Developing structure sense is an important part of learning algebra. We investigated learners' structure sense of algebraic expressions involving brackets. This led us to propose the constructs "surface structure" sense and "systemic structure" sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we…

Central elements of adaptive expertise in arithmetic problem solving are flexibility, using multiple strategies, and adaptivity, selecting the optimal strategy. Research shows that the strategies children actually use do not fully reflect the strategies they know: there is hidden potential. In the current study a sample of 147 third graders from…

This study aimed to reveal the conceptual and operational conceptions of sixth-grade students in the process of division. The focus of the study included the strategies used in the division process, the students' understanding of the division algorithm, and their ability to interpret the remainder in a real-life context. Being qualitative in…

This research investigated students' sources and causes of errors and misconception in solving routine problems involving addition, subtraction, multiplication, and division of integers. This qualitative study involved observation of eight Year 7 classes and interviews with the respective classroom teachers. Sixteen Year 7 students who exhibit…

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…

Using a randomized placebo controlled design, we examined the direct and follow-up effects (at 6 and 12 months) of a mathematics tablet intervention. Math training focused primarily on basic arithmetic (addition and subtraction facts up to 12), and secondarily on number knowledge and word problems. We investigated the moderating effects of IQ and…

This study aims to investigate the mathematical word problem-solving skills of preschool children 5-6 ages. To achieve this objective, the data were collected in four preschools (n = 162). A mathematical word problem test was used as data collection tools. In this study, it was found that the children's skills at solving mathematical word problems…

The purpose of this study was to better understand how students with learning disabilities, including those who struggle specifically with mathematics, engage with fraction computation. In particular, we examined error patterns, the influence of like and unlike denominators on these patterns, and correct solution methods. Although skill-related…

Over the last two decades, students in Singapore consistently scored above students from other nations on the Trends in International Mathematics and Science Study (TIMSS; Provasnik et al., 2012). In contrast, students in the United States have not performed as well on international and national mathematics assessments and students with…

Does solving subtraction problems with negative answers (e.g., 5-14) require different cognitive processes than solving problems with positive answers (e.g., 14-5)? In a dual-task experiment, young adults (N=39) combined subtraction with two working memory tasks, verbal memory and visual-spatial memory. All of the subtraction problems required…

This paper reports a study aimed at revealing special-educational-needs pupils' learning potential by means of an ICT-based assessment including a dynamic visual tool that might help pupils when solving mathematics problems. The study focused on subtraction problems up to 100, which require "borrowing". These problems, in which the value…

Second and third graders from six Dutch elementary schools (N = 168) solved two sets of almost identical addition and subtraction sums at a two-week interval. Inconsistency in strategies, which characterized half the subjects, was related to unfamiliar sums and resulted in misinterpreted errors. (TJH)

The degree to which test item bias techniques can lead to interpretable results when groups are defined in terms of specified differences in the cognitive processes involved in problem-solving strategies was studied. Data from two groups of junior high school students (N=545) were used. (TJH)

Diagnostic score reports linking assessment outcomes to instructional interventions are one of the most requested features of assessment products. There is a body of interesting work done in the last 20 years including Tatsuoka's rule space method (Tatsuoka, 1983), Haertal and Wiley's binary skills model (Haertal, 1984; Haertal & Wiley, 1993),…

As part of a 3-year study of arithmetic problem-solving skills in young children, pretests were administered to 180 middle class first grade students. Following each of three instructional units, another achievement test was administered. The three first grade units corresponded to the Developing Mathematical Processes curriculum and involved…