
How to Remove Obstacles to Learning Math - bootload
http://ww2.kqed.org/mindshift/2015/11/30/not-a-math-person-how-to-remove-obstacles-to-learning-math
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abarrettjo
1\. 'Kids considered to be “gifted” suffer from ability grouping the most
because they develop the ultimate fixed mindset. They become terrified that if
they struggle they’ll no longer be considered smart.'

2\. 'Removing the time pressure from math is another important issue for
Boaler. Neuroscience research... has shown that time pressure often blocks the
brain’s working memory from functioning. This is particularly bad for kids
with test anxiety. “The irony of this is mathematicians are not fast with
numbers,” Boaler said. “We value speed in math classrooms, but I’ve talked
with lots of mathematicians who say they’re not fast at all.” '

I have experienced the truth of both of these points during my math education,
and have recently started talking with professors (I'm an undergrad stat
major) about the idiocy of timed exams in math. Timed exams test for speed,
which is not something that matters in real mathematics (if you can prove a
theorem in one week vs. two it doesn't really matter), and this can push
people out of the discipline who would otherwise stay. As people discuss
retention rates in stem fields, particularly with under-represented groups, I
hope they will consider getting rid of time limits as an avenue of effective
policy change.

~~~
Retra
I think STEM students should be writing more papers across the board. You
shouldn't just solve problems and write down the solutions, you should be
writing exposition on the methods you use, why they work, and what other
options are available.

~~~
InclinedPlane
My writing ability developed in high school and college due to a few specific
causes. 1: Being forced to write for my AP European History course in HS (the
regular assignments were just lists of questions/prompts to be answered with a
few sentences or a paragraph or so, it's amazing how valuable that experience
was). 2: Writing proofs in advanced math courses (elementary analysis,
abstract algebra, etc.) 3: Participating in usenet newsgroups (by far the
biggest contributor).

P.S. I meant to point out the irony that English classes contributed
comparatively little. Actually writing about something and putting in the
effort to string together something coherent is what really exercises and
builds writing abilities. It's nice to have some of the groundwork laid, but
practice is by far the most important component.

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Jtsummers
> Boaler said a big problem is that math teachers themselves are math-
> traumatized. They came through a system very similar to the one in which
> they work. Elementary school teachers in particular often feel insecure
> about math.

This is incredibly important to understand. I know a number of middle grades
teachers (not math or science) who "aren't math people". Their anxieties
significantly hamper their ability to help their students when math-related
things come up in class (statistics in a social sciences class, for instance).
Or if a student wants to go to a trusted teacher for help outside that
teacher's subject area.

Similarly, and this is really bad, they can't calculate students' grades! I've
witnessed this one several times with a friend, and wish I could sit with her
every time she worked out her grades so it will stop happening:

Test is out of 100 points. 10 points of extra credit. Calculate the students
percentage as X/110\. WTF, it's no longer extra credit, the top score (110) is
still 100% (instead of 110%), and now 90 points (should be 90%, an A-) becomes
an 82% (B-)!

~~~
lacker
Math teachers in the US often don't have a math degree. Of course they feel
insecure! - they are not really equipped to teach their subject well.

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mathgenius
So much to say about this.

I absolutely refused to learn the times-table in school. Even to this day I
struggle to add seven and eight. That one seems to confuse me every time. I
think the long division algorithm is one of the most difficult things in
mathematics, and they teach this to ten year olds! (or they did when i was
ten.)

So, fast forward many years, and I started doing really well studying advanced
mathematics in my undergrad. But somewhere along the line I hit a wall: most
math textbooks are written ass-backwards for my brain. I really don't get
maths by looking at equations. It has taken another 20 some years to move
beyond this, and to not be shy about being a disaster when it comes to
algebra. Because when it's about _shape_ or _process_ that is when I really
start to move.

My research today is in theoretical quantum physics (finally doing my
postgrad.) I've started to see that there are others like me out there: we
often sound like nutjobs when talking about maths, because it's all a confused
mess internally. But somehow from the chaos miracles emerge. This is in
contrast to the heavily-linear-thinking types: these people produce sparkling
sentences one after another, but often get lost seeing the big picture. The
"nutjobs" are a minority, and are so easily criticized. But I sure wish there
were more of us doing this hard stuff.

One of my favourite math lessons in school occurred when I was about six years
old. The teacher had some coloured shapes scattered across the floor, some
yellow, some red, some triangles, some discs, etc. She placed a big hoop
around all the yellow shapes, and another separate hoop around all the
triangles. But there was a problem with this scheme: what to do about the
yellow triangles? She let us all stew on this for a few moments, and then the
magic happened. If you place one of the hoops overlapping the other, the
yellow triangles could inhabit both hoops at the same time.

~~~
nextos
Do you mind sharing math textbooks you like (undergrad & grad).

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ajarmst
A lot of problems here. (1) "This study shows that all kids can learn math
when taught effectively". Well, as the definition of "teaching effectively" is
that students learn from it, this observation really isn't all that startling.
We could do a similar study to prove that all children arrive at school when
driven there. What would be startling would be if the same technique worked
equally well with all students (and this one won't). (2) Ah, it wouldn't be a
paper about educational techniquese without some Gladwelling (which I define
as using a vastly over-simplified and facile interpretation of scientific
findings in order to advance a puerile generalization). Yes, research shows
that connections in the brain are modified when learning. It would be shocking
if learning didn't have an effect on the brain. By FMRIs and other imaging is
far,far too blunt to detail what is happening in any useful detail. Taking a
scientific finding that "people seem to use these particular areas of the
brain when learning" as justification for an entire philosophy of pedagogy is
absurd. And, for the umpteenth time --- multiplying two numbers is no more
"Mathematics" than learning how to drive a screw is "Mechanical Engineering".
And encouraging children to explore driving a screw with a hammer, a pair of
pliers, their teeth, a teammate and then having them do a class presentation
on their findings does not help them in their later careers as mechanics. Far
better to show them the most effective technique, let them practice it, and
move on. "Exploration" learning is only effective when applied to skills that
already have mental infrastructure provided by evolution. You learn your first
language by exploration. You learn to walk by exploration. Riding bikes and
mathematics were never evolutionarily selected for, so we have to learn them
by, well, learning them.

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Jtsummers
> Far better to show them the most effective technique, let them practice it,
> and move on.

This can work for the base levels of what most folks think as mathematics,
namely arithmetic and algebra. But it starts falling apart as students get to
more advanced algebra and mathematical topics. Memorizing a particular
algorithm does _not_ lend to understanding mathematics. In particular, the
parallels between algebra (and some arithmetic) and geometry are non-obvious
and not easily conveyed via a series of exercises and then jumping to the next
topic. See the visualization examples of `18x5` in the linked article. Letting
students see the correlation between the numbers and the objects (squares and
rectangles) greatly helps their understanding of the subject. _Discussing_ it
reinforces this experience and gets them to see it beyond the exercises
they've been doing, abstracting the concept beyond a handful of cases and to
the general case.

> Riding bikes and mathematics were never evolutionarily selected for, so we
> have to learn them by, well, learning them.

There are many ways to learn and to teach. Teacher-tell, student-regurgitate
is one method. And it works for some (many) subjects, at least in getting
facts and figures into students heads. Teacher-tell, student-explain gets the
students past thinking about facts and thinking about whys and hows of the
world. (You can expand tell beyond spoken word to shown, demonstrated, etc.)
Teachers can take it further by starting on a mathematical topic, and
directing the student conversation and discussion towards understanding (I
think this is the example I'm looking for, graph theory for eight-ear olds:
[http://jdh.hamkins.org/math-for-eight-year-
olds/](http://jdh.hamkins.org/math-for-eight-year-olds/)).

~~~
jwdunne
To supplement this comment, How to Solve It by Polya is a nice little handbook
on the education of mathematics. I'm reading through this at the moment and
I've learned quite a bit. It's especially useful to see how I have unknowingly
applied some heuristic to a problem I've solved in the past.

As a side note, I'm finding both Calculus Made Easy and Concrete Mathematics
incredibly useful. Thanks for the suggestions.

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droithomme
Every child can easily learn all the math they would need in life.

Inability to understand math does not come naturally to any child. It is
something that must be taught by specialists at intense effort and great
expense.

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dbpokorny
I found this video on Hungarian math education (elementary) fun to watch:
[https://www.teachingchannel.org/videos/teaching-
elementary-m...](https://www.teachingchannel.org/videos/teaching-elementary-
math-hungary)

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rukuu001
High school math was hell for me.

The teacher would explain something on the board. Everyone but me would say
'Ohhh, I see' or similar (think Bart Simpson and the 'RDRR' gag).

The teacher would explain the concept to me again. I still wouldn't get it. I
got a 'Really?' look from the teacher, who then walked off.

So I wasn't a 'math person'.

Then halfway through a thesis I encountered some math that I had to understand
and use, or give up the thesis.

I discovered I could some math after all.

