Justifying and generalizing are essential forms of mathematical reasoning, yet, teachers struggle both to produce and identify justifications and generalizations. In comparing elementary school teachers' self-reported levels of noticing justifying and generalizing in their own classrooms and the levels researchers observed in two consecutive…

The aim of the present study is to explore strategies in enumerating units of three dimensional (3D) arrays. We analyse enumeration strategies of students in grade 3 (ages 8 to 9) in situations of cubical and spherical representations of units of 3D arrays. By exploring students' strategies in these two situations, we find that difficulties in…

In this report, we analyze students' learning of compound probability by describing connections they generated while engaged with tasks involving two independent events. Several of their connections were compatible with the development of expertise, such as recognizing the need to determine sample spaces across a variety of situations and noting…

Rational number and fractions concepts are inherently difficult; and lack of mastery often holds students back from success in subsequent mathematics courses. This paper describes design characteristics of a software based, adaptive, rational number tutor with virtual manipulatives, realistic contexts, and procedural feedback. Then, the paper…

Integrating history of mathematics in classes could be a hard task with young pupils. Indeed, original historical sources have a language that is far from the modern one. Such texts represent cultural artefacts that can give access to mathematical knowledge. The teacher can exploit such potential acting as a mediator between the mathematical signs…

"Nature-based learning" is learning through exposure to nature and nature-based activities (Jordan and Chawla 2019). Nature and mathematics can be connected through teaching and learning with natural materials (objects from nature) or teaching and learning in outside spaces. In this article, the authors elaborate on the rationale for…

With facilitation of advanced technologies, design and application of "smart" become promising research issues in education. Although it is potential for students to learn geometric in authentic contexts, there were still lack of studies addressing "smart" learning issue in authentic context for geometry. This study aim to…

This article illustrates and differentiates the unique role cognitive interviews and think-aloud interviews play in developing and validating assessments. Specifically, we describe the use of (a) cognitive interviews to gather empirical evidence to support claims about the intended construct being measured and (b) think-aloud interviews to gather…

Parent-teacher conferences are considered an important bridge between home and school, but there are little data on what teachers discuss during these conferences and whether it is linked to parents' involvement in children's schooling. Parent-teacher conferences (N = 431) with parents of young elementary school children (mean age 7.68 years) were…

Recently, teacher recruitment and retention has been the focus of the government and a step taken to support recruitment was the abolishing of the skills tests. Initial teacher training providers became responsible for assessing trainees' mathematicsrather than having it externally assessed. The purpose of this literature review is to synthesise…

Memorizing the multiplication table is a major challenge for elementary school students: there are many facts to memorize, and they are often similar to each other, which creates interference in memory. Here, we examined whether learning would improve if the degree of interference is reduced, and which memory processes are responsible for this…

Co-teaching is a prevalent model to address student needs in an inclusive classroom, therefore it is critical that both the general and special education teacher are implementing high leverage and evidence-based practices. The present study used peer coaching in an elementary co-taught classroom to evaluate the effectiveness of teachers' use of…

This dissertation presents three studies exploring mathematics interventions for students with autism spectrum disorder (ASD) including a review of literature and two intervention studies using manipulative based interventions. Specifically, the researcher conducted a systematic review of literature exploring the current state of the literature on…

This study's first purpose was to investigate effects of a fourth- and fifth-grade "next-generation" fraction intervention, which included six enhancements over a previously validated fraction intervention, designed to address career- and college-readiness standards. The study's second purpose was to assess effects of the next-generation…

This study is an attempt to design and develop as well as validate sets of Online Instructional Materials in Mathematics VI at selected elementary schools in DCS, Manila, specifically, focused on the study of Geometry and Measurement. Using both documentary analysis and descriptive method of study, two (2) major groups of respondents were chosen…