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

ABSTRACT

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.

KEYWORDS:

• Worked example
• representation
• deep question
• inverse relation
• classroom instruction
• video analysis

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Science Foundation CAREER award (No. DRL-1350068) at Temple University. Any opinions, findings, and conclusions in this study are those of the authors and do not necessarily reflect the views of the funding agency.