/pdf/review-of-principles-to-actions-ensuring-mathematical-2na9nugf41.pdf

Review of Principles to Actions: Ensuring Mathematical Success for All

Observation-based frameworks of instructional quality differ largely in the approach and the purposes of their development, their theoretical underpinnings, the instructional aspects covered, their operationalization and measurement, as well as the existing evidence on reliability and validity. The current paper summarizes and reflects on these differences by considering the 12 frameworks included in this special issue. By comparing the analysis of three focal mathematics lessons through the lens of each framework as presented in the preceding papers, this paper also examines the similarities, differences, and potential complementarities of these frameworks to describe and evaluate mathematics instruction. To do so, a common structure for comparing all frameworks is suggested and applied to the analyses of the three selected lessons. The paper concludes that although significant work has been pursued over the past years in exploring instructional quality through classroom observation frameworks, the field would benefit from establishing agreed-upon standards for understanding and studying instructional quality, as well as from more collaborative work.

Classroom observation frameworks for studying instructional quality: looking back and looking forward

Member checking is commonly used in qualitative research as a means to maintain validity; however, little has been published about the effects the member checking process may have on participants. In this article, I provide the experiences of two participants in a qualitative case study and argue how member checking should be used as a reflective space for participants.

/pdf/exploring-the-function-of-member-checking-tzywmhuhy7.pdf

Exploring the Function of Member Checking

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students' responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research, are discussed.

A Response to Mathematical Problem Posing as a Measure of Curricular Effect on Students’ Learning

A disability studies in mathematics education review of intellectual disabilities: Directions for future inquiry and practice

The Instructional Quality Assessment (IQA) identifies the nature and quality of classroom instruction by considering students’ opportunities to engage in cognitively demanding mathematical work and discussions The IQA assesses ambitious mathematics instruction based on the following dimensions: potential of the task, task implementation, rigor of the discussion, teacher’s questions, and accountable talk (eg, teacher’s and students’ talk moves related to linking and press) The IQA rubrics have been tested for reliability and validity by the IQA team and external researchers The IQA has previously been used in research to assess ambitious mathematics instruction Through looking at three episodes of classroom instruction, this article will highlight how the IQA can go beyond assessing instruction and serve as a tool to enhance instruction by providing formative feedback to mathematics teachers targeted towards planning and implementing cognitively demanding tasks While the IQA’s specific focus on assessing ambitious mathematics instruction may limit its applicability in research, when used as a professional learning tool, the IQA rubrics can provide explicit pointers to frame teachers’ learning, self-reflection, and instructional change

The Instructional Quality Assessment as a tool for reflecting on instructional practice

This special issue was inspired by the Critical Approaches to Disability in Mathematics Education working group, founded at the Psychology of Mathematics Education North America conference in Tucso...

https://www.tandfonline.com/doi/pdf/10.1080/19477503.2018.1463006

Rehumanizing the Mathematics Education of Students with Disabilities; Critical Perspectives on Research and Practice

We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.

Discourse Actions to Promote Student Access

This chapter will provide readers with an overview of professional development created and enacted to support teachers' selection and implementation of cognitively demanding tasks using the Instructional Quality Assessment as the professional development tool. This case study seeks to give voice to mathematics teachers in third through eighth grades who participated in the professional development as they share their perspectives on using the instructional quality assessment rubrics and structure of professional development. The goal of this chapter is to provide an overview of the structure of the professional development, and share the aspects of the professional development the teachers identified as supportive or a hindrance when planning and implementing tasks in their mathematics classrooms. With this information, the article concludes by discussing ideas for future professional development aimed at providing teachers with instructional practices to incorporate into classrooms.

Amber G. Candela

Papers

Exploring the Function of Member Checking

The Instructional Quality Assessment as a tool for reflecting on instructional practice

Rehumanizing the Mathematics Education of Students with Disabilities; Critical Perspectives on Research and Practice

Discourse Actions to Promote Student Access

Teachers' Perspectives Using the Instructional Quality Assessment as a Professional Development Tool