The decomposition of numbers when solving subtraction tasks is regarded as more powerful than counting-based strategies. Still, many students fail to solve subtraction tasks despite using decomposition. To shed light upon this issue, we take a variation theoretical perspective (Marton, 2015) seeing learning as a function of discerning critical…

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All…

A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…

Although the general development of mathematical abilities in primary school has been the focus of many researchers, the development of place value understanding has rarely been investigated to date. This is possibly due to the lack of conceptual approaches and empirical studies related to this topic. To fill this gap, a theory-driven and…

This study used a multiple probe across participants design, replicated across two interventions and counterbalanced across participant groups to examine the effects of number sense intervention and extensive practice intervention on strategy transformation when students with mathematics learning disabilities (MLD) solved basic fact problems. In…

The language that students use with whole numbers can be insufficient when learning integers. This is often the case when children interpret addition as "getting more" or "going higher." In this study, we explore whether instruction on mapping directed magnitudes to operations helps 88 second graders and 70 fourth graders solve…

Experts think in patterns and structures using the specific "language" of their domains. For mathematicians, these patterns and structures are represented by numbers, symbols and their relationships (Stokes, 2014a). To determine whether elementary students in the United States could learn to think in mathematical patterns to solve…

Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the…

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…

Number sense is critical to the development of higher order mathematic abilities. However, some children have difficulty acquiring these fundamental skills and the knowledge base of effective interventions/remediation is relatively limited. Based on emerging neuro-scientific research which has identified the association between finger…

The purpose of the study was to examine differences in early numerical competencies, as well as subtraction skill, as a function of children's mathematics difficulty (MD) status: computational difficulty (CD), word problem-solving difficulty (PD), concurrent difficulty (CDPD), or neither difficulty (i.e., typically developing; TYP). Based on…

This paper highlights the Indonesian's road transportation contexts, namely, angkot, that used in learning and teaching of addition and subtraction in first grade and second grade MIN-2 Palembang. PMRI approach that adopt from RME [Realistic Mathematics Education] was used in this design research. From teaching experiment was founded that the…

This paper reports on a study to examine mental computation strategies used by Year 1, Year 2, and Year 3 students to solve addition and subtraction problems. The participants in this study were twenty five 7 to 9 year-old students identified as excellent, good and satisfactory in their mathematics performance from a school in Penang, Malaysia.…

The purpose of the research is to explore second graders' concept of number development and quantitative reasoning. For this purpose, there were two stages of trials for the children. The first trial was concrete objects. After three months, the children participated in the second trial of half concrete objects. Since understanding the process of…

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…