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Thread: The WHY of Mathematics

  1. #1
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    The WHY of Mathematics

    I find that many schools do not teach students to learn math. Most schools concentrate on getting students to focus on passing exams. For example, many calculus 1 students know that d/dx [sin x] = cos x.

    However, they do not know that cos x is the derivative of sin x. I will go deeper by saying that most cannot define the word derivative. The same applies to integration.

    Another good example is y = mx + b. Students know how to use this formula but do not actually know anything about slope. They have no idea what y, m, x, and n represent in the formula. What do you say? Should students be taught to learn or simply to pass exams?
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    Re: The WHY of Mathematics

    Obviously students should be taught to learn, but while governments persist in evaluating schools using exam results, there are strong incentives to teach them to pass exams.
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    Re: The WHY of Mathematics

    Quote Originally Posted by Archie View Post
    Obviously students should be taught to learn, but while governments persist in evaluating schools using exam results, there are strong incentives to teach them to pass exams.
    In what way should math be taught?
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    Re: The WHY of Mathematics

    Understanding the language of mathematics is paramount. Understanding why you do what you do in mathematics is much more important than being able to "get the right answer" by following a process. Teaching (and learning) must aim for understanding, particularly if you want to further your studies and not just "pass the exam" to get to where you want to be.
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    Re: The WHY of Mathematics

    Quote Originally Posted by Debsta View Post
    Understanding the language of mathematics is paramount. Understanding why you do what you do in mathematics is much more important than being able to "get the right answer" by following a process. Teaching (and learning) must aim for understanding, particularly if you want to further your studies and not just "pass the exam" to get to where you want to be.
    While this is obviously true for people that want to be able to extend mathematics it's less obviously true for those who just want to use it.

    There are lots of good people in this world who need to know arithmetic and that's about it. They don't care about why. They want to be able to balance their checkbook, make sure they aren't being ripped off in their paycheck, and maybe be able to split a bar tab.

    Even engineers who use mathematics extensively don't necessarily need to understand the why of things to accomplish their job. Trust me, very few of the engineers I ever worked with could explain the behavior of Fourier reconstructions at discontinuities but nevertheless they were able to make cellphones and sensor systems work.

    Time is a resource and must be managed like all other resources and if you have to slack a bit on the deep understanding of mathematics in order to have enough recreation time to stay sane then so be it.
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    Re: The WHY of Mathematics

    Quote Originally Posted by Debsta View Post
    Understanding the language of mathematics is paramount. Understanding why you do what you do in mathematics is much more important than being able to "get the right answer" by following a process. Teaching (and learning) must aim for understanding, particularly if you want to further your studies and not just "pass the exam" to get to where you want to be.
    The biggest problem is lack of time. There aren't enough hours in a day.
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    Re: The WHY of Mathematics

    Quote Originally Posted by romsek View Post
    While this is obviously true for people that want to be able to extend mathematics it's less obviously true for those who just want to use it.

    There are lots of good people in this world who need to know arithmetic and that's about it. They don't care about why. They want to be able to balance their checkbook, make sure they aren't being ripped off in their paycheck, and maybe be able to split a bar tab.

    Even engineers who use mathematics extensively don't necessarily need to understand the why of things to accomplish their job. Trust me, very few of the engineers I ever worked with could explain the behavior of Fourier reconstructions at discontinuities but nevertheless they were able to make cellphones and sensor systems work.

    Time is a resource and must be managed like all other resources and if you have to slack a bit on the deep understanding of mathematics in order to have enough recreation time to stay sane then so be it.
    I believe that math majors should know the WHY of math topics. If a person is majoring in pure mathematics and cannot derive the quadratic formula, something is wrong.
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    Re: The WHY of Mathematics

    Quote Originally Posted by mathdad1965 View Post
    I believe that math majors should know the WHY of math topics. If a person is majoring in pure mathematics and cannot derive the quadratic formula, something is wrong.
    This doesn't exist. Such a person would have been weeded out of any credible mathematics program.

    That being said I have interviewed people with a BS in electrical engineering who couldn't analyze a passive voltage divider.

    I've interviewed people with a BS in computer science that would have been hard pressed to write the "Hello, world." program.

    I have to say though I've never interviewed any people with a BS in mathematics that weren't pretty sharp. Interesting that.
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    Re: The WHY of Mathematics

    That is so true! It is so frustrating as a teacher when you are forced, due to time restrictions and a packed syllabus, to skip over derivations of formulae. I've been "guilty" of saying for example "Here's the rule (eg cosine rule), this is how you use it, if you want to know where it came from, read page blah blah blah in your textbook". Hate doing that.
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    Re: The WHY of Mathematics

    Quote Originally Posted by Debsta View Post
    That is so true! It is so frustrating as a teacher when you are forced, due to time restrictions and a packed syllabus, to skip over derivations of formulae. I've been "guilty" of saying for example "Here's the rule (eg cosine rule), this is how you use it, if you want to know where it came from, read page blah blah blah in your textbook". Hate doing that.
    This is common language among most math teachers.
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    Re: The WHY of Mathematics

    Quote Originally Posted by romsek View Post
    This doesn't exist. Such a person would have been weeded out of any credible mathematics program.

    That being said I have interviewed people with a BS in electrical engineering who couldn't analyze a passive voltage divider.

    I've interviewed people with a BS in computer science that would have been hard pressed to write the "Hello, world." program.

    I have to say though I've never interviewed any people with a BS in mathematics that weren't pretty sharp. Interesting that.
    I know people with a B.A. and/or B.S. in Mathematics that can easily solve calculus questions but have forgotten, to a great extent, elementary school math. Are you smarter than a 5th grader?
    Last edited by mathdad1965; Jan 3rd 2017 at 01:13 PM.
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    Re: The WHY of Mathematics

    Quote Originally Posted by mathdad1965 View Post
    I know people with a B.A. and/or B.S. in Mathematics that can easily solve calculus questions but have forgotten, to a great extent, elementary school math. Are you smarter than a 5th grader?
    I'm sorry but I find it hard to believe that someone who has forgotten arithmetic and algebra can solve calculus problems.

    I'm also going to remark... don't you have pre-calc homework to do?
    Last edited by romsek; Jan 3rd 2017 at 02:06 PM.
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    Re: The WHY of Mathematics

    Quote Originally Posted by romsek View Post
    I'm sorry but I find it hard to believe that someone who has forgotten arithmetic and algebra can solve calculus problems.

    I'm also going to remark... don't you have pre-calc homework to do?
    At the age of 51, I have no homework. I was born in 1965. This is true. No homework.
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    Re: The WHY of Mathematics

    Quote Originally Posted by mathdad1965 View Post
    At the age of 51, I have no homework. I was born in 1965. This is true. No homework.
    shrug, you're the one who has set yourself this quest.
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    Re: The WHY of Mathematics

    Why not study math? I am 51. I am not popular with females. My family is scattered.

    I passed precalculus with an A minus in the Spring semester 1993. I have not been a classroom student in more than two decades. I think my math is ok considering this information.
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