Cognitive instructional principles in elementary mathematics classrooms: a case of teaching inverse relations

• Published in: International journal of mathematical education in science and technology Vol. 52; no. 8; pp. 1195 - 1224
• Main Authors: Ding, Meixia, Hassler, Ryan, Li, Xiaobao
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 14.09.2021; Taylor & Francis Ltd
• Subjects: Algebra; Barriers; classroom instruction; Classrooms; Cognitive Science; Correlation; deep question; Elementary School Teachers; inverse relation; Lesson Plans; Mathematics Instruction; Principles; Problem Solving; Questioning Techniques; Questions; representation; Representations; Students; Teacher Student Relationship; Teachers; Teaching; Teaching Methods; video analysis; Video Technology; Worked example
• ISSN: 0020-739X; 1464-5211
• DOI: 10.1080/0020739X.2020.1749319

Instructional principles gleaned from cognitive science play a critical role in improving classroom teaching. This study examines how three cognitive instructional principles including worked examples, representations, and deep questions are used in eight experienced elementary teachers' early algebra lessons in the U.S. Based on the analysis of 32 videotaped lessons of inverse relations, we found that most teachers spent sufficient class time on worked examples; however, some lessons included repetitive examples that also included irrelevant practice problems. Most teachers also situated new teaching in concrete contexts, which were faded into abstract representations. However, connections between concrete and abstract were not always made. The largest challenge was rooted in teachers' inability to ask deep questions that elicited students' deep explanations. Some teachers focused on key words and provided students with direct explanations. Implications are discussed.