Writing in the Mathematics Classroom: Does It Have an Effect on Students’ Mathematical Reasoning?

In this action research study of my classroom of 5th grade mathematics, I investigate how to improve students’ written explanations to and reasoning of math problems. For this, I look at journal writing, dialogue, and collaborative grouping and its effects on students’ conceptual understanding of the mathematics. In particular, I look at its effects on students’ written explanations to various math problems throughout the semester. Throughout the study students worked on math problems in cooperative groups and then shared their solutions with classmates. Along with this I focus on the dialogue that occurred during these interactions and whether and how it moved students to a deeper level of conceptual understanding. Students also wrote responses about their learning in a weekly math journal. The purpose of this journal is two-fold. One is to have students write out their ideas. Second, is for me to provide the students with feedback on their responses. My research reveals that the integration of collaborative grouping, journaling, and active dialogue between students and teacher helps students develop a deeper understanding of mathematics concepts as well as an increase in their confidence as problem solvers. The use of journaling, dialogue, and collaborative grouping reveals themselves as promising learning tasks that can be integrated in a mathematics curriculum that seeks to cultivate students’ thinking and reasoning.

Unifying Representations and Responses: Perseverative Biases Arise From a Single Behavioral System

A dominant account of perseverative errors in early development contends that such errors reflect a failure to inhibit a prepotent response. This study investigated whether perseveration might also arise from a failure to inhibit a prepotent representation. Children watched as a toy was hidden at an A location, waited during a delay, and then watched the experimenter find the toy. After six observation-only A trials, the toy was hidden at a B location, and children were allowed to search for the toy. Two- and 4-year-olds’ responses on the B trials were significantly biased toward A even though they had never overtly responded to this location. Thus, perseverative biases in early development can arise as a result of prepotent representations, demonstrating that the prepotent-response account is incomplete. We discuss three alternative interpretations of these results, including the possibility that representational and response-based biases reflect the operation of a single, integrated behavioral system.