Tuesday, June 30, 2015

Confusing math with math education

It strikes me that much of what is wrong with math education results from a confusion of math with math education. Is the goal to teach kids how to do math, or how to be math teachers?

Consider two tasks common to today’s math assignments but rare before Reform Math: explaining answers verbally, and explaining what’s wrong with other people’s solutions. Variants include having third graders write letters to second graders about why, say, 1/3 is bigger than 1/4, or to Jack “telling him what he did right, and what should do to fix his mistake.”

I and others have argued here and elsewhere that explaining your answers verbally is often a counterproductive waste of time that, in particular, shortchanges second language learners and students with language delays. Similar arguments apply to explaining why someone else’s answers are wrong. But, if you’re in a teacher education program training to be a math or a K6 general education teacher, then suddenly being able to provide these types of verbal explanations is absolutely essential.

Ironically, these explanation demands are especially common in elementary school, when students are least able to verbalize things clearly. Perhaps this has to do with the profile of the typical elementary school math teacher, who, in his or her teacher training program, has had to take courses in math education, but not in actual math. To some extent, however, such teachers are simply following the math curriculum that others have written and/or selected for them. So what about those most responsible for creating and selecting math curricula--the Deborah Balls and Andy Isaacs and Jo Boalers of the world? Is it possible that most of them get more training in math education than in math?

When it comes to educating K12 students, math education should primarily involve math, and not the infinite regress, as it were, that comes from educating students in math education.


Auntie Ann said...

I always trip on the social aspects of asking fairly young children to tell other young children what they are doing wrong.

Kids don't have the experience to say things nicely, don't have the emotional maturity to take criticism the right way (it's not easy for adults either--no one likes having to sit with their boss for job evaluations!), nor do they have the security in themselves and their social position to be honest with someone either far above or far below them in the pecking order. It's a great opportunity, sanctioned by the teacher, to bully and be bullied.

Kids simply aren't mature enough to handle this.

SteveH said...

I consider it a matter of turf. It disappears to a great extent in high school when you get teachers who are trained and certified in their subjects. However, in K-6, it's not about skills and content, but pedagogy and process. That's their turf and they are bound and determined to make them the dominant variables in education. When I told my son's first grade teacher that he loved geography and could find any country in the world, she said "Yes, he has a lot of superficial knowledge." When we finally got his Kindergarten teacher to admit to a reading test they gave kids, she went out of her way to tell us that some kids can read encyclopedias but they don't know what they are reading. They talk about "kids spelling."

There is also a competence issue going on. They talk about differentiated instruction as the main justification for full inclusion, but just try to ask about details. Don't assume that there is much supporting their justifications.