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…

Developing a positive relationship with mathematics in early elementary is vital for success in future mathematics education. Students who do not develop an understanding of mathematical number sense in early grade levels struggle to make connections in later courses. Mathematical discourse sessions, specifically Number Talks, encourage students…

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…

The problem addressed in this study was students who have not been able to demonstrate proficiency in performing mathematical computation, algebraic and geometrical reasoning, number sense proficiency and mathematical processing while in grades 3 through 8 are not prepared to successfully complete the high school high stakes Algebra 1 ECA…

Children's ability to place fractions on a number line strongly correlates with math achievement. But does the number line play a causal role in fraction learning or does it simply index more advanced fraction knowledge? The number line may be a particularly effective representation for fraction learning because its properties align with the…

Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a…

This paper reports on results of a targeted and extended (two school terms) program for building Grade 3 and Grade 4 students' facility with number facts and application for mental computation. As part of a larger project, this paper reports results from two schools. Results indicated strong gains in number fact recall and mental computation for…

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses…

Annual National Assessment (ANA) performance in Mathematics across the primary grades in South Africa indicates a decrease in mean performance across Grades 1-6. In this paper, we explore the apparently high performance in Grade 1 through a comparative investigation of learner responses on two assessments: the Grade 1 ANA taken in February 2011 by…

This article reports the findings from a comparative analysis that examined several mathematical content strands, reasoning processes, and emphasis on technology in prior K-8 state mathematics standards and the Common Core State Standards for Mathematics (CCSSM). Various methodological tools were utilized to compare and contrast CCSSM with prior…

Research literature is reviewed, identifying a need to design instruction to support multi-digit mental computation and critiquing conventional place value instruction. A distinctive instructional domain is proposed, called conceptual place value (CPV)--incrementing and decrementing numbers by units of ones, tens and hundreds. A design research…

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…

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.…

This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…

Four hundred and three 3rd- and 5th-grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole-number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based…