesting thing --- it's definitely a tough problem. There is an opensource program for it: https://github.com/Jack000/SVGnest (and I believe MakerCAM may have had functionality for it).

Jim Koepke
10-05-2018, 4:44 PM
But there is the odd one who can't help but beat the world over the head with their mastery. Not surprisingly, most of that lot are surgeons. Surgery seems not to breed humility.

This brings to mind an old riddle:

What is the difference between God and a surgeon?

God doesn't think he is a surgeon.


I don't remember a thread this long.

You must have never opened a sharpening thread in the Neanderthal Haven. Some of those got long, then a bit too hot, then closed and removed from view.

jtk

Bob Glenn
10-06-2018, 12:04 PM
There are 10 kinds of people in this world: those who understand binary and those who don't.


Actually, there are ll kinds of people in the world, those that can read Roman numerals and those that can not.

Jason Roehl
10-07-2018, 8:17 AM
There are two kinds of people in the world: those who understand extrapolation.

Steve Demuth
10-07-2018, 9:57 AM
Surgeons have much less uncertainty in their practice than do physicians who practice in primarily cognitive fields ... Also, medical training leads to a lot of self-selection. People who are repulsed by arrogance stay away from surgery, and those who enjoy the one-upsmanship gladly go into surgery.

There are obviously many things at work in my observation. I think the biggest is the combination of self-selection that you mention with the need for a command and control environment in the OR. That puts a premium on certainty, warranted by the procedure at hand or not. It means that for much of their working time, the system demands certainty and command from surgeons. Nevertheless, it has always intrigued me that the anesthesiologists I know are almost uniformly self-effacing, humble people, notwithstanding that they literally take over their patients' physiology wholesale for hours in complex surgeries (which my organization specializes in), maintaining homeostasis and hemodynamic stability in bodies under the most demanding of assaults, when the bodies can't do it themselves.

Steve Demuth
10-07-2018, 10:05 AM
God doesn't think he is a surgeon.


Not long ago we did a 50 hour surgery at our hospital, involving a rotating cast of half a dozen or more surgeons. The teamwork was mind blowing, not even counting the 50 or more supporting MDs and nurses. So take everything I say about surgeons with a grain of salt. To the degree I'm making a negative observation, I'm really talking about a subset, and not the most representative subset at that.

Jim Koepke
10-07-2018, 12:16 PM
Nevertheless, it has always intrigued me that the anesthesiologists I know are almost uniformly self-effacing, humble people

What else can one be but humble when they tell people they pass gas for a living?

jtk

Charlie Velasquez
10-07-2018, 1:18 PM
There are two kinds of people in the world: those who understand extrapolation.

Now that good, it took me a few seconds.
;)