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…

The adaptive use of strategies, that is selecting a strategy which allows an efficient solution for a given problem, can be considered as an important individual ability relevant in various domains. Based on models of subjects' skills of adaptive use of strategies, two idealized instructional approaches are suggested to foster students in their…

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

In contrast to previous studies on Spontaneous Focusing on Quantitative Relations (SFOR), the present study investigated not only the "extent" to which children focus on (multiplicative) quantitative relations, but also the "nature" of children's quantitative focus (i.e., the types of quantitative relations that children focus…

Pupils' difficulties in solving word problems continue to attract attention: while researchers highlight the importance of relational reasoning and modelling, school curricula typically use short word problems to develop pupils' knowledge of arithmetic operations and calculation strategies. The Relational Paradigm attributes the leading role in…

Math fact fluency is critical for understanding complex mathematics. Explicit timing interventions have shown promise for improving math fluency, and they may benefit from being paired with group-oriented contingencies. Further, investigations of independent and dependent group-oriented contingencies would help to identify their relative…

The focus of this study is the relationship between students' performance in mental calculation and the strategies they use when solving three-digit mental addition problems. The sample comprises 78 4th grade students (40 boys and 38 girls). Their mean age was 10 years and 4 months. The main novelties of the current research include (1)…

A team of teachers from the same New York City public school met to discuss and compare the Common Core State Standards for Mathematics (CCSSM) to their current math curriculum. The group consisted of four kindergarten teachers, a representative from the first-grade teaching team, and the school's math coach. During the first meeting, the…

Researchers and practitioners indicate students require explicit instruction on mathematics vocabulary terms, yet no study has examined the effects of an embedded vocabulary component within mathematics tutoring for early elementary students. First-grade students with mathematics difficulty (MD; n = 98) were randomly assigned to addition tutoring…

Principal aim of this study is to show the effectiveness of the program prepared by researchers in order to enable 6 year-old children attending pre-school educational institutions to effectively gain addition subtraction skills through a drama-related method. The work group in the research comprised of 80 kids who continued their education in…

This study examined the isolated effects of Cover, Copy and Compare (CCC) and the effects of CCC paired with performance feedback (CCC + PF) and rewards (CCC + RW) on the mathematical calculation skills of first grade students identified with math difficulty. Four research questions were addressed in this study. 1. Does Cover, Copy, and Compare…

This study investigated the effects of the nature of the algorithm, reinforcement, and level of problem difficulty on the ability of fourth graders to solve addition problems as measured by the number of problems correctly solved and the number of columns attempted. Subjects were selected for high scores on a test of basic addition facts; only…

Two experiments examined the use of a number-line metaphor presented with interactive multimedia to help sixth graders with varying levels of mathematics achievement or spatial ability build connections between addition and subtraction of signed numbers and existing conceptual knowledge. Results indicated that use of multiple representations…