Abstract
The concept of negative numbers has been documented to not only be difficult for mathematicians of the past, but also math students of the present. Numerous instructional models, procedures and analogies have been developed to help students learn how to add and subtract negative numbers; however, low proficiency in integer arithmetic continues to be a concern and a hinderance to student success in higher mathematics. Researchers have studied this phenomenon by documenting the various ways which students reason about integer arithmetic before and after exposure to instruction; those that study the former usually work with students that have not experienced instruction on even the concept of negative numbers. This qualitative study presents insight into the thinking of those students that have been exposed to formal instruction on negative numbers but not on arithmetic of negative numbers. Twenty-one 6ᵗʰ grade students were interviewed using task-based interviews. Using the Knowledge in Pieces (diSessa, 1988) perspective, reasoning was defined to be the use of knowledge resource to solve the tasks. Participants’ verbal explanation and written work were used to make interpretation of knowledge resources that were invoked to solve tasks with negative and positive integers. Numerous knowledge resources were identified as well as their usage was compared across different types of tasks, specifically tasks of adding a negative and subtracting a positive. Conclusions are made about the participants’ knowledge resources, language that was used, and the influence of different types of tasks. This study adds to the growing research on understanding the types of knowledge that students bring into the classroom. Implications are provided about the instruction of integer addition and subtraction, aimed at helping teachers create learning experiences for integers that build on students’ existing knowledge.