CONCEPTUAL ANALYSIS OF MATHEMATICAL IDEAS: SOME SPADEWORK AT THE FOUNDATION OF MATHEMATICS EDUCATION 1

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A Study of Students’ Readiness to Learn Calculus (2015, background): “The ideas of angle measure and trigonometric functions have been documented to be under-developed in inservice teachers (Thompson 2008; Thompson et al. 2007) and precalculus level students (Moore 2012, 2013) and preservice teachers (Moore 2012; Moore et al. 2012).”
A model of students' combinatorial thinking (2013, unknown): “Thompson (2008) elaborates this idea and makes a case for the importance of developing such conceptual analyses.”
Quantifying exponential growth: Three conceptual shifts in coordinating multiplicative and additive growth (2015, background): “Thompson and Carlson (in press) further distinguish between smooth continuous variation and chunky continuous variation. Smooth continuous variation entails thinking about the variation of a quantity’s value as its magnitude increases in bits while anticipating simultaneously that within each bit th”