MATHEMATICAL THINKING: A SEMIOTIC COORDINATION OF IDEAL-MATERIAL COMPONENTS.
- A qualifying paper submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Education. Abstract: Abstract. In this case study, I provide evidence for, and operationalize (fill the gaps and provide specific analytic methods to replicate) the “dynamic unity of material and ideal components” framework for mathematical cognition (Radford, 2014, p. 268). Mathematic... read moreal thinking, according to this framework, is a “semiotic coordination” (Radford, 2014, p. 268) of ideal and material components, such as speech, gestures, tactility, rhythm, perception, sensuous imagination, and actions with cultural artifacts. The analytical methods in the present case study involve a frame-by-frame analysis of data collected during an interview with a seventh grade student exploring the shadow of a figurine. In this case study, I identified the following six ideal-material components described by Radford: outer speech, gestures, tactility, rhythm, perception, and actions with cultural artifacts. To illustrate Radford’s framework, I identify ideal-material components that co-occur in space and time, discuss ways in which they might be semiotically coordinated in terms of carrying identical, supporting, complementary or additional meaning, and argue that these are the components of learner’s mathematical thinking. Lastly, I draw implications for mathematics education and research.read less