Alison Castro Superfine

Exploring the Mathematical Knowledge Needed for Teaching Teachers

The purpose of this study is to explore the knowledge demands of teacher educators as they teach disciplinary content to preservice elementary teachers, specifically in mathematics, and to understand how such knowledge is different from that used by K-12 teachers. Drawing from a database including teaching and learning artifacts from five iterations of a content course for preservice teachers, the authors illustrate different forms of knowledge observed across different mathematics teacher educators’ practice and discuss how the observed knowledge forms are different from knowledge used by K-12 teachers in their practice. Finally, the authors discuss how the process used in this study can identify potential components of a knowledge base for teacher education.

Examining the Process of Developing a Research-Based Mathematics Curriculum and Its Policy Implications

The implementation of “research-based” mathematics curricula is increasingly becoming a central element of mathematics education reform policies. Given the recent focus on grounding mathematics curriculum policies in research, it is important to understand precisely what it means for a curriculum to be research-based. Using the Curriculum Research Framework (CRF), this paper examines the development process of Math Trailblazers to help situate decision-making processes related to curricula in the broader mathematics education policy landscape. In the process of developing and revising the curriculum, the development and research teams have specifically developed field test materials, researched ways in which teachers and students use and learn with the materials in a small number of classrooms, and then completed research-based revisions of the curriculum materials. While certain elements of the CRF are represented in the research and revision process, other elements, such as why and under what conditions the curriculum is effective, are underrepresented. Making visible research and development processes of research-based mathematics curricula has profound implications for understanding the effectiveness of certain policy initiatives. Merging policy, practice, and research is a difficult activity, but a critical one for enhancing the effectiveness of these fields in education. As these fields become increasingly intertwined, policymakers should be sensitive to the different demands of each field, and look for opportunities to enhance the capacities of organizations that exist at this nexus.

Fidelity of Implementation: Bringing Written Curriculum Materials into the Equation.

Fidelity of curriculum implementation (FOI) is an important area of research because of the critical role it plays in understanding how and why curriculum materials work and how they can be improved. This analysis explores written features within the Math Trailblazers curriculum that may influence the ways teachers implement mathematics curriculum materials. In particular, we examine FOI data from prior research in order to identify features within the materials themselves that may influence why teachers adhere to the intended curriculum to varying degrees. This paper reports on our analysis of examining five whole number lessons previously analysed for level of FOI alongside an analysis scale of written curriculum features. Our purpose in this analysis is to examine features of the written curriculum that potentially mediate teachers’ implementation of the materials in line with the intended curriculum. In doing so, our analysis further emphasises the critical role teachers play in curriculum implementation, and thus may provide some insight for curriculum developers as they consider ways in which to design the written curriculum that increase the likelihood that teachers will adhere to the intended curriculum.

Integrating Algebra and Proof in High School: Students' Work with Multiple Variables and a Single Parameter in a Proof Context

In the United States, researchers argue that proof is largely concentrated in the domain of high school geometry, thus providing students a distorted image of what proof entails, which is at odds with the central role that proof plays in mathematics. Despite the centrality of proof, there is a lack of studies addressing how to integrate proof into other mathematical domains. In this article, we discuss a teaching experiment designed to integrate algebra and proof in the high school curriculum. Algebraic proof was envisioned as the vehicle that would provide high school students the opportunity to learn not only about proof in a context other than geometry but also about aspects of algebra. Results from the experiment indicate that students meaningfully learned about aspects of both algebra and proof in that they produced algebraic proofs involving multiple variables and a single parameter, based on conjectures they themselves generated.

Understanding the Work of Mathematics Teacher Educators from a Knowledge of Practice Perspective

The work of mathematics teacher educators (MTE) is far from understood. In this study, we explore the nature of knowledge drawn upon MTEs as they connect pre-service teachers’ content learning to the practice of teaching mathematics to children. Using data from a two-year project focused on the professional development of university-based teacher educators, we illustrate MTEs’ work of teaching pre-service elementary teachers mathematics. In doing so, we identified three MTE practices of connecting to teaching practice, including MTEs supporting pre-service teachers in making sense of and remedying children’s errors, MTEs modeling for pre-service teachers how to modify a mathematical task appropriate to children’s current level of understanding, and MTEs engaging pre-service teachers to consider children’s common conceptions. The nature of knowledge MTEs draw upon in their teaching practices is discussed.

Shifting Perspectives on Preservice Teachers’ Noticing of Children’s Mathematical Thinking

Noticing children’s mathematical thinking is an important aspect of what teachers need to know. Researchers generally agree that noticing involves two main processes, namely attending to and making sense of particular events in an instructional setting. We report on our work involving preservice teacher noticing and our efforts to scaffold their noticing. We argue for a shift in perspective on preservice teacher noticing, a perspective that considers interpreting classroom events as an important first step for preservice teachers in their development of noticing, which then positions preservice teachers to attend to important and noteworthy events.