This article investigates two children's intuitive thinking in solving multiplication problems from different educational backgrounds. One of the children is in a southern elementary school in the US. He was given the same problems both in first and second grades. The other child was a first grader in a southwest region of China, and she was given…

Although the topic of division by zero has been widely discussed in the literature, this subject is still confusing for students, pre-service teachers and teachers. Because of this, teachers at various grade levels may encounter difficulties in conveying the concept to their students. Therefore, in order to provide students with a strong…

Aim of the research was to investigate possible impact of visuals on primary school 4th graders' problem-solving success. 108 fourth graders studying at four primary schools in Bartin city center were assigned as participants of the study. The research was carried out in 2016-2017 academic year. The model of the study was post-test control group…

Howe (2014, Three pillars of first grade mathematics, and beyond. In: Li Y. & Lappan G. (eds), Mathematics curriculum in school education, Springer, Dordrecht, pp 183-207) identified three pillars of first grade mathematics and beyond that described central mathematical and sense-making aspects of major Common Core State Standards Math…

Recent research suggests that children in elementary grades have some facility with variable and variable notation in ways that warrant closer attention. We report here on an empirically developed progression in first-grade children's thinking about these concepts in functional relationships. Using learning trajectories research as a framework for…

Quartiles are usually introduced early, often in primary school together with box-and-whisker plots. Various methods are used, and in lack of explanation in many textbooks at elementary level, this leads to unnecessary confusion. We discuss some elementary methods that are consistent with the most common definition and are also easy to understand.

This paper describes kindergarten children's engagement with two patterning activities. The first activity includes two tasks in which children are asked to choose possible ways for extending two different repeating patterns and the second activity calls for comparing different pairs of repeating patterns. Children's recognition of the unit of…

Elementary school students often lack a conceptual understanding of linear measurement, which is revealed by their poor performance when the object to be measured is not aligned with the start of the ruler. Instead of correctly counting the units that correspond to the object (e.g., inches or centimeters), children often use 1 of 2 incorrect…

This study examines four of the most commonly-used core mathematics curricula in the USA for evidence of support for research-based instructional strategies for mathematics vocabulary in first and second grade. Content analyses of the teachers' editions of two units for each grade level were analyzed per curriculum (n = 16). Statistically…

To assess the strength of conceptual understanding of number sense, a three-tier number sense test (TTNST) for fifth-grade students was developed and validated in this study. The three-tier test includes a content tier that assesses content knowledge of number sense, a reason tier that assesses a reason given for selecting a first-tier response,…

In this study, we investigated the potential of a hypothesized geometrical measurement learning progression (LP) to examine students' thinking and understanding in this domain.We interviewed 30 third to fifth graders using 3 LP-based cognitive tasks that asked the students to find the length, perimeter, area, surface area, and volume measurement…

Recent multiplication with regrouping research shows that the combination of the concrete-representational-abstract (CRA) sequence and the Strategic Instruction Model (SIM) has been effective in several studies. More evidence is needed to demonstrate CRA-SIM's effectiveness across settings and students. Therefore, the purpose of this study was to…

Understanding fractions has been a pervasively difficult skill for struggling math learners, yet it is essential for success in secondary level mathematics skills. The present systematic review examined the evidence base of fraction interventions for elementary level students identified as struggling math learners. Twelve studies met inclusion…

Solving word problems is challenging in elementary schools, both for the teacher in teaching students to solve word problems and for the student in learning to solve them. This paper examines how the ideas of learning trajectory and variation pedagogy could be integrated as an instructional principle for teaching this content in the context of…

Teaching mathematics in children's first language has both cognitive benefits and assists with developing cultural and mathematical identity. In Papua New Guinea, many different Indigenous languages are used for instruction in elementary schools and teachers often need to identify or develop mathematics terminology themselves. Building on prior…