Amanda Brown

University of Michigan | U-M · School of Education

In this article we examine an analytical framework generated by secondary mathematics teachers for tracking changes to their own instructional practices across time. We describe the journey of this group of teachers through professional development focused on improving instructional practice. In the midst of that experience, teachers struggled to f...

Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

We show how we used a national distribution of responses from 416 practicing teachers to items of a test of mathematical knowledge for teaching geometry to estimate changes in knowledge by a group of 11 practicing teachers who participated in a 2-year practice-based professional development programme. To draw a reliable interpretation of the change...

We describe how a group of secondary mathematics teachers posed and solved a real-world problem. The problem was posed by teachers on a sandbar off the coast of an island in the Bahamas, where panoramic views of water meeting sky spurred the teachers to wonder how far away they could see. We analyze how the teachers translated the natural question,...

This chapter focuses on how digital technologies provide affordances for Practice-Based Mathematics Teacher Education (PBMTE) and maps needed research on technologically mediated teacher education. The chapter elaborates on Grossman’s pedagogies of practice, describing how they can be enacted in digital environments. Using LessonSketch as a prototy...

Technology-mediated simulations of teaching are used increasingly to represent practice in the context of professional development interventions and assessment. Some such simulations represent students as cartoon characters. An important question in this context is whether simplified cartoon representations of students can convey similar meanings a...

We contribute to the understanding of teacher noticing by focusing on what a teacher may notice in students' mathematical contributions in the context of problem‐based lessons. Complementing approaches to research on noticing that focus on individual teachers' perceptual, cognitive, or situated skills, this conceptual article offers four categories...

For centuries, there has been a debate about the role of undergraduate education in society. Some have argued that universities should focus on practical skills and knowledge to prepare students for the workforce, while others have supported the idea that universities should prioritize providing a broad understanding of disciplinary knowledge and p...

This research article contributes to the growing literature highlighting the potential for innovation in mathematics education through design cycles that involve creative risk-taking and failure-based learning. Specifically, we explore how “failed” cycles of StoryCircles—a practice-based professional development approach that centers on teacher col...

This paper contributes to understanding the work of teaching the university geometry courses that are taken by prospective secondary teachers. We ask what are the tensions that instructors need to manage as they plan and teach these courses. And we use these tensions to argue that mathematics instruction in geometry courses for secondary teachers i...

A central goal of lesson-centered professional development programs (PD) for mathematics teachers is to learn by constructing an artifact, for example, by designing and improving a lesson plan together. That leads to the questions, what does it mean, for mathematics teachers, to improve a lesson? And how can improvements be accounted for in the ana...

Building on student work (SW) in mathematics classroom discussion requires complex decision-making from mathematics teachers. Previous literature on problem-based lessons recommends selecting and sequencing pieces of SW in a way that creates a mathematical storyline, but there is rarely any empirical evidence on how mathematics teachers can master...

A key characteristic of problem-based lessons in mathematics is centering students' ideas in classroom discussions. Thus, teachers need to decide which pieces of student work (SW) to share with the class. Previous studies suggest that this decision is informed by teachers' attention to the features of SW. This study focuses on this preliminary stag...

To leverage pedagogies of approximation to improve teacher education, educational researchers must first tackle the methodological question, "How can we determine the potential of pedagogies of approximation for supporting the growth of prospective teachers' knowledge and practices for teaching?" In this paper, we offer a model called the Dual Acti...

The investigation at scale of the tensions that teachers need to manage when deciding to follow recommendations for practice has been hampered by the problem of occurrence: The conditions in which those decisions could be made need to occur during an observation in order for observers to document how teachers handle them. Simulations have been reco...

In this conceptual chapter, we illustrate how a professional-development innovation called contingency cards can be used to elicit teachers’ subject-specific pedagogical decisions in an online learning environment. Contingency cards are representations of practice that can be used by facilitators to occasion conversations about realistic contingenc...

The concept of teacher noticing has been a powerful methodological tool for understanding teachers’ decision-making and professional judgment. In this line of inquiry, researchers usually try to identify elements of classroom practice salient to teachers. Data about teacher noticing and decision making can be collected at scale through the use of s...

In this chapter, we contribute some insights from project SimTeach (Herbst P, Chieu VM, SIMTEACH: What can practical knowledge modeled in a teaching simulator contribute to support mathematics teacher learning? National Science Foundation Grant, EHR, DRL-1420102, 2014) concerning the role that technologically mediated teaching simulations can play...

OPEN ACCESS LINK: http://www.learntechlib.org/p/216903/ ABSTRACT: We describe how we further developed StoryCircles to support teacher learning online during COVID-19. In StoryCircles, a facilitator gathers teachers to collectively represent a lesson through iterative phases of scripting, visualizing, and arguing about alternatives. We share new i...

We offer a framework for analyzing teachers' practice of responding to students' mathematical contributions. This work builds on a framework developed by secondary mathematics teachers that we then augmented with one developed by linguists to create a modified framework that addresses pedagogic responding moves in detail. We show, through in-depth...

Novel tasks are valuable, yet discussions of novel tasks are often challenging to manage. In this paper, we describe a U.S. high school geometry lesson taught by two teachers in six different classes, in which students were assigned a novel task that the teacher framed as an instance of two familiar instructional situations — constructing a diagram...

This chapter addresses the role of technological tools in mathematics teacher learning within a perspective that conceives of this learning as practice-based and work-specific. The notion of practice-based and work-specific mathematics teacher education is envisioned as a just-in-time endeavor emphasizing important continuities between prospective...

This paper reports on an ongoing project aimed at developing an inter-institutional system of professional support for the improvement of the Geometry for Teachers (GeT) courses that mathematics departments teach to preservice secondary teachers. In alignment with the literature on improvement science (see Bryk et al., 2015; Lewis, 2015), it is ess...

As educational researchers and policy makers advocate for algebra classrooms to become places where students share ideas and compare approaches to solving problems, the question remains open as to whether and how much these ideas have penetrated actual practice. For example, how do algebra teachers respond to a correct, but unexpected way of solvin...

Teacher educators understand that the preparation of teachers needs to be rooted in the practice of teaching. This understanding, paired with the advancement in digital technologies capable of delivering practice-based teaching experiences, requires that those charged with preparing teachers consider how to best to position these technologies withi...

This paper reports on a project aimed at developing a system of professional support for the improvement of the Geometry for Teachers course that mathematics departments teach to preservice secondary teachers. We share data from interviews with 20 instructors to report on how they perceive their position of geometry instructors and the work they do...

There is growing interest in the field of education for leveraging emerging digital technologies to support teachers' learning in online or blended settings. This paper builds on Clarke and Hollingsworth's (2002) Interconnected Model of Professional Growth by investigating an alternative instantiation of professional experimentation. In particular,...

This chapter conceptualizes and illustrates StoryCircles, a form of professional education that builds on the knowledge of practitioners and engages them in collective, iterative scripting, visualization of, and argumentation about mathematics lessons using multimedia. The drive to invent and study new forms of professional education for mathematic...

This paper is part of a three-year inquiry that supports and investigates the work of groups of mathematics teacher educators using technological tools to design and implement multimedia practice-based teacher education curriculum materials. This paper describes the kinds of activities, interactions, and tools used by mathematics teacher educators...

We discuss affordances and liabilities of using a storyboard to depict a written case of a teacher’s dilemma that involves race, opportunity to learn, and student community. We rely on reflections by the teacher educator who authored the written case and later depicted it as a storyboard to use it with his preservice teachers (PSTs). The analysis i...

The primary goal of this paper is to investigate whether a computer-based simulation can detect the difference between novice and expert teachers’ decision-making in mathematics instruction, which is complex in nature. The design of the simulation is grounded in a sociological perspective on practical rationality of mathematics teaching. The simula...

In this paper, we report on the potential of StoryCircles, a process of collaboratively representing a lesson using a storyboarding tool, for engaging teachers in substantive discussions about teaching mathematics. The analysis focuses on the interactions amongst a group of inservice teachers during which they wrestled with several dilemmas of prac...

This study describes an investigation exploring relationships between pre-service teachers' (PSTs') mathematical knowledge for teaching geometry (MKT-G) and their educational experiences. Our data from 108 pre-service teachers from 6 universities suggest that PSTs' experience in the classroom had the most significant effect on their MKT-G scores. T...

A challenge inherent in improving mathematics instruction is whether new practices will be adopted and sustained by practitioners. In order to better understand the circumstances under which mathematics teachers are willing to depart from customary instruction, we report on findings from a study in which K-12 mathematics teachers were asked to eval...

This paper compares two analytical frameworks for 'reacting', a highly studied idea from linguistics, identified as critical in mathematics teaching (most famously within the triadic dialogue of IRF/E). The first framework was generated by secondary mathematics teachers engaged in improving their instructional practices. The second framework was ge...

Records of what takes place in mathematics classrooms are indispensable in mathematics teacher education and in research on mathematics teaching. We describe here the LessonSketch environment, an online platform for creating and analyzing representations of mathematics classrooms. We describe the authoring and analytic tools of LessonSketch with a...

In this study, we examine the use of a nondescript cartoon graphics for representing emotion in professional scenarios. The results from fifteen inservice teachers who took 33 forced-choice items identifying emotions of 20 photos of human actors and 13 nondescript cartoon graphics of students represented in classrooms will be discussed. Findings sh...

We investigate the potential of a mode of professional development called StoryCircles for engaging pre-service teachers (PSTs) in iterative approximations of the work of teaching (Grossman et al., 2009) in settings of reduced complexity. StoryCircles are a facilitated process of collaboratively representing a lesson using a multimedia storyboardin...

A teacher's reactions to students’ mathematical contributions have critical implications for shaping both teaching and learning. We present a framework for describing reacting moves that resulted from a comparative analysis between two existing frameworks; one developed by secondary teachers for parsing instructional practice and the other develope...

We discuss findings from a study of 226 K-12 mathematics teachers who rated the appropriateness of instructional actions in a scenario-based assessment. The teaching actions shown in the scenarios were designed to represent mathematics teachers fulfilling their obligation to the discipline of mathematics. Our analysis of the participants' follow-up...

https://deepblue.lib.umich.edu/bitstream/2027.42/143807/1/Milewski_Erickson_NCTM_Research_2015_FinalProposal.pdf

The development of several microworlds of topological surfaces using The Geometer's Sketchpad for exploring topological ideas with a representation, is discussed. The design of microworlds encourages researchers to explore a new domain that combines both geometry and topological ideas and techniques. Topologists use rectangular diagrams that repres...