Surveying Teachers About the Teaching of Algebra Word Problems and Mathematics Education Reform

• In Event: 66.072 - Multimedia Online Experiences as Research Tools to Study Mathematics Teaching Knowledge at Scale

Abstract

Mathematics education reform (NCTM, 1989, 2000) has suggested the value of consideration of multiple methods for solving the same problem. In the context of the algebra curriculum, these developments challenge traditional approaches to doing word problems. Gerofsky (1996) suggests that, traditionally, in the curricular genre of word problems, students must write and solve algebraic equations.
Earlier work with teacher study groups (blinded) explored teacher expectations and norms when solving word problems in algebra (an instruction situation for Herbst, 2006). The teachers in the sample viewed as legitimate mathematically correct solutions that do not involve equations, suggesting that practicing algebra teachers share with reformers more flexible views of what constitutes a viable solution to word problems than those portrayed by Gerofsky (2004).
The question of how widespread reform ideas have become motivates our current instrument development. We are exploring the feasibility of rich media based surveys that will allow us to ascertain with larger numbers of teachers:
What types of students’ solutions to word problems algebra teachers consider appropriate?
What kinds of responses to students’ solutions to word problems that do not involve equations teachers view as appropriate?
To overcome the limitations of text-only surveys (Cohen et al., 2000), we are developing an instrument that invites teachers to interpret rich media representations of classroom scenarios. The instrument utilizes a combination of forced-choice items and open responses (Onwuegbuzie & Teddlie, 2003); it consists of a section in which teachers assess students’ solutions to word problems that do not involve equations and one that explores the perceived appropriateness of teacher responses to non-standard student work. This section asks participants to assess moving on with the lesson, insisting on a traditional, equation-based solution, engaging in discussion of a non-standard approach, or highlighting the limitations or advantages of such an approach.
The instrument was piloted with 45 practicing algebra teachers. For the initial pilot, teachers’ quantitative responses were analyzed with descriptive statistics, paired samples t-tests, and one-way ANOVA. The qualitative data were analyzed for identification of appraisals of students’ work, teacher responses to it, and the types of justifications used to support teacher responses (Herbst, et al., 2013).
Analysis of the pilot data corroborates study group findings and suggests that mathematics teachers are willing to accept solutions to word problems that do not involve equations (indeed 54% rated preference for standard solutions as inappropriate). However, the data suggests the need for greater experimenter control of the scenarios in which teachers insist on the use of equations or highlight limitations of approaches that do not involve equations (13% of responses suggested difficulties interpreting scenarios).
Against the backdrop of scholarly arguments for stability in teaching (e.g., Cuban, 1993), the capacity to carry out fine-grained understanding of the influence of reform ideas on teaching, and to compare the doing of word problems with the solving of equations, has the potential to help educators better understand how and when reforms are more likely to alter practice in schools.

Authors

• Daniel I. Chazan, University of Maryland

• Orly Buchbinder, University of New Hampshire