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Thread: Why are we still teaching algebra?

  1. #136
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    Quote Originally Posted by Jim Koepke View Post
    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?
    Yoga class makes me feel like a total stud, mostly because I'm about as flexible as a 2x4.
    "Design"? Possibly. "Intelligent"? Sure doesn't look like it from this angle.
    We used to be hunter gatherers. Now we're shopper borrowers.
    The three most important words in the English language: "Front Towards Enemy".
    The world makes a lot more sense when you remember that Butthead was the smart one.
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  2. #137
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    Quote Originally Posted by Lee DeRaud View Post
    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
    "A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty."
    - Sir Winston Churchill (1874-1965)

  3. #138
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    Quote Originally Posted by Bob Glenn View Post
    ..... 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.
    Comments made here are my own and, according to my children, do not reflect the opinions of any other person... anywhere, anytime.

  4. #139
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    Quote Originally Posted by Jim Koepke View Post
    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

  5. #140
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    Quote Originally Posted by John K Jordan View Post
    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.

  6. #141
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    Quote Originally Posted by John K Jordan View Post
    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.
    Yoga class makes me feel like a total stud, mostly because I'm about as flexible as a 2x4.
    "Design"? Possibly. "Intelligent"? Sure doesn't look like it from this angle.
    We used to be hunter gatherers. Now we're shopper borrowers.
    The three most important words in the English language: "Front Towards Enemy".
    The world makes a lot more sense when you remember that Butthead was the smart one.
    You can never be too rich, too thin, or have too much ammo.

  7. #142
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    Quote Originally Posted by Charlie Velasquez View Post
    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.

  8. #143
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    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.

  9. #144
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    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 havenít used in sooooooo long. I was so wrong.

  10. #145
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    Quote Originally Posted by Travis Porter View Post
    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 havenít 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....

  11. #146
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    We were always told, to get credit, you must not only have the right answer but also show your work.
    Life's too short to use old sandpaper.

  12. #147
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    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.

  13. #148
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    Okay, okay......But if you're going 80 MPH how long will it take to travel 80 miles?
    Life's too short to use old sandpaper.

  14. #149
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    Quote Originally Posted by Bob Glenn View Post
    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
    "A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty."
    - Sir Winston Churchill (1874-1965)

  15. #150
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    Quote Originally Posted by Bob Glenn View Post
    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.
    Brett
    Peters Creek, Alaska

    Man is a tool-using animal. Nowhere do you find him without tools; without tools he is nothing, with tools he is all. ó Thomas Carlyle (1795-1881)

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