

What math (and programming) teachers should know about memory - ColinWright
http://www.blog.republicofmath.com/?p=2946

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rottencupcakes
Where is this happening?

I don't think I've had a math teacher say "memorize it" since Geometry in
middle school, where we had to memorize pretty useful things to generally
know, like SOHCAHTOA.

Basically every math test I've had since that has required nearly any type of
memorization has been open note.

Also, at the end of the day, some memorization is necessary to advance in
mathematical complexity. If you can't remember solutions to basic differential
equations or the integrals of trigonometric functions, it will severely limit
your ability to build useful things out of that basic knowledge.

I'm not saying I remember what the integral of arctan is off the top of my
head, I'm just saying that there are practical reasons why teachers may
require certain things to be memorized.

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joe_the_user
I was attracted to math in elementary school _because_ it required less
memorization and rote learning. Spell - that was the subject where rote
memorization was required. I essentially failed spelling until it stopped
being a subject - somewhere around Middle School.

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rdtsc
I remember being so flooded with information that memorizing it would lead to
failure. In other words, my classmates that tried to memorize formulas and
steps would fail because there were so many of them. Those who internalized
the relationship between components and understood why the steps were needed
did alright.

One of the best tests to see if rote memorization is taking place, or there is
actual understanding is word problems. In ex-Soviet schools they emphasized
word problems heavily. In case of a word problem it is very hard to memorize
the steps like one would do for a Gaussian reduction.

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Natsu
You're right about making connections, but one difficult part is that
sometimes you just have to derive too much if all you have are connections and
you haven't memorized things that could have created shortcuts for you.

I actually used to have trouble running out of time on tests sometimes when I
had all the knowledge connected, but not enough of the right things memorized.

~~~
rdtsc
Depends on how the tests are structured. You could structure the tests so that
rote memorizers win or those who have truly understood the relations win. And
then sometimes it is not just he tests that are structured mostly one way or
the other, but whole educational systems.

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chad_oliver
This is a great article. I've thought for a while that the way we teach maths
is broken - not because we use too much rote or muscle memory, but because we
separate teaching from practicing. We spend an hour learning a concept, and
only practice using it when we get home. We spend six weeks teaching the
basics of differentiation, and then move on to integration. While we do
integration, we totally forget how to differentiate.

The article mentioned that memory retention is an exponential curve. Science
has also shown that the best time to practice a concept is right before we
would forget it. Put together, these two principles allow us to devise
revision plans that make learning efficient.

Why are we stuck in the 18th century? We know so much more about how memory
works, but we still keep doing the things we've always done.

~~~
teach
The math books by the late John Saxon are a superb example of keeping teaching
and practicing better connected. Unfortunately, I'm not aware of any large
public schools (in my area, anyway) that use them.

~~~
chad_oliver
Hey, I googled the textbooks and they sound intriguing. I may have to get one,
just to see how it works in practice (I'm at university now, but it's never to
late to go over old material). Thanks for sharing!

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bstar
"She has this thing where she makes us do reviews that are about 10 questions
and then she calls us up to the board to answer each question putting us on
the spot."

My 10th grade geometry/trig teacher did this to us. Confidence issues I had as
a result of this class lasted many years. I got over it and have done well for
myself, but I still have some resentment.

~~~
archgoon
My AP Calc teacher had us do the same thing with our homework assignments. I
cannot say if this resulted in confidence issues among his students, but 58
out of the 60 students in the class received 5's on the AP exam.

It is not clear to me that this is obviously a bad teaching method. It
definitely accomplishes 'engaging the student'.

~~~
andrewce
It can be a good teaching method or a bad one, depending on how it's used.

Personally, I enjoy having students come up to the whiteboard. But when we do
so, I present it as the student at the board is a representative of the class.
The whole thing is collaborative, and I have students who are sitting explain
what the student at the board is doing.

What this means is that students who know what's going on are able to take the
lead (when at the board), whereas students who are less confident can rely a
bit on their classmates. The whole time, I stress "Look, we're learning new
stuff and it's going to be challenging. Work together and you'll get it." This
makes a different vibe than if we just sat and watched before I determine if
the answer is correct or incorrect.

I don't use this for individual assessment, and I don't attach any guilt or
shame. It's purely done to get students working in the Zone of Proximal
Development and to get someone other than me talking.

