Abstract
ABSTRACT This case study investigated the relationship between five undergraduate interior design students’ reasoning with numerical units and reasoning about length and area. The multiplicative concepts frame participants’ coordination of numerical units. Differences were found between participants’ reasoning about length and area, based on their multiplicative concept. Specifically, participants who had constructed more sophisticated multiplicative concept stages fluidly coordinated centimetres within inches on a ruler, and leveraged the coordination of numerical units to represent the relationship between two square units as a ratio. In contrast, participants who had constructed less sophisticated multiplicative concept stages struggled to coordinate centimetres within inches on a ruler, and did not reason about the ratio between two areas. These results contribute by illustrating the ways undergraduates reason about length and area, building on literature related to younger students’ difficulties with length and area, and filling a noted gap about the relationship between numerical units and area.
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