Conclusion

This chapter concludes the book by revisiting its overall goal and synthesizing insights from the contrasting cases in Chapters 3–6 through the Teaching through Example-based Problem Solving (TEPS) approach. By linking key features of TEPS—representation use and deep questioning—to cross-case analyses, the chapter demonstrates how teachers’ instructional choices influence students’ cognitive engagement, as framed by the Interactive, Constructive, Active, and Passive (ICAP) model. The TEPS cases focus on worked examples rather than full lessons, illustrating how problem-solving in real-world contexts can be unpacked to promote deep mathematical learning and worked example effects. Through guided comparisons, preservice teachers can observe how strategies such as concreteness fading and deep questioning foster inference-making, a hallmark of deep learning. While the book emphasizes early algebra, the TEPS approach is applicable across elementary mathematics domains. The chapter concludes by highlighting the value of contrasting cases and the ICPA framework in teacher education and suggesting future directions, including leveraging technology and AI to further support preservice teachers’ learning and development.