The purpose of this article is to demonstrate how students' mathematics identities were developed and how their agency was fostered through the use of a mathematical action technology (MAT), Desmo, during stages of learning beyond noticing and wondering. The authors describe how they enacted an eighth-grade mathematics lesson depicting students…

The development and use of learning trajectories is a body of research that has made enormous contributions to the field of mathematics education, offering insight into the teaching and learning of topics at all levels. Simultaneously, the work of building learning trajectories can benefit from explicitly adopting an anti-deficit stance,…

It is beneficial for students to discover intuitive strategies, as opposed to the teacher presenting strategies to them. Certain proportional reasoning tasks are more likely to elicit intuitive strategies than other tasks. The strategies that students are apt to use when approaching a task, as well as the likelihood of a student's success or…

Genius Hour is a time built into the school day or week to enable students to actively create their learning rather than passively consume it. During the time set aside for Genius Hour, students choose what they will learn about, the strategies they will use to learn it, the pace of their work, the materials and resources they will use, and the…

What "is" mathematics? What does it mean to "do" mathematics? The answers to these two questions critically influence the ways in which learners respond to a mathematical problem. On the other hand, if they see questions as having only one correct answer and as needing to be solved in one particular way, they will be prone to…

Three mid-level mathematics teachers (grades 7 and 8) and a university mathematics educator formed a year-long professional learning community. The objective was to collectively look at how they were promoting the Standards for Mathematical Practice (SMP) (CCSSI 2010) in their classes. The monthly discussions followed an iterative cycle in which…

Even those with no interest in the philosophy of mathematics take positions on a range of philosophical issues when they teach mathematics. Some of these issues are intimately related to common student confusions. These include the nature of mathematical objects and relations such as real numbers and equality; how we come to conclude a…

An interesting change has been occurring in the author's middle school mathematics classes. Some students have become creative, free-thinking inventors. If they have had little experience with an operation, they invent strategies of their own. Sometimes these strategies have been well informed and supported by strong mental math skills and a good…

Just as ready-made clothes may not provide a perfect fit for all bodies, math lessons may not be a perfect fit for all students. Published instructional tasks, including problems in mathematics textbooks, often need to be tailored to be meaningful, relevant, or accessible to each student. Ways are possible to take high-level reasoning tasks and…

The history of strategies research during the past quarter century has been a story of significant conceptualizations and reconceptualizations regarding the nature, development, and teaching of cognitive and metacognitive strategies. Theoretical models, empirical research, and discussions contributed by Michael Pressley have been central to…

When the author and her teaching colleague assessed their 7th and 8th grade students' research papers, they realized that although the papers demonstrated proper structure, the students had not gained meaningful understanding of their topics. Although the teachers had carefully prepared students to write, they had not ensured that students had…

According to Kilpatrick (1987), in the mathematics classrooms problem posing can be applied as a "goal" or as a means of instruction. Using problem posing as a goal of instruction involves asking students to respond to a range of problem-posing prompts. The main goal of this article is a classification of mathematics questions created by Years 8…