Kara Jackson

Assessing the Quality of the Common Core State Standards for Mathematics

The authors comment on Porter, McMaken, Hwang, and Yang’s recent analysis of the Common Core State Standards for Mathematics by critiquing their measures of the focus of the standards and the absence of an assessment of coherence. The authors then consider whether the standards are an improvement over most state mathematics standards by discussing whether the core mathematics ideas on which they focus are appropriate, whether individual standards are organized into coherent learning progressions, and whether their implementation is feasible. They question whether schools and districts currently have the capacity to support effective implementation, and they call for improvement-oriented investigations that can inform the development of effective implementation models.

Supporting African American Students’ Learning of Mathematics: A Problem of Practice

This article reports on a review of the mathematics education research literature 1989-May 2011 specific to K-12 African American students’ opportunities to learn mathematics. Although we identify important developments in the literature, we conclude that the existing research base generally remains at the level of broad principles or orientations to teaching and is therefore inadequate for specifying forms of instructional practice that support African American students’ participation in rigorous mathematical activity. We suggest a research agenda focused on specifying forms of practice that are empirically shown to support African American students’ learning of mathematics and development of productive mathematical identities.

The Consequences of Experimentalism in Formulating Recommendations for Policy and Practice in Mathematics Education

In this response to Foundations for Success: The Final Report of the National Mathematics Advisory Panel (2008), the authors argue that the Panel’s assumption that only experimental research studies can produce scientific evidence limits the power of the Panel’s recommendations to improve mathematics teaching and learning. The authors first discuss the theoretical underpinnings, potential contributions, and limitations of experimental studies. Against this background, they focus on three issues that are central to improving mathematics learning and teaching, those of equity, the nature and content of textbooks, and graduate education. In doing so, the authors illustrate the limitations of developing implications for policy and practice by relying exclusively on research conducted using a single methodology.

Approaching Participation in School-Based Mathematics as a Cross-Setting Phenomenon.

This article reports on an ethnographic study of a 10-year-olds pursuit of school-based mathematics across school and home to suggest that participating in school-based mathematics is a cross-setting phenomenon in at least 2 ways. First, I illustrate how accomplishing school-based mathematics literally extends into the home and how individuals recruit resources from their histories of participation in alternative settings to accomplish the work of school-based mathematics. Second, I show how a youths social identification in the classroom is shaped by his teachers partial accounts of how learning is arranged for in the home. Approaching participation in school-based mathematics as a cross-setting phenomenon illustrates the complexity inherent in participating in schooling and raises questions about how to coordinate schooling across school and home settings.

Examining Relations between Teachers’ Explanations of Sources of Students’ Difficulty in Mathematics and Students’ Opportunities to Learn

The nature of mathematical activity and discourse that teachers foster in classrooms is likely influenced by their explanations of sources of students’ difficulty. Several small-scale qualitative studies suggest that how teachers make sense of student difficulty matters for whether they engage all of their students in rigorous mathematical activity. In this article we extend such work to a sample of 165 teachers in four large urban districts. In particular, we investigated the extent to which teachers’ explanations of sources of students’ difficulty in mathematics (as due to traits of students or the communities they come from, or as in relation to the opportunities to learn provided in classrooms) are related to students’ participation in quality mathematical discourse. We found that they are significantly related and that they depend on the racial and linguistic classroom composition of students they teach.

Articulating the “How,” the “For What,” the “For Whom,” and the “With Whom” in Concert: A Call to Broaden the Benchmarks of our Scholarship

Cognition and Instruction has developed a well-deserved reputation for publishing empirically grounded scholarship that makes rich theoretical contributions to what it means to “think, learn, know, and teach” (Enyedy & Hall, 2017, p. 2). As described in our Aims & Scope, the commitment to theory building in this journal “preferentially attends to the ‘how’ of learning.” From the establishment of the journal in 1984, prioritizing the how has been an intellectual endeavor to push back on frameworks that diminish the complexity and contextuality of learning. At least implicitly, if not explicitly, this journal’s emphasis has been a political stance that strives to influence and redesign the environments in which people learn. As editors, we hope to build on this rich tradition of Cognition and Instruction. We call on those of us who intend to publish in this journal to more clearly attend to the ways in which the for what, for whom, and with whom of teaching and learning are necessarily intertwined with the how of learning—an effort that asks us to carefully examine and address the cultural and political contexts and consequences of our scholarship. We also hope to unequivocally broaden this journal’s usage of teaching and learning to include and appeal to scholars whose work on culture and politics may fall outside traditional notions of cognition and instruction. Our invitation is meant to enrich and not diminish the theoretically and methodologically rich contributions to teaching and learning for which Cognition and Instruction has become known. As a scholarly community, we continue to develop a wide array of theoretical, methodological, and analytical lenses and tools to attend to cognition and its social and interactional nature.We have also becomemore responsive to moves across the social and behavioral sciences to attend to the diversity of human cognition and development beyond participants, methods, and purposes that are rooted in the epistemologies and values of dominant groups in Western, industrialized nations (Henrich, Heine, & Norenzayan, 2010; Bang et al., 2016; Medin, Ojalehto, Marin, & Bang, 2017; Smith, 1999).We are asking this scholarly community to join the effort in the broader fields of the social and behavioral sciences to expand what we know about human possibilities. Indeed, we are already headed in that direction. A growing body of research published in this journal has started tomake headway on how power, race, and culture intersect with cognition, learning, and teaching (Bang & Vossoughi, 2016; Jurow et al, 2016; Philip, 2011; Philip, Olivares-Pasillas, & Rocha, 2016; Rubel et al., 2016; Vakil, Royston, Nasir, & Kirshner, 2016; Zavala, 2016). These perspectives emphasize that socially and locally meaningful forms of power differentially shape opportunities to learn, aswell as the values and consequences ofwhat is learned (Gutiérrez& Jurow, 2016). They elucidate how power, itself, is partially constituted and contested through learning. These collective advances in our scholarly community highlight new possibilities for bringing the for what, for whom, and with whom to bear on studies of the how of cognition and instruction. The unique opportunity that this journal presents—to generate scholarship in which these four dimensions of teaching and learning are fundamentally tethered—is what we find most promising in contributing to foundational knowledge and learning contexts that matter for young people, their families, and communities.

Supporting Improvements in the Quality of Mathematics Teaching on a Large Scale

Research on the teaching and learning of mathematics has made significant progress in recent years. However, this work has had only limited impact on classroom instruction in many countries. We report on an eight-year project in which we partnered with several large urban school districts in the U.S. that were attempting to support mathematics teachers’ development of ambitious, inquiryoriented instructional practices. We first give an overview of the project and describe these researcher-practitioner partnerships, which were conducted as design research studies at the system level. We then present findings as they relate to key elements of a coherent system for instructional improvement. These elements include: explicit student learning goals and an associate vision of highquality mathematics instruction; curriculum materials and associated resources; pull-out teacher professional development; school-based teacher collaborative meetings; teachers’ informal professional networks; teacher leaders’ practices in providing job-embedded support for other teachers’ learning; and supplemental supports for currently struggling students. We conclude by arguing that additional studies are needed that frame large-scale instructional improvement as an explicit focus of investigation if mathematics education research is to realize its potential by contributing to improvements in the quality of mathematics instruction for large numbers of students.

Educational Design Research to Support System-Wide Instructional Improvement

In this chapter, we describe a methodology for conducting educational design research to support system-wide instructional improvement in mathematics and draw on one of the few design studies that does this as an illustrative case. Design studies conducted at the level of an educational system are interventionist in nature, and can address both the complexity of educational settings and the problems that educational system leaders, school leaders, and teachers encounter as they work to improve the quality of classroom instruction, school instructional leadership, and ultimately, students’ mathematics learning. This chapter describes the theoretical background for this approach, in which the issue of what it takes to support instructional improvement on a large scale is framed as an explicit focus of empirical investigation.

Storytelling in a Fifth Grade Mathematics Classroom: Matters of Content and Personhood

Grounded in an analysis of “storytelling” in a fifth grade mathematics classroom, this chapter highlights the importance of explicitly attending to matters of personhood as well as content in mathematics classrooms. Data sources include field notes based on ethnographic observations of 60 lessons across a year, and semi-structured interviews with the teacher and two focal students. The teacher regularly told stories to the students in which numbers, mathematics operations, and/or procedures were anthropomorphized in an effort to spark students’ interest and engagement in the content and to serve as resources for the students to draw on when solving mathematics problems. However, the stories told served to construct mathematics and personhood in problematic ways. On the basis of this case, I suggest the importance of putting front and center concerns with personhood when making pedagogical decisions; and of employing a critical lens in doing so.