I love math. I hate the way it is taught. If you feel similarly, and want to do something about, then this manifesto is for you.
I am on a mission to improve math education. I’ve had some success writing puzzle books and bringing games into classrooms. I’m inspired by wonderful books, movies, exhibitions and web sites that bring math to life. But those efforts have hardly made a dent in the school experience for the vast majority of students. And I want to change things in a big way.
The problem is that schools resist change. Teachers must conform to district wide standards of what topics are taught on what days. Textbooks must conform to detailed state standards about what topics should be taught at what ages. A fourth grade teacher can’t decide to teach a different curriculum, because then their students will not be prepared for fifth grade math. Students who fall behind struggle to catch up to a moving train, and students who jump ahead are abandoned. Pressure to conform is everywhere.
And it is not just schools that resist change. Parents, administrators, policy makers all cling to the way math has always been taught, even though it works poorly, because they can’t imagine any other way to do it. Even those who recognize the need for change often have no vision of how to do it better — all we can think of doing is to move first grade math into kindergarten or condense three years of middle school math into two.
This mass acceptance of the status quo has resulted in a society in which it is socially acceptable to casually remark that you were never any good at math, and expect that everyone else in the room will nod in agreement. Imagine remarking to the same group of people that you were never good at reading. Not so acceptable. Something is very wrong.
So how do we make a bigger dent in math education? By working together. We need a bigger vision that will unify everyone's work into a revolution. My proposal: we should aim for universal math literacy, the same way we already aim for universal English literacy.
Of course language education is far from perfect. Nonetheless math education has much to learn from language education — in almost every aspect of language education our standards are much higher and teaching more effective than they are in mathematics.
To dramatize the difference between math and language education, let’s imagine what would happen if English were taught the way math is taught.
If English were taught the way math is taught there would be no reading. No novels, no poetry, no myths, and certainly no creative writing. There wouldn’t even be model dialogs that illustrate using language in conversation. Only graduate students would be allowed to enter a library or pick up a pen and writing.
Instead English teachers would focus entirely on grammar and spelling — the mechanics of language. We would learn how to add suffixes, conjugate verbs, and match tenses. Occasional we would encounter example sentences, but never in the context of a meaningful story. Students would complain “when are we ever going to use this?”
And we would teach the mechanics of language poorly. Forget mastery. If you didn’t learn all twenty six letters, too bad you move on to spelling. Don’t know what half the words mean? Too late, it’s time for grammar. And forget learning language with multiple senses. All language would be written, and all testing would be multiple-choice tests, graded on speed and accuracy.
A nightmare? Definitely. But reverse the nightmare and we get a prescription for how to improve math education. Here are the six pillars for achieving universal math literacy.
- Mastery — Most problems that college students have with math can be traced back to much earlier gaps in their knowledge, like fractions and place value. Prescription: let students work at their own pace, and do not let them go forward until they have mastered necessary basics. Tip: Online math resources like Kahn Academy enable teachers to manage a whole classroom of self-paced learners.
- Multiple senses — If language were taught only as written language, far fewer kids would be literate. Fortunately kids grow up speaking language in a hands-on multisensory environment where words have immediate meaning — home. Prescription: teach math in a hands-on immersive environment where every concept taught in symbols is also taught with pictures and hands-on activities. For instance, kids should be familiar with the visual model of multiplication as finding the area of a rectangle.
- Testing — Multiple choice and fill-in-the-blank tests assess only rote computational skills. Prescription: test math the same way we test language comprehension, with essay questions, reports and class discussion. One of the biggest innovations in the new Common Core math standards is that the standardized tests now include essay questions where students write about how they solved problems, and these questions are graded by human beings, not computers.
- Using math to do real things — Schools teach math mostly as an abstract subject, where the only reality check is passing tests. Prescription: get kids out of their desks, and have them use math to solve real world problems. My friend Warren Robinett told me “a middle-school teacher I knew would, after teaching the Pythagorean Theorem, take the kids out to the gym, and measure the length and width of the basketball court with a tape measure. Then they would go back to the classroom and predict the length of the diagonal. Then they would go back to the gym, and measure the actual diagonal length. She said some of the kids would look at her, open-mouthed, like she was a sorceress.”
- Reading about math — Parents read picture books to their kids to expose them to the world of words, people and ideas long before kids are able to read. Prescription: parents should play math games and read math stories with their kids long before the kids learn formal math, to expose them to the ideas and thinking behind math.
- Writing math — when students write original stories and essays, they integrate everything they have learned about language. Prescription: math students should not just solve other people’s problems, but also create their own questions and methods of solving problems, and teach what they have learned to others. When you create and teach ideas, the ideas truly become your own. Mathfair.com advocates this approach to math education in their wonderful idea of student-created math fairs.
In future blog posts I will expand on these six pillars, showcase outstanding examples of how these goals can be achieved, and recommend what we need to do next. Let's raise our standards and settle for nothing less than universal math literacy.