The Carlisle Mosquito Online

Friday, December 17, 1999


Math program from manipulative to abstract

The Carlisle math curriculum pays attention to the process of how children learn, as well as what they learn, math teacher Rob Quaden told the school committee at their meeting on December 7. Rather than just review the math curriculum again, he and middle school math teacher Liz Perry demonstrated the usefulness of manipulative materials for teaching the subject at all grade levels.

Handing out small plastic tiles and graph paper, Perry set up a series of shapes that followed a pattern, then asked school committee members if they could tell what shape would come next. They then came up with several sets of mathematical expressions that could describe the pattern. Taking it a step further, they were asked if they could abstract the formula to get the nth shape.

Quaden explained that the point was that someone starting with concrete materials, can do the same activity at many different levels. In this way, younger students would just look at the patterns and try to make the next one or two. By fourth and fifth grades, students could start using numbers to describe the patterns, and in sixth grade, they might be asked to describe the tenth or twentieth pattern in the series. Seventh- and eighth-graders would also be asked to find a formula for the nth pattern. By starting with the manipulative, then working to the abstract, students get a better grasp of the concepts, Quaden said.

Systems lessons

Systems thinking mentor Alan Ticotsky reported that three classroom lessons using systems dynamics, which were developed and tested in Carlisle classrooms for the past few years, have been written up by former school committee member Deb Lyneis and are ready for distribution to other interested schools.

1999 The Carlisle Mosquito