Connections is one of the Process Standards set forth by the National Council of Teachers of Mathematics (NCTM 2000), whereby teachers provide students with learning opportunities to "recognize and apply mathematics in contexts outside of mathematics." Similarly, the Standards for Mathematical Practice (NGA Center and CCSSO 2010) call…

This observation study documents the amount and quality of mathematics instruction provided to students with intellectual and developmental disabilities in kindergarten through second grade in self-contained special education settings. We observed six special education teachers and their students (N = 12) during a total of 967 min allotted to…

The importance of ratio and proportional reasoning is regularly emphasised, however, the teaching and learning of these concepts continues to present challenges. In this article the authors explore a hands-on task, designed to encourage student visualisation of the concept of ratio. Teacher perceptions of this task were positive, indicating the…

Scaling up educational interventions in the STEM (Science, Technology, Engineering, and Mathematics) field is critical but under-researched. We review and draw implications from a series of studies investigating the long-range impact of an implementation of an early mathematics scale-up model based on learning trajectories. Lasting effectiveness…

As a parent, the author stepped into his child's class on a Friday morning to a room buzzing with activity. Parents walked around the room, coffee and bagel in hand, reading stories that their child (and others) had drafted, revised, written, and illustrated. Students eagerly shared their stories and drawings, cherishing the comments and praise…

This case study of a third grade classroom details the ways that competence was jointly constructed by students and the teacher in relation to students' efforts to engage with each other's mathematical ideas. By creating consistent opportunities for students to share and make sense of others' ideas, and by supporting students to take up these…

How can educators encourage and better prepare students to pursue science, technology, engineering, and mathematics (STEM)-based fields? To start, students are more likely to pursue these fields if they enjoy and perceive themselves to be good at them. This means introducing relevant concepts and skills at an early age and embedding them…

The aim of this research was to examine science and mathematics teaching efficacy beliefs of pre-school teachers in terms of some variables. The sample of the study was comprised of 191 pre-school teachers working in a city in Aegean Region of Turkey. Since it attempted to define self-efficacy beliefs of pre-school teachers toward science and…

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

The aim of this study was to determine pre-school teachers' beliefs about teaching mathematics to young learners. In this context, we compared preschool teachers' beliefs with mathematical learning, talent-development-age appropriateness for mathematical learning, the nature of mathematics, the curriculum, teacher efficacy, and the teacher's role…

This paper presents discussions on stochastic education in early childhood, based on two doctoral research projects carried out with groups of preschool teachers from public schools in the Brazilian cities of Suzano and São Paulo who were participating in a continuing education program. The objective is to reflect on the analysis of two didactic…

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…

To what extent can instructional design be based on principles for instilling a culture of problem solving and conceptual learning? This is the main focus of the study described in this paper, in which third grade students participated in a one-year course designed to foster problem solving and mathematical reasoning. The design relied on five…

The purpose of this three-paper manuscript dissertation is to add value to the limited knowledge base of research surrounding the quality of teacher-child interactions in pre-k mathematics contexts. The first paper, based on an extensive review of literature, presents a theoretical basis for using five-frames to support children's development of…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…