Children's intuitive understandings of mathematical ideas--both correct, generalizable strategies alongside misconceptions--showcase the complexity of their thinking. However, recognizing children as complex thinkers is one thing but it is another thing altogether to leverage their ideas to plan for and carry out mathematics instruction. The…

The purpose of the dissertation is to investigate three particular aspects that may affect the transition between a third grade Montessori system and a fourth grade non-Montessori system, specifically within the context of teaching and learning mathematics. These aspects are 1) the change in pacing and structure of the classroom, 2) the removal of…

In this paper, we report on how Year 5 and 6 students (10 to 13 years old) solve reverse fraction problems; that is, where students are required to find the quantity of an unknown whole given a known partial quantity and its equivalent fraction of the unknown whole. To what extent do students' solutions generalise fraction structures that indicate…

In this article, we investigate the artistic puzzle of designing mathematics experiences (MEs) to engage young children with ideas of group theory, using a combination of hands-on and computational thinking (CT) tools. We elaborate on: (1) group theory and why we chose it as a context for young mathematicians' experiences with symmetry and…

Spatial reasoning, an emerging transdisciplinary area of interest to mathematics education research, is proving integral to all human learning. It is particularly critical to science, technology, engineering and mathematics (STEM) fields. This project will create an innovative knowledge framework based on spatial reasoning that identifies new…

This study examined mathematics strategy instruction that primes the common underlying structures of word problems using explicit instruction in a rural elementary classroom with fourth- and fifth-grade students with and without disabilities (n = 27). Although intervention students did not outperform control condition students on a word problem…

Acknowledging the critical role of mathematics coaches in enhancing teacher capacity, positively influencing teacher beliefs, and increasing teacher investment in professional development, NCTM's "Principles to Actions: Ensuring Mathematical Success for All" (2014) calls on coaches to "take action." However, coaches seek…

This study examined the performance gap experienced by high achieving grade four and five students at the Kallang International Day School (KIDS) who were not demonstrating growth in math results from fall to spring as measured by the Measures of Academic Progress (MAP) test (NWEA, 2017). The purpose of this study was to apply the gap analysis…

Improving students' achievement scores has been a critical issue for both educators and legislators. Eliminating or reducing recess to increase instructional time has become a common practice. The purpose of the study was to examine the impact of recess on the academic achievement in reading and mathematics among third and fourth grade students.…

Policy and practice communities increasingly are emphasizing conceptual, cognitively demanding, and "ambitious" instruction. Within this context, we examine whether such practices serve the needs of students with specialized academic needs. Across upper-elementary classrooms in four districts, we find that exposure to…

This article highlights the main ideas that underlie the differences in potential pragmatic knowledge constructs students experience when solving problems, between the zone of proximal development (ZPD) and the zone of potential construction (ZPC). This qualitative research is based on a phenomenological approach to finding the meaning of things…

Moving among levels of abstraction is an important skill in mathematics and computer science, and students show similar difficulties when applying abstraction in each discipline. While computer science educators have examined ways to explicitly teach students how to consciously navigate levels of abstraction, these ideas have not been explored in…

Data-based decision making (DBDM) is presumed to improve student performance in elementary schools in all subjects. The majority of studies in which DBDM effects have been evaluated have focused on mathematics. A hierarchical multiple single-subject design was used to measure effects of a 2-year training, in which entire school teams learned how…

This paper presents primary school teachers' perceptions associated with their engagement in a project aimed at building Year 3 and Year 4 students' number fact and computational fluency. Throughout the project, teachers were provided with classroom ideas and suggestions for engaging students in number fact practice and for generating student…

Students' success with fourth-grade content standards builds on mathematical knowledge learned in third grade and creates a conceptual foundation for division standards in subsequent grades that focus on the division algorithm. The division standards in fourth and fifth grade are similar; but in fourth grade, division problem divisors are only one…