The design of tasks in support of teachers’ development of coherent mathematical meanings

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The Precalculus Concept Assessment: A Tool for Assessing Students’ Reasoning Abilities and Understandings (2010, background): “The following section provides a review of research that has provided insights into the foundational understandings and reasoning abilities that students need for success in a first course in calculus (Carlson, 1995, 1997, 1998; Monk, 1992; Kaput, 1992; Dubinsky & Harel, 1992; Carlson, Jacobs, Coe, ”
CONCEPTUAL ANALYSIS OF MATHEMATICAL IDEAS: SOME SPADEWORK AT THE FOUNDATION OF MATHEMATICS EDUCATION 1 (2008, methodology): “We could satisfy this constraint (the circle’s size cannot matter) by using any unit that is proportional to the circle’s circumference ( Thompson, Carlson, & Silverman, 2007 ).”
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).”