Judit Moschkovich

A Situated and Sociocultural Perspective on Bilingual Mathematics Learners

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 mathematical practices. The 3rd perspective is based on sociocultural and situated views of both language and mathematics learning. In 2 mathematical discussions, I illustrate how a situated and sociocultural perspective can complicate our understanding of bilingual mathematics learners and expand our view of what counts as competence in mathematical communication.

Learning to Graph Linear Functions: A Case Study of Conceptual Change

This case study shows how a students 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 students strategies and conceptions and describe how these changed. We show how the student did not erase his original conception or replace it with a conception supported by instruction, but instead refined his initial strategies and conceptions.

Beyond Words to Mathematical Content: assessing English Learners in the Mathematics Classroom

In the U.S., approximately 4.5 million (9.3%) students enrolled in K–12 public schools are labeled English learners [NCES 2002]. In California, during the 2000–2001 school year 1.5 million (25%) K–12 public school students were labeled as having limited English language skills [Tafoya 2002]. For numerous reasons, the instructional needs of this large population warrant serious consideration. Assessment is particularly important for English learners because there is a history of inadequate assessment of this student population. LaCelle-Peterson and Rivera [1994] write that English learners “historically have suffered from disproportionate assignment to lower curriculum tracks on the basis of inappropriate assessment and as a result, from over referral to special education [Cummins 1984; Duran 1989; Ortiz and Wilkinson 1990; Wilkinson and Ortiz 1986].” Previous work in assessment has described practices that can improve the accuracy of assessment for this population [LaCelle-Peterson and Rivera 1994]. Assessment activities should match the language of assessment with language of instruction and “include measures of content knowledge assessed through the medium of the language or languages in which the material was taught.” Assessments should be flexible in terms of modes (oral and written) and length of time for completing tasks. Assessments should track content learning through

How Equity Concerns Lead to Attention to Mathematical Discourse

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 practices, and challenges with ethno-mathematical approaches. Next, I summarize what research tells us about equitable discourse practices for students from non-dominant communities in mathematics classrooms. In closing, I use the four chapters and my own work (Moschkovich, Language(s) and learning mathematics: Resources, challenges, and issues for research. In Moschkovich, J. (Ed.), Language and mathematics education: Multiple perspectives and directions for research (pp. 1–28). Charlotte: Information Age Publishing, 2010) to make recommendations for future research.

Issues Regarding the Concept of Mathematical Practices

In the first chapter of Alan Schoenfeld’s 2011 book How we think, he describes his original framework (1985) for the study of mathematical problem solving as having four components: knowledge base, problem solving strategies, metacognition, and beliefs.

Recommendations for Research on Language and Learning Mathematics

This paper describes recommendations for research on language and learning mathematics. I review several issues central to conducting research on this topic and make four recommendations: using interdisciplinary approaches, defining central constructs, building on existing methodologies, and recognizing central distinctions while avoiding dichotomies. I make four recommendations to address these issues.

Student agency and counter-narratives in diverse multilingual mathematics classrooms : Challenging deficit perspectives

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 see how such learners productively use existing resources to engage in mathematics. In this chapter we examine potentially fruitful ways of framing identity and learning centered on student agency that can be brought to bear on the analysis of emergent multilinguals’ mathematical activity. We then illustrate the utility of agency-centered framings with vignettes of student interactions that focus on how emergent bilinguals used multiple linguistic resources in powerful ways. The vignettes are drawn from a variety of international mathematics classroom contexts and focus on students as creative users of linguistic resources in ways that serve a variety of functions during mathematical activity.

Proficiency and Beliefs in Learning and Teaching Mathematics

This volume was sparked by the fact that Alan Schoenfeld and Gunter Torner were both celebrating their 65th birthdays in July 2012. The book started out as part of a Festschrift to celebrate that event. Although the volume was not ready in time for their birthdays, the result is a belated celebration in print to recognize their contributions to the field of mathematics education.

International Perspectives on Language and Communication in Mathematics Education

This chapter introduces this volume, which arose from the conversations among 90 scholars from 23 countries within the topic study group on Language and Communication in Mathematics Education at the 16th International Congress of Mathematical Education, which convened in Hamburg, Germany. The chapter describes the goals of the topic study group and the diversity of contributions, and it introduces the papers that were selected for elaboration and publication in this volume.

Reading Graphs of Motion: How Multiple Textual Resources Mediate Student Interpretations of Horizontal Segments

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-modal and multi-semiotic. Data from a bilingual classroom and transcript excerpts illustrate the multimodal and multi-semiotic nature of mathematical language. The analysis describes how pairs of students interpreted stories of bicycle trips using multiple modes, sign systems, and texts. The analysis examines how multiple modes provided tools for students to make sense of mathematical ideas and how inter-textuality functioned as students negotiated the mathematical meaning of motion through multiple texts (graphs, written questions, written responses, and oral discussions). We describe how four pairs of eighth-grade bilingual students interpreted horizontal segments on a distance versus time graph as they answered questions using a story about a bicycle trip. While students shifted between two interpretations (moving and not moving) of the three horizontal segments above the x-axis, pairs interpreted the segment located on the x-axis as representing the biker not moving. We examine how students shifted among alternative interpretations of the horizontal segments and describe how the graph and the written text mediated these student interpretations.