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posted by mrpg on Saturday May 13 2017, @04:31AM   Printer-friendly
from the 2x²+x+64 dept.

If you've ever had to help your child with math homework, you really appreciate their teachers, who do it every day. "Math anxiety" isn't something only kids experience.

Maybe you haven't seen an algebra formula in years, and weren't that comfortable with them when you were a student. Maybe you're a skilled mathematician, but don't know how to explain what you're doing to a child. Whatever the case, math homework can leave parents feeling every bit as frustrated as their children. Homework doesn't have to lead to unpleasantness, though.

What I've learned through my own experience—as a teacher, a researcher, from helping my own children, and now watching my daughter work as an elementary school mathematics teacher—is that communication is (excuse the pun) the common denominator when it comes to making math homework a positive experience.

The National Science Foundation (NSF), where I work, is dedicated to research. We support scientists across the country who study learning and education systems. But we're also teachers at heart. On lunch breaks in the past, a group of us gathered to help our NSF peers with their own questions about how to help their kids learn math.

Here are a few tips from what we've learned:

Do Soylentils have better tips, things that have really helped their own kids learn math?


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  • (Score: 5, Insightful) by bradley13 on Saturday May 13 2017, @05:54AM (10 children)

    by bradley13 (3053) on Saturday May 13 2017, @05:54AM (#509023) Homepage Journal

    I have to disagree with you. Part of math - or indeed any subject - is rote memorization. Personally, I remember having to memorize the multiplication tables in 3rd grade: 6*7 = 42, 6*8=48, etc.. Boring, repetitive, but utterly essential if you want kids to be able to multiply arbitrarily large numbers. Part of what I see in "new-fangled" teaching methods are futile attempts to make the rote-learning parts magically disappear.

    The second part of math is teaching systems, and systematic work. Being a math nut, I taught my kids a lot of their basic math before they got to it in school. When we made the transition from adding single-digit numbers to multiple digits: I emphasizes the system: If you carry from digit 1 to digit 2, then you've discovered the system that works for digit 3 and digit 4 and digit 5 and... Schools stop at 2-digit numbers, and the students in their class "didn't know how" to add three digit numbers. That's a huge error in presentation by the teachers.

    Building on those foundations comes the problem solving. At each level, teachers need to find practical, interesting problems for the kids to solve. At the lowest level, these are the word problems: "Billy has 15 pieces of candy. He wants to share equally with his two friends. How many pieces of candy does each kid get?". The mistake I see made by teachers (and parents) at this level: They try to retreat back into rote learning,so kids memorize the answers to individual problems, instead of understanding how to solve entire classes of problems.

    If you pull off all three steps correctly, kids see that math is a useful tool, something that does apply to their daily lives. The problem is: kids with math-allergic parents won't get the support they need. And far too many elementary school teachers are math-allergic themselves, and don't understand even basic math well-enough to pull of the steps described above. Not sure how to solve that problem, unless it's by having separate math instruction from the earliest ages.

    --
    Everyone is somebody else's weirdo.
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  • (Score: 2, Insightful) by Ethanol-fueled on Saturday May 13 2017, @06:41AM (4 children)

    by Ethanol-fueled (2792) on Saturday May 13 2017, @06:41AM (#509036) Homepage

    " The problem is: kids with math-allergic parents won't get the support they need. "

    Kids don't need math parents to do well in math, there are plenty of non-parental resources available for B̶l̶a̶c̶k̶ ̶s̶t̶u̶d̶e̶n̶t̶s̶ kids with busy parents, what they do need is a parent or guardian or two willing to kick their ass if the kids don't do what it takes to pass math.

    Unfortunately, the threat of violence is no longer a deterrent because in America that can get your kid taken away and you charged with a felony. Which means the kid can scream and cry all night wanting to play X-Box instead of doing boring things like memorizing multiplication tables and parents literally have no choice between appeasing the kid and being ran through the courts.

    • (Score: 3, Insightful) by anubi on Saturday May 13 2017, @09:35AM (3 children)

      by anubi (2828) on Saturday May 13 2017, @09:35AM (#509064) Journal

      Ethanol... your observation about physical parental discipline:

      the threat of violence is no longer a deterrent because in America that can get your kid taken away and you charged with a felony. Which means the kid can scream and cry all night wanting to play X-Box instead of doing boring things like memorizing multiplication tables and parents literally have no choice between appeasing the kid and being ran through the courts.

      I was raised with physical discipline. I would say in retrospect that it was best that my Dad did it than to have a Law Enforcement Officer do it.

      I would not consider a lack of interest in math a reason for discipline, no more than I would consider a lack of interest in sports ( guilty as charged ) a reason.

      I was really good in math. That did not mean I was a success in the workforce. I believe STEM is really overhyped by those wanting cheap minions.

      However, I will not tolerate things like bullying, shoplifting, vandalism, or other social nuisances which would be sure to make my kid end up in prisons.

      So, today, its a felony if Dad has to resort to physical means... so why is it not a felony for our Law Enforcement Officers to do what Dad was supposed to have done?

      Believe me, they will also resort to physical means if they have to.

      Our Law Enforcement Officers do not need to be tasked with doing what Dads should have done.

      You just nailed one of my biggest fears on being a dad.

      The other main fear I have is divorce law.

      I do not believe the modern guy stands a chance in today's legal environment when it comes to family things. I do not even know where to start. My reaction to all this law was to avoid this part of life.

      Probably just as good for all concerned, anyhow, except for the lawyers.

      --
      "Prove all things; hold fast that which is good." [KJV: I Thessalonians 5:21]
      • (Score: 3, Insightful) by aristarchus on Saturday May 13 2017, @09:56AM (2 children)

        by aristarchus (2645) on Saturday May 13 2017, @09:56AM (#509070) Journal

        The other main fear I have is

        Quadratic equations?

        Infinitesimals parading around as integers.

        Irrational relations, Pi, Theta, and their kin.

        Prime numbers, how do they work? Is it like magnets?

        And you are afraid of divorce law? Wow, just wow.

        • (Score: 4, Touché) by maxwell demon on Saturday May 13 2017, @10:16AM

          by maxwell demon (1608) on Saturday May 13 2017, @10:16AM (#509071) Journal

          I never heard for someone whose private life failed because of the failure to solve a quadratic equation. On the other hand, the consequences of a a divorce can certainly lead to a failed life.

          --
          The Tao of math: The numbers you can count are not the real numbers.
        • (Score: 0) by Anonymous Coward on Saturday May 13 2017, @04:30PM

          by Anonymous Coward on Saturday May 13 2017, @04:30PM (#509199)

          I'm affraid of The Donald. He's an irrational number.

  • (Score: 1, Interesting) by Anonymous Coward on Saturday May 13 2017, @06:49AM

    by Anonymous Coward on Saturday May 13 2017, @06:49AM (#509040)

    You seem to misunderstand what I am trying to say. Every single part of human knowledge requires understanding of facts, and You cannot understand something without first remembering what it is -- I agree with that. And I'm not trying to push something that will magically make memorization disappear. The crux of the problem is in what You had said: teachers at some level retreat to rote learning. But that is just a symptom of a problem -- that educators have to teach people who have no interest nor ability in the subject. The only way for a teacher to do so to a class of X, where X is sufficiently large, is rote memorization -- which for mathematics looks like it works, because each year students show that they can solve progressively more complicated "problems". So that is the first thing that I'm trying to say: stop teaching it to everybody.
    Maths is still required for some tasks, though -- but mostly to show precise relations between real world objects. But the problem I see with education, is that kids are shown the solution to a problem before they even know what the problem is.
    The candy example is almost good: but make kids actually do things, and then show them a solution. Show them two heaps of candies and make them choose which one they want. Or show them two heaps of peas, and make them choose which one they prefer to eat. Which one is smaller, and why? After several attempts, on different objects, they will get it, although they will probably be unable to describe how they do it. That's the second thing: don't start by making students learn the solutions to problems they don't know about, but describe (or even better: help them describe) ways of solving problem they already know. This can show them that mathematical notation is useful for describing general solutions, which can be applied to various classes of problems. But, as You hopefully see, this is totally impossible without rote memorization (I have to remember the tasks that I have done). But mathematical notation actually requires less memorization and is more general to problem solving, than solving the same problem over and over again for different kinds of objects. Rote memorization of mathematical notation is also required, but this can be done eagerly by children only after they can understand that it actually helps them, and saves them effort.
    Now for systematic work: again, children learn by doing, and not by me saying things to them. They have to be shown that systematic work pays off, right now. But that can only be understood by them iff they show interest in a solution -- and that is usually not so in the case of mathematical problems shown in class and at home. If anything, mathematical problems are reduced so much because they not only have to be described in one class, but usually a solution to them has to be describable within the duration of the same class. There simply is no time for systematic testing of hypotheses -- systematic work and systematic reasoning are two different things. When can a child have the leisure time to sit down and think for an arbitrary amount of time, to employ their minds to come up with different solutions to problems and allow them to test each one systematically? Certainly not at school, next period is biology, drop that maths, and after that is history, stop thinking about that biology. I think, the reason why You were able to teach Your children before they went to school is because they have had the time to understand the terms You tried to teach them in their own time.

  • (Score: 0) by Anonymous Coward on Saturday May 13 2017, @07:34AM (2 children)

    by Anonymous Coward on Saturday May 13 2017, @07:34AM (#509049)

    I have to disagree with you. Part of math - or indeed any subject - is rote memorization.

    Why are you doing this? You say that "part of path" is rote memorization, but schools concentrate almost entirely on rote memorization. Your comment is therefore irrelevant. Our school system is an utter abomination and it always has been.

    Of course you need to retain information to some degree, because otherwise you'd never learn anything. I don't know a single person who says otherwise, which is why I get tired of the 'But some memorization is required!' responses.

    Part of what I see in "new-fangled" teaching methods are futile attempts to make the rote-learning parts magically disappear.

    No such thing is happening. Instead, they pretend they're not doing rote memorization, but in reality, they are heavily relying on it. What is missing is a true, deep understanding of the subject. We are not encouraging people to be real academics, but mindless drones.

    • (Score: 2, Interesting) by anubi on Saturday May 13 2017, @10:18AM (1 child)

      by anubi (2828) on Saturday May 13 2017, @10:18AM (#509072) Journal

      When I help the neighbor's kids with math ( usually algebra ), I take over an old DOS laptop loaded with GWBasic, MathCad for DOS, Borland Eureka, and Borland C++ for DOS.

      The kids always get hung up on word problems, and how to convert a word problem into equations - and what they even mean.

      So, we start off talking about the word problem. What the unknowns are, and their relationship to each other.

      Throwing all the arithmetic into the fray quickly derails the understanding I am trying to teach the kid... so I have the computer deal with it until I can get the kid seeing the larger picture of how to abstract some unknown number as a variable. In my experience, that has been the biggest hurdle of Algebra. Once I can get the kid knowing that "X" represents a number, but we don't know what that number is... I am pretty well on the way.

      I start off pretty simple. Let X=10. Print X. Let X = X + 5. Print X. Then once the kid catches on, go from there.

      When I get done, the kid can conceptualize the word problem into an equation.

      I will use the MathCad for more intensive maths, such as calculus or linear algebra, just so we can concentrate on the math, not the arithmetic.

      Otherwise, I fear the kid will get lost in the minutiae just as I got so lost in the minutiae of interpolation of logarithm and steam tables in my college thermodynamics classes that for years I did not see the big picture. Not until a computer shouldered the burden of all that arithmetic minutiae and let me focus on what was really going on.

      There is no call for me to calculate square roots the long way. Just knowing what they are is what I need. Same with integration and differentiation. Knowing what and why I am doing this operation is what is important. I did analytic solutions in college to get a grade. I do calculus all the time, yet never have I had to resort to analytical methods anymore, as I never knew the exact equations to that which I was analyzing! It was streams of data. Knowing how to tell a computer what I wanted it to do with the streams of numbers I was feeding it was what was important. ( things like Simpson integration methods ).

      Another thing - computers made it easier to show kids how statistics works and why we do things the way they are done. MathCad is really handy for that one, that I can show how discrete and continuous solutions both come up with the same answer. You know... the bell curve probability functions.

      This new graphic apps stuff coming out is too good though. One can't peek under the cover to see whats going on behind the display. I much prefer the older stuff for trying to teach a kid. For the same reason I would teach using GWBasic instead of delving right into C++. I will fire up Borland C++ for DOS later just to show how one can write stuff for fitting into much larger stuff, but that's for way later when the kid is ready to tie the whole shebang together.

      --
      "Prove all things; hold fast that which is good." [KJV: I Thessalonians 5:21]
      • (Score: 0) by Anonymous Coward on Saturday May 13 2017, @06:03PM

        by Anonymous Coward on Saturday May 13 2017, @06:03PM (#509218)

        In my failed quest to get cisfemale programmers to precipitate out of the æther, which I have given up out of sheer frustration with third-wave feminism and their sexually abusive, homophobic white knights (not to be confused with their blatant transphobia and blind, right-wing-authoritarian-follower's reverence of the gender dichotomy wrapped up in oppression Olympics), QBasic and GWBasic were two that I considered: QBasic for being one of the first IDEs that I used (also Turbo Pascal), GWBasic for resembling TI-Basic on the TI-99/4A (not to be confused with the Basic interpreter on TI's graphing calculators). One co-worker even suggested that it might not be a bad idea to load up a TI-99/4A emulator and use that.

        I settled with Ruby because it supported both. Perhaps in hindsight I should have done Python, but I knew Ruby at the time and not Python. (Also significant whitespace is against my religion.) Vim became our IDE, and irb became the line-mode equivalent of GWBasic/TI-Basic. I felt it worked very well. We even tangented into a few side-quests having to do with basic algebra, and I was left with the impression that my mentorship had helped at least put a dent in her math anxiety.

        Unfortunately, my last student became infested with evil and is now a Deadite. If it's not obvious, I write bombastic comments to cover up for my own pain at the betrayal and abuse I've experienced at the hands of feminists. I have been crying a lot lately....

  • (Score: 2) by AthanasiusKircher on Saturday May 13 2017, @02:05PM

    by AthanasiusKircher (5291) on Saturday May 13 2017, @02:05PM (#509146) Journal

    Great comment. I agree that practical problems are the key, and primary teachers often don't find ways to integrate this stuff.

    The problem is: kids with math-allergic parents won't get the support they need. And far too many elementary school teachers are math-allergic themselves, and don't understand even basic math well-enough to pull of the steps described above.

    This is the really hard part. Math is a kind of language. Like actual speaking or reading, it takes TONS of practice to become fluent, particularly in terms of abstract reasoning or broad understanding. Lots of parents and unfortunately primary teachers never actually achieved that -- instead, they learned the "crutch" of symbolic manipulation and symbolic algorithms as a proxy for actual math intuition.

    Then the teachers are faced with kids whose natural inclination is to explore the world and develop intuition about things, and inevitably kids figure out other methods of doing problems (sometimes good alternatives, sometimes things that are wrong). Teachers who are "math-allergic," as you put it, can't cope with this intuitive childhood exploration of math concepts, so they at best smile and nod when the kid comes up with the right answer through alternate means, and at worst shut down such exploration pre-emptively. They often aren't competent/intuitive enough with math to recognize whether the kid has happened upon a good way of doing things or whether the kid's method is actually something that will fail when applied generally. Instead, focus on symbolic algorithms that they KNOW work. (This, I think, is even a bigger problem than rote memorization.)

    Kids rapidly pick up this "math-allergy," because (1) they learn it's NOT about exploration (which is fun), (2) symbolic algorithms are the most abstract representation, so kids often find them the hardest to understand, thus making the math seem harder than it is, and (3) abstract symbolic manipulation is BORING for most kids. They may even pick up the anxiety directly from the teacher.

    It's a real problem.