Judit Moschkovich

University of California, Santa Cruz | UCSC · Department of Education

The concept of scaffolding can be used to describe various types of adult guidance, in multiple settings, across different time scales. This article clarifies what we mean by scaffolding, considering several questions specifically for scaffolding in mathematics: What theoretical assumptions are framing scaffolding? What is being scaffolded? At what...

Oral student contributions are important for learning mathematics, but without a written record of students' reasoning, revising is difficult or impossible. While writing makes revising possible, research needs to theoretically frame what to revise, how to revise, and how to support revisions. The chapter addresses the question: How can the academi...

This article addresses the relationship between language and mathematical thinking by reconsidering early work on language and number names. The analysis examines theoretical assumptions, later empirical data, and critiques of those early studies. Researchers, practitioners, and curriculum designers in mathematics education working in multilingual...

This invited lecture summarized my work on language and learning mathematics. I described a theoretical framework for academic literacy in mathematics (Moschkovich, ABCDa, ABCDb) that can be used to analyze student contributions and design lessons. The presentation included a classroom example and recommendations for instruction that integrates att...

How can school mathematics prepare citizens for a democratic society? Answers to this question are not static; they change as society and its problems change. The SARS-CoV-2 pandemic with its corresponding disease COVID-19 presents such a problem: what is needed to navigate this complex situation that involves, among other things, mathematics? Usin...

This chapter examines the strengths multilingual and non-dominant learners bring to school for learning mathematics or science. We connect research on learners’ strengths from two sets of literature: research in mathematics education and in science education. The examples illustrate how research in mathematics and science education can inform polic...

After four decades of research and development on language in mathematics classrooms, there is consensus that enhancing language is crucial for promoting students' mathematics learning. After briefly sketching the theoretical contexts for work on this topic, in this paper we present six design principles for instruction that enhances language for m...

In this paper, we propose increasing the focus on research on writing in k-12 mathematics classrooms. Although considerable research has explored discourse in mathematics classrooms, this work has largely focused on talk rather than writing. Discourse, which has been shown to support mathematics learning (Hufferd-Ackles, Fuson, & Sherin, 2004; Mich...

This chapter provides an introduction to integrating a naturalistic paradigm and ethnographic methods into research in mathematics education. The chapter addresses methodological issues specific to designing and conducting research in mathematics education framed by a naturalistic paradigm that includes ethnographic methods and, in particular, usin...

This paper illustrates how the academic literacy in mathematics framework (Moschkovich, J Math Behav 40:43–62, 2015) can be used to uncover the multiple layers of work bilingual learners accomplish during mathematical discussions. Using this framework allows researchers to examine students’ joint mathematical activity in terms of mathematical profi...

This article addresses the relationship between language and mathematical thinking by reconsidering early work on language and number names. The analysis examines theoretical assumptions, later empirical data, and critiques of those early studies. Researchers, practitioners, and curriculum designers in mathematics education working in multilingual...

This chapter analyzes interpretations of a graph of motion by bilingual adolescents using multiple representations of motion: a written story, a graph, and an oral description. The chapter uses a socio-cultural conceptual framework, complex views of language and academic literacy in mathematics, and assumes that mathematical discourse is multi-moda...

This Working Group will continue the work of last year's Working Group in considering multiple aspects of research and practice related to mathematics learning and teaching with English Learners. Our goals include: (1) developing further the collaborative endeavors that began during the 2015 meeting and (2) fostering new collaborations and supporti...

This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf learners, new media and tertiary education. Each chapte...

This white paper describes the Elementary Mathematical Writing Task Force's recommendations for the types of and purposes for elementary mathematical writing. It presents how the group distinguished "mathematical writing" from other kinds of writing that take place in mathematics classrooms and considerations of this work. Download at http://mathwr...

This chapter provides the introduction to this ICMI Study 21 volume. It includes: a discussion of the place of this study and its topic within ICME; a discussion of what is meant by the study title; and a brief historical account of research on this topic in mathematics education. The chapter also recounts the various stages of the study, including...

Mathematics classrooms around the world serve students who are learning the dominant language of instruction. These students’ forms of participation in mathematical activity have often been examined from deficit perspectives. Mathematics education research is in great need of counter-narratives to such prevailing deficit assumptions so that we can...

This Working Group will consider multiple aspects of research and practice related to mathematics learning and teaching with English Learners. Our goals for the Working Group include: (1) developing a shared understanding of the research questions, issues, challenges, and contributions that research studies focusing on English learners can make to...

In this essay, the author describes principles for equitable mathematics teaching practices for English Language Learners (ELLs) and outlines guidelines for ma-terials to support such practices. Although research cannot provide a recipe for equitable teaching practices for ELLs, teachers, educators, and administrators can use this set of research-b...

This article shares the authors' views on language-diversity issues in research in mathematics education. Described are tensions, questions, and myths that they have regularly faced as researchers. They use similarities and differences in two settings (multilingual classrooms in South Africa and U.S. mathematics classrooms with Latino/a students) t...

This paper is based on the Iris M. Carl Equity Address the author delivered at the 2012 annual meeting of the National Council of Teachers of Mathematics. That invited keynote considered the question of equitable teaching practices in mathematics classrooms for students from non-dominant communities. Although research cannot provide quick answers t...

This chapter traces the history of the concept of mathematical practices, describes how it has been used in research in mathematics educations, and raises four issues to consider about this concept: how we define mathematical practices, theoretically frame the concept, connect practices to other forms of mathematical activity, and describe how prac...

This is a dialogue extracted from a conversation among some members of the Equity Special Issue Editorial Panel (Beatriz D'Ambrosio; Marilyn Frankenstein; Rochelle Gutierrez, Special Issue editor; Signe Kastberg; Danny Martin; Judit Moschkovich; Edd Taylor; and David Barnes) about racism in mathematics education. It raises issues about the use of t...

This is a dialogue extracted from a conversation among members of the Equity Special Issue Editorial Panel about the role of a researcher's position in mathematics education. It raises issues about the non-neutrality of research; the relationship between a researcher's identity and the design, analysis, and conclusions of a research study; the bene...

This article provides an introduction to the JRME Equity Special Issue. It includes a rationale for the special issue, the process for selecting articles, and a description of the kinds of articles that will appear in the special issue. It concludes with a set of questions that teachers and researchers can and should ponder as they read the article...

This is a dialogue extracted from a conversation among some members of the Equity Special Issue Editorial Panel (Beatriz D'Ambrosio; Marilyn Frankenstein; Rochelle Gutiérrez, Special Issue editor; Signe Kastberg; Danny Martin; Judit Moschkovich; Edd Taylor; and David Barnes) about racism in mathematics education. It raises issues about the use of t...

This is a dialogue extracted from a conversation among members of the Equity Special Issue Editorial Panel about the role of a researcher's position in mathematics education. It raises issues about the non-neutrality of research; the relationship between a researcher's identity and the design, analysis, and conclusions of a research study; the bene...

This chapter traces the history of the concept of mathematical practices, describes how it has been used in research in mathematics educations, and raises and raises four issues to consider about this concept: how we define mathematical practices, theoretically frame the concept, connect practices to other forms of mathematical activity, and descri...

We analyze how three seventh grade mathematics teachers from a majority Latino/a, linguistically diverse region of Texas taught the same lesson on interpreting graphs of motion as part of the Scaling Up SimCalc study (Roschelle et al., 2010). The students of two of the teachers made strong learning gains as measured by a curriculum-aligned assessme...

This chapter examines the connections between equity and mathematical discourse and explores how discourse is relevant to equity. Through commentary on the preceding three chapters, I discuss four issues raised by different approaches to equity and to discourse: multiple approaches to equity, definitions of ‘discourse’, aspects of school discourse...

This study analyzes patterns of interaction among bilingual middle school students while they engaged in peer mathematical discussions. Using a sociocultural lens on learning the practice of school mathematics, this study addresses three questions: (1) What kind of mathematical discourse practices did the students engage in? (2) What discourse patt...

Students often voice computations during group discussions of mathematics problems. Yet, this type of private speech has received little attention from mathematics educators or researchers. In this article use excerpts from middle school students' group mathematical discussions to illustrate and describe “computational private speech.” We analyze f...

This paper explores representation- and language-rich mathematics instruction in two classrooms with low-income Latino/a students. The two classroom teachers were part of a larger study investigating the use of SimCalc in middle school, and their classrooms had learning gains greater than the mean gains for the study overall. Prior analyses documen...

This article reviews two sets of research studies from outside of mathematics education to consider how they may be relevant to the study of bilingual mathematics learners using two languages. The first set of studies is psycholinguistics experiments comparing monolinguals and bilinguals using two languages during arithmetic computation (language s...

This article examines a classroom discussion of multiple interpretations of the scales on two distance versus time graphs. The analysis describes how two students and a teacher used multiple meanings for phrases of the form "I went by" and coordinated these meanings with different views of the scales. Students' ambiguous and shifting meanings did n...

Testing matters! It can determine kids' and schools' futures. In a conference at the Mathematical Sciences Research Institute, mathematicians, maths education researchers, teachers, test developers, and policymakers gathered to work through critical issues related to mathematics assessment. They examined: the challenges of assessing student learnin...

In this article I examine the notion of mathematical Discourse practices. I use a classroom vignette to examine two features of Discourse practices, the situated meanings for utterances and the focus of attention. I consider the multiple Discourse practices that inform views of mathematical Discourses, describe the characteristics of academic mathe...

A statement to the National Mathematics Panel, as a representative of TODOS: Mathematics for All, an organization that advocates for an equitable and high quality mathematics education for all students, in particular Hispanic/Latino students as well as students from minority populations such as Native Americans, African Americans, and others.

This case study uses a sociocultural perspective and the concept of appropriation (Newman, Griffin and Cole, 1989; Rogoff, 1990) to describe how a student learned to work with linear functions. The analysis describes in detail the impact that interaction with a tutor had on a learner, how the learner appropriated goals, actions, perspectives, and m...

My aim in this article is to explore 3 perspectives on bilingual mathematics learners and to consider how a situated and sociocultural perspective can inform work in this area. The 1st perspective focuses on acquisition of vocabulary, the 2nd focuses on the construction of multiple meanings across registers, and the 3rd focuses on participation in...

This chapter examines the mathematical activities in a middle-school mathematics classroom during an architectural design project. By looking at three instances of assessment activities during this project--design reviews, final presentations, and classroom conversations--I examine student mathematical activities during assessments and compare math...

This chapter examines two recommendations for classroom practices from curriculum and instruction Standards (National Council of Teachers of Mathematics [NCTM], 1989; 2000) and research in mathematics education. One recommendation, informed in part by research uncovering the mathematical practices in everyday activities (Carraher, Carraher, & Schli...

This case study shows how a student's strategies and associated conceptions emerged and changed over the course of a 6-session tutoring curriculum designed to develop conceptual knowledge of linear functions. Using microgenetic and sequential analyses, we identify the student's strategies and conceptions and describe how these changed. We show how...

Curriculum guidelines and research in mathematics education have outlined the characteristics of reform-oriented mathematics classrooms (National Council of Teachers of Mathematics (NCTM) 1989). These characteristics include an increased emphasis on communication and collaborative work. It is important in designing classroom instruction for Latino...

This article uses an evolutionary perspective of conceptual change to consider in detail a conception in the domain of linear functions. The analysis focuses on the nature of students' use of the x-intercept in equations of the form y = mx + b by summarizing the results of written assessments and presenting two case studies of students exploring an...

In this article, I describe the refinement of a conception in the domain of linear functions, the use of the x-intercept in equations of the form y = mx + b, to illustrate the resources used by students to refine a conception. The examples presented show how students refined their use of the x-intercept by (a) narrowing the problem contexts in whic...

Examines assessment practices in a middle school mathematics classroom using two criteria for authenticity. Uses two frameworks to examine how well assessment practices meet the two criteria and to consider when the two criteria may be at odds. Contains 24 references. (ASK)

This study examines mathematics learning in the context of peer discussions by focusing on students' descriptions of lines graphed on a computer screen. The article describes how these discussions provided a rich context for negotiating shared descriptions, supported conceptual change, and resulted in convergent meanings through reciprocal elaborat...

Thesis (Ph. D. in Education)--University of California, Berkeley, April 1992. Includes bibliographical references (leaves 230-239).

This study analyzes patterns of interaction among bilingual middle school students while they engaged in mathematical discussions. Using a sociocultural lens on the practice of school mathematics and methods from discourse analysis, this study addresses three questions: 1) What kinds of mathematical discourse practices did the students engage in du...