## About

114

Publications

57,696

Reads

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2,686

Citations

Citations since 2016

Introduction

Chazan studies the teaching of mathematics in compulsory high school settings as a practice, embedded inside societal institutions, within a society with particular kinds of structure, that is carried out by individuals with their own identities and knowledge. This challenges him to integrate theoretical perspectives and orientations toward mathematics as a discipline, school as an institution, and students and teachers as members of communities with particular positions in our society.

Additional affiliations

August 2002 - present

September 1990 - August 2002

September 1985 - June 1990

Education

August 1985 - May 1989

**Harvard Graduate School of Education**

Field of study

- Education

August 1981 - May 1982

**Harvard Graduate School of Education**

Field of study

- Education

September 1978 - May 1981

## Publications

Publications (114)

This book tells a single story, in many voices, about a serious and sustained set of changes in mathematics teaching practice in a high school and how those efforts influenced and were influenced by a local university. It includes the writings and perspectives of high school students, high school teachers, preservice teacher candidates, doctoral st...

In this article, we explore how the solving of linear equations is represented in English-language algebra text books from the early nineteenth century when schooling was becoming institutionalized, and then survey contemporary teachers. In the text books, we identify the increasing presence of a prescribed order of steps (a canonical method) for s...

Background/Context
This opening article, like the other articles in this special issue, is situated in scholarship that attempts to understand the racialized nature of mathematics education in the United States and to examine the racial identities of students and teachers in the context of school mathematics. It is designed to respond to the curren...

Concerns about the use of computer-aided empirical verification in geometry classes lead to an investigation of students' understandings of the similarities and differences between the measurement of examples and deductive proof. The study reports in-depth interviews with seventeen high school students from geometry classes which employed empirical...

This editorial considers elements of an infrastructure that can support research that situates mathematics education research as a practice occurring in specific places and times. We explicitly acknowledge that our research practices as mathematics educators allow us to make contributions to the progress of knowledge not only by using intellectual...

https://blogs.ams.org/matheducation/2020/10/05/reflecting-on-mathematics-as-the-art-of-giving-the-same-name-to-different-things-part-2-averages-finite-and-continuous/

https://blogs.ams.org/matheducation/2020/07/15/pedagogical-implications-of-mathematics-as-the-art-of-giving-the-same-name-to-different-things/

Addressed towards course coordinators and departmental leaders interested in redesigning an undergraduate mathematics course, we highlight the steps our team at the University of Maryland, College Park has taken in bringing active learning to our Precalculus course. We provide examples of ways in which we have coordinated active learning across red...

How should we expect growing understandings of the nature of mathematical practice to inform classroom mathematical practice? We address this question from a perspective that takes seriously the notion that mathematics education, as a societal enterprise, is accountable to multiple sets of stakeholders, with the discipline of mathematics being only...

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...

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...

Many research studies have sought to explain why NCTM's vision for mathematics classrooms has not had greater impact on everyday instruction, with teacher beliefs often identified as an explanatory variable. Using instructional exchanges as a theoretical construct, this study explores the influence of teachers' institutional positions on the solvin...

This chapter explores a way of describing the teacher education curricular materials being developed by mathematics teacher educators through their interaction with the LessonSketch online platform (www.lessonsketch.org). We briefly describe the platform and the larger project and then using the experiences created by two fellows illustrate the kin...

Both the fields of mathematics teacher education and research on mathematics teachers have been making extensive use of representations of teaching, whether through written cases, video clips of actual practice, or a range of designed representations (like storyboards or animations with cartoon characters, e.g., Chazan and Herbst in Teachers Coll R...

This chapter seeks to understand the resistance of the school mathematics tradition (Gregg, J. J Res Math Educ 26(5): 442–466, 1995) to calls for reform, specifically to calls that would have mathematics classrooms outside of geometry instruction more closely follow disciplinary norms regarding justification and proof. It argues that writing script...

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...

This article explores the ways in which a teacher educator uses digital technology to create a virtual field placement as a way to blur the boundaries between a university methods course and teacher candidates' field placements. After describing his goals for the course, the teacher educator provides a description of three Lesson Sketch experiences...

This chapter comprises a conversation between the two authors focused on half-a-dozen core words concerned with teaching and their mutual interaction: dilemmas, tensions, commitments, obligations, ambivalence and, indirectly, technique. Additionally, we engage Jill Adler in an indirect conversation through her writing on the dilemmas teachers face...

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...

This paper describes instruments designed to use multimedia to study at scale the instructional decisions that mathematics teachers make as well as teachers’ recognition of elements of the context of their work that might influence those decision. This methodological contribution shows how evidence of constructs like instructional norm and professi...

We describe how multimedia scenarios delivered online can be used in instruments for the study of professional knowledge. Based on our work in the study of the knowledge and rationality involved in mathematics teaching, we describe how the study of professional knowledge writ large can benefit from the capacity to represent know-how using multimedi...

Against the backdrop of mentor teachers’ reasoning about practice, we seek to understand shifts in intern teachers’ reasoning about practice during a year in which they take their final methods course in the fall and then do intern teaching in the spring. The data we analyze consist of intern and mentor teacher study group discussions of repeated v...

Background/Context: Teachers in urban schools are sometimes seen as a large part of the problem with such schools. They are often spoken of as not knowing the content they need to know to teach, and they are not seen as committed to excellence or to reform-minded teaching; therefore, they are not seen as a resource for school improvement. Purpose/O...

Teachers in urban schools are sometimes seen as a large part of the problem with such schools; they are often spoken of as not knowing the content they need to know to teach, are not seen as committed to excellence or to reform-minded teaching, and therefore are not seen as a resource for school improvement. The case of Madison Morgan presented in...

We elaborate on the notion of the instructional triangle, to address the question of how the nature of instructional activity can help justify actions in mathematics teaching. We propose a practical rationality of mathematics teaching composed of norms for the relationships between elements of the instructional system and obligations that a person...

Background/Context
For decades, teacher educators and professional developers have been using video recordings of actual classroom practice to help teachers reflect on their teaching (e.g., van Es & Sherin, 2002, 2008) and to help preservice teachers come into contact with practice (Lampert & Ball, 1998). However, the use of video records of actual...

We illustrate a method, which is modeled on “breaching experiments,” for studying tacit norms that govern classroom interaction around particular mathematical content. Specifically, this study explores norms that govern teachers’ expectations for the doing of word problems in school algebra. Teacher study groups discussed representations of classro...

teacher education, technology, representations of practice, teaching, mathematics, comics, cartoon, animation, pedagogy, cases

In this chapter, we describe the use of an animation of classroom interaction to support conversation with prospective teachers.
The animation is used to examine establishing norms for the discussion of multiple answers to algebra word problems. This
chapter comes from the work of the “Thought Experiments in Mathematics Teaching” (ThEMaT) project,...

This article presents a way of studying the rationality that mathematics teachers utilize in managing the teaching of theorems in high-school geometry. More generally, the study illustrates how to elicit the rationality that guides teachers in handling the demands of teaching practice. In particular, it illustrates how problematic classroom scenari...

This article situates comic-based representations of teaching in the long history of tensions between theory and practice in teacher education. The article argues that comics can be semiotic resources in learning to teach and suggests how information technologies can support experiences with comics in university mathematics methods courses that (a)...

Secondary school mathematics teachers are often exhorted to incorporate reasoning into all mathematics courses. However, many feel that a focus on reasoning is easier to develop in geometry than in other courses. This article explores ways in which reasoning might naturally arise when solving equations in algebra courses.

We consider the functions of proof in mathematics from the perspective of the work of the mathematics teacher. The work of proving and the time spent on proving, what can a teacher account it to? How can he or she justify it? We frame that problem in a descriptive theory of teaching and place within that frame the work of scholars who have inquired...

The introductory content of this paper is taken from the first author???s Pattishall Award Lecture at the UM School of Education in May 2010.

In this chapter, we describe how two experienced and well-respected teachers grapple with a specific example of a problem
that all teachers confront, helping students build more sophisticated understandings from more limited ones. And we illustrate
how, in the context of their grappling, they have developed their own knowledge of the content for te...

RÉSUMÉ Dans ce texte, nous rendons compte d'une problématique méthodologique concernant l'étude du fonctionnement des classes de mathématiques. Nous considérons l'unité d'analyse des recherches et nous discutons la manière dont elle peut varier en fonction des objets de recherche. Nous posons aussi le problème de l'instrumentation des recherches et...

This interview study takes place in the context of a single small district in the United States. In the algebra curriculum of this district, there was a shift in the conception of equation, from a statement about unknown numbers to a question about the comparison of two functions over the domain of the real numbers. Using two of Shulman’s [Shulman,...

mathematical notions, starting is always difficult. Starting places can be too abstract or formal, and as a result divorced from students’ experience (as critics argued with New Math set theoretic definitions of number). Or, starting places can be too specific and concrete. In such a case, students must abstract the essential aspects of a concept f...

We report on the development of representations of teaching based on sequential-art sketches of classroom stories. We demonstrate with focus group data that these resources can help sketch compelling classroom stories and elicit the practical rationality of mathematics teaching. For quite some time policy makers have looked for levers for instructi...

Investigated recent developments in the teching and learning of algebra and provided participants with a forum for sharing and discussing therir research endeavors, development projects, ans experiences. The teaching and learning of algebra is a difficult area for study because across different countries and even within countries, what is done in c...

To view this videopaper online, see https://terpconnect.umd.edu/~dchazan/SchneppVP/
The navigation buttons do not work completely.

For a cultural outsider to shadow a French secondary mathematics teacher for a week during the first year of teaching is perhaps repeatedly to be surprised. The work required is varied and not even predominantly based in a single institution, a school. Indeed, at first sight, it may seem an error even to consider stagiaires (as all first-year teach...

A PREVIEW of this book can be found on Google Books at:
https://www.google.com/books/edition/Beyond_Formulas_in_Mathematics_and_Teach/E-GbNh2vi8cC?hl=en&gbpv=1&dq=daniel+chazan+beyond+formulas&printsec=frontcover