Mathematics Teacher Educator Podcast

Episode 24: Representing Student Voice in an Approximation of Practice: Using Planted Errors in Coached Rehearsals to Support Teacher Candidate Learning

January 4th, 2021  |  Season 6  |  29 mins 55 secs

approximations of practice; authenticity; coached rehearsal; responding to errors; whole-class discussion

Approximations of practice provide opportunities for teacher candidates (TCs) to engage in the work of teaching in situations of reduced complexity. A problem of practice for teacher educators relates to how to represent student voice in approximations to engage TCs with interactive practices in meaningful ways. In this article, we share an analysis of our use of “planted errors” in coached rehearsals with secondary mathematics TCs focused on the practice of responding to errors in whole-class discussion. We highlight how different iterations of the planted errors affect the authenticity of how student voice was represented in the rehearsals and the resulting opportunities for TC learning. We offer design considerations for coached rehearsals and other approximations of practice.

Episode 26: Fostering Middle School Teachers’ Mathematical Knowledge for Teaching via Analysis of Tasks and Student Work

January 4th, 2021  |  Season 6  |  36 mins 59 secs

proportional reasoning; mathematical knowledge for teaching; middle school teachers; student work

Mathematical knowledge for teaching is a complex web of knowledge domains. In this article, we share findings from an 18-month professional development project that aimed to improve middle school mathematics teachers’ mathematical knowledge for teaching (MKT) of proportional reasoning by focusing on the critical analysis of mathematical tasks and student work. Although multiple studies have shown that professional development can contribute to teachers’ MKT globally, little is known about how this knowledge grows and how specific domains of MKT can be targeted through professional development. Findings in this study show how professional development positively influenced participants’ knowledge of content and teaching and knowledge of content and students, two domains of MKT, through teachers’ twinned analyses of tasks and student work in proportional reasoning.

Episode 23: Exploring Real Numbers as Rational Number Sequences With Prospective Mathematics Teachers

January 4th, 2021  |  Season 6  |  35 mins 22 secs

prospective mathematics teachers; quantitative reasoning; real numbers

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students’ understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real numbers as rational number sequences. We found that the instructional sequence enhanced prospective teachers’ understanding of real numbers by considering them as quantities and explaining them by using rational number sequences. In particular, results showed that prospective teachers reasoned about fractions and decimal representations of rational numbers using long division, the division algorithm, and diagrams. This further prompted their reasoning with decimal representations of rational and irrational numbers as rational number sequences, which leads to authentic construction of real numbers. Enacting the instructional sequence provides lenses for mathematics teacher educators to notice and eliminate difficulties of their students while developing relationships among multiple representations of real numbers.

Episode 25: Creating a Third Space for Learning to Design Technology-Based Mathematics Tasks

January 4th, 2021  |  Season 6  |  35 mins 28 secs

preservice teachers; technology; school based partners

In this article, we examine the ways in which the creation of a third space can bridge the divide between coursework and practice for preservice secondary mathematics teachers (PSTs) taking a technology, pedagogy, and content course. A university-based instructor partnered with two high school teachers to create a space in which PSTs draw upon and use both academic and practitioner knowledge while creating technology-based tasks for high school students to use. Our results revealed increased focus on pedagogical decisions in areas such as technology-task design and questioning techniques. The data also indicate that the success of this collaboration was connected to fair distribution of work, feeling valued, and personal benefit and challenges centered on maintaining rejection of hierarchy.

Episode 22: Interventions, Tools, and Equity-Oriented Resources in the MTE Journal

December 13th, 2020  |  Season 6  |  24 mins 9 secs

The Mathematics Teacher Educator journal is co-sponsored by the National Council of Teachers of Mathematics and the Association of Mathematics Teacher Educators. In June, both organizations released statements that call for mathematics teachers and mathematics teacher educators (MTEs) to “engage in anti-racist and trauma-informed education in our daily practices as processes of learning and adjustments” (NCTM, 2020) and to “actively work to be anti-racist in our acts of teaching, research, and service” (AMTE, 2020). This editorial highlights equity-related interventions and tools that can be implemented by MTEs. We reiterate statements made by NCTM and AMTE, describe key features of interventions and tools, and share equity-related resources published in the journal for MTEs to use with teachers.