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Submitted via IRC for chromas
Think you're bad at math? You may suffer from 'math trauma'
I teach people how to teach math, and I've been working in this field for 30 years. Across those decades, I've met many people who suffer from varying degrees of math trauma – a form of debilitating mental shutdown when it comes to doing mathematics.
When people share their stories with me, there are common themes. These include someone telling them they were "not good at math," panicking over timed math tests, or getting stuck on some math topic and struggling to move past it. The topics can be as broad as fractions or an entire class, such as Algebra or Geometry.
[...] One of the biggest challenges U.S. math educators face is helping the large number of elementary teachers who are dealing with math trauma. Imagine being tasked with teaching children mathematics when it is one of your greatest personal fears.
(Score: 5, Insightful) by Anonymous Coward on Monday November 05 2018, @02:36AM (15 children)
When I used to tutor students in math, I ran into people who were convinced that they "just didn't get it" or "were just bad at math". While it's possible that I was just a better teacher, most of them actually already knew what to do but were paralyzed by low confidence and frustration would make them give up.
Something like:
Me: Alright, what's the problem?
Them: I don't know what to do.
Me: What did you think you should do?
Them: Isolate the variable?
Me: Why don't you try that?
Them: Oh, now this kinda looks like that other problem I solved. What do I do now?
Me: What did you do for that other problem?
Them: Cancel things out and simplify. But that problem was different?
Me: Do you have any better ideas to try?
Them: No.
Me: Then why don't you try simplifying and see what happens.
(Score: 2, Insightful) by Anonymous Coward on Monday November 05 2018, @02:49AM (4 children)
In my experience, there's a number of things that happen. But, this is one of the big ones. A refusal to try unless absolutely certain that you're on the right track. It's very, very difficult to learn anything if you refuse to try unless you've already got the answer.
This is one of the reasons why I advocate against having too many tutors available for the students. If they don't try before getting help, then there's no way of knowing if they could do it on their own. And there's no way of developing any sort of self-confidence as you only build that via either succeeding or handling failure gracefully. Neither of which happen if you've got support right there immediately on demand.
I'm not sure who it is that gives students the idea that it's possible to advance in math without making any mistakes. Sometimes you can't reasonably determine the appropriate method without first trying a few things because either the rule that would tell you what to do doesn't exist, or more commonly, is more complicated than just taking a few educated stabs.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @03:26AM (2 children)
Idiot parents who themselves have math trauma and think rote memorization can get one through algebra.
It can't.
And I wish somebody would tell the people always going "I wanna be a programmer" that if you barely passed algebra, chances are that you will never be a programmer, no matter how much you blame half the planet's population. In the next life you'll realize how much of a childish jackass you were being with that approach.
(Score: 2) by hendrikboom on Monday November 05 2018, @03:18PM
Except that the procedural intuition you build up doing things in the real world can carry you far enough to gain confidence and bypass the blocks you set yourself up with in algebra.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @11:00PM
Can you cook? You can be a programmer. What else a recipe?
Do you knit? You can be a programmer. What else is pattern?
Remember the first programs where punched metal plates, strung together in a loop for the loom.
Now, will write code in less than 2k and use it pilot a spaceship to moon? Maybe not. But just like math, there are many different skill levels that required for the many facets of the business.
Go watch "Hidden Figures".
(Score: 0) by Anonymous Coward on Monday November 05 2018, @10:22AM
This applies to much more than math.
(Score: 3, Interesting) by BsAtHome on Monday November 05 2018, @07:03AM (1 child)
This is how you go from a "closed mindset" to an "open mindset". Many pupils and students have had bad experiences, which causes them to lock-up (mindset: "I think it is hard, so I rather not try as to prevent another bad experience").
The trick is to get the student into an open mindset as in "lets try, it can't ever get any worse and only better" and in "I don't know it yet, but I might in a moment". This is where the quality and experience of the teacher comes into play...
(Score: 0) by Anonymous Coward on Monday November 05 2018, @07:50AM
I feel like pointing out that that's most common with computers. People cannot figure things out because they are afraid to do anything wrong, and thus never manage to use a computer unassisted.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @12:19PM (6 children)
I have tutored also...
Most do not understand or "get" (came to realize) the fundamentals of math...
1) Addition is just counting up the number line (ruler)
2) subtraction is just down counting the number line (ruler)... or Addition with a counting sign (-)
3) Multiplication doing Addition repetitively.
4) Division doing Subtraction repetitively.
5) ... and so on
It is taught to slow and disjointed... it was assumed *ALL* will see the patterns. Yup, math is about patterns.
So in our language:
1) X + Y
2) X - Y --> X + -Y
3) X * Y --> S=0 : c=0 : while c D=0 : R=X : while R >= Y : R = R - Y : D++ : loop : print D, R
5) ...
Don't you see math as computer program too?
(Score: 1, Insightful) by Anonymous Coward on Monday November 05 2018, @02:56PM (1 child)
I never really realized this until more than ten years after I took multivariable calculus. I knew it in theory, but I never applied it to common mental math problems:
5%: take 10%, then divide by 2.
12%: take 10%, then add 1% two times.
142-59: subtract 60, then add 1; add 1 and subtract 1 from the initial problem (142-59 = 143-60).
39*39: 40*40 (forty, forty times), then subtract 40 (forty, thirty-nine times or thirty-nine, forty times), then subtract 39 (thirty-nine, thirty-nine times), which is also 40*40 -80 +1.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @03:27PM
You are VERY right... It is one of those things in early programming to find the fastest way to do something.
Had two programmer working on 80186 trying to figure out how to quickly (fewest clock steps) to calculate the the position of the curosr on a 24x80 screen.
So they where going to use MULT instruction to multiply by 80, and could not see how to speed it up. I looked a the Assemebler book (I was Z-80 ASM and IBM mini ASM knowledgeable.
80 is 16 (2^4) * 5 (2^2 + 1)...
Save ACC
Shift left twice (x 4)
Add saved back to ACC (+ 1)
shift left 4 tiems (x 16)
If i remember right 12 clocks total. The MULT function 5 to setup and 2 per 1, so X * 80 = 165 clocks.
(Score: 2) by hendrikboom on Monday November 05 2018, @03:22PM (2 children)
I've always seen mathematical induction over the integers as being a for-loop in a proof.
There's a remarkable correspondence between proofs and programs.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @04:35PM (1 child)
And there should be a lot of similarity, proofs are what you do if you need to know that the program is correct over whatever set of inputs you need to run it on. For many programs that's overkill, but if you're wanting to make sure that your plane doesn't kill people from above, that's the kind of thing you do.
(Score: 0) by Anonymous Coward on Monday November 05 2018, @11:03PM
And even if you do!! Military need those.
(Score: 2) by acid andy on Tuesday November 06 2018, @04:56PM
That's not the problem for me.
More or less, yes.
The problem for me is when the teachers get lazy / sloppy and start skipping over steps in those patterns. Disjointed? Yep. Assume? Yep. I don't know about "too slow" though. I think part of the reason they skip over steps is to save time and go faster.
If a cat has kittens, does a rat have rittens, a bat bittens and a mat mittens?
(Score: 2) by tangomargarine on Monday November 05 2018, @05:27PM
Sounds about right. I had to retake pretty much all my advanced math courses in college twice (should've gone to a tutor way earlier).
My problem was that, the book would explain some way to solve for whatever/simplify whatever, and it would make sense. Couple example problems, okay I think I get it.
Then the assignment/test problems would be 3 times as complicated to solve, and half the time my efforts at simplification wouldn't actually get anywhere. Sometimes you can't tell if the simplification will actually work until you get to the last step and everything collapses and cancels out.
--
That, plus fairly frequently I wouldn't "get" the crucial logical step of how you connected one concept to the next. "Okay, so we do blah blah blah...but why?" And the teacher would give you an explanation that made sense to them, of course, because they know how the entire puzzle fits together. But they teach you one concept at a time, which literally involves lying to the student a lot of the time to keep the complexity down for the moment, then they yank the rug out from under you later "well actually that assumption you've been working on so far is something you have to work out for yourself each time."
And yes, fortunately programming has very little to do with advanced math unless you're writing a graphics engine or some other from-scratch project. Libraries--and not having too much pride to use them--are great.
"Is that really true?" "I just spent the last hour telling you to think for yourself! Didn't you hear anything I said?"