Author Pam Harris argues that teaching real math--math that is free of distortions--will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math…

Mathematical coherence is a goal within the Common Core State Standards for Mathematics. One aspect of this coherence is how student mathematical thinking is developed across concepts. Unfortunately, mathematics is often taught as isolated ideas across grades. The multiplicative field is an area of study that needs to be examined as a space to…

Digital formative assessment tools have been identified as a promising support for mathematics teachers' practices of monitoring and enhancing students' understanding. However, more research is required to align these support affordances better with teachers' practices. In a qualitative expert-novice comparison, we investigated how expert and…

For several decades, digital formative assessment tools and platforms have been promoted as promising for supporting adaptive teaching. For learning goals such as procedural fluency, this promise has been held across a range of subject-matter topics. For conceptual learning goals, however, the available digital formative assessment tools are much…

Many educators face the challenge of engaging students in science and mathematics, often struggling to bridge the gap between theoretical concepts taught in classrooms and their real-world applications. This disconnect can lead to disinterest and disengagement among students, hindering their learning outcomes. "Cases on Informal Learning for…