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Heather West, Emily Elrod, Karen Hollebrands, and Valerie Faulkner

In this editorial, an analysis of articles published in the Mathematics Teacher Educator journal (MTE) from 2012 to 2020, which describes the knowledge base for mathematics teacher educators addressed by MTE authors, is presented. This analysis builds on similar work conducted four years ago (). These more recent findings demonstrate that articles focusing on teacher knowledge; mathematical content; student thinking and reasoning; and models of teacher preparation or in-service professional development (PD) have been the most frequently published in MTE. In contrast, a limited number of articles have focused on discourse; diversity, equity, and language; technology; and methods of research. This examination allows us to assess as a community where we were, where we are, and where we might go in the future.

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M. Kathleen Heid, Karen F. Hollebrands and Linda W. Iseri

This article describes the successful use of a computer algebra system (CAS) by Kevin, a seventh-grade student, as he worked on a problem involving functions far more difficult than the functions that he encountered in his mathematics class. CAS clearly supported Kevin's reasoning but did not provide the solution. What place does this powerful technology have in our classrooms? For classroomtested CAS uses and for thought-provoking articles about CAS experiences, watch for the November 2002 CAS focus issue of the Mathematics Teacher.

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M. Heid, Glendon Blume, Karen Hollebrands and Cynthia Piez

More than with any other recent technology, thinking about incorporating computer algebra systems (CASs) in secondary mathematics raises major concerns. Teachers and others wonder whether CAS use will hamper development of or lead to atrophy of by-hand symbolic-manipulation skills. We also wonder about the mathematics that students might learn when the large quantity of time usually spent on those by-hand skills is used for other mathematical purposes. Fifteen years of research on CAS use can inform our curricular decisions.

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Karen F. Hollebrands, AnnaMarie Conner and Ryan C. Smith

Prior research on students' uses of technology in the context of Euclidean geometry has suggested it can be used to support students' development of formal justifications and proofs. This study examined the ways in which students used a dynamic geometry tool, NonEuclid, as they constructed arguments about geometric objects and relationships in hyperbolic geometry. Eight students enrolled in a college geometry course participated in a task-based interview that was focused on examining properties of quadrilaterals in the Poincaré disk model. Toulmin's argumentation model was used to analyze the nature of the arguments students provided when they had access to technology while solving the problems. Three themes related to the structure of students' arguments were identified. These involved the explicitness of warrants provided, uses of technology, and types of tasks.

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P. Holt Wilson, Hollylynne Stohl Lee and Karen F. Hollebrands

This study investigated the processes used by prospective mathematics teachers as they examined middle-school students' work solving statistical problems using a computer software program. Students' work on the tasks was captured in a videocase used by prospective teachers enrolled in a mathematics education course focused on teaching secondary mathematics with technology. The researchers developed a model for characterizing prospective teachers' attention to students' work and actions and interpretations of students' mathematical thinking. The model facilitated the identification of four categories: describing, comparing, inferring, and restructuring. Ways in which the model may be used by other researchers and implications for the design of pedagogical tasks for prospective teachers are discussed.

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Richard Lesh, Kathryn B. Chval, Karen Hollebrands, Clifford Konold, Michelle Stephan, Erica N. Walker and Jeffrey J. Wanko

For roughly 35 years, the NCTM Research Presession has been held 1 or 2 days prior to the NCTM Annual Conference—hence the word presession. Beginning with the 2014 meeting in New Orleans, the NCTM Research Presession will be rebranded as the NCTM Research Conference. This change of name is intended to emphasize the critical role that research should play in our efforts to improve mathematics education. The NCTM Research Committee thought this an appropriate occasion to invite Richard Lesh, who was instrumental in the founding of the Research Presession, to join the members of the current Research Committee in reflecting on its formation, the hopes he and other kindred spirits had in mind when they started it, and the current state and future of research in our field.

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James E. Tarr, Erica N. Walker, Karen F. Hollebrands, Kathryn B. Chval, Robert Q. Berry III, Chris L. Rasmussen, Cliff Konold and Karen King

During the past 2 decades, significant changes in mathematics curriculum standards and policies have brought greater attention to assessment instruments, practices, purposes, and results. In moving toward stronger accountability, the No Child Left Behind Act (NCLB) of 2001 (NCLB, 2002) mandates that school districts receiving funding under NCLB formulate and disseminate annual local report cards that include information on how students and each school in the district performed on state assessments. This mandate has not only facilitated a growth in state testing (Wilson, 2007) but also influenced the teaching of mathematics (Seeley, 2006). More recently, the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO) crafted and launched the Common Core State Standards for Mathematics (NGA Center & CCSSO, 2010), which have been formally adopted by the vast majority of U.S. states and territories. The Common Core State Standards for Mathematics (CCSSM) specifies standards for mathematical content by grade in K–8 and by conceptual categories at the secondary level and identifies key Standards for Mathematical Practice that should be present in K–12 instruction. The CCSSM represents an unprecedented initiative to raise academic standards in school mathematics that will inevitably influence the development of curriculum materials, teaching, and assessment practices.

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Daniel J. Heck, James E. Tarr, Karen F. Hollebrands, Erica N. Walker, Robert Q. Berry III, Patricia C. Baltzley, Chris L. Rasmussen and Karen D. King

The National Council of Teachers of Mathematics (NCTM) espouses priorities to foster stronger linkages between mathematics education research and teaching practice. Of the five foundational priorities, one is directly focused on research, indicating NCTM's commitment to “ensure that sound research is integrated into all activities of the Council” (NCTM, n.d.). Another priority specifically references the relationship between research and mathematics teaching; the priority on curriculum, instruction, and assessment states that NCTM pledges to “Provide guidance and resources for developing and implementing mathematics curriculum, instruction, and assessment that are coherent, focused, well-articulated, and consistent with research in the field [emphasis added], and focused on increasing student learning” (NCTM, n.d.).