An essential understanding of the uses and practices of algebra remain out of reach for many students. In this book, award-winning researcher Dr. Nicole Fonger addresses the issue of how to support all learners to experience algebra as meaningful. In a highly visual approach, the book details four research-based lenses with examples from 9th-grade…

In this paper I analyze a problem solving event in a secondary mathematics classroom. As the event unfolds, the teachers, including me, understand the event as involving interactions that were not related to learning. By adopting an expansive view of learning, I advance a different interpretation, that the interactions tell a story of student…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

Learning analysts often consider whether learning processes across time are related (1) to one another or (2) to learning outcomes at higher levels. For example, are a group's temporal sequences of talk (e.g., correct evaluation [right arrow] correct, new idea) during its problem solving related to its group solution? I show how to address these…

This article continues to challenge the robust myth that mathematical smartness is exemplified in individuals who consistently complete mathematics problems quickly and accurately. In so doing, I present a set of counterstories from three students in one ninth-grade Algebra 1 classroom. These students described transformative experiences in their…

The flipped classroom is a growing trend within the education field; specifically at the colligate level. When examining the flipped classroom, teachers assign students material to review prior to attending class. Such materials could be videos, lecture notes, reading assignments, or work/activity sheets. During class time, students collaborate…

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

Representational fluency (RF) includes an ability to interpret, create, move within and among, and connect tool-based representations of mathematical objects. Taken as an indicator of conceptual understanding, there is a need to better support school algebra students' RF in learning environments that utilize both computer algebra systems…

Background/Context: Research shows that teachers' understandings of students, subject, and teaching influence their classroom practice. Additionally, teachers' colleagues have a role in shaping individuals' approaches to teaching and their responses to reform. Focus of Study: To understand how interactions with colleagues support teachers'…