This paper stems from calls for methodological advancement in two areas of research: primary mathematics education and dialogical education. We respond to these calls from the commognitive standpoint by introducing the "Grove of Realizations" as a tool for capturing and visualizing individual students' learning through collaborative work…

Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…

Research on number sense presents contradictory arguments and results regarding the effects of context-based tasks and activities on students' number sense. The aim of this study was to examine fourth-grade elementary school students' number sense as they solve context-based (CB) and non-context-based (NCB) items. A survey design was employed and…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

The research examined the calculation methods used by pupils in Grades 3-6 when they were presented with problems that could be worked out efficiently and flexibly by applying number sense. The study was conducted with a convenience sample of 179 pupils between the ages 7 years and 10 months to 12 years and 10 months. in mainstream education in…

Purpose: Most literature has focused solely on either knowledge about number sense or understanding of fractions. To fill the research gap, this study examined pupils' abilities in both number sense and fractions. In particular, it investigated Year 4 and Year 5 pupils' use of strategies in developing their fraction sense. Methodology: This study…

Many studies in the past decades have focused on low and typical mathematics achievers, yet little is known about children with high mathematics achievement, particularly at a young age. The current study aimed to fill this gap and started from the early work of Krutetskii (1976) as a theoretical lens to study the characteristics of high…

During a time when students are accessing instruction virtually because of COVID-19, reflecting on the sixth of the Standards for Mathematical Practice (SMP 6) is a vital step for educators to take. Although the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010) identifies SMP 6 as Attend to precision, associated expertise…

In this study, we examined how curricular resources supported three expert teachers in their enactment of progressions. Using a video-stimulated interview process, we documented the multiple types of progressions identified, described, and enacted by the teachers. Results indicate that the teachers used four different types of…

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a…

This qualitative study was conducted to identify the potential of using iPad as a supplement to teach math to students with learning disabilities. Ten teacher candidates from a university in the south provided one-on-one math tutoring services to ten students in a self-contained classroom at a local high poverty elementary school. The students…

We examined the role of executive attention, which encompasses the common aspects of executive function and executive working memory, in children's acquisition of two aspects of mathematical skill: (a) knowledge of the number system (e.g., place value) and of arithmetic procedures (e.g., multi-digit addition) and (b) arithmetic fluency (i.e.,…

Exploring number systems of other cultures can be an enjoyable learning experience that enriches students' knowledge of numbers and number systems in important ways. It helps students deepen mental computation fluency, knowledge of place value, and equivalent representations for numbers. This article describes how the author designed her…

Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…