@article{unal_hollebrands_mcculloch_scher_steketee_2022, title={Prospective High School Mathematics Teachers' Uses of Diagrams and Geometric Transformations While Reasoning about Geometric Proof Tasks}, volume={29}, ISSN={["2045-2519"]}, DOI={10.1564/tme_v29.1.02}, abstractNote={The purpose of this study was to examine prospective teachers’ uses of diagrams and approaches to congruence while solving proof tasks. Eight prospective high school mathematics teachers were given three proof tasks to solve at the beginning and end of a mathematics education course. The course used the history of mathematics as the context for assisting teachers in making connections between important mathematical ideas. A unit of instruction used technology-based activities to support a transformational approach to congruence. Analysis revealed that at the beginning of the course teachers approached congruence proofs using perceptual or correspondence approach and used a descriptive mode of interaction with diagrams. At the end of the course, their approaches to congruence included more instances of transformations and measures and their interactions with diagrams included fewer uses of the descriptive mode and more instances of representational, generative, and functional modes.}, number={1}, journal={INTERNATIONAL JOURNAL FOR TECHNOLOGY IN MATHEMATICS EDUCATION}, author={Unal, Deniz Ozen and Hollebrands, Karen and McCulloch, Allison and Scher, Daniel and Steketee, Scott}, year={2022}, pages={13–24} }
 @article{mcculloch_lovett_dick_sherman_edgington_meagher_2020, title={Eliciting the coordination of preservice secondary mathematics teachers' definitions and concept images of function}, ISBN={1464-5211}, DOI={10.1080/0020739X.2020.1821107}, abstractNote={ABSTRACT Given the vast experiences pre-service mathematics teachers (PSMTs) have with functions, one may assume that they have existing personal definitions and concept images. The purpose of this paper is to build an understanding of the variety of images that one might associate with a definition of function that includes ‘for each input there is one output’ and how these images are coordinated with the definition to determine whether an object is a function or not. Two cases are presented to describe PSMTs who were working from the same personal definition of function, yet used that definition differently within a task designed around the function concept. The task itself was novel in that it is presented in a non-algebraic context, namely a vending machine. As such, PSMTs were required to coordinate their personal definition and images within the novel context. Attending to PSMTs’ concept images revealed that though they were working from the same personal definition, images they drew upon to determine whether or not an object is a function were varied.}, journal={INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY}, author={McCulloch, Allison W. and Lovett, Jennifer N. and Dick, Lara and Sherman, Milan and Edgington, Cyndi and Meagher, Michael}, year={2020} }
 @book{marshall_decuir-gunby_mcculloch_2015, title={When critical multiculturalism meets mathematics: A mixed methods study of professional development and teacher identity}, ISBN={9781475808483}, publisher={Lanham, Maryland: Rowman & Littlefield Pub Inc}, author={Marshall, P. L. and DeCuir-Gunby, J. T. and McCulloch, A. W.}, year={2015} }