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Abstract
We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways. Many students represented the situation numerically without invoking negative numbers, whereas others wrote equations involving negative numbers. When asked to interpret equations involving negative numbers in relation to the story, students did so in two ways. Their responses reflect distinct perspectives concerning the relationship between arithmetic equations and borrowing/owing. We discuss these findings and their implications regarding the role of contexts in integer instruction.
Acknowledgements
These interviews were conducted as part of an National Science Foundation (NSF)-funded research project entitled Mapping Developmental Trajectories of Students’ Conceptions of Integers. Any opinions, findings, conclusions, and recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NSF. We thank the students for their participation, and we thank the cooperating teachers and other school staff for their help in arranging the interviews.
Notes
1. To be clear, we did not select this story problem for instructional purposes. The interviews were not intended to teach students anything about integers, and we are not suggesting that this context should be used in integer instruction. We investigated how students thought about the money problem because it is the kind of problem that is often used in integer instruction.
2. Student names are pseudonyms.