Equity is a core principle of the current mathematics education reform movement. "All students, regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to study -- and support to learn -- mathematics." (Principles and Standards for School Mathematics, p. 11.) Much has been written about our need to reach minorities, girls, and inner city children -- populations that have been underrepresented in advanced math classes in high school and college. But there is another population that I think we are in danger of leaving behind, a population that used to do well in school mathematics: tidy math fans.
What is tidy math? Worksheets containing orderly rows of computation problems, all essentially the same problem, but with different numbers. Textbooks or teachers that cleanly demonstrate a method step by step and then ask students to do thirty problems using that same method. These are examples of tidy math.
Who are tidy math fans? Students who are neat and well-organized. Students who may not be too creative, but who pay attention and follow directions well. Students who are satisfied with knowing how and who are not bothered by not knowing why. Students who grow up, meet math teachers like myself at parties, and say "Oh, I've always liked math. I love how there's always one right answer to a problem." These are tidy math fans.
Tidy math fans do well in what we now call "traditional" math programs. But as some schools adopt new programs like Investigations, some of these students face a sudden drop in status, from one of the best math students in the class to an average, sometimes struggling student. Their self-esteem about their math ability plummets. It's no wonder that some of their parents (who themselves grew up with tidy math) put up a fuss about the new program and teaching style that is causing their children's loss of confidence.
Certainly not all students who enjoy tidy math are less successful with Investigations or similar programs. Some of them rise to the challenge and find that they are able to generate their own strategies instead of just following the teacher's strategy, and that they actually feel better about what they are doing now that they understand why it works. But there are still some tidy math fans who do not adapt well. The rules for success and the very definition of what it means to do math have changed on them. Math is much harder now.
You might argue that this change is for the students' good. What tidy math fans were successful at before really wasn't mathematics anyway, and we do all students a favor by showing them what doing mathematics is really about. "Doing math has to do with thinking and reasoning about problems or situations that call for applying mathematical ideas and skills . . . Skills should be learned in the context of problems and situations and should not exist isolated from the problems and situations that give them their purpose." (Burns, p. 69.)
In Beyond Arithmetic, Investigations authors advocate that students work on nonroutine mathematical problems. "With nonroutine problems, students should expect "messiness." There may be different paths to a solution, and there may be several different good solutions to a problem . . . Doing mathematics often means rough drafts, tentativeness, challenge, and hard work." (Mokros et al., p. 53.)
I couldn't agree more: students need to learn and experience that mathematics isn't tidy, it's messy. Most people do not do well at tidy math anyway. Far more common responses I get at parties when people learn that I am a math teacher is "Ick! I hate math" or "I was never good at math" or "I never understood math." I believe a constructivist approach would have helped these people to enjoy mathematical success.
In contrast, most students LOVE Investigations, messiness and all. I am excited about the many students who are turned on by Investigations, students who used to think math is boring. I'm thrilled to hear the stories of students who would rather continue with math time than go to recess. But I am also troubled by the few students who liked math better the old way.
We need to recognize how hard the adaptation to "messy math" is for a few children. To achieve our vision of equity, we must support these children too, but how? I would love to hear from Investigations users on this issue. Here are some questions I would appreciate responses to:
- How do we teach these students with a background in and a talent at tidy math?
- Should we include traditional worksheets as one choice during choice time? Or is this sending the wrong message?
- Do you find that these students are easily turned on to "messy math" or not?
- Is this a problem in your classroom or do you think this piece is way off base?
Susan James, Grade 5 teacher, Winston-Salem, NC
March 2001
Bibliography
Burns, Marilyn. Math: Facing an American Phobia. Sausalito, CA: Math Solutions Publications, 1998.
Mokros, Jan, Susan Jo Russell, and Karen Economopoulos. Beyond Arithmetic: Changing Mathematics in the Elementary Classroom. Palo Alto, CA: Dale Seymour, 1995.
This information was reprinted with permission of CESAME, Northeastern Univ., and the Educational Alliance, Brown University.
