Regular Numbers and Mathematical Worlds
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Rather than describing the challenges of integer learning in terms of a transition from positive to negative numbers, we have arrived at a different perspective: We view students as inhabiting distinct mathematical worlds consisting of particular types of numbers (as construed by the students). These worlds distinguish and illuminate students' varied responses. Proficient students and adults may also inhabit multiple mathematical worlds from moment to moment. In our framework of mathematical worlds, we focus on the contrast between regular numbers and signed numbers in analyzing cases of student thinking. Implications of these ideas for educators and researchers are presented.