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1. Theoretical report: A framework for examining prospective teachers’ use of mathematical knowledge for teaching in mathematics courses.

   Lai, Y.; Strayer, J.; Lischka, A.; Anhalt., C.; Quinn, C.; Reed, S. (January 2019, Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education)

   This theoretical report addresses the challenge and promise of improving prospective secondary mathematics teachers’ experiences in undergraduate mathematics courses through 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. 

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2. Analyzing the development of MKT in content courses

   Lai, Y.; Strayer, J.; Lischka, A. E. (January 2018, Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of 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. 

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3. Analyzing the development of MKT in content courses

   Lai, Y.; Strayer, J. F.; Lischka, A. E. (November 2018, 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)

   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. 

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4. Mathematical Errors When Teaching: A Case of Secondary Mathematics Prospective Teachers’ Early Field Experiences

   Bieda, K.; Voogt, K. (January 2019, Proceedings of the 22nd Annual Conference on Research in Undergraduate Education)

   The construct of mathematical knowledge for teaching (MKT) has transformed research and practice regarding the mathematical preparation of future teachers. However, the measures used to assess MKT are largely written tasks, which may fail to adequately represent the nature of content knowledge as it is used in instructional decision making. This preliminary report shares initial findings into one measure of MKT in practice – mathematical errors made during planning and enactment of mathematics instruction. We analyzed lesson plans and classroom video from prospective secondary mathematics teachers (PSTs)’ supervised field experiences in college algebra course. We found that there tended be more errors related to understanding of functions (especially logarithmic), but relatively few errors happened overall during instruction. Of the errors made during planning, the majority of these errors were issues of mathematical precision. Implications for the mathematical preparation of secondary PSTs, as well as research on MKT in practice, are discussed. 

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5. Opportunities for reasoning and proving in mathematical tasks: A discursive perspective.

   Weingarden, M.; Buchbinder, O.; Liu, J. (January 2022, Proceedings of the 44th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N.; Strayer, J.; Drown, S. (Ed.)

   In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the curricular-based mathematical discourse and as participation in the meta-discourse about proof, which is focused on the aspects of deductive reasoning. By cluster analysis performed on 106 tasks designed by prospective secondary teachers, we identify four types of tasks corresponding to four types of ORP: limited ORP, curricular-based reasoning ORP, logic related ORP, and fully integrated ORP. We discuss these ORP and the contribution of this framework in light of preparing beginning teachers to integrate reasoning and proving in secondary mathematics classrooms. 

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