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Marvin Minsky: What makes mathematics hard to learn? (2008)

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Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#71

Post by anon4 »

j2kun wrote: post #56
crispyambulance wrote: post #42

Earlier quoted context omitted.

Disagree. Kids disengage from math for many different reasons. There is no single pattern to it. If it were that simple, it would not have remained an issue since schools were commonplace. Minsky solidly makes the point that when math is taught as nothing more than an endless series of tedious drills with no purpose in sight, of course it demotivates kids. No one likes pointless Sisyphean tasks. Many students, howeve…

> Many students, however, "rediscover" math when they get to their first class that involves theorems and proofs (often in high-school geometry) High school geometry (at least in the US, and in my experience) is the worst of them all! Two-column proofs should be banned.

Two-column proofs

I had never heard of that monstrosity before and having googled it, it looks worse than programming in COBOL.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#73

Post by anon4 »

elementalest wrote: post #11
thomasahle wrote: post #2

> Anecdote: I asked a certain 6-year-old child “how much is 15 and 15”and she quickly answered, “I think it’s 30.” I asked how she figured that out so fast and she replied, “Well, everyone knows that 16 and 16 is 32, so then I subtracted the extra two 1’s.” Wait, is this girl some kind of base-2 native?

This is how i often work with things. I break them down into things that i know how to work with. I search my knowledge for elements that most closely represents the problems and then combine them. For example, rather than remembering 12 * 6 = 72, i recall that 10 * 6 = 60 and 2 * 6 = 12, hence 60 + 12 = 72. I don't need to remember as many things and for me i can do that much faster than trying to recall it. My memo…

Remembering the multiplication table up to 12 seems to be an American thing. We only did up to 9 and from then on learned how to multiply many-digit numbers going digit by digit.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#74

Post by lordCarbonFiber »

anon4 wrote: post #69
nothis wrote: post #60

That old topic. Ironically, I find people who work with math ( chosen to work with math, that is) to probably be quite unqualified to truly understand the problem. He opens by saying that learning avoiding mistakes before any bigger concepts is a major root of this but then again, people do make mistakes in math (even math professors) and it's a field where any mistake can completely invalidate the work. Also most pe…

I'm not sure how you would define the Fourier Transform geometrically without needing 4 spatial dimensions, at which point intuitive geometric reasoning is impossible.

Far from impossible, it's even reasonably intutitive. Wikipedia has an excellent graphic https://en.wikipedia.org/wiki/File:Fourier_transform_time_an....

Then for people for which that's too abstract, I find this graphic helps a lot in explaining. http://static.nautil.us/1635_42a3964579017f3cb42b26605b9ae8e...

You picked a really bad example for the unintutiveness of mathematics.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#75

Post by cmrdporcupine »

kazinator wrote: post #38

While kids may find arithmetic to be boring and demotivating, they're able to do it. It's when math gets symbolic that you get the permanent attrition. For instance, most people never get to calculus. When you progress from arithmetic to abstract, it hardly gets easier . Moreover, memorizing. You go from memorizing multiplication tables to other kinds of tables, like tables of equations giving various identities, row…

I failed math all through elementary school but somehow got into this industry despite that. The reality is I'm terrible at arithmetic, but fine at what most of CS is: logic in the form of boolean logic, symbolic stuff. As a kid I was much better with the symbolic than the arithmetic -- which I almost always got _wrong_. My brain stumbles over numbers. I'm terrible at it. I feel like my childhood education did a horrible disservice to me telling me I'm terrible at math, when I'm really just terrible (to the point of what I think might be a physical disability) with numbers.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#76

Post by echo_oddly »

anon4 wrote: post #69
nothis wrote: post #60

That old topic. Ironically, I find people who work with math ( chosen to work with math, that is) to probably be quite unqualified to truly understand the problem. He opens by saying that learning avoiding mistakes before any bigger concepts is a major root of this but then again, people do make mistakes in math (even math professors) and it's a field where any mistake can completely invalidate the work. Also most pe…

I'm not sure how you would define the Fourier Transform geometrically without needing 4 spatial dimensions, at which point intuitive geometric reasoning is impossible.

Doing a Fourier transform is simply applying a set of inner products from the function, f, onto a set of orthonormal basis functions. Put a post in the ground, measure the length of the shadow cast by the sun. That's how to do an inner product. So you can at least describe the process using few dimensions. Then you can scale it up to higher dimensions from there.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#77

Post by tdaltonc »

I really like the educational policy recommendation in Where Mathematics Comes From [0]. Even the most abstract mathematics is an analogy with our intuitive embodied experience.

One striking example: Training children to individually articulate their fingers makes them better at processing arabic numerals. [1]

[0] https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From [1] https://www.researchgate.net/profile/Marie-Pascale_Noel/publ...

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#78

Post by [deleted] »

nothis wrote: post #60

That old topic. Ironically, I find people who work with math ( chosen to work with math, that is) to probably be quite unqualified to truly understand the problem. He opens by saying that learning avoiding mistakes before any bigger concepts is a major root of this but then again, people do make mistakes in math (even math professors) and it's a field where any mistake can completely invalidate the work. Also most pe…

[deleted]

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#79

Post by jimmaswell »

j2kun wrote: post #56
crispyambulance wrote: post #42

Earlier quoted context omitted.

Disagree. Kids disengage from math for many different reasons. There is no single pattern to it. If it were that simple, it would not have remained an issue since schools were commonplace. Minsky solidly makes the point that when math is taught as nothing more than an endless series of tedious drills with no purpose in sight, of course it demotivates kids. No one likes pointless Sisyphean tasks. Many students, howeve…

> Many students, however, "rediscover" math when they get to their first class that involves theorems and proofs (often in high-school geometry) High school geometry (at least in the US, and in my experience) is the worst of them all! Two-column proofs should be banned.

These? https://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/a8e3...

I had those in high school and I hardly see any problem with them. It's just writing the proof neatly organized into a table, with the reasons for each step given.

Re: Marvin Minsky: What makes mathematics hard to learn? (2008)

#80

Post by socrates1998 »

It's hard to know exactly what would work for ALL students.

Honestly, for me, the issue is "one size fits all" that the vast majority of our students get.

I learned math just fine the way it was taught. Sure, it was boring at times, and I was mathematically inclined, but it worked for me.

For others, it clearly doesn't work.

We have to ask ourselves, what exactly do we want people to know who don't want to learn math. What is the "bottom line" that we need a citizen to know?

Algebra 2? Trig? Some combination of Algebra and basic math finance concepts?

That's the main question. And it's very difficult to answer for ALL students.

I don't know what the answer is, but adopting one method for all students isn't the answer.

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