In Math Cram Sessions, Solving for Why
nytimes.com
In Math Cram Sessions, Solving for Why
1–10 of 83 posts
Re: In Math Cram Sessions, Solving for Why
#2"This was the key. If you knew hhhhwwhy you didn’t have to memorize equations, or solve equations in the exact same way they did in the book..."
I feel like this is a valuable lesson a lot of people could benefit from.
Re: In Math Cram Sessions, Solving for Why
#3A good example of why well educated parents is more important than getting into the "the best schools".
Re: In Math Cram Sessions, Solving for Why
#4A 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.
Re: In Math Cram Sessions, Solving for Why
#5"This was the key. If you knew hhhhwwhy you didn’t have to memorize equations, or solve equations in the exact same way they did in the book..." I feel like this is a valuable lesson a lot of people could benefit from.
I agree as a generalization, but that does presume that the syllabus itself doesn't need rote interpretation.
“No, we haven’t learned about some of the vectors yet, so for the sake of the problem, we just take this one out,”
Re: In Math Cram Sessions, Solving for Why
#6"This was the key. If you knew hhhhwwhy you didn’t have to memorize equations, or solve equations in the exact same way they did in the book..." I feel like this is a valuable lesson a lot of people could benefit from.
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, sometimes for other reasons.)
Re: In Math Cram Sessions, Solving for Why
#7A good example of why well educated parents is more important than getting into the "the best schools".
Uhm, no - asking students to prove theorems and lemmas and answer all the "whys", instead of just applying a set of problem solving rules was one of the main reasons why the high school I went to was so good at math education. Our physics teacher constantly told us not to memorize the formulas, but to understand the logic behind them so we could just figure them out if we needed them. It's a better way to learn math and physics indeed, but a good teacher can do it too.
Re: In Math Cram Sessions, Solving for Why
#8Yeah, 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 transfer of attitude works in the negative direction too. If the teacher is out of their comfort zone (e.g. parent touching math for the first time in 20 years), then the learner might pick up on the anxiety and start to consider the subject to be unpleasant or hard---if your parent was stressing out about helping you with algebra, then algebra must be a thing of formidable complexity!
As another example, you can think of a teacher bored with the subject (e.g. prof who is teaching this course for the 17th time this semester) who will then transmit "this is stupid shit you have to know, because you're forced to take this course" attitude and students will pick up on this too...
Luckily these days there are really good resources (youtube, free books, interactive demos) so hopefully we'll have more STEM people in the future. We won't make 100% of the population into STEM-experts, but it's not unrealistic to hope that everyone can become at least STEM-literate. I'd like to believe that I contribute to this with my books. This one in particular would be good for adult readers who want to rekindle their relationship with the subject: https://www.amazon.com/dp/099200103X/noBSmath
Re: In Math Cram Sessions, Solving for Why
#9"This was the key. If you knew hhhhwwhy you didn’t have to memorize equations, or solve equations in the exact same way they did in the book..." I feel like this is a valuable lesson a lot of people could benefit from.
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 enjoyable to derive and 'see' why it works but also just used so much. That said, I wouldn't encourage memorizing it without first understanding it.
Re: In Math Cram Sessions, Solving for Why
#10I think understanding the why of mathematics makes all the difference between forgetting it soon after an exam, and being able to use it later in life.
I sometimes find myself needing to return to something I once knew in high-school / university to solve some problem, not being able to remember the specific methods, but the underlying bigger picture of the concepts comes back to me, and I can make progress from there.