Hypothesis

Students will more easily learn operations with signed numbers if they have a concrete, real-world model underlying the numbers and operations to be applied.

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 three workspaces that focused on helping students understand negative numbers as opposites (related to absolute value).

We built workspaces with different interactive manipulatives to support understanding signed numbers and their operations on a number line. In the Kangaroo condition, operations on the number line were displayed as a kangaroo jumping forwards or backwards, according to pre-defined abstract addition or subtraction problems. In the Thermometer condition, operations on the number line were displayed as a thermometer, with associated problems contextualized as a real-world example (e.g., "The current temperature is 20 degrees, and it decreases by 10 degrees"). Following use of the manipulative, students completed a mastery workspace presenting addition and subtraction problems using signed integers.

Design

Participants were randomly assigned to receive either the Kangaroo (concrete manipulative with abstract problems), or the Thermometer (concrete manipulative with real-world problems) version of the workspaces.

Outcome measures

Since the mastery portion of the task is identical for both conditions, we use performance in this mastery section as a measure of the impact of the manipulatives. We measure both the amount of time and the number of problems that students need to reach mastery following use of the manipulative, as well as the percentage of students who are able to reach mastery. We also look at the amount of time spent using the manipulative.