Students are presented with problems involving three scenario types of addition and subtraction in elementary mathematics: one dynamic ("Change") and two static ("Combine, Compare"). Previous studies have indicated that the dynamic type is easier for school children, whereas the static types are more difficult and comprehended only gradually…

This paper describes a case study of a math teacher working with a math coach and the effects of their interaction. A guiding question was whether the coaching intervention had affected the teacher's classroom practices and, if so, in what way. The study utilized data from teacher/coach planning sessions, classroom lessons, follow-up debriefing…

In this research report we consider the kinds of knowledge needed by a mathematician as she implemented an inquiry-oriented abstract algebra curriculum. Specifically, we will explore instances in which the teacher was unable to make sense of students' mathematical struggles in the moment. After describing each episode we will examine the…

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a…

Discourse has always been at the heart of teaching. In more recent years, the mathematics education community has also turned its attention towards understanding the role of discourse in mathematics teaching and learning. Using earlier classifications of discourse, in this paper, we looked at three types of classrooms: classrooms that engage in…

In considering mathematics problem solving as a model-eliciting activity (Lesh & Doerr, 2003; Lesh & Harel, 2003; Lesh & Zawojewski, 2008), it is important to know "what" students are modeling for the problems: situations or solutions. This study investigated Grade 3 students' mathematization process by examining how they modeled different…

Rhythm is a fundamental dimension of human nature at both biological and social levels. However, existing research literature has not sufficiently investigated its role in mathematical cognition and behavior. The purpose of this article is to bring the concept of "incarnate rhythm" into current discourses in the field of mathematical learning and…

The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent…

Justification is a core mathematics practice. Although the purposes of justification in the mathematician community have been studied extensively, we know relatively little about its role in K-12 classrooms. This paper documents the range of purposes identified by 12 middle grades teachers who were working actively to incorporate justification…

This study examined prospective middle grade mathematics teachers' knowledge of algebra for teaching with a focus on knowledge for teaching the concept of function. 115 prospective teachers from an interdisciplinary program for mathematics and science middle teacher preparation at a large public university in the USA participated in a survey. It…

We analyze how three seventh grade mathematics teachers from a majority Latino/a, linguistically diverse region of Texas taught the same lesson on interpreting graphs of motion as part of the Scaling Up SimCalc study (Roschelle et al., 2010). The students of two of the teachers made strong learning gains as measured by a curriculum-aligned…

This paper elaborates the notion of a personal example space as the set of mathematical objects and construction techniques that a learner has access to as examples of a concept while working on a given task. This is different from the conventional space of examples that is represented by the worked examples and exercises in textbooks. We refer to…

We investigated how students use the representation of data in a given example appearing in an interactive diagram (ID) and how they create additional examples with the ID. Students who worked with the ID that offered limited representations and tools ("illustrating ID") looked for ways to bypass the designed constraints: they changed the…

The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to…

We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which…