Concrete Fading and its Effect on Students’ Algebraic Problem Solving and Computational Skills

Abstract

Algebra I encompasses several topics that serve as a basis for students’ subsequent mathematics courses as they progress in school. Some of the key topics that students struggle with is solving linear equations and algebraic word problems. There are several factors that may contribute to this ongoing struggle for students such as the structure of the textbooks, the teacher instruction and misconceptions of components of algebraic equations. A promising solution to the potential contributing factors is concrete fading. In this study, concreteness fading refers to an instructional technique that represents topics in a particular sequence from a concrete, real-world representation to a semi-concrete diagram (e.g., tape diagram) to an abstract representation (e.g., algebraic equations). The current study aims to investigate the influence concrete fading has on student learning while studying concrete fading in two ninth grade Algebra I general education classes at an urban high school. In particular, the study aims to answer the following: 1) What are some ways that students who received concrete fading think differently than the control group? 2) How do these differences seem to be related to the intervention? Both classes were taught by the same teacher. One class was assigned to the treatment group that received the concrete fading lessons and the other class was assigned to the control group that was taught as business as usual by the teacher. The study was intended to be quasi-experimental study, but due to challenges, it was primarily qualitative in nature focusing on eight students where the analysis included analyzing student work and student interviews responses along with quantitative analysis of the pre and two post-tests. Results revealed that the treatment group does think differently than the control group based on student work and the interview responses.