In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

This article reports on elementary students' understanding of time in the context of common classroom manipulatives and notational systems. Students in Grades 2 (n = 72) and 4 (n = 72) participated in problem-solving interviews involving different clocks. Quantitative results revealed that students' performances were significantly different as a…

This paper introduces a revised model for the development of basic computation skills. The model draws on four key phases, which have proven to be important for the development of calculation strategies and stresses the use of gestures and the verbalisation of concrete and mental images. This seems to be of crucial importance for children with…

Research on young children's reasoning show the complex relationships of knowledge, theories, and evidence in their decision-making and problem solving. Most of the research on children's reasoning skills has been done in individualized and formal research settings, not collective classroom environments where children often engage in learning and…

This study examined how small groups of second-grade children developed understandings of the concept of congruence while collaboratively exploring and solving problems with dynamic representations of triangles using Sketchpad on the iPad. One case study is presented to illustrate how young learners can infer geometrical relationships between…

Argumentation as a form of introducing children to science has received increasing attention over the past decade. Argumentation tends to be studied and theorized through the lens of individual speakers, who contribute to a conversation by means of opposing statements. M.M. Bakhtin and L.S. Vygotsky independently proposed a very different approach…

The perception of what a teacher says s/he does in the classroom may or may not match the reality of their actual teaching practice. This case study considers one second-grade teacher's instructional methods and pedagogical decisions when teaching number sense and her perception of what informed her teaching practice. This teacher supported…

Teachers' ability to elicit and build on students' mathematical thinking during instruction is critical in order to support students' mathematical growth. An emerging hypothesis in the field is that the construct of a "learning trajectory" (LT) has the potential to support teachers in making sense of and using student…

This paper presents a case study designed to educate students in pre-service teacher education programs about the importance of a comprehensive eye exam. The case study chronicles a family's multi-year search for solutions to their child's reading difficulties. The research supporting the case study explores the connection between vision…

This case study consisted of an examination of the perspectives of students, teachers, and administrators at the Shuangling Primary School, a rural Chinese school in Shaanxi Province, as they relate to themes of China's most recent curricular reform efforts. The intent was to understand these perspectives and determine how to best assist teachers…

Based on a mixed methods research design that included an examination of the impact of summer, case study analyses, and survey findings, English learners appear to have an advantage over their non-English learner peers in resisting summer loss and developing social competence. This study examined the effect of summer vacation on the oral reading…

The No Child Left Behind (NCLB) Act of 2001 requires states to ensure that all students make adequate yearly progress in achieving proficiency in English language arts and math. This study examines how six diverse schools have responded to the challenge of educating their students in math, particularly students with disabilities and other…

Within a major numeracy project, there were marked differences in achievement between classes, which, as reported in Sullivan and McDonough (2002), we attribute to the teachers. To gain insights into the practices of effective teachers, six case studies of highly effective teachers at the Prep (first year of school) to Grade 2 level were…