I followed my students to math yesterday.
It was painful trying to teach them afterwards.
The teacher had used a flashcard game called Around the World with division, meant to reinforce basic fact memorization. You can find the rules at the link above. It was pretty fast-paced.
Students started muttering about the possibility that some were giving others answers in their native languages. The girls seemed to go quiet. The boys ( I use that term loosely. Our boys are pretty nearly, if not already, men.) got very competitive. And they had to be reminded not to get physical as they switched seats.
Harmless fun, the teacher says.
But I think there’s more to it.
Class really did not go well when we had them. Angry faces. Dagger eyes. Good thing we had Lindsay and were working on some relaxation.
We tried to do some new work, but it didn’t go so well. It wasn’t the content. It was that students came in so wound up. We started with trying (again) to put feelings in our bodies:
When I do math, I feel (emotion, or what we’re using for emotions) in (body part).
So my answer?
When I do math, I feel angry in my shoulders.
We had some happy people. We had one thirsty person. (Thirsty for what???) But mostly, we had tired and/or angry people who felt it in their hands, their necks, their arms, their eyes…
And that got us thinking. Suzy suggested we retest a student who says he is bored in ELL math. So we gave him our screener again. He still has pretty big holes. He’s in the right math class. But he is really frustrated.
The screener was created 20 years ago by my colleague and friend, David Rome. It’s not perfect. But the math department stands behind it. They say it does the job.
I think they are right. But are these symbols universal? Or are we testing Western math?
The other thing that happened in math is that we started long division.
And we only had a few minutes left in class. Students were really confused. They didn’t understand what the teacher was doing. And he was using simple words, but they really needed time to be taken to explain the symbols.
Suzy had asked me questions about the screener and the symbols that are used, whether they were culturally universal. So I asked Tim Whiteford, a math education professor I know at St. Michael’s College, to come by and check out our tests. He’s going to get back to me with his assessment of our assessment, but here’s what he told me:
Ninety percent of all schools focus on procedural knowledge over conceptual knowledge.
I showed him how our frustrated student was trying to solve the problem. It looked kind of like this:
But our student wasn’t getting the problem right. He was confused. Tim says this likely is because he started to learn it in his home culture, but he didn’t reach fluency. And now we’re changing the procedure. And it’s very frustrating. What we are used to looking at, and what the students were being exposed to was this:
I found this during my research tonight:
Symbols and representations can be seen as tools for conveying mathematical information. The problem, however, is to understand how immigrant students come to understand the meaning of symbols and representations that may not be part of their former reality. Immigrant students that attend schools in the United States have interesting mathematical experiences. One of these experiences is related to the long division algorithm; in this case, algorithm is defined as a rule or procedure for solving problem (Philipp, 1996). The procedures that are taught in schools in the United States, sometimes, look so different from what was learned in schools in their home countries.
And so, in order to find out what our students know, we may have to do a little research to find out what they really know. Because we don’t know. Even with an effective screener that attempts to remove language from the equation.
Because what are symbols, anyway?