Episode 12: Complex and Contradictory Conversations: Prospective Teachers Interrogating Dominant Narratives Within Mathematics Education Discourse
April 4th, 2020 | Season 3 | 26 mins 26 secs
In this conceptual piece, I explore complex and contradictory conversations during an idea mapping task in which prospective elementary teachers interrogated dominant discourses within mathematics education, such as “mathematics is everywhere” and “being a math person.” I argue that this exercise of engaging with contradictions provided prospective teachers with opportunities to tease out nuances for reconstructing ideas that generate new perspectives for teaching and learning mathematics. Sharing my experience with the idea mapping task as a case study, I offer an alternative role for mathematics teacher educators to consider—as facilitators who create spaces for prospective teachers to interrogate complex and contradictory conversations within mathematics education.
Episode 11: Using Coordinated Measurement with Future Teachers to Connect Multiplication, Division, and Proportional Relationships
March 26th, 2020 | Season 3 | 29 mins 43 secs
We report results from a mathematics content course intended to help future teachers form a coherent perspective on topics related to multiplication, including whole-number multiplication and division, fraction arithmetic, proportional relationships, and linear functions. We used one meaning of multiplication, based in measurement and expressed as an equation, to support future teachers’ understanding of these topics. We also used 2 types of length- based math drawings—double number lines and strip diagrams—as media with which to represent relationships among quantities and solve problems. To illustrate the promise of this approach, we share data in which future secondary mathematics teachers generated and explained without direct instruction sound methods for dividing by fractions and solving proportional relationships. The results are noteworthy, because these and other topics related to multiplication pose perennial challenges for many teachers.
Episode 10: Engaging Preservice Secondary Mathematics Teachers in Authentic Mathematical Modeling: Deriving Ampere’s Law
March 21st, 2020 | Season 3 | 19 mins 56 secs
Incorporating modeling activities into classroom instruction requires flexibility with pedagogical content knowledge and the ability to understand and interpret students’ thinking, skills that teachers often develop through experience. One way to support preservice mathematics teachers’ (PSMTs) proficiency with mathematical modeling is by incorporating modeling tasks into mathematics pedagogy courses, allowing PSMTs to engage with mathematical modeling as students and as future teachers. Eight PSMTs participated in a model-eliciting activity (MEA) in which they were asked to develop a model that describes the strength of the magnetic field generated by a solenoid. By engaging in mathematical modeling as students, these PSMTs became aware of their own proficiency with and understanding of mathematical modeling. By engaging in mathematical modeling as future teachers, these PSMTs were able to articulate the importance of incorporating MEAs into their own instruction.
February 26th, 2020 | Season 3 | 21 mins
In the last decade, mathematics teacher educators have begun to design learning opportunities for preservice mathematics teachers using a pedagogies-of-practice perspective. In particular, learning cycles provide a structure for engaging PSTs in learning to teach through the use of representations, approximations, and decompositions of practice (Grossman et al., 2009). In this article, we provide details of one learning cycle designed to support secondary mathematics preservice teachers’ learning to elicit and use evidence of student thinking and pose purposeful questions (National Council of Teachers of Mathematics, 2014). Through qualitative analyses conducted on learning reflections, we provide evidence of the impact on engagement of this cycle through the lens of the Framework for Learning to Teach (Hammerness et al., 2005).