Let’s be rational: worked examples supplemented textbooks improve conceptual and fraction knowledge

Abstract

The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students’ fraction number line acuity, rational number concepts and procedures. Finally, the study assessed whether individual differences in prior knowledge of rational numbers moderate the effect of the textbooks. The experimental textbooks resulted in significantly greater improvements overall in fraction number line estimation skills than control textbooks. Further, example-supplemented textbooks were more effective than control textbooks at improving understanding of rational number concepts for those with low prior conceptual knowledge. Both textbooks were equally effective at improving procedural skills.

Keywords:

• Rational number
• numerical cognition
• fraction magnitude
• numerical magnitude
• mathematics education

Disclosure statement

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

Additional information

Funding

Funding for this research was provided by the Institute of Education Sciences, the United States Department of Education, through Grant R305C100024 to West Ed. The data that support the findings of this study are available on request from the corresponding author.