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In 1908, Felix Klein suggested that to mend the discontinuity that prospective secondary teachers face, university instruction must account for teachers’ needs. More than a century later, problems of discontinuity remain. Our project addresses the dilemma of discontinuity in university mathematics courses through simulating core teaching practices in mathematically intensive ways. In other words, we interpret teachers’ needs to include integrating content and pedagogy. We argue that doing so has the potential to impact teachers’ competence. To make this argument, we report fndings from the Mathematics of Doing, Understanding, Learning, and Educating for Secondary Schools (MODULE(S2)) project. The results are based on data from 324 prospective secondary mathematics teachers (PSMTs) enrolled in courses using curricular materials developed by the project in four content areas (algebra, geometry, modeling, and statistics). We operationalized competence in terms of PSMTs’ content knowledge for teaching and their motivation for enacting core teaching practices. We examined pre- and post-term data addressing these constructs. We found mean increases in PSMTs’ outcomes in content knowledge for teaching and aspects of motivation. 

This Perspectives on Practice manuscript focuses on an innovation associated with “Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task” from Volume 7, Issue 2 ofMTE. We built on Aguirre et al.’s (2019) integration of mathematical modeling and social justice issues in mathematics teacher education to similarly integrate statistical investigations with social justice issues. 

Research in prospective teachers’ development of mathematical modeling knowledge for teaching is gaining momentum. The Mathematics of Doing, Understanding, Learning, and Educating for Secondary Students [MODULE(S2)]* project developed a curriculum in modeling for teacher education that includes simulations of practice, in which prospective teachers reflect on and plan a discussion around student thinking, their models, and the contextualization of their results. We present an analysis of prospective teachers’ modeling work on the decreasing area of Indigenous reservation land in the U.S., and a simulation of practice which explores different methods for finding the area of land in connection to the injustice deeply rooted in the treatment of Indigenous people. This problem explores a critical social issue and calls for explicit attention to pedagogical knowledge in structuring discussions around the contextualization of the mathematical results. 

This study examines prospective elementary teachers’ growth and development of competencies, conceptions, and perceptions of mathematical modelling in a mathematics content course for ele- mentary teachers. A series of lessons were implemented that engaged students in the modelling process through modelling tasks. The goal was to capture prospective teachers’ thoughts and per- ceptions on the meaning of mathematical modelling and their conceptions of teaching and learning modelling at the elementary and middle school level. The research questions were: (1) How do prospective teachers translate the mathematical modelling cycle into their practice of doing modelling? and (2) How do prospective teachers’ conceptions of modelling and teaching and learning modelling evolve throughout the implementation of a series of mathematical modelling lessons? Data sources included posters, modelling reports, responses to a pre- and post-intervention questionnaire, and semi-structured interview dialogue. Data analyses included mixed methods using provisional coding, open coding, and a categorical rubric. Findings from this study indicate that (1)Prospective elementary teachers translated the modelling cycle into their practice by developing their range of modelling competencies including multiple components of the modelling cycle, and (2) They developed a professionally appro- priate conception of mathematical modelling along with productive perceptions of the benefits of teaching and learning modelling. 

Undergraduate mathematics instructors are called by many cur- rent standards to promote prospective teachers’ learning of geometry from a transformation perspective, marking a change from previous standards. The novelty of this situation means it is unclear what is involved in undergraduate learning and teaching of geometry from a transformation perspective. To approach this problem, we illustrate how specific in-class activities and design principles might help prospective teachers make conceptual links between congruence proofs and a transformation approach to geometry. Additionally, to illustrate these activities for instruc- tors, we provide examples of prospective teachers’ work on some of these problems.