Textbooks as a Resource for Teaching Mathematics Through Problem Posing: Catalyzing Instructional Change

TL;DR

This study examines how middle school teachers use Illustrative Mathematics (IM) textbooks as resources for problem-posing-based learning (P-PBL), analyzing existing Co-Craft Questions tasks and cases of teacher redesign. It finds that problem posing can catalyze instructional change, but changes must stay tied to textbook lesson learning goals and proceed in small steps.

Key findings

• IM middle school textbooks contained 70 Co-Craft Questions tasks in all: 19 in Grade 6, 27 in Grade 7, and 24 in Grade 8. The most common representations were informational statements (26%), pictures (21%), and graphs (14%); Grade 6 had the greatest variety of representations (10 types).
• PP prompts were mostly “Write down possible mathematical questions that might be asked about the situation” (76%) and “Write down possible mathematical questions that could be answered about the situation” (21%), which the authors say suggests PP incorporation is not yet entirely systematic.
• Teachers developed additional PP tasks from textbooks through three strategies: changing prompts to convert problem-solving tasks into PP tasks, modifying problem situations to increase engagement while maintaining learning goals, and involving students in designing assessment tasks.
• Textbooks mediated instructional change: IM provided footholds but minimal implementation support, teachers sometimes conflated PP with PS, and the ASSSC discussion protocol helped center posed-problem handling on textbook lesson learning goals; small incremental changes were more feasible than large lesson overhauls.

Methods

• Qualitative curriculum analysis and case study within the 4-year P-PBL Project; the team searched all IM middle school textbooks for existing PP tasks, especially Co-Craft Questions, cataloguing features such as grade level, representations, and prompt wording.
• The project worked with 35 middle school mathematics teachers across three school districts; this paper drew examples from four teachers. Data sources included IM textbooks, teacher journal entries, recorded professional learning meetings and summer workshops, classroom observations, and individual planning meetings.
• Thematic analysis of journal entries identified themes about shifts in teachers’ practices and agency; the larger project uses a quasi-experimental design coupled with design-based research and improvement science, but this paper reports curriculum analysis and cases.

Limitations

• Stated: the authors do not claim their strategies are the only viable P-PBL approaches; they are in the early stages of exploring the ASSSC protocol; and they chose IM, a high-quality curriculum, while other textbooks may have fewer affordances.
• Stated: careful interpretation of textbook design choices tests the limits of what many teachers can practically afford, and district pacing constrained richer PP activities in Ms. Khan’s case.
• Evident from the text: the illustrative cases come from only four of 35 project teachers, and this paper reports no student outcome effect sizes; the findings are qualitative and context-specific rather than generalizable.