October 2007 — News
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Homework: A Math Dilemma and What To Do About It
Without accommodating learner differences, we set students up for failure or boredom when, in fact, we can do something about that in the design of experiences outside of school that are meant to reinforce learning. As educators, we can also recall the many reasons a particular assignment was not turned in even by our best students. One of the more original I received was from a high school student who accidentally spilled soda on the homework paper. She said it burned it up when she put it into the microwave to dry.
I am not saying to eliminate a homework requirement. In spite of research design flaws, a synthesis of research from 1987 to 2003 on homework reveals "generally consistent evidence for a positive influence of homework on achievement." We do need to consider grade level and student characteristics, however, as "simple homework-achievement correlations revealed evidence that a stronger correlation existed (a) in Grades 7-12 than in K-6 and (b) when students rather than parents reported time on homework" (Cooper, Robinson, & Patall, 2006, p. 1).
What I also suggest is taking a closer look at current literature on teaching and learning, which calls for differentiated instruction and attention to learning styles, thinking styles, and multiple intelligence theory. When it comes to math homework, differentiation does not seem to carry over, and it should be considered beyond assigning the problems out of a text by level of difficulty.
Dimensions of Learning Math
As Richard Strong, Ed Thomas, Matthew Perini, and Harvey Silver (2004) indicate, student differences in learning mathematics tend to cluster into four mathematical learning styles. Those with a mastery style tend to work step by step; individuals with an understanding style search for patterns, categories, reasons. Students prone to an interpersonal style tend to learn through conversation, personal relationships, and association. The self-expressive learner tends to visualize and create images and pursue multiple strategies. Students can work in all four styles but tend to develop strengths in one or two of the styles.
So where does homework fit into this? Each of these styles tends toward one of four dimensions of mathematical learning: procedural, conceptual, contextual, and investigative. "If teachers incorporate all four styles into a math unit, they will build in computation skills (Mastery), explanations and proofs (Understanding), collaboration and real-world application (Interpersonal), and nonroutine problem solving (Self-Expressive)" (Strong et al., 2004, p. 74). If you have ever solved Sudoku puzzles, you can appreciate the motivational value of options. Everyone might be solving a puzzle of the same size but has selected an easy, medium, hard, or evil challenge based on his/her understanding of how such puzzles are solved and a self-determined ability to do so. But, I'd soon lose motivation, if that was the only puzzle type I ever attempted. By providing options, adding variety, and differentiating homework into those categories, as well as in instruction, learning math might be better achieved for all.
