I am going through some old flagged links. This one is from a couple years ago. The New York Times looks at what might be a better way to teach math:
In particular, math teachers often fail to make sufficient allowances for the limitations of working memory and the fact that we all need extensive practice to gain mastery in just about anything. Children who struggle in math usually have difficulty remembering math facts, handling word problems and doing multi-step arithmetic (pdf). Despite the widespread support for “problem-based” or “discovery-based” learning, studies indicate that current teaching approaches underestimate the amount of explicit guidance, “scaffolding” and practice children need to consolidate new concepts. Asking children to make their own discoveries before they solidify the basics is like asking them to compose songs on guitar before they can form a C chord.
Mighton, who is also an award-winning playwright and author of a fascinating book called “The Myth of Ability,” developed Jump over more than a decade while working as a math tutor in Toronto, where he gained a reputation as a kind of math miracle worker. Many students were sent to him because they had severe learning disabilities (a number have gone on to do university-level math). Mighton found that to be effective he often had to break things down into minute steps and assess each student’s understanding at each micro-level before moving on.
Before having read this, I actually started doing this when I was trying to teach math to sixth graders. I really think that there is something to it. The totality of the problem can be really daunting, especially for those who come into it believing that they are not equipped for it. This is one of the ways that I think computer programming is a helpful tool for life. Computer programming encourages people to break down large problems into much smaller ones and attacking them one at a time until you get there.
The premise of the book behind the article and the book – that anyone can do higher-level math – is likely to be met with some scoffing amongst y’all. And actually, I am inclined to agree. I am not nearly as optimistic as the author of the book. I do think, though, that even within someone’s range of ability, you can get better results or worse results. To some extent, it’s not going to be worth the time and effort to get above a certain level, but I think even those for unfavorable demographics or lineage can get further along than they do. You never know what might produce some pretty incredible results.
About the Author
6 Responses to A Better Way To Teach Math
Leave a Reply
please enter your email address on this page.
This isn’t directly relevant to the article you link to, but I only really started to be decent at math (although I never became “good” at it), until I took trig and my teacher used an approach that none of my other teachers had used. She assigned the problems first, and we had to go home, teach ourselves how to do the problems (by, for example, reading the chapter in the textbook) and then the next day, she’d go over the problems and how to solve them. In other words, we had to “teach ourself” so we could know what we didn’t understand, and then use class time to shore up what we didn’t know.
It didn’t work for some students, but for me it was empowering. It meant I didn’t have to struggle through class lecture hoping to understand enough to do that night’s problems.
This wasn’t how I was supposed to be taught, but the “teach ourself” is mostly what I did. I found classroom instruction to be boring at best, grating at worst. So I’d work on the previous class’s homework and then try to figure it out for myself in the next class.
I really would have been a prime candidate for home or virtual ed, I guess.
I will assume that the first “higher” math class is Calc I.
The reason some students do poorly in Calc I is not because it is inherently difficult, but because they don’t REALLY know algebra, geometry, and trig. If you don’t know those three subjects very well, calc becomes a miserable experience.
I had the opposite problem. My first college class was basically a duplicate of what I learned in high school.
This being a “problem” because I was bored out of my mind.
Do you think that the guy is right, though, that most anybody can do it if they’re taught properly?
Generally speaking, no I don’t think the guy is right. I think the situation can be improved, but there is a certain cognitive ability that has to be in place in order to succeed at that level.
If students don’t hae an intuitive grasp of HS level math, then they don’t have the foundation for college math. They are going to be questioning every little step, making problems very time consuming. Imagine if factoring trinomials was something you couldn’t do easily, or if you converting between degrees and radians was confusing…
That’s kind of my thought. I can imagine it vaguely possible for a sub-par student if they were very motivated, but in my experience it’s almost never the case that people who aren’t intuitively good at something like math are going to be motivated.