A new curriculum to introduce rational numbers was devised, using developmental theory as a guide. The 1st topic in the curriculum was percent in a linear-measurement context, in which halving as a computational strategy was emphasized. Two-place decimals were introduced next, followed by 3- and 1-place decimals. Fractional notation was introduced last, as an alternative form for representing decimals. Sixteen 4th-grade students received the experimental curriculum. Thirteen carefully matched control students received a traditional curriculum. After instruction, students in the treatment group showed a deeper understanding of rational numbers than those in the control group, showed less reliance on whole number strategies when solving novel problems, and made more frequent reference to proportional concepts in justifying their answers. No differences were found in conventional computation between the 2 groups.
Joan Moss and Robbie Case
Katherine Baker, Naomi A. Jessup, Victoria R. Jacobs, Susan B. Empson and Joan Case
Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.