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Tracking may not be the issue

Posted By: Gabriel Della-Piana on December 5, 2002
I have not kept up with the research so I speak from experience recently of doing classroom observations. I have been adapting an instrument developed by Lawrenz, Hamilton, and Appledoorn to better tap what is going on in local initiatives in systemic reform. The major problem that I see thus far is the difficulty in handling individual differences regardless of whether the group is heterogeneous or ability grouped. There is always diversity of ability to contend with. Maybe an example will help.

The POD (problem of the day): Tina had to get ready for the 26 mile marathon ... She ran every day. The first day she ran one mile, the second day she ran one and one-half miles. The third day .. two miles. If this pattern continues, how many days will it take her to run the 26 miles?

This is a sixth grade class. The teacher did everything she had been trained to do. Students began work on the POD without prompting. After about 10 minutes the teacher suggested students work in pairs or small groups continuing their problem solving and justifying process and solutions to each other. She moved around the room and answered questions without "giving the answer" using more scaffolding type interaction. After about another 15 minutes she asked for volunteers to put a solution on the board and justify it to the entire class. She picked 5 students with diverse abilities (or so it seemed to me). Two students layed out the entire sequence of days and miles day by day and finally came to 51 days to run 26 miles in a day. The other three students tried to find a short-cut. None of them succeeded. One student carried the series out to 13 miles which took 25 days, doubled the number of days and concluded that it would take 50-days. Students struggled with the different answers both of which seemed logical. But they agreed that the ansswer had to be 51 days because the logic of the completed series was incontrovertable. When the "short-cut group" was asked to check their work, they checked computation but had no strategies (yet, in this instructional unit)for checking the "rule" they applied. The period was over.

In a school with a culture of inquiry in which teachers conducted "lesson study" this teacher would have presented this experience and go help in how to get groups working more productively, how to teach looking for patterns and formulating a "rule" "formula" or what the state test calls a "number statement" and how to test it. The alternative of grouping within the class heterogeneously for part of the period and ability groupe in part might be discussed. But all students could benefit from the heterogeneity.

It seems to me that it is possible to do within-class tracking for part of the day and still benefits of the wider range of students working on the same curriculum, working toward conceptual understanding and problem solving with multi-step open-ended multi-solution problems.

That is how I see it at present. I taught 7th and 8th grade mathematics years ago in a diverse community (Italian laborers, Jewish professionals, and military) and did the within class grouping at times. But I am open to considering a wider range of solutions than the one I proposed. Or did I propose one?

Gabriel Della-Piana
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 Tracking....good or bad? by Christina Rhoades on November 24, 2002
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