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In Math Cram Sessions, Solving for Why

nytimes.com

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Re: In Math Cram Sessions, Solving for Why

#31

Post by saagarjha »

tesin wrote: post #4
rb808 wrote: post #3

A good example of why well educated parents is more important than getting into the "the best schools".

Isn't that just a matter of chicken and the egg timing tautology? The parents are well educated presumably because they went to good schools.

No, I think you’re getting the relation backwards. Many parents who were well educated have the opportunities to send their children to good schools, regardless of whether they went to a good school themselves, because they realize that it makes it easier to be well educated there.

Re: In Math Cram Sessions, Solving for Why

#32

Post by paulddraper »

unpythonic wrote: post #22

As much as the Common Core standards are criticized here in California, I have to say that the emphasis on the "why" behind every operation is really fantastic. It's usually in the last section of each homework, but it provides a good discussion point when going over the homework each night. Asking students to answer questions like the following are easy to zip through, but they provide a good place to pause and find…

I don't know whether or not Common Core is the "right" solution for math education, but on face value it is.

A good math student understands the subject in a principled way, which shapes inference and intuition for future discovery, and results in rock solid grasp of the subject.

Supposedly, this is the point of the Common Core math curriculum, right?

Re: In Math Cram Sessions, Solving for Why

#33

Post by rambl30n »

ummonk wrote: post #17
Koshkin wrote: post #6

Earlier quoted context omitted.

Knowing "why" is exteremely helpful in many cases. But let's not forget that, on the other hand, memorization plays a huge part in learning, and not only in mathematics. Learning "why" multiplication works will not help you to retain the multiplication table in your head. (Also, in many cases the answer to a question "why" you might get will be plain wrong - sometimes because the correct answer is too complicated, so…

You can just do a lot of multiplications, and let your brain cache the results over time.

This. Although said tongue-in-cheek, is a basic principle. Once you understand the concept and the mechanics behind something, what rote learning buys you is to free cycles in the future so that you can take up the next-level task. Skipping this step is like expecting someone to play the piano just by learning how to read a music sheet and where each note is in the keyboard. You build up your muscle memory so that you're able to take on more complex pieces as you progress.

Re: In Math Cram Sessions, Solving for Why

#34

Post by saagarjha »

ivansavz wrote: post #8

Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn. I think equally important is the transmission of a relaxed, exploratory attitude towards the STEM subjects. When a learner sees their teacher take on positive attitudes towards complexity, they too develop this attitude and can go on to solve problems on their own. Unfortunately, this t…

> Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn.

I really disagree with your choice of words here, specifically, “just-in-time”. This makes it seem like the tutor is teaching things to the student right before they need it for an exam, which is an unfortunate effect I’ve seen happen because in the long run it doesn’t really teach anything. But where a private tutor really does excel is having a better understanding of how to tailor the curriculum to the student (this includes both simplifying or making it more challenging, depending on the student and the topic).

Re: In Math Cram Sessions, Solving for Why

#35

Post by saagarjha »

unpythonic wrote: post #22

As much as the Common Core standards are criticized here in California, I have to say that the emphasis on the "why" behind every operation is really fantastic. It's usually in the last section of each homework, but it provides a good discussion point when going over the homework each night. Asking students to answer questions like the following are easy to zip through, but they provide a good place to pause and find…

> As much as the Common Core standards are criticized here in California, I have to say that the emphasis on the "why" behind every operation is really fantastic.

The one reason why I dislike Common Core is that this kind of explanation get quickly become tedious if you already understand what’s going on and it’s “obvious” to you. And many teachers seem to like to use this section as an excuse to waste their students’ time at home by forcing to write much more than they really need to.

Re: In Math Cram Sessions, Solving for Why

#36

Post by typomatic »

saagarjha wrote: post #34
ivansavz wrote: post #8

Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn. I think equally important is the transmission of a relaxed, exploratory attitude towards the STEM subjects. When a learner sees their teacher take on positive attitudes towards complexity, they too develop this attitude and can go on to solve problems on their own. Unfortunately, this t…

> Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn. I really disagree with your choice of words here, specifically, “just-in-time”. This makes it seem like the tutor is teaching things to the student right before they need it for an exam, which is an unfortunate effect I’ve seen happen because in the long run it doesn’t really teach an…

> This makes it seem like the tutor is teaching things to the student right before they need it for an exam

On the contrary, I found it really precise. JIT processes in manufacturing are about providing the correct inputs at the time they're needed. If your desire is mastery over the material, a teacher who can predict or extemporize tutorials on the subject as you need them is invaluable.

Re: In Math Cram Sessions, Solving for Why

#37

Post by Zeebrommer »

chrisweekly wrote: post #13
ivansavz wrote: post #8

Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn. I think equally important is the transmission of a relaxed, exploratory attitude towards the STEM subjects. When a learner sees their teacher take on positive attitudes towards complexity, they too develop this attitude and can go on to solve problems on their own. Unfortunately, this t…

Great post. FWIW in discussing this topic I've heard and now adopted the term "(in)numerate" vs "STEM-(il)literate" -- though the latter might be intended to be broader in scope?

I don't think it's very helpful to make such a distinction between people who "get it", and those who don't. It's a spectrum. Unless of course when it's relating to a disorder, like dyslexia for example.

Re: In Math Cram Sessions, Solving for Why

#38

Post by ivansavz »

saagarjha wrote: post #34
ivansavz wrote: post #8

Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn. I think equally important is the transmission of a relaxed, exploratory attitude towards the STEM subjects. When a learner sees their teacher take on positive attitudes towards complexity, they too develop this attitude and can go on to solve problems on their own. Unfortunately, this t…

> Yeah, private tutoring is the best. The custom, just-in-time curriculum that a tutor can prepare is the most efficient way to learn. I really disagree with your choice of words here, specifically, “just-in-time”. This makes it seem like the tutor is teaching things to the student right before they need it for an exam, which is an unfortunate effect I’ve seen happen because in the long run it doesn’t really teach an…

Ah no, my intended meaning of “just-in-time” was definitely not in the sense of just-in-time-for-the-exam. In fact I think there is very little use for last-minute cramming... at most you can survive the test, but definitely not build fluency or understanding.

I was using “just-in-time” in the sense of just-in-time-for-the-lesson, e.g., if the tutor wants to teach concept X which requires knowledge of prerequisite concepts α1, α2, and α3, then the tutor can provide a quick review of these concepts before explaining X. Tutors can do this "custom filling in of gaps," whereas in a groups setting the teacher might be forced to say "you should know this already."

Re: In Math Cram Sessions, Solving for Why

#39

Post by aj7 »

somethingroma wrote: post #9
Koshkin wrote: post #6

Earlier quoted context omitted.

Knowing "why" is exteremely helpful in many cases. But let's not forget that, on the other hand, memorization plays a huge part in learning, and not only in mathematics. Learning "why" multiplication works will not help you to retain the multiplication table in your head. (Also, in many cases the answer to a question "why" you might get will be plain wrong - sometimes because the correct answer is too complicated, so…

Memorizing multiplication tables is over rated. Seeing connections between those early multiples up to 12 is more interesting. Can be helpful I suppose in factorization. Maybe I just don't trust my memory (as in how am I sure that 7*8 is 56) and why I despise rote memorization and rather retain memory from use and practice. Regardless a good example of something to remember in math is the quadratic formula Still enjo…

No. If you can’t multiply in your head, you are crippled in any quantitative reasoning. You have interjected too many steps in estimating, calculating, judging, etc.

This is not to say there aren’t useful, non-quantitative pursuits.

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