Investigating Seventh Grade Students’ Mathematization Processes and Mathematical Models: The Lawnmower Problem

Abstract

As part of a comprehensive study which investigated 7^th grade (12-13 years of age) students’ mathematical modeling processes as they worked on three mathematical modeling problems over several weeks, this study reports on the mathematization processes that six students used in constructing their models for the third modeling problem, the Lawnmower Problem. In this study, the students worked in two groups of three each for a total of nearly 90 minutes (two class periods). Data sources included audio- and video-tapes of students’ responses to the problem, students’ written worksheets, and focus group interviews. Audiotapes of both groups were transcribed and analyzed in terms of the mathematical operations and ideas students applied, the types of transformations they made through these operations, the representations they used in documenting their models, and the interpretations of tables and models the students developed. The findings show that students in both groups used “Scoring” in order to mathematize procedures while developing their models; however, some differences were observed in their approaches. The findings also indicate that both groups were nearly able to deal successfully with a complex mathematical modeling problem.