Virginia Mathematics Teacher Fall 2016

Enhancing Pedagogical Practices Through Professional Development in Proportional Reasoning Padmanabhan Seshaiyer and Jennifer Suh

higher level mathematics. Teachers have also been urged to focus students’ attention on the meaning of problems and to help students value different mathematically correct solutions to a single problem (NCTM, 2000). There is a great need for research in evaluating the effect of solving one proportional situation via multiple solution strategies for example using unit rate strategy; repeated subtraction strategy; equivalent fractions strategy; size-change strategy; cross multiplication using equal rates or ratios strategy, relative and absolute thinking strategy and; reasoning up and down strategy (Lamon, 2007). Teaching proportional reasoning through problem solving therefore requires depth of mathematical knowledge for teaching that not only includes understanding of general content but also having domain specific knowledge of students. Research has shown that a content-focused PD leads to improvements in teacher content knowledge with a focus on student learning goals, highlighting the concepts being addressed, how they are developed over time, difficulties students may encounter, and how to monitor student understanding (Suh and Seshaiyer 2013, 2014a, 2014b). To evaluate the collaborative nature of designing PD, Suh, Seshaiyer, Freeman and Jamieson (2011) used the collective self-study method to examine how purposively designed experiences such as the content-focused institute in the summer with school-based follow-up Lesson Study cycles in the fall encouraged vertical articulation of algebraic connections. In this work, we present one such PD program that systematically introduced the concept of proportional reasoning through problem based learning activities. Specifically, the paper presents how the pedagogical practices of a group of 85 elementary and middle grades teachers that participated in a summer PD institute were impacted in proportional reasoning. The study explored the following research question: How can professional development for mathematics teachers be designed and implemented so that the teachers develop deep understanding of proportional reasoning? The goals for our project were for elementary and middle grades teachers to relearn

Abstract

There is a continuous need to develop more content-focused professional development (PD) programs for teachers that can help lead to improvements in teacher content knowledge in proportional reasoning. This work presents how the pedagogical practices of a group of 85 elementary and middle grades teachers that participated in a summer institute through a Mathematics and Science Partnership (MSP) program, were impacted in proportional reasoning through problem solving activities. The observations on their understanding of proportional reasoning through poster artifacts, the reflections on their work through journals as well as misconceptions in their problem solving found in this work are presented. Impact on student learning through follow-up lesson study are also discussed. Over the last seven years, the Center for Outreach in Mathematics Professional Learning and Educational Technology (COMPLETE) at George Mason University (GMU) has been supported by the Virginia Department of Education MSP Program to coordinate projects that has helped to provide PD to teachers from various school districts in the Northern Virginia area. Topics in these PD have included Building numbers and number sense for elementary grades; Rational numbers and Proportional reasoning in middle grades and; Expeditions in Science Technology Engineering Education through Mathematics at high school level. The projects were coordinated by a mathematician and a mathematics educator from GMU in collaboration with partnering districts that included Alexandria, Arlington, Fairfax, Fall Church, Frederick, Loudoun, Manassas City, Manassas Park, Prince William and Virginia Council for Private Education. The project website provides more details: http://completecenter.gmu.edu . Project Overview

Introduction

Proportional Reasoning is fundamental to many important mathematical concepts and is often regarded as the pathway to performing well in

Virginia Mathematics Teacher vol. 43, no. 1

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