Reasoning-and-proving opportunities in elementary mathematics textbooks

Abstract

Over the past two decades, standards documents have emphasized the importance of developing students’ abilities to generate and critique mathematical arguments across all grade levels. However, little is known about the opportunities elementary textbooks provide for students to learn mathematical argumentation. We analyzed seven upper elementary (ages 9–11) mathematics textbooks published in the U.S., focusing specifically on reasoning-and-proving opportunities in written tasks, and found that the average percentage of such tasks was 3.7%. Further, analyses of the task purpose and type of justification warranted revealed distinctions between the text materials in terms of the kinds of reasoning-and-proving activities prompted and the placement of tasks in the lesson sections. Specifically, textbooks developed based on research and written to align with curriculum and instruction standards were more likely to have reasoning-and-proving tasks within the narrative and student exercise sections than other texts. We discuss implications for the opportunities to learn reasoning-and-proving in elementary classrooms.