Algebra for everyone? Sometimes I wonder...

Discussion in 'Debate & Marathon Threads Archive' started by atomic, Mar 7, 2010.

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  1. Grover

    Grover Cohort

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    Is algebra for everyone? Absolutely not! Of course, neither is reading. There is nothing that everyone is capable of learning- some kids are born without brainstems for crying out loud. There are, however, pretty compelling reasons for trying to teach algebra to almost everyone. The basic algebraic concept of formulas, constants and variables is a very important way of looking at the world, even if you're not good at all the calculations. All public policy comes down, at some point, to crunching variables through formulas to see what is or is not affordable, what benefits justify what costs, etc. There's not much that is effected by economics or government legislation that doesn't have some algebra hidden in it somewhere, so it does certainly affect your life, even if you aren't the one doing the calculations. Understanding those calculations might help you make better choices about things, though.
     
  2. markinca

    markinca Rookie

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    As a high school math teacher myself, I wonder the same question. Even when you teach the algebra, it seems like it's useless. For example, a couple of weeks ago we went over graphing linear equations. We went over all the different forms, and the different ways to graph those lines, and by the end of it, my kids were getting pretty good at it - they could graph pretty much anything I threw at them. But when I asked them a simple question "Ok, so what does this line represent?"... you could hear a pin drop.

    I guess it's sort of like what one of my college professors told me - if we taught driving like we teach math, we would go over turning the key one day, then go over turning on the blinkers the next day, then go over shifting gears the next, and so on and so on and by the end of the semester you should know how to drive a car, right?
     
  3. indigo-angel

    indigo-angel Companion

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    Mar 30, 2010

    This post is coming from another self proclaimed "not a math person." I think it is important that students learn algebra in high school because as teachers, I strongly feel that we need to teach our students how to think. I think students should be pushed to think critically and abstractly. Most people don't use algebra in their daily lives, but we think every day; we analyze and criticize, we weigh pros and cons,and we use logic. As for the argument that algebra isn't relevant because it doesn't have much real world application, I'd argue that most of what is taught in school involve abstract concepts and thought; things we can't "see" or use every day.
     
  4. Emily Bronte

    Emily Bronte Groupie

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    Some of the earlier posts in this thread mentioned counting on fingers and the like as wrong. I thought that myth was put to rest a long time ago. I could be wrong, but that is what I thought.
     
  5. chessimprov

    chessimprov Rookie

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    Since college is becoming oh that much so important with the economy going down, employers being picky, colleges being picky, and one country competing against another, I consider Algebra a basic course for complex math of Calcalculus and beyond. Most colleges I know require Calculus to be passed for any major now! If nothing else, at least the exposure does not hurt. It can be stressful sure, but I think it's necessary. Of course, you're talking to a math teacher, so I am a bit biased in this regard.

    Algebra is used in everyday life even though you may not realize it. If you're trying to look for that missing number for the number of items leftover, you are in a sense using Algebra. Life is not always something like "5 - 4 = x." Sometimes it could be more like
    "5 - x = 4" and you could be manipulating "5 - x = 4" to
    "5 - 4 = x" without realizing it.

    Something that is very tricky with algebra is that students think they understand it, but they really do not. They can figure out the missing number sometimes, but they do not actually do the steps to work it out. And then if you put the same or very similar math problem in, whether it's in the real world or a problem to do for homework, my students get confused. There's a certain amount of patience and understanding required to understand even basic algebra. I feel like if they could get over this hurdle, they could truly go a long way.

    I ask my students to write out their work and there is this constant struggle of "I have the answer, so that must mean I know what I'm doing" when they probably just copied from someone else, etc. Many of my students never seem to try to do even fun assignments even though they may have fun doing a similar task in-class. The lack of motivation and support, and lack of support for my extra curricular activity and program to use for motivation is frustrating sometimes!
     
  6. hatima

    hatima Devotee

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    This reminds me of two of my high school math teachers, (geometry and Algebra) and my remedial math class in college. Algebra, especially word problems helps you solve other problems because you can approach them better.

    I think that computation is put on the back burner in high school. My teachers assumed we were experts, we probably should have been, at multiplication and adding. We weren't and I wasn't. I'm better at it now.

    In life I use some algebra in my daily life, but it is more basic, and it isn't always recognized as such. (doing longer problems mentally when shopping and have multiple prices with different variables-I don't recognize this as algebra when I do it, but it is--I learned that algebra is real world (some of it) in remedial math)--I guess this is like what chesimprov is saying.

    I see kids using algebra, in a very basic form, in first grade and I'm surprised we don't just call it algebra---wouldn't this help students, who like me have strong anxiety over math? Any thoughts from math teachers on this? Basically 25+n=100 is the same as a elementary text (not using "variables") 25+____ =100? When I thought of algebra like this in college it scared me a lot less.
     
  7. ecl

    ecl Rookie

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    I was standing in line at a store, and a father and son who were in line behind me were having a discussion. The son was asking the father about something they were purchasing, a question that involved simple proportions, and the father did not know the answer. I was stunned that an adult would be lacking this simple knowledge. I wanted to jump in and tell them, but didn't because I did not want to embarrass the father.

    I believe that people would use algebra more often if they were more proficient with it. Learning algebra helps people to conquer that fear of math that seems so prevalent.
     
  8. Marci07

    Marci07 Devotee

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    Apr 11, 2010

    Well for that matter, lets also remove any subjects that we, personally, don't think we need. I honestly didn't see a value of learning history. In fact, I thought I could easily survive with just learning a few facts. I dreaded history, it was the most difficult subject for me because I had to memorize pages of dates and events when I had a brain of teflon, nothing would stick.

    Now as an adult I see great value of learning even subjects that I don't consider essential for my daily living because they make me well rounded.

    Math enhances our ability to problem solve and will make students less intimidated when they read credit cards statements, mortgage papers, and other financial stuff. Using formulas is part of daily lives and involves algebra. Formulas are needed when it comes to remodeling such as installing wood floors. I know for sure that I feel confident knowing how much square footage of tiles I would need for a room.
     
  9. Special-t

    Special-t Enthusiast

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    From what I've seen (subbing elementary and secondary) kids are sorely lacking in multiplication, division and fractions. How are they supposed to understand algebra when the don't know their x-tables?

    I'm very skeptical of the elementary math books I've seen where they give the kids those multiplications boxes to use so they don't have to memorize their x-tables, then they teach them a lot of "new math tricks" to solve problems before they even get the basic concepts.

    Many kids don't even understand what the process of multiplication actually does. So, how are these kids supposed to get Algebra?

    To further impede success, I was told by a math teacher that (in our district) Algebra is taught in phases that supposedly don't require mastery of the prior lesson.

    And, I just have to throw in this wrench, if class sizes were smaller, kids would have the personal attention required to master these skills. This goes against everything I know about learning math.

    I believe that Algebra can be for everyone if they have the proper foundation.
     
  10. Marci07

    Marci07 Devotee

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    I totally agree that students would have a much easier time learning algebra if they had their basics well learned. How is it that this is happening? I dont' know.

    In my opinion students are required to learn a little bit of everything every year. As a result, many don't learn it well and it's forgotten by the next year. Instead, standards should focus on 3 or 4 per year and move on until you master it well.

    Another thing is the fact that there are many teachers who are not proficient in math and pass that fear on to students. They follow textbooks word by word because of their own weakness. I had a teacher once showing me how a textbook addressed times tables in only one lesson. That's all she did.
     
  11. cutNglue

    cutNglue Magnifico

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    I'm with Marci on this one. I think the problem comes down to know having the basics well mastered. This is one area where it is important to differentiate a little more and not just barrel ahead.
     
  12. Grover

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    Apr 12, 2010

    Part of the problem is how one defines 'the basics'. Unfortunately, these are usually considered to be simple arithmetic computations. I would suggest that simple algebra is, in fact, more 'basic', as it directly addresses the fundamental concepts of mathematical relationships. While I believe it's important to give students basic computational skills as well, I think it's critical to keep in mind the difference between 'understanding' and 'doing'. A computer 'does' math very quickly and accurately, but doesn't 'understand' any of it. Basic algebra can, in fact, be understood by people with very limited computational skills. In fact, if one takes a linguistic approach rather than a computational approach, very young children can grasp algebraic concepts very quickly. In my experience, it takes less time and effort to reach the same over-all level of comprehension and computational skill starting from that end than from starting with simple addition, moving to subtraction, etc. And, it makes learning advanced algebra much easier later on.
     
  13. Muttling

    Muttling Devotee

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    Apr 12, 2010

    Algebra for everyone??? Heck no, it's just like saying geometry is for everyone.


    When's the last time you had to think about what 20% off really means?

    When on God's green Earth does a carpentar use a 3-4-5 triangle?

    Who cares about understanding why you'll have twice as much retirement savings if you start at age 25 than if you wait until age 35 to start saving?


    Nah....These are silly concepts that just don't apply to real life and are a waste of time to learn.
     
  14. hatima

    hatima Devotee

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    Apr 13, 2010

    I use the X% off all the time. Thought I am REALLY, REALLY bad at it and use that calculator on my phone! Shouldn't I be able to do that mentally?

    I understand the retirement part is true but don't understand why 10 years makes such a big difference. The compounding of interest confused me and it is so useful. I was shocked to learn $300 max out on a parade sponsor credit card could take me over 3 years to pay off, and the "fee" out weighs the minimum payment. I wish I'd have understood this in HS, then maybe I'd have it down now and would stop getting into debt!
     
  15. Muttling

    Muttling Devotee

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    I can do most of it in my head using short cuts, but I'm constantly doing math.

    If you know how to set the problem up and use a calculator, you know how use the technology. You are still able to get to the answer and that is what really matters in the real world. Don't ding yourself for not being a math teacher who can run the numbers in his head, I do this stuff 40+ hours a week and I started with a real nack for it.


    Exponential growth/decay is my all time favorite subject I teach it 100% contextual (e.g. real world problems and nothing abstract.)

    The answer to your question is simple, the interest earned builds upon itself. Think about another example, animal breeding. If the average female mouse gives birth to 3 female mice every year then it goes something like this....

    Start with 1 female who gives birth to 3 females. Thus, you end the year with 4 females.

    Now you have 4 females who give birth to 12 females in the second year.

    Now you have 16 females who give birth to 48 females in the third year.

    Then you have 64 females who.......in the 4th year


    Imagine what the numbers will be like in 14 years.



    This is a very contrived example, but it is exactly how exponential growth (e.g. compound interest) operates. The growth builds upon itself and operates at an constantly accelerating rate. It starts out slow but keeps getting faster and faster and faster. 10 years makes a monster difference because it gives you 10 more years when that growth is getting incredibly fast. If you could go 20 more years the numbers get really insane.
     
  16. Aliceacc

    Aliceacc Multitudinous

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  17. Mrs Ski

    Mrs Ski Companion

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    Apr 13, 2010

    I think algebra is very important. Have you painted, re-carpeted, tiled your house? and these are just things that popped in to my head. The other day I was standing in the tile aisle at lowe's and actually used an x= equation, because i wanted to know how much the 9x12 tile would cost a square foot, I tired to do it in my head but knew the answer i was getting was wrong. So I set it up and solved. Maybe I am a nerd, and yes there are calculators for that. But I am glad that I have those skills.
     
  18. sue35

    sue35 Habitué

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    Apr 13, 2010

    I am also a "non math person" and I can see needing basic algebra but can someone tell me why we need to know Calculus? I was horrible at in in high school and college and have blocked it out for the most part so I can't remember what is needed from it. For all I know I am using it all the time but don't remember:)
     
  19. mmswm

    mmswm Moderator

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    Apr 13, 2010

    Okay, so I'm REALLY late in this discussion, and I'm really tired, so I don't want to think about a detailed response (I will later, maybe...but not now). But, I did want to throw one thing out there...

    Atomic, you mentioned not being able to convince your students about the usefulness of piece-wise functions. I have a great lesson plan with that.....

    Go get some take out menus from a few restaurants that have different menus for different times of the day (breakfast, lunch, dinner). Have your students predict what it will cost them to take a group of certain size to a couple of different places at different times of day. Ask them to show you, in a single picture, a way to predict the cost at a particular place on any given time of day. The result will be a peice wise function :D.
     
  20. Muttling

    Muttling Devotee

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    Most of algebra II and beyond are what I call the "scientific level maths." You're highly unlikey to find yourself using a cubic or quartic function, log arithmic functions, differential equations, integrals, etc. unless you work in some form of a scientific/ engineering field.

    I spent my first 15 years as a civil/environmental engineer, but I never used needed work a calculus problem. Tons of algebra problems and I lived by logarithms, but I've never done an integral in the real world.

    Calculus is a method of evaluating curves and relationship to find the area under the curve (2 dimensional calculus....you can also do 3, 4, 5, etc dimensional calculus.) This is particularly useful when analyzing certain relationiships. For example, if you graph Speed versus time, the distance traveled will be the area underneath the curve. It's easy to calculate for a constant speed, but lets say that the speed is changing in an exponential pattern. Calculus is what you need to calculate the distance traveled.
     
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