Paying the Price for "Sugar and Spice": Shifting the Analytical Lens in Equity Research

The analytical stance taken by equity researchers in education, the methodologies employed, and the interpretations that are drawn from data all have an enormous impact on the knowledge that is produced about sources of inequality. In the 1970s and 1980s, a great deal of interest was given to the issue of women's and girls' underachievement in mathematics. This prompted numerous different research projects that investigated the extent and nature of the differences between girls' and boys' achievement and offered reasons why such disparities occurred. This work contributed to a discourse on gender and mathematics that flowed through the media channels and into schools, homes, and the workplace. In this article, I consider some of the scholarship on gender and mathematics, critically examining the findings that were produced and the influence they had. In the process, I propose a fundamental tension in research on equity, as scholars walk a fine and precarious line between lack of concern on the one hand and essentialism on the other. I argue in this article that negotiating that tension may be the most critical role for equity researchers as we move into the future.     

Research,Reform, and Equity in U.S. Mathematics Education

This article discusses mathematics education research in relation to equity and current U.S. reforms. Although mathematics education researchers and reformers give attention to equity, work in this area tends to ignore relevant social and cultural issues. I begin by surveying articles on equity published in recent, mainstream education journals, highlighting the lack of attention given to social class and ethnicity. I discuss the implications of this limited research base. Specifically, I argue that current mathematics education reforms have been shaped by good intentions and existing research, neither of which offers adequate guidance to address the complexities of equity in mathematics classrooms today. Drawing from a study of social class differences in students' experiences in one reform-oriented classroom, I discuss the challenges and dilemmas inherent in sociocultural approaches to research in mathematics education and their potential contributions. I call for research from a sociocultural perspective, focusing on ways in which students from underrepresented groups can struggle when encountering particular instructional approaches, and ways in which teachers and students are able to address such struggles.     

Research, Reform, and Equity in U.S. Mathematics Education

This article discusses mathematics education research in relation to equity and current U.S. reforms. Although mathematics education researchers and reformers give attention to equity, work in this area tends to ignore relevant social and cultural issues. I begin by surveying articles on equity published in recent, mainstream education journals, highlighting the lack of attention given to social class and ethnicity. I discuss the implications of this limited research base. Specifically, I argue that current mathematics education reforms have been shaped by good intentions and existing research, neither of which offers adequate guidance to address the complexities of equity in mathematics classrooms today. Drawing from a study of social class differences in students' experiences in one reform-oriented classroom, I discuss the challenges and dilemmas inherent in sociocultural approaches to research in mathematics education and their potential contributions. I call for research from a sociocultural perspective, focusing on ways in which students from underrepresented groups can struggle when encountering particular instructional approaches, and ways in which teachers and students are able to address such struggles.     

Enabling the Practice of Mathematics Teachers in Context: Toward a New Equity Research Agenda

In this article, I address the need for a more clearly articulated research agenda around equity issues by proposing a working definition of equity and a focal point for research. More specifically, I assert that rather than pitting them against each other, we must coordinate (a) efforts to get marginalized students to master what currently counts as "dominant" mathematics with (b) efforts to develop a critical perspective among all students about knowledge and society in ways that ultimately facilitate (c) a positive relationship between mathematics, people, and equity on the planet. I make this argument partly by reviewing the literature on (school) contexts that engage marginalized students in mathematics. Then, I argue that the place that holds the most promise for addressing equity is a research agenda that emphasizes enabling the practice of teachers and that draws more heavily on design-based and action research, thereby redefining what the practice of mathematics means along the way. Specific research questions are offered.     

Enabling the Practice of Mathematics Teachers in Context: Toward a New Equity Research Agenda

In this article, I address the need for a more clearly articulated research agenda around equity issues by proposing a working definition of equity and a focal point for research. More specifically, I assert that rather than pitting them against each other, we must coordinate (a) efforts to get marginalized students to master what currently counts as “dominant” mathematics with (b) efforts to develop a critical perspective among all students about knowledge and society in ways that ultimately facilitate (c) a positive relationship between mathematics, people, and equity on the planet. I make this argument partly by reviewing the literature on (school) contexts that engage marginalized students in mathematics. Then, I argue that the place that holds the most promise for addressing equity is a research agenda that emphasizes enabling the practice of teachers and that draws more heavily on design-based and action research, thereby redefining what the practice of mathematics means along the way. Specific research questions are offered.     

Equity in mathematics education: unions and intersections of feminist and social justice literature

Traditional models of gender equity incorporating deficit frameworks and creating norms based on male experiences have been challenged by models emphasizing the social construction of gender and positing that women may come to know things in different ways from men. This paper draws on the latter form of feminist theory while treating gender equity in mathematics as intimately interconnected with equity issues by social class and ethnicity. I integrate feminist and social justice literature in mathematics education and argue that to secure a transformative, sustainable impact on equity, we must treat mathematics as an integral component of a larger system producing educated citizens. I argue the need for a mathematics education with tri-fold support for mathematical literacy, critical literacy, and community literacy. Respectively, emphases are on mathematics, social critique, and community relations and actions. Currently, the integration of these three literacies is extremely limited in mathematics.     

Economy: the absent centre of mathematics education

Social and political turns in mathematics education research have brought into the field postmodern theorisations that researchers have been using to dismantle traditional philosophies of mathematics, to posit mathematics in the sociocultural terrain, and to spell out the role mathematics has in school exclusion. Sociopolitical perspectives constitute a privileged field of research to address the influence of economy on mathematical achievement. However, instead of investigating the role of economy in students’ achievement, sociopolitical studies have been contributing to a disavowal of the economic dimension of school mathematics. This paper synthesises a set of investigations carried out by the author in the last 5 years endeavouring to posit mathematics education in the political and economic spectrum of our time. It takes advantage of the contemporary combination of Hegel’s dialectics, Lacanian psychoanalysis and Marx’s critique of political economy, carried out by Slavoj ?i?ek, to develop a critique of the way research within the so-called ‘sociopolitical turn’ deals with the issue of equity; and marks out the contours of mathematics education’s ideological belonging.     

Gender perspectives in mathematics education: intentions of research in Denmark and Norway

A framework is presented for analyzing gender perspectives in mathematics education (structural, symbolic, personal and interactional gender), and the Danish and Norwegian researchers’/teachers’ work within the field of gender and mathematics is presented with reference to these four perspectives. Furthermore, the gender issue in TIMSS and PISA is briefly discussed. The main thread through the article is the researchers’ willingness and intentions of investigating the gender perspectives in mathematics education. However, so far, these research intentions have not been realized in Denmark and Norway.     

Inquiry as an entry point to equity in the classroom

ABSTRACT

Although many policy documents include equity as part of mathematics education standards and principles, researchers continue to explore means by which equity might be supported in classrooms and at the institutional level. Teaching practices that include opportunities for students to engage in active learning have been proposed to address equity. In this paper, through aligning some characteristics of inquiry put forth by Cook, Murphy and Fukawa-Connelly with Gutiérrez's dimensions of equity, we theoretically explore the ways in which active learning teaching practices that focus on inquiry could support equity in the classroom.     

Discursive psychology as an alternative perspective on mathematics teacher knowledge

Research on mathematics teacher knowledge, including work on mathematical knowledge for teaching, draws heavily on Shulman’s categories of teacher knowledge. These categories have been adopted, developed and modified by mathematics education researchers. This approach has led to some valuable insights. In this paper, I draw on discursive psychology to develop a critique of this work. This critique highlights some of the unstated assumptions of much research inspired by Shulman’s work, including, in particular, a representational view of knowledge and argues that the resulting theories do not reflect the discourses of knowledge that arise in mathematics classrooms. These ideas are illustrated with discussion of two examples, with the aim of showing how discursive psychology can offer an alternative perspective.     

Mother and Child Emotions during Mathematics Homework

Mathematics is often thought of as a purely intellectual and unemotional activity. Recently, researchers have begun to question the validity of this approach, arguing that emotions and cognition are intertwined. The emotions expressed during mathematics work may be linked to mathematics achievement. We used behavioral measures to identify the emotions expressed by U.S. mothers and their 11-year-old children while solving pre-algebra tasks in the home. The most notable positive emotions displayed by mothers and children included positive interest, affection, joy, and pride, whereas the most notable negative emotions expressed included tension, frustration, and distress. Reflecting the social aspects of doing homework together, mothers' and children's emotions were highly correlated. Independent of pre-existing differences in knowledge, children's emotions were associated with their performance on a mathematics post-test: tension was linked to poorer performance while positive interest, humor, and pride were linked to better performance. We found no evidence of gender differences in the emotions while working the tasks, although boys responded with more tension following an incorrect solution than did girls.     

The role of the researcher’s epistemology in mathematics education: an essay on the case of proof

Is there a shared meaning of “mathematical proof” among researchers in mathematics education? Almost all researchers may agree on a formal definition of mathematical proof. But beyond this minimal agreement, what is the state of our field? After three decades of activity in this area, being familiar with the most influential pieces of work, I realize that the sharing of keywords hides important differences in the understanding. These differences could be obstacles to scientific progress in this area, if they are not made explicit and addressed as such. In this essay I take a sample of research projects which have impacted the teaching and learning of mathematical proof, in order to describe where the gaps are. Then I suggest a possible scientific programme which aspires to strengthen the research practice in this domain. Eventually, I make the additional claim that this programme could hold for other areas of research in mathematics education.     

A case for combinatorics: A research commentary

In this commentary, we make a case for the explicit inclusion of combinatorial topics in mathematics curricula, where it is currently essentially absent. We suggest ways in which researchers might inform the field’s understanding of combinatorics and its potential role in curricula. We reflect on five decades of research that has been conducted since a call by Kapur (1970) for a greater focus on combinatorics in mathematics education. Specifically, we discuss the following five assertions: 1) Combinatorics is accessible, 2) Combinatorics problems provide opportunities for rich mathematical thinking, 3) Combinatorics fosters desirable mathematical practices, 4) Combinatorics can contribute positively to issues of equity in mathematics education, and 5) Combinatorics is a natural domain in which to examine and develop computational thinking and activity. Ultimately, we make a case for the valuable and unique ways in which combinatorics might effectively be leveraged within K-16 curricula.     

Students' Critical Awareness of Voice and Agency in Mathematics Classroom Discourse

This account of my extended conversation with a high school mathematics class focuses on voice and agency. As an investigation of possibilities opened up by introducing mathematics students to what Fairclough (1992) called “critical language awareness” (p. 2), I prompted the students daily to become ever more aware of their language practices in class. The tensions in this conversation proved parallel to the tension in mathematics between individual initiative and convention, a tension that Pickering (1995) called the “dance of agency” (p. 21). Participant students in this classroom-based research resisted the idea of linguistic reference to human agency, although their actual language practice revealed some recognition of human agency.     

Factors Influencing Elementary Teachers' Positioning of African American Girls as Science and Mathematics Learners

Despite recent progress toward gender equity in science and mathematics education, the underachievement of low‐income African American girls remains a challenge when compared with their white counterparts. Furthermore, the causes of this persistent underachievement have not been explored thoroughly. We have initiated a three‐year longitudinal study of how African American girls position themselves in relation to science and mathematics learning from fifth to seventh grade, including the impact, if any, of the positioning of teachers, counselors, and parents on this process. In this article, we share findings examining science and mathematics teachers' actions and perceptions and their positioning of African American girls. This qualitative study used an interpretive design with multiple data sources including classroom observations, interviews, and field notes. Findings reveal that school‐wide policies and teachers' autonomous decisions impact the regularity of science and mathematics instruction, and that teachers do not always conceptualize the girls as science and mathematics achievers, positioning them in negative ways.     

New Perspectives on the Gender Stereotyping of Mathematics

Historically, mathematics has been stereotyped as a male domain, and there is considerable evidence to support this belief. In the last 30 years, mathematics education researchers have uncovered a range of factors contributing to the documented achievement and participation differences that favored males and sought to redress them. Mathematics as a male domain, one of the subscales of the Fennema-Sherman Mathematics Attitude Scales (1976), has been used widely to assess the extent to which mathematics is stereotyped as a masculine sphere. It has been argued that some of the items comprising the subscale are anachronistic and that the subscale scores can no longer be interpreted reliably. In this article we outline the development of two new instruments-the mathematics as a gendered domain instrument and the who and mathematics instrument-that have been designed to overcome the limitations of the original Fennema-Sherman mathematics as a male domain subscale. We also present findings from the administration of the two instruments in Australia, where they were developed, and in the United States, the site of the trials of the original Fennema-Sherman scales. The results indicate that females feel more strongly than males about some aspects of gender stereotyping in mathematics although, in general, most students feel that mathematics is gender neutral.     

New Perspectives on the Gender Stereotyping of Mathematics

Historically, mathematics has been stereotyped as a male domain, and there is considerable evidence to support this belief. In the last 30 years, mathematics education researchers have uncovered a range of factors contributing to the documented achievement and participation differences that favored males and sought to redress them. Mathematics as a male domain, one of the subscales of the Fennema-Sherman Mathematics Attitude Scales (1976), has been used widely to assess the extent to which mathematics is stereotyped as a masculine sphere. It has been argued that some of the items comprising the subscale are anachronistic and that the subscale scores can no longer be interpreted reliably. In this article we outline the development of two new instruments-the mathematics as a gendered domain instrument and the who and mathematics instrument-that have been designed to overcome the limitations of the original Fennema-Sherman mathematics as a male domain subscale. We also present findings from the administration of the two instruments in Australia, where they were developed, and in the United States, the site of the trials of the original Fennema-Sherman scales. The results indicate that females feel more strongly than males about some aspects of gender stereotyping in mathematics although, in general, most students feel that mathematics is gender neutral.     

Scientific World Building on the Edge of Chaos: High School Students' Beliefs About Mathematics and Science

This study investigated high school students' beliefs about mathematics and science during a four week summer residential mathematics and science program. Beliefs about mathematical and scientific truths, the value and importance of mathematics and science inquiry, gender equity and ability with respect to pursuit of mathematics and science careers, the relationship between mathematics and technology, and the role of science in society were examined. Habermasian ways of knowing were used to categorize student beliefs and determine student world views. Implications of this study include suggested changes in the organizational dynamics of schooling to better prepare our students for surviving in the complexity of the 21st century and reducing dissonance between the “classical” educational viewpoints and the “chaotic” world.