This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

In this commentary, we explore tensions between engaging students in authentic disciplinary mathematical activity and insights from critical theorists who analyze equity in mathematics education. The tensions arise as engaging students in authentic mathematical activity usually involve having students adopt the language and norms of another…

A clear relationship exists between the consistent selection and implementation of cognitively demanding tasks and students' conceptual understanding of mathematics. However, mathematics teachers often struggle to maintain the cognitive demand of implemented tasks, with a number of factors identified as contributing to this decline. As many…

These educators share the "how" and "why" behind their use of open middle tasks in the classroom. In this article, the authors share a type of mathematics task, called Open Middle, that exhibits the characteristics outlined above. The authors frequently use Open Middle tasks in their classrooms because they teach students that…

Even in math class, English learners can work on their oral language development. The math tasks described here, designed for K-3, illustrate how.

Out-of-class activities play a crucial role in student learning. However, student opinions on the design of these activities are rarely measured across several different classes. The purpose of this study is to understand students' preferences and attitudes towards new "Engaged Mathematics Labs" in which professors and teaching…

Technology will not inherently make students in any classroom more mathematically inquisitive, however, the use of technology can foster student-centered inquiry. This article explores the impact technology has on mathematics learning when it emphasizes the ways it supports student-centered pedagogies. Through this lens, the authors focus on…

Collaborative problem solving (CPS) has been shown to both engage and benefit students' learning of mathematics. However, there is evidence that group work is not always easy to facilitate, in part because educators lack details about learners' engagement during group work: the processes of problem solving involved, and how these are engaged. In…

In this paper, we share about specific tenets of joy in mathematics and conditions for supporting joy. A pair of students, Julia and Javier, young Latinx mathematicians in Grades 3 and 4 respectively, participated in a study that involved addition and subtraction with negative integers within game play. Drawing on descriptions of joy and…

Teaching introductory statistics is a service requirement for many mathematics faculty, and the audience is often anxious about the subject and not always excited about the material. Making class fun, relevant, and visually stimulating is key to keeping students engaged in the material and also in promoting student learning. Collecting data from…

In this paper, we revisit a long-running conversation about situated learning and the design of environments for disciplinary engagement. Throughout the 1970s and 1980s, scholars advanced an anthropological critique of the then-dominant acquisitionist paradigm of formal schooling with a situated view focused on membership in communities and…

Although it is now more commonly acknowledged that young children can engage with mathematics, it is not as commonly acknowledged that really young children (such as those aged under three years) can engage with and think mathematically. One of the reasons for this is the inability of adults to recognise mathematics in what these young children…

In this paper, we offer a theoretical account of the emotion-cognition dialectic (i.e. the unit of feeling and cognition in thought) in identity formation (or identification), focusing on early childhood and mathematics. We consider how contradictory (emotional-cognitive) experiences which arise in different forms of mathematical activity (a…

This study examined a game-based teaching activity on "Factors and Multiples" designed for the 6th grade students. The game aims to create a differentiated and enriched learning environment targeted the curriculum standard "The students determine prime numbers using their properties. The students find prime numbers using the…

We explore the mathematics engagement of a group of mathematics coaches, working in k-12 mathematics education. The incenter of a triangle is used to derive an alternative formula for the area of a triangle inspired by Usiskin, Peressini, Marhisotto, and Stanley (2002).