One ManifestoJanuary 25, 2009
Link: One Manifesto
People have been writing about the failure of math education for a long, long time. For example:
S. K. Stein, Strength in Numbers, John Wiley & Sonse, 1996
If you browse through The Mathematics Teacher, the main journal devoted to instruction in mathematics you will find constant lamentation, going back to its first volume in 1908, where one teacher wrote, “One of the most obvious facts about mathematics in our schools is a general dissatisfaction.” The tone in 1911 was even less cheery, “Our conference is charged with gloom. I have attended funerals, but I do not remember a more mournful occasion than this. We are failures and our students are not getting anything worthwhile.”
Year after year, the complaints in The Mathematics Teacher persist. I will skip ahead to 1958, when we read, “The traditional curriculum is meaningless, and by heading for abstract mathematics the modernists are moving further from reality.” … Still, in 1994, the University of Chicago School Mathematics Project complained, “The student today still encounters a variant of the elementary school curriculum designed for the pupil of a hundred years ago.”
I cribbed this tidbit from the website this title links to. I think the author of this site does a good job laying out a comprehensive manifesto—if you have some free time, check it out. There are plenty of specific anecdotes and quotes that are worth reading (and I’ll be putting my favorites of those up here from time to time). There are also lots of math puzzles. A warning though—most of them look pretty tricky. If you’re timid about math, this probably is not a good place to start. If you’re more experienced and looking for a challenge, it may be right up your alley.
To return to education for a moment, I quoted Stein above to make the point that there is virtually no time period we can point to where mathematics was generally well taught. Personally, I think that the problem is deeper than math education. The point is to teach students to think independently and creatively; everything else should support this goal. But the particular problem of mathematics is that most people don’t understand that it is a subject where creative and independent thought is possible. To quote the great mathematician and teacher G. Polya:
“A teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking.”
There are long standing arguments about how best to teach math. At this moment, they tend to be polarized between entrenched, immovable opponents. Both sides, of course, have plenty of valid points, and both sides, at some level, miss the whole picture. To be taught well, mathematics needs to be motivated. The reason to learn it is not because you’ll need to use it someday—it’s because it’s interesting now, and because you have questions now that you want to answer.
In my experience, there is a near universal interest in math. I’ve seen students who were classified as lost get joy out of the subject. But we have to get people—students, teachers, and the public—to do math in order to see that they actually enjoy it. Music you can listen to. Art you can look at. Math you have to do.