The purpose of this multiple comparative case study was to examine how professional development sessions based on the IQA Mathematics Toolkit rubrics influenced teachers' ambitious teaching practices, including approaches to selecting, adapting, and implementing high-cognitive demand tasks during small-group instruction in mathematics. Guided by the Instructional Quality Assessment (IQA) and the Mathematical Task Framework (MTF), this qualitative inquiry gathered data through informal interviews; participant portfolios of tasks, rubric scores, and student work samples; observation tools; and transcripts during weekly professional development sessions from two in-service elementary school teachers at a K-8 charter school in Florida. Two research questions drove this study: (a) What factors influence the selection, adaptation, and implementation of high-quality mathematical tasks for small-group instruction; and (b) In what ways are teachers' approaches to planning and implementing instruction impacted by using the IQA rubrics? Qualitative analysis of the data revealed five themes pertaining to the experiences of participants: (a) pressures from pandemic concerns; (b) perceptions of students' ability and motivation; (c) understanding of state standards and school prescriptions; (d) teachers' level of interest and exposure to outside distractions; and (e) level of experience. Teachers' approaches to high-quality tasks when mixed with heterogeneous grouping were found to best support opportunities for teacher change and provide students with opportunities to make sense of mathematics. Results show reflection of practice using the IQA rubrics can influence teachers' approaches to planning, adaptation, and implementation of tasks and support changes in classroom practice. Discussion of the findings in relation to the relevant literature, their implications, and recommendations for further research are provided. These findings add to the research in the field of mathematics education in equitable grouping strategies for small-group instruction, approaches to high-quality tasks to promote sense making in small groups and assessing ambitious teaching practices in mathematics.


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Graduation Date





Dixon, Juli


Doctor of Philosophy (Ph.D.)


College of Community Innovation and Education


School of Teacher Education

Degree Program

Education; Math Education









Release Date

August 2024

Length of Campus-only Access

3 years

Access Status

Doctoral Dissertation (Campus-only Access)

Restricted to the UCF community until August 2024; it will then be open access.