Hypothesis

Students benefit from a conceptual understanding of where the circle area formula comes from, and will gain this understanding from an interactive manipulative using real-world objects that helps them explore the relationship between the area of a circle and its parts, compared with a manipulative that involves only abstract shapes.

Student population

This study was conducted over Carnegie Learning's general user population, with the exception of those who requested to be excluded from product improvement research.

Intervention

The experiment involved a single workspace explaining the area and circumference of a circle. In this workspace, many students were not reaching mastery, meaning that they may not be making appropriate connections between the vocabulary, formulas, and visual object. We created two versions of a new interactive manipulative to highlight the relationships between parts of a circle. One version of the circle manipulative showed the circle manipulative as a real-world object (like a pizza pie), and the other version of the circle manipulative was simply the abstract geometric shape. Following their interaction with the manipulative, students work on circle area problems until they reach (or fail to reach) mastery.

Design

Participants were randomly assigned to receive either the Concrete (real-world), or the Abstract version of the circle manipulative.

Outcome measures

Since the area problems presented to students following the manipulative are the same for both groups, we can use performance on this mastery section to understand which manipulative led to more rapid mastery of circle area. The mastery workspace presents problems for students to complete until they have mastered all skills associated with the workspace. Outcomes include the time it takes students to master the circle area problems, measured both as clock time and number of problems required. We also look at the percentage of students who are able to reach mastery.