TODOS: Mathematics for All, June 21-23, 2021 (virtual)
Are achievement “gaps” due to some racial groups being less interested in education than others? In educating future mathematics teachers, we counter untrue stereotypes related to inequities in education with data-based activities. The MODULE(S^2) project includes teacher education statistics curriculum materials that have equity and social justice as a major component. Come engage in our activities and learn about the project.
Presenters: Andrew Ross, Stephanie Casey, Melody Wilson, Samantha Maddox
Mathematical modeling is in the unique position of being part of the K-12 curriculum, a topic in undergraduate mathematics, a technique used by professionals, and an active area of research. Yet, most teacher preparation programs do not require a mathematical modeling course. In many cases, mathematics faculty are not familiar with approaches to teach modeling in K-12. For this reason, it is important for mathematicians and mathematics educators to come together and advance collaboratively the preparation of future teachers in a manner that is connected with the way practitioners construct and use mathematical models. The NSF-funded project, the Mathematics of Doing, Understanding, Learning, and Educating for Secondary Schools [MODULE(S2)], supports collaborative development of mathematical modeling modules that are first piloted around the country, and will be eventually made available widely. The authors will present the structure of the material, highlight modeling tasks, and the use of simulations of practice (SoPs) from the curriculum materials. Participants will engage in discussion of the context of selected modeling tasks, possible solution approaches, and comment on the usefulness of the material.
Cortez, R., Anhalt, C. and Kohler, B. (2020). Mathematical Modeling Modules: Curriculum Material for Secondary Teacher Education. Proceedings of the ninth annual Mathematics Teacher Education Partnership conference. Online Conference. June 28–30, 2020.
In this chapter, we argue that providing opportunities for prospective teachers to build MKT requires educative curricular materials (Davis & Krajcik, 2005) that simultaneously support the learning of university mathematics instructors as well as the prospective teachers themselves. In addition, we describe an emergent, research-based design for developing and implementing these curriculum materials and propose priorities for those seeking to capitalize on the NIC model in future work. The efforts described in this chapter contribute to the overall vision for the transformation of secondary mathematics teacher preparation programs presented in this book by addressing the Mathematics Teacher Education Partnership (MTE-Partnership)’s Guiding Principles for Secondary Mathematics Teacher Preparation Programs (2014) that focus on teacher candidate knowledge, skills, and dispositions.
Lischka, A. E., Lai, Y., Strayer, J. F., & Anhalt, C. (2020). Developing mathematical knowledge in and for teaching in content courses. In G. W. Martin, B. R. Lawler, A. E. Lischka, & W. M. Smith (Eds.) The Mathematics Teacher Education Partnership: The Power of a Networked Improvement Community to Transform Secondary Mathematics Teacher Preparation (pp. 119-141). Charlotte, NC: Information Age Publishing.
In our project, we develop curricular materials to support prospective secondary teachers’ development of MKT and provide professional development (PD) opportunities for instructors who will teach with these materials. In this paper, we examine the ways in which mathematics faculty engage in the teaching rehearsal debriefs included in the PD to answer the question: To what instructional interactions do instructors of mathematics content courses attend during rehearsal debriefs enacted in PD? Findings show that mathematics instructors attend to all types of interactions but attention is influenced by instructors’ mathematical knowledge.
Czap, L., Ahrens, S., Lischka, A. E., & Lai, Y. (2020). Mathematics instructors’ attention to instructional interactions in discussions of teaching rehearsals. In Proceedings of the 2020 PME-NA Conference (in press).
Today’s math teachers face significant social and political challenges for which they receive little preparation. Mathematics content courses can potentially provide additional preparation in this regard by providing future teachers with experiences to mathematically explore social justice issues. This provides them with opportunities to increase their awareness and sensitivity to social justice issues, develop greater empathy for their future students, and serve as examples for high quality instruction that they can emulate in their future careers. This dissertation recounts the development and revision of three social justice mathematical modeling projects, and shares evidence from student work samples of the ways in which the experience impacted students’ lives. The implications of this work for teacher preparation and modeling education are discussed.
Seegmiller, P., (2020) Social Justice Mathematical Modeling for Teacher Preparation. [Dissertation]. Utah State University.
This theoretical report addresses the challenge and promise of improving prospective secondary mathematics teachers’ experiences in undergraduate mathematics courses by incorporating tasks embedded in pedagogical contexts. The objective of this approach, used by multiple nationally- funded projects, is to enhance the development of teachers’ MKT. We report on the construction of a framework for observing and analyzing the development of teachers’ MKT. This framework is the result of integrating several existing frameworks and analyzing a sample of prospective secondary teachers’ responses to tasks embedded in pedagogical contexts. We discuss the methods used to build this framework, the strengths and weaknesses of the framework, and the potential of the framework for informing future work in curriculum design and implementation.
Lai, Y., Strayer, J., Lischka, A., Anhalt., C., Quinn, C. & Reed, S. (2019). Theoretical report: A framework for examining prospective teachers’ use of mathematical knowledge for teaching in mathematics courses. In A. Weinberg, D. Moore-Russo, H. Soto, & M. Wawro (Eds.), Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education (pp.765-773). Oklahoma City, Oklahoma.
We are called by recent standards to promote teachers’ learning of a transformation approach in geometry and its proofs. Teachers who learned geometry from a perspective based on Euclid’s Elements are now called to teach geometry using different proofs and axioms from what they learned. Moreover, there is little literature on teachers’ learning of geometry from a transformation perspective. To begin to address this problem, we analyze the teachers’ use of the conceptual link between congruence and transformation in the context of constructing proofs. We identify possible key developmental understandings involved in using the definition of congruence and in the construction of transformation proofs, pointing to concepts that may need to be specifically addressed in teacher education.
St. Goar, J., Lai, Y., & Funk, R. (2019). Prospective secondary teachers’ conceptions of congruence proof from a transformation perspective. Paper proposal 2019 Annual Conference on Research in Undergraduate Mathematics Education.
To improve teaching and learning in content courses for secondary mathematics teachers, we take the approach of supporting faculty who teach these courses – often mathematics faculty – in developing their own mathematical knowledge for teaching (MKT) at the secondary level. We describe a framework that has informed the design of educative curricula for a set of these courses. This framework integrates theory for knowledge development, empirical work on dimensions of knowledge used in teaching, and findings on observable behaviors in teaching that reveal prospective secondary teachers’ knowledge development.
Lai, Y., Strayer, J., & Lischka, A. E. (2018). Analyzing the development of MKT in content courses. In T.E. Hodges, G.J. Roy, & A.M. Tyminski, A. M. (Eds.), Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 496-499). Greenville, SC: University of South Carolina & Clemson University.
Developing Preservice Teachers’ Mathematical Knowledge for Teaching in Content Courses
In this paper we present evidence that a) providing opportunities for PSMTs to engage with simulations of practice and b) making connections between advanced perspectives on geometry and 7-12 mathematics allows PSMTs to develop MKT in university mathematics content courses.
Strayer, J. F., Lischka, A., Quinn, C. M. & Watson, L. (2018). Workshop: Engaging Statistics Teachers through Connections to the Teaching of School Statistics and Educational Equity Issues. Developing preservice teachers’ mathematical knowledge for teaching in content courses. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, and S. Brown (Eds.), Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education (pp. 826-833). San Diego, California.