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Research paper thumbnail of Becoming More Mathematical: New Directions for Describing and Designing for Positive Dispositions Toward Mathematics

This symposium brings together researchers interested in studying mathematical proficiency throug... more This symposium brings together researchers interested in studying mathematical proficiency through a focus on students’ dispositions toward mathematics their ideas and affect about mathematics and their patterns of engagement with it. While dispositions are useful for connecting important aspects of students’ proficiency, they are also broad and challenging to operationalize in empirical contexts. This symposium aims to promote dialogue around the meaning of dispositions as an analytic construct and to explore their relationship to other constructs relevant to helping learners become mathematical. We also aim to demonstrate that different methodological orientations allow us to see different aspects of what we all agree to call “dispositions”. We present empirical work which address two foci within research on dispositions –operationalizing in ways that enable documentation in a classroom context, and designing learning environments which foster positive dispositions to mathematics ...

Research paper thumbnail of Why Engaging in Mathematical Practices May Explain Stronger Outcomes in Affect and Engagement: Comparing Student-Driven With Highly Guided Inquiry

Journal of the Learning Sciences, 2014

This article investigates why students reported liking a student-driven learning design better th... more This article investigates why students reported liking a student-driven learning design better than a highly guided design despite equivalent gains in knowledge assessments in both conditions. We created two learning designs based on the distinction in the literature between student-driven and teacher-led approaches. One teacher assigned each of her two 5th-grade classes to one design (n = 52); both designs addressed the mathematical concepts for the same amount of time. Data were collected using written assessments, surveys, and video. Students in both classes improved equivalently on assessments. On surveys, students in the studentdriven condition were significantly more positive about learning. Video was coded to examine why students were more positive in the student-driven design. This analysis showed students engaging more frequently with data in discussing strategies, questioning peers, and aligning outcomes with prior experiences. We trace the association between students' positive responses to learning and richer engagement in mathematical practices to specific features of the student-driven design. Furthermore, we reject competing explanations (e.g., amount of off-task behavior or adult intervention). We conclude that designing learning opportunities that promote mathematical

Research paper thumbnail of Re-storying practice: Using stories about students to advance mathematics education reform

Teaching and Teacher Education, 2013

ABSTRACT

Research paper thumbnail of Not in their name: re-interpreting discourses of STEM learning through the subjective experiences of minoritized girls

Race Ethnicity and Education, 2019

This paper problematizes the enduring conscription of STEM learning in discourses of U.S. global ... more This paper problematizes the enduring conscription of STEM learning in discourses of U.S. global ascendancy, neoliberalism and militarism. Drawing on ethnographic data, we explore how girls of color make meaning of their everyday experiences in two settings: a racially tracked mathematics class in a suburban high school and a STEAM based after-school program in a working class urban community. The stories of these girlsseparated by time, place, age, and social histories but bound by sensibilities grown in their Immigrant families and learning contextscontest U.S. hegemony as the primary rationale for STEM learning; challenge individual gain at the expense of another; problematize what counts as science while insisting on its creative convergence with joy; and honor their ingenuity and humanity. Challenging representational and respectability politics, we consider how dignity may better account for the complexity of their experiences and serve as a resource for research, pedagogy and design.

Research paper thumbnail of Integrating Power to Advance the Study of Connective and Productive Disciplinary Engagement in Mathematics and Science

Cognition and Instruction, 2019

Engle and Conant's productive disciplinary engagement (PDE) framework has significantly advanced ... more Engle and Conant's productive disciplinary engagement (PDE) framework has significantly advanced the study of learning in mathematics and science. This artilce revisits PDE through the lens of critical education research. Our analysis synthesizes two themes of power: epistemic diversity, and historicity and identity. We argue that these themes, when integrated into PDE, strengthen it as a tool for design and analysis of disciplinary learning in relation to power and personhood, and describe the broadened framework of connective and productive disciplinary engagement (CPDE). By comparing and contrasting the use of PDE and CPDE in relation to two cases of classroom learning-for science, Warren et al.'s metamorphosis and for mathematics, Godfrey and O'Connor's measurement-we demonstrate how CPDE surfaces issues of history, power, and culture that may otherwise be overlooked by PDE alone. In particular, we analyze how CPDE makes visible unseen identities and generative resources of disciplinary knowing and doing among minoritized students. We discuss how the revised framework redresses epistemic injustice experienced by minoritized learners held to the narrow rubric of western epistemologies and compels close attention to the diversity of human activity in mathematics and science. Further, we elaborate how it provides a structure for teachers, teacher educators, and researchers to design and analyze learning environments as safeguarding the rightful presence of minoritized learners in STEM classrooms and beyond. Among its many contributions, the learning sciences has progressed our understanding of students' disciplinary engagement in and out of school. Within this body of research, Engle and Conant's (2002) productive disciplinary engagement (PDE) has made an indelible mark as a framework of design and analysis of disciplinary learning in relation to cultural and linguistic diversity (Engle, 2012). It emerged through the study of science learning in Fostering

Research paper thumbnail of Mathematics as a Discursive and Embodied Practice

This chapter examines major lines of inquiry in mathematics education through the prism of cultur... more This chapter examines major lines of inquiry in mathematics education through the prism of cultural historical activity theory, focusing on the language and discursive practices in the teaching and learning of school mathematics. We make an analytic distinction between the language in and of mathematics learning in classrooms, noting the pitfalls of dichotomizing the language of the classroom and the language in mathematical learning or ignoring their interrelations. Specifically, we reviewed work that framed the role of everyday discourse practices as supporting the development of scientific discourse practices. In line with several mathematics education scholars, we challenge this framing by revisiting the theoretical principles from the work of Vygotsky, Engestrom, and Cole, among others, to show how scientific or school-based mathematical learning “grows down into” the everyday, and

Research paper thumbnail of When Dissent and Debate Risk Fracturing Mathematics Learning Communities

Research paper thumbnail of Another Step Forward: Engaging the Political in Learning

Cognition and Instruction

Research paper thumbnail of Nature, Neglect and Nuance: Changing Accounts of Sex, Gender and Mathematics

The SAGE Handbook of Gender and Education, 2006

In this section, authors examine past and present research in a range of school subjects. In almo... more In this section, authors examine past and present research in a range of school subjects. In almost every case, they point out historical shifts that have occurred in the study of gender and school subjects. In many of these fields, early research worked within static notions of gender and identity, and focused on making girls fit into male-defined notions of success and achievement in school. From work that accepted dichotomous positioning of girls and boys, research has shifted more recently to work that examines the construction of gendered selves within discourses that often privilege existing gender positions in political, social and economic structures. Current researchers also explore the importance of geopolitical location, local knowledge and practice, which are necessary for understanding the negotiation of gendered selves within different school subjects and fields of study. The authors in this section note that research in gender and school subjects is inherently political; much of it documents the changes that need to be made to address inadequacies and inequalities in schools and disciplines. In Chapter 15, 'Nature, Neglect And Nuance: Changing Accounts Of Sex, Gender And Mathematics', Jo Boaler and Tesha Sengupta-Irving point out that some of the prior work on gender and mathematics has contributed to a discourse about girls' and women's inadequacies in the field of mathematics. They argue for an approach to studying gender and mathematics that is situated, relational and focused on the interactions between people and environments that promote or inhibit inequality. In Chapter 16, 'Engaging Girls in Science', Angela Calabrese Barton and Nancy Brickhouse argue that rather than focusing on standard achievement in school-related activities and assessments, educators need to encourage SECTION III

Research paper thumbnail of Becoming More Mathematical: New Directions for Describing and Designing for Positive Dispositions Toward Mathematics

This symposium brings together researchers interested in studying mathematical proficiency throug... more This symposium brings together researchers interested in studying mathematical proficiency through a focus on students’ dispositions toward mathematics their ideas and affect about mathematics and their patterns of engagement with it. While dispositions are useful for connecting important aspects of students’ proficiency, they are also broad and challenging to operationalize in empirical contexts. This symposium aims to promote dialogue around the meaning of dispositions as an analytic construct and to explore their relationship to other constructs relevant to helping learners become mathematical. We also aim to demonstrate that different methodological orientations allow us to see different aspects of what we all agree to call “dispositions”. We present empirical work which address two foci within research on dispositions –operationalizing in ways that enable documentation in a classroom context, and designing learning environments which foster positive dispositions to mathematics ...

Research paper thumbnail of Why Engaging in Mathematical Practices May Explain Stronger Outcomes in Affect and Engagement: Comparing Student-Driven With Highly Guided Inquiry

Journal of the Learning Sciences, 2014

This article investigates why students reported liking a student-driven learning design better th... more This article investigates why students reported liking a student-driven learning design better than a highly guided design despite equivalent gains in knowledge assessments in both conditions. We created two learning designs based on the distinction in the literature between student-driven and teacher-led approaches. One teacher assigned each of her two 5th-grade classes to one design (n = 52); both designs addressed the mathematical concepts for the same amount of time. Data were collected using written assessments, surveys, and video. Students in both classes improved equivalently on assessments. On surveys, students in the studentdriven condition were significantly more positive about learning. Video was coded to examine why students were more positive in the student-driven design. This analysis showed students engaging more frequently with data in discussing strategies, questioning peers, and aligning outcomes with prior experiences. We trace the association between students' positive responses to learning and richer engagement in mathematical practices to specific features of the student-driven design. Furthermore, we reject competing explanations (e.g., amount of off-task behavior or adult intervention). We conclude that designing learning opportunities that promote mathematical

Research paper thumbnail of Re-storying practice: Using stories about students to advance mathematics education reform

Teaching and Teacher Education, 2013

ABSTRACT

Research paper thumbnail of Not in their name: re-interpreting discourses of STEM learning through the subjective experiences of minoritized girls

Race Ethnicity and Education, 2019

This paper problematizes the enduring conscription of STEM learning in discourses of U.S. global ... more This paper problematizes the enduring conscription of STEM learning in discourses of U.S. global ascendancy, neoliberalism and militarism. Drawing on ethnographic data, we explore how girls of color make meaning of their everyday experiences in two settings: a racially tracked mathematics class in a suburban high school and a STEAM based after-school program in a working class urban community. The stories of these girlsseparated by time, place, age, and social histories but bound by sensibilities grown in their Immigrant families and learning contextscontest U.S. hegemony as the primary rationale for STEM learning; challenge individual gain at the expense of another; problematize what counts as science while insisting on its creative convergence with joy; and honor their ingenuity and humanity. Challenging representational and respectability politics, we consider how dignity may better account for the complexity of their experiences and serve as a resource for research, pedagogy and design.

Research paper thumbnail of Integrating Power to Advance the Study of Connective and Productive Disciplinary Engagement in Mathematics and Science

Cognition and Instruction, 2019

Engle and Conant's productive disciplinary engagement (PDE) framework has significantly advanced ... more Engle and Conant's productive disciplinary engagement (PDE) framework has significantly advanced the study of learning in mathematics and science. This artilce revisits PDE through the lens of critical education research. Our analysis synthesizes two themes of power: epistemic diversity, and historicity and identity. We argue that these themes, when integrated into PDE, strengthen it as a tool for design and analysis of disciplinary learning in relation to power and personhood, and describe the broadened framework of connective and productive disciplinary engagement (CPDE). By comparing and contrasting the use of PDE and CPDE in relation to two cases of classroom learning-for science, Warren et al.'s metamorphosis and for mathematics, Godfrey and O'Connor's measurement-we demonstrate how CPDE surfaces issues of history, power, and culture that may otherwise be overlooked by PDE alone. In particular, we analyze how CPDE makes visible unseen identities and generative resources of disciplinary knowing and doing among minoritized students. We discuss how the revised framework redresses epistemic injustice experienced by minoritized learners held to the narrow rubric of western epistemologies and compels close attention to the diversity of human activity in mathematics and science. Further, we elaborate how it provides a structure for teachers, teacher educators, and researchers to design and analyze learning environments as safeguarding the rightful presence of minoritized learners in STEM classrooms and beyond. Among its many contributions, the learning sciences has progressed our understanding of students' disciplinary engagement in and out of school. Within this body of research, Engle and Conant's (2002) productive disciplinary engagement (PDE) has made an indelible mark as a framework of design and analysis of disciplinary learning in relation to cultural and linguistic diversity (Engle, 2012). It emerged through the study of science learning in Fostering

Research paper thumbnail of Mathematics as a Discursive and Embodied Practice

This chapter examines major lines of inquiry in mathematics education through the prism of cultur... more This chapter examines major lines of inquiry in mathematics education through the prism of cultural historical activity theory, focusing on the language and discursive practices in the teaching and learning of school mathematics. We make an analytic distinction between the language in and of mathematics learning in classrooms, noting the pitfalls of dichotomizing the language of the classroom and the language in mathematical learning or ignoring their interrelations. Specifically, we reviewed work that framed the role of everyday discourse practices as supporting the development of scientific discourse practices. In line with several mathematics education scholars, we challenge this framing by revisiting the theoretical principles from the work of Vygotsky, Engestrom, and Cole, among others, to show how scientific or school-based mathematical learning “grows down into” the everyday, and

Research paper thumbnail of When Dissent and Debate Risk Fracturing Mathematics Learning Communities

Research paper thumbnail of Another Step Forward: Engaging the Political in Learning

Cognition and Instruction

Research paper thumbnail of Nature, Neglect and Nuance: Changing Accounts of Sex, Gender and Mathematics

The SAGE Handbook of Gender and Education, 2006

In this section, authors examine past and present research in a range of school subjects. In almo... more In this section, authors examine past and present research in a range of school subjects. In almost every case, they point out historical shifts that have occurred in the study of gender and school subjects. In many of these fields, early research worked within static notions of gender and identity, and focused on making girls fit into male-defined notions of success and achievement in school. From work that accepted dichotomous positioning of girls and boys, research has shifted more recently to work that examines the construction of gendered selves within discourses that often privilege existing gender positions in political, social and economic structures. Current researchers also explore the importance of geopolitical location, local knowledge and practice, which are necessary for understanding the negotiation of gendered selves within different school subjects and fields of study. The authors in this section note that research in gender and school subjects is inherently political; much of it documents the changes that need to be made to address inadequacies and inequalities in schools and disciplines. In Chapter 15, 'Nature, Neglect And Nuance: Changing Accounts Of Sex, Gender And Mathematics', Jo Boaler and Tesha Sengupta-Irving point out that some of the prior work on gender and mathematics has contributed to a discourse about girls' and women's inadequacies in the field of mathematics. They argue for an approach to studying gender and mathematics that is situated, relational and focused on the interactions between people and environments that promote or inhibit inequality. In Chapter 16, 'Engaging Girls in Science', Angela Calabrese Barton and Nancy Brickhouse argue that rather than focusing on standard achievement in school-related activities and assessments, educators need to encourage SECTION III