WORKING WITH Jerry Acton, Math and Science Teacher see value and usefulness to math, without my having to persuade them of that idea. Blending the Social and Emotional with the Cognitive Jerry Acton teaches math, chemistry, and physics in high school. I wanted to interview him to learn more about how students think about these traditionally "cog- nitive" subjects. What I learned, though, was that suc- cess in these subjects depended heavily on social and emotional factors-on students' attitudes and motiva- tions, and not just on their thinking abilities as such. The blending of the domains of development was especially evident in Jerry's tenth-grade math class, the one we spent most time discussing. Kelvin: I've heard a lot of generalizations about math-stereotypes about learning it, so to speak. I've heard that math is inherently abstract, for example, and that it's very sequentially orga- nized, and that you have to be willing to work independently if you want to do well in math. What do you think about these ideas? Do they explain why some students do better in math than others? Tell me about your own classes. Jerry: For my classes, I would say that matu- rity makes the biggest difference. Maybe it's because these are tenth-graders-people who have just arrived at senior high school and are still getting used to it. The more successful stu- dents in math classes are the ones who are the most mature. Kelvin: What do you mean by "mature"? Jerry: I mean the ones who are prepared to come to class to work, to listen, to ask questions, and to do work in class, as opposed to coming to class because it is a convenient place to socialize with friends. The mature ones already seem to Kelvin: That makes it sound like there's not much need for you as the teacher-like students either choose to work or they don't, and there's not much you can do about it. Surely that's not what you mean? Jerry: Oh no, there's still lots to do! One thing I do to motivate the less self-motivated students is give them a structured environment: one where our tasks are predictable, where there's routine. With a good routine, they know what to expect and the tasks are organized into steps that they understand and can do. We always do mental math first, then review the day's homework, then start a new lesson, and so on. I find that varia- tions from the format inevitably throw some stu- dents "off their stride," and less gets done. Kelvin: That reminds me of the sequencing idea. People sometimes say that you have to learn math concepts in a certain sequence or else you risk getting hopelessly lost in the long term. Is that true? Jerry: Yes, in a sense it is true. But teachers can do things to keep students from getting lost as a result. In our new curriculum, for example, we use "spiral sequencing," where we revisit topics peri- odically and give daily review in between visits. If you're sick for a whole week, you don't miss out altogether on a particular math topic. And all the teachers in my school now use cumulative testing, which gives students incentives for consolidating WORKING WITH Jerry Acton, Math and Science Teacher Blending the Social and Emotional with the Cognitive continued what they know so that there are no "holes" in their math knowledge at the end of the course. Kelvin: Still, by its nature, math must be pretty abstract, even in tenth grade. Jerry: You're right about that. Especially in the course called "precalculus," which actually says in its advertising that it is abstract and is intended for students who already enjoy math. How do you offer concrete, hands-on activities related to factoring? What are the everyday uses for factoring? [Smiles.] Most students do learn better if you can make the material more down to earth and relate it to familiar activities. But I have found ways to move in that direc- tion. This year we used graphing calculators, for example, which the students really enjoy. The calculators make it a lot easier to create graphs-much faster and less laborious. With the calculators, you can actually play around with graphing different functions instead of tak- ing fifteen minutes just to draw one by hand. When we get tire computer lab set up properly, we'll be able to do even more. Kelvin: Sounds like with the calculators, stu- dents could even work together. They could do problems and projects cooperatively. Jerry: That's indeed the case. Students can do problems independently, for example, and then compare their results. We'll be able to do more joint work, in fact, when we get the computer lab set up. Kelvin: I often think of math as being an espe- cially "solitary" activity, not one that lends itself to working with others. Would you agree? Jerry: I've found that there are ways for students in math to work together, like with the graphing calculators. Sometimes, in fact, I've actually had trouble with students cooperating too much; it seems like they're always wanting to consult with each other about how to do certain problems or about what the answers are. Then I wish they would function more independently of each other. A mix is best: cooperation combined and independence combined. What Do You Think? 1. Given Jerry Acton's comments, would you describe mathematical success as a "cognitive" skill, a "social" skill, or as some combination? Explain your reasoning. 2. Do you believe there is indeed truth in the stereotypes or expectations about mathematics that Kelvin expressed at the beginning of the interview? How would you qualify these ideas, taking into account both Jerry's comments and your own knowledge and beliefs? 3. Sometimes mathematics is traditionally thought of as a "boy's" subject more than a "girl's." Judging by Jerry's comments, do you think this is true for his class? Do you still think it could be true for mathematics students in general?