Re:Learning algebra in my 60s
by ravi-delia on Monday August 08, 2022 @01:28PM
(#32388440)
I think there are smarter drills to do. In another comment I lauded the way I was taught math, and how it built intuition, but it certainly had lots of drills too. I think what worked was that we were taught more than one way to do each thing, usually one more theory-heavy and another more technique-heavy, and we had lots of drills focused just on the primitive operations. There was lots of focus on mental math, which is just super handy for understanding more complicated problems since you don't even have to think about the simpler steps. While they did go over how fractions were just division in disguise (with pictures, which I found very helpful), knowing how to find a least common denominator is much faster than improvising every time, so even if I hated it I'm glad we did lots of drilling with those too.
A lot of what you describe has become the standard way to teach elementary math-- from the "new math" onwards to Common Core pushing aspects of looking at problems the same way
Our school does the much-lauded Singapore Math in elementary, which definitely tries to build intuition and looks at many approaches, and supplements with drills.
And I teach a competitive math class which definitely is all about finding different ways around problems and comparing and contrasting.
Re:Learning algebra in my 60s
by ravi-delia on Monday August 08, 2022 @01:41PM
(#32388599)
I'm thrilled to hear it's popular! In my hometown it was killed by doubters, but perhaps with expanding evidence they'll reconsider. I think perhaps it was lumped in with disastrous testing efforts, but the math at least was pretty great.
:D I'm not sure it's popular: it's controversial with parents, in general. But I think it's a good thing, overall.
I do think most programs implementing it end up taking out a little too much rote and algorithms.
A good math education in arithmetic, algebra, and calculus is a combination of concepts and drill. This was a concept that I rejected back in school. Now I'm teaching-- not mathematics, but I have tutored and helped students catch up who have had problems.
There's a fair number of students struggling in pre-calc who have all the concepts just fine, from the bottom to the top. But when they're dealing with lots of terms and keeping a higher level goal in mind, their performance on a few simpler things, like fractions and quotient properties, falls apart. Maybe they missed a week or two in 6th grade when this was really solidified and practiced.
The terrible thing that tends to happen, once you stumble in math: the amount of concept content you have falls. The focus moves even more to rote, but focused on the "more difficult" stuff--- leaving whatever core deficit there is intact. There's solid reasons for this, but the outcomes are not great.
I also have a kid who is going into AP Calculus pretty young. I'm kinda nervous that he just has not had enough reps of practice, even though he scores very high on placement tests.