Examining Geometry Teachers’ Changes to Design-based Lessons for Engaging Students in Math Modelling

• In Event: Innovations and Advances in Mathematics Instruction

Abstract

Research studies show that engaging K-12 students in design-based challenges has a positive impact on their learning of the discipline and the development of life-long learning skills (Rusmann & Ejsing-Duun, 2021). Empirical research studies in the field of design-based learning and mathematical modelling in middle and high school mathematics show that design-based challenges can motivate students by giving them the opportunity to apply mathematical concepts to real-world problems (e.g. Alsina & Salgado, 2022). However, creating these challenges requires curricular expertise.

In this work, we examine six design-based geometry lessons addressing middle school and high school math standards. The lessons were created by a group of teachers and researchers during online lesson study sessions. Lesson study is a professional development model that is composed of four phases: study, plan, teach, and reflect (Lewis et al. 2006). Involving the teachers in creating these lessons is key, as many of the principles rely on the students’ mathematical prior knowledge, grade level and personal circumstances, and authentic real-world connections. We anticipate that our work can guide the creation of design challenges in other K-12 settings and disciplines.

During each lesson study cycle, the teachers were presented with three design-based lesson prototypes as examples of lessons that they can teach. The researchers created these prototypes following a framework developed by Authors (2024). The framework is based on three research supported perspectives: 1) the lessons must be supported by the curricular standards, 2) the lessons must be guided by a design thinking model, and 3) the lessons must address a challenge that is relevant to them and their communities. Each lesson prototype was composed of an Overview with three sections: The Problem, The Design Challenge, and Your Task. The student worksheet had three phases: Engage, Experiment, and Explain. Sections and phases had information and scaffolding prompts to facilitate students’ engagement and application of geometry concepts during the design challenge.

During the lesson study cycle, the teachers selected one of the lesson prototypes and adapted the lesson to include design thinking processes with the researchers’ support. In this study we ask, what changes did the teachers make to the lesson prototypes to support students’ engagement in math modeling? We compared the content of the selected lessons before and after the teachers made the changes. We marked any changes to each section of the lesson indicating the type of this change (addition, modification, or deletion). Then, we used the Design and Implementation Framework for Mathematical Modelling Tasks (DIFMT) (Geiger et al., 2022) to develop a coding scheme (see Table 1a) that was used to categorize the change.

Table 1b shows that most of the changes were additions or modifications to the Experiment phase. Table 1c shows that the categories of the changes varied between the lessons; however, changes were focused on relevance/motivation and accessibility. This indicates that when teachers adapt design-based lessons to engage students in math modeling, their focus is on making it more relevant, meaningful, and accessible to the students given their prior knowledge.

Authors

• Saadeddine S. Shehab, University of Illinois at Urbana-Champaign

• Gloriana Gonzalez, University of Illinois at Urbana-Champaign

• Edward Powers, University of Illinois at Urbana-Champaign