Michelle Stephan

Participating in Classroom Mathematical Practices

In this article, we describe a methodology for analyzing the collective learning of the classroom community in terms of the evolution of classroom mathematical practices. To develop the rationale for this approach, we first ground the discussion in our work as mathematics educators who conduct classroom-based design research. We then present a sample analysis taken from a 1st-grade classroom teaching experiment that focused on linear measurement to illustrate how we coordinate a social perspective on communal practices with a psychological perspective on individual students’ diverse ways of reasoning as they participate in those practices. In the concluding sections of the article, we frame the sample analysis as a paradigm case in which to clarify aspects of the methodology and consider its usefulness for design research.

Improving the Quality of Mathematics Teaching with Effective Planning Practices.

Although it has been two decades since National Council of Teachers of Mathematics Standards were published, research underlines the lack of essential practices for quality reform teaching. The literature also emphasizes the importance of planning in reform teaching although few studies focus directly on the planning of the teacher. This study attempts to shed light on teacher planning through a particularistic case study within a design research experiment which was performed to improve the quality of teaching. In particular, this study aims to extract the planning practices of an expert seventh-grade mathematics teacher before and during instruction on integers. The extracted practices were interpreted through the teaching-in-context theory, which uses beliefs, goals, and knowledge as the backbone of the analysis. The results indicate that five core practices underlay the development of effective planning: preparation, reflection, anticipation, assessment, and revision. Each practice included multiple actions performed in an environment of collaboration.

Guided Reinvention: What Is It and How Do Teachers Learn This Teaching Approach?

In this chapter, the theoretical construct of guided reinvention is extended to include desirable pedagogical practices for teachers implementing RME sequences. First, we explain what a guided reinvention teaching approach looks like and how it evolved out of over 25 years of research. We then articulate the planning and teaching practices of guided reinvention teachers and describe how those practices move beyond what many call “inquiry approaches” to mathematics teaching. We end the chapter by offering a set of learning goals that professional developers might use when mentoring aspiring guided reinvention teachers.

Teaching Integers to Students with Disabilities: Three Case Studies

The main purpose of this chapter is to document the reasoning of three students, two with disabilities and one with mathematical difficulties, as they participated in and contributed to the classroom mathematical practices established by a seventh-grade class during integer instruction. The integer instructional sequence was designed to support students’ increasingly sophisticated reasoning about integers and meaning making for integer addition and subtraction. This chapter builds on our prior work that identified the classroom mathematical practices established by the teacher and students during implementation of the integer sequence (Stephan M, Akyuz D, J Res Math Edu 43:428–464, 2012). In particular, because the integer sequence was implemented in an inclusive setting, we have the unique opportunity to document the learning of two students with disabilities and one with difficulties as they participated in an inquiry environment, contributing to the development of the classroom mathematical practices. These three students participated in a classroom teaching experiment held in a co-taught classroom in which students with disabilities were included with regular education students. Therefore, the three case studies we present illustrate a rare analysis of the integer learning of students with disabilities. The primary research question that we seek to answer through this chapter is, how do students with learning disabilities make meaningful contributions to the development of classroom mathematical practices and gain intellectual autonomy in the process of learning integer concepts and operations?

Correction to: Introduction to this Special Issue (found in Int J of Sci and Math Educ (2017) 15 (Suppl 1):S1–S4)

This correction stands to correct the reference found in the reference list of the introductory paper above.

Correction to: Epilogue (found in Int J of Sci and Math Educ (2017) 15 (Suppl 1):S1–S4)

This correction stands to correct the reference found in the reference list of the closing paper above.

Contributing to the Development of Grand Challenges in Maths Education

David Barnes, Associate Executive Director for Research, Learning and Development, National Council of Teachers of Mathematics Trena Wilkerson, Professor, Curriculum and Instruction Graduate Program Director, Department of Curriculum & Instruction, Baylor University & NCTM Board of Directors Michelle Stephan, Assistant Professor, Department of Middle, Secondary, and K-12 Education. University of North Carolina – Charlotte.