This study examined the engagement of preservice elementary teachers (PSTs) with mathematics tasks that were open in various ways and to varying extents. In K-12 settings, practitioners who have implemented recently popular open tasks report increased engagement and from a wider variety of students. While these anecdotal reports and related…

Professional noticing of children's mathematical thinking (Jacobs et al. in J Res Math Educ 41(2):169-202, 2010) is a construct that is used frequently to understand the ways in which teachers attend to, interpret, and respond to children's mathematical thinking. In this paper, we present our analysis of prospective elementary mathematics…

The purpose of this article is to report how Year 6 teachers used geometric reasoning tasks to foster students' mathematical attitudes and dispositions by encouraging communication as students constructed mathematical meaning for themselves. The Year 6 teachers implemented two tasks to provide a rich mathematical assessment opportunity…

In our multi-method study, feedback levels derived from the well-known feedback model of Hattie and Timperley were used in conjunction with feedback that was related to subject-specific content; here, mathematical reasoning tasks in primary school. Feedback needs to be aligned with the learning process; in the beginning, more task feedback is…

This paper presents research that exists at the crossroad of scholarly practice and scholarly inquiry. We outline the process in the design, enactment, and empirical examination of an elementary methods course activity, Exploring and Supporting Student Thinking (ESST), which engaged 18 elementary prospective teachers (PTs) in two sessions of…

This study examines how elementary preservice teachers notice children's mathematical thinking and how this noticing influences the evaluation of technological resources. In particular, we explore the aspects of thinking to which preservice teachers attend and how they interpret evidence about children's thinking when using the Spatial-Temporal…

Incorporating computational thinking (CT) ideas into core subjects, such as mathematics and science, is one way of bringing early computer science (CS) education into elementary school. Minimal research has explored how teachers can translate their knowledge of CT into practice to create opportunities for their students to engage in CT during…

Mathematics discourse is a teaching approach that encourages student discussion and reveals an understanding of concepts as students engage in mathematical reasoning and debate (Cobb 2006). Grabowski and Ke (2007) posit that students have significantly higher achievement and positive attitudes toward mathematics after participating in gaming…

As computational thinking (CT) is increasing in focus in K-12 education, it is important to consider how teacher education programs may better prepare teacher candidates (TCs). Previous studies have found that TCs do not always have a firm understanding of what CT involves, and they might not have clear ideas about how to develop CT in their…

Developing pre-service teachers' (PSTs') knowledge of pedagogical practices can be particularly challenging within university classrooms. Teacher educators are well placed to provide PSTs with theoretical perspectives on pedagogical practices; what is particularly challenging, however, is linking theory with practice and developing PSTs' breadth…

This study examines how collective activity related to multiplication evolved over several class sessions in an elementary mathematics content course that was designed to foster prospective elementary teachers' number-sense development. We document how the class drew on as-if-shared ideas to make sense of multidigit multiplication in terms of…

This article describes activities in which students deepen their relational understanding of the equals sign through exploring inequalities in a competitive dice game, built around the familiar fairy-tale "The Three Little Pigs" and "The Big Bad Wolf." The activity can be adapted to different abilities by choosing more or less…

Researchers have linked teachers' use of mathematical tasks and questions to students' achievement in mathematics, and also have documented that the types of tasks and questions posed might change throughout the year in grades that include high-stakes tests of student achievement. This qualitative research study explored 3 elementary school…

In this paper, I examine the utility of a mathematics learning trajectory as a tool to support teachers' attention to students' mathematical thinking. I present findings from one second grade teacher's use of a learning trajectory as she planned a sequence of three mathematics lessons. Findings suggest learning trajectories support teachers in…

This book reviews alternative assessment. Suggestions include portfolios, interviews, observations, journals, and tests utilizing various rubrics. This book contains suggestions and materials that teachers can use to assess students' progress in problem solving, reasoning, and communication. Many performance tasks and problem-specific rubrics for…