Melissa D. Boston

Middle School Mathematics Instruction in Instructionally Focused Urban Districts.

Direct assessments of instructional practice (e.g., classroom observations) are necessary to identify and eliminate opportunity gaps in students’ learning of mathematics. This study examined 114 middle school mathematics classrooms in four instructionally focused urban districts. Results from the Instructional Quality Assessment identified high percentages of lessons featuring cognitively challenging tasks, but declines in cognitive challenge during implementation and discussions. Overall instructional quality exceeded results from studies with nationally representative samples and paralleled results of studies of instructionally focused urban middle schools. Significant differences existed between districts, favoring the district with veteran teachers, long-term use of Standards-based curricula, and professional development initiatives.

Investigating How to Support Principals as Instructional Leaders in Mathematics

We present a framework for considering principals’ knowledge and actions to support high-quality instruction in a specific content area (mathematics). Using design research, we engaged principals in professional development and assessed principals’ ability to identify aspects of high-quality mathematical tasks and instruction through pre–post task sort analyses and classroom video analyses. Significant differences occurred in principals’ identification of high-quality mathematics tasks and instruction, students’ thinking, and teachers’ actions. Subsequent data identified changes in principals’ feedback to mathematics teachers; however, this change was not sustained in following years. We hypothesize necessary conditions for supporting principals as instructional leaders in specific content areas.

Assessing Instructional Quality in Mathematics Classrooms Through Collections of Students’ Work

This chapter explores the use of collections of students’ work as a reflection of instructional quality. Sets of students’ written work can provide indicators of the conditions of learning, representing the norms and instructional practices impacting students’ mathematical thinking as they produced the work. I present a methodology for analyzing sets of students’ written work using the Instructional Quality Assessment (IQA) Mathematics Assignment rubrics. I will summarize research validating the use of students’ work as an indicator of instructional quality, provide examples to illustrate how to use the IQA rubrics to evaluate collections of students’ work, describe ways of analyzing IQA data, and share research projects in which student-work collections and the IQA rubrics were used to (1) assess instructional quality in mathematics at the district level and (2) evaluate the effectiveness of professional development initiatives. The chapter will close with a discussion of the strengths and limitations of the IQA specifically and the use of students’ work as a data source more broadly.

Preservice Mathematics Teachers’ Effective Use of Technology: Analyzing the Cognitive Demands of Technology-Based Instructional Activities

This study examined pre-service teachers’ (PST) ability to integrate technology into instructional activities in ways that support students’ mathematical thinking and reasoning, using the Instructional Quality Assessment to assess the cognitive demand of: (a) instructional tasks, (b) description of how tasks would be implemented or were implemented during the lesson, and (c) level of response expected from or produced by students. Results show that PSTs designed technology-based instructional activities with high-level cognitive demands and aimed to maintain high-level implementation and student response. Results suggest that focusing on cognitive demands of tasks and implementation may be productive for supporting PSTs to incorporate technology in ways that enhance students’ mathematical learning.