Conventional coordinate systems are often considered representational tools for reasoning about mathematical concepts. However, researchers have shown that students experience persistent difficulties as they engage in graphing activity. Using examples from research and textbooks, we present a framework based on a conceptual analysis of the use of…

We explored the effects of task-related factors on reasoning processes in geometry focusing on a comparison-of-perimeters task in which the irrelevant feature area interferes with the reasoning process. We studied the effects of congruity, salience, and complexity on participants' accuracy of responses and reaction times. The study shows that…

Two experiments explored the effect of linguistic input on 18-month-olds' ability to form an abstract categorical representation of support. Infants were habituated to 4 support events (i.e., one object placed on another) and were tested with a novel support and a novel containment event. Infants formed an abstract category of support (i.e.,…

We examine eight cases of argumentation in relation to a proportional reasoning task--the "Paint" task--in which the "constant sum" strategy was a significant factor. Our analysis of argument follows Toulmin's (1958) approach and in the discourse we trace factors which seem to facilitate changes in argument. We find that the arguments of "constant…