Lesson Experiment Cycles: Examining Factors that Affect Prospective Teachers’ Learning of Area Measurement

Michelle Chamberlin

doi:10.29333/iejme/11469

Abstract

For teachers to provide students with meaningful instruction in area measurement, teachers need robust understandings of area. Here, I describe two cycles of a lesson experiment used to investigate prospective teachers’ understandings of area units in an undergraduate mathematics class. For each cycle, I collected and analyzed the prospective teachers’ written work and videotaped class discussions. The first cycle yielded a learning trajectory for helping prospective teachers better understand area units, which led to more teachers attaining the lesson goals in the second cycle. The paper articulates these classroom lessons and the lesson experiment process for fellow mathematics instructors and teacher educators.

Highlights

Area measurement is a significant concept in school mathematics due to its many physical applications
The purpose of this paper is to present classroom lessons learned about supporting prospective teachers (PSTs) with understanding area measurement and area units
One purpose of this paper was to present classroom lessons learned about supporting PSTs with understanding area measurement

Summary

INTRODUCTION

Area measurement is a significant concept in school mathematics due to its many physical applications. My overarching research question asked, “What did the PSTs learn about area units, and how and why did instruction impact such learning?” My data collection entailed gathering all written mathematical work from the PSTs and videotaping all whole-class discussions of our lesson activities (step two of a lesson experiment). To evaluate my hypotheses for supporting the PSTs in attaining the learning goals, I returned to my written summaries of the PSTs’ mathematical understandings on the class activity, during the whole-class discussion, and on the Formative Assessment. For the tessellating area units (hexagon, rhombus, square, rectangle, and trapezoid), the PSTs again aligned the area units along the boundary of the Funky Shape, often orienting the area unit in different directions, leaving gaps between repetitions of the area unit and failing to partition the region as an array.

Area units need to cover the region without gaps or overlaps

DISCUSSION