Student Strategies Suggesting Emergence of Mental Structures Supporting Logical and Abstract Thinking: Multiplicative Reasoning

Abstract

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills are built. The purpose of this study is to recognize indicators of multiplicative reasoning among fourth-grade students. Through cross-case analysis, the researcher used a test instrument to observe patterns of multiplicative reasoning at varying levels in a sample of 14 math students from a low socioeconomic school. Results indicate that the participants fell into three categories: premultiplicative, emergent, and multiplier. Consequently, 12 new sublevels were developed that further describe the multiplicative thinking of these fourth graders within the categories mentioned. Rather than being provided the standard mathematical algorithms, students should be encouraged to personally develop their own unique explanations, formulas, and understanding of general number system mechanics. When instructors are aware of their students' distinctive methods of determining multiplicative reasoning strategies and multiplying schemes, they are more apt to provide the most appropriate learning environment for their students.

Building Conceptual Understanding of Multiplicative Reasoning Content in Third Graders Struggling to Learn Mathematics: A Feasibility Study

“…Treating MR as an approach to quantitative thinking is challenging for teachers to develop in their students (Carrier, 2014), and because of the well–documented difficulty many students have in constructing MR, we carried out a feasibility study in a school setting prior to conducting a randomized control trial. The study consisted of a 6–week intervention of daily lessons focused on making MR explicit both to teachers and their students struggling in mathematics.…”

Teaching the partial products algorithm with the concrete representational abstract sequence and the strategic instruction model

“…In addition, the development of multiplicative reasoning skills in younger students is imperative to the future success of students in advanced mathematical courses (Carrier, 2014). The line of research regarding the importance of developing students' multiplicative reasoning is extensive (Barmby, Harries, Higgins, & Suggate, 2009; Van Dooren, DeBock, & Verschaffel, 2010).…”