Solving Equations: Exploring Instructional Exchanges as Lenses to Understand Teaching and Its Resistance to Reform

Abstract

Many research studies have sought to explain why NCTM's vision for mathematics classrooms has not had greater impact on everyday instruction, with teacher beliefs often identified as an explanatory variable. Using instructional exchanges as a theoretical construct, this study explores the influence of teachers' institutional positions on the solving of equations in algebra classrooms. The experimental design uses surveys with embedded rich-media representations of classroom interaction to surface how teachers appraise correct solutions to linear equations where some solutions follow suggested textbook procedures for solving linear equations and others do not. This paper illustrates the feasibility of studying teaching with rich-media surveys and suggests new ways to support changes in everyday mathematics teaching.

Identifying Student Responsibilities While Watching Mathematics Instructional Videos

“…Participants seemed to be looking for a reproducible process for solving the problem. For those that had prior knowledge of completing the square, this process was the specific steps given to them by their teacher or professor that I will call -the canonical process‖ (Buchbinder et al, 2019). In the case of this study, the canonical process was shown by the Math Meeting video.…”

“…This is especially true if the teacher is requiring students to use the process that is taught in the classroom. Buchbinder et al (2019) established that teachers held a responsibility to teach the canonical process for solving equations in one variable. Moreover, researchers found that teachers viewed alternate solutions as unnecessary and potentially confusing.…”

“…Another suggestion for future research would be to investigate whether students hold the responsibility to use the canonical process because they knew that they would be assessed by the teacher on this process, meaning, the students believe that any deviation will result in reduced points. I suggest a study that includes an interview with the teachers of student participants as well as an analysis of their assessments to see if the teachers were requiring their students to use a particular set of steps for completing the square as is proposed by Buchbinder et al (2019). Perhaps an intervention could be introduced to encourage teachers to allow students to explore different processes for solving quadratic functions using completing the square.…”

Framing, responsiveness, serviceability, and normativity: Categories of perception teachers use to relate to students' mathematical contributions in problem‐based lessons

“…Other students might think of the convenience of working with smaller numbers, deciding to first divide out common factors and write instead 4 x + 1 = x + 13. While the second case might not reproduce the steps shown in a worked‐out example from a typical textbook (Buchbinder et al, 2019), a teacher might notice the reasonableness and the algebraic nature of the second student's work. But it bears consideration that students might also think about things quite different from solving equations with symbolic manipulation.…”

Discipline-Based Education Research (Dber) – What Is It, and Why Should Engineering Education Research Scholars Be Talking About It More?

“…• "Flat Earth theory: an exercise in critical thinking" (Physics Education journal) [15] • "Using high speed smartphone cameras and video analysis techniques to teach mechanical wave physics" (Physics Education journal) [16] • "Solving Equations: Exploring Instructional Exchanges as Lenses to Understand Teaching and Its Resistance to Reform" (Journal for Research in Mathematics Education) [17] • "Machine Learning for Fluid Property Correlations:…”