The purpose of this study was to identify affordances and limitations of using order and value comparison tasks versus number placement tasks to infer students’ negative integer understanding and growth in understanding. Data came from an experiment with kindergarteners (N = 45) and first graders (N = 48), where the experimental group played a numerical linear board game and the other group did control activities, both involving negative integers. Performance on the number placement task connected to students’ ability to use endpoints but did not help us infer students’ integer understanding. Changes in students’ pattern of responses on integer order and value comparison tasks better aligned with the experimental group’s improvement (especially for students with a whole-number mental number line). Implications include the potential for better incorporation of integer values in linear board games and revising the number placement task, which may be overestimating students’ whole-number conceptions.
Bofferding, L. & Hoffman, A. (2019). Children’s Integer Understanding and the Effects of Linear Board Games: A Look at Two Measures. The Journal of Mathematical Behavior.