Why are we still teaching algebra?

[Kev Williams]

Here's why I failed algebra... below is a screenshot of a 'kids introduction to algebra'..,

================================================== ==

================================================== ======

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]

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]

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]

Here's why I failed algebra... below is a screenshot of a 'kids introduction to algebra'..,

================================================== ==

================================================== ======

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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.