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…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

The probability is exceptional in the teaching of mathematics because students often have difficulties to understand the basic terms and the problem solving strategies. Understanding lacks of the probability concept and various types of misconceptions arise from the misleading intuition and misinterpretations of experience with the stochastic…

We report a novel survey that narrows the gap between information about teachers' knowledge of fraction arithmetic provided, on the one hand, by measures practical to administer at scale and, on the other, by close analysis of moment-to-moment cognition. In particular, the survey measured components that would support reasoning directly with…

Insightful problem solving is a vital part of human thinking, yet very difficult to grasp. Traditionally, insight has been investigated by using a set of established "insight tasks," assuming that insight has taken place if these problems are solved. Instead of assuming that insight takes place during every solution of the 9 Dot, 8 Coin,…

The strategy choice model (SCM) is a highly influential theory of human problem-solving. One strength of this theory is the allowance for both item and person variance to contribute to problem-solving outcomes, but this central tenet of the model has not been empirically tested. Explanatory item response theory (EIRT) provides an ideal approach to…

This study used a person-centered approach to examine mother-daughter dyad behaviors when jointly solving addition problems during a card game. The goal was to identify maternal and child profile behaviors during the interaction as predictors of children's autonomous addition accuracy and strategy use at the end of first grade. Videotaped…

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…

Arithmetic is a major mathematical focus in elementary school curriculum, and researchers such as Mason (2008) claim that "algebraic thinking is required in order to make sense of arithmetic" (p. 58). When adding, subtracting, multiplying, and dividing, learners must rely on a small set of fundamental properties also important for the…

This study investigated 111 pre-service teachers' (PSTs') flexibility with referent units in solving a fraction division problem using a length model. Participants' written solutions to a measurement fraction division problem were analyzed in terms of strategies and types of errors, using an inductive content analysis approach. Findings suggest…

This study was conducted to determine the degree of relationship that exists between learners' level of comprehension and solving skills on mathematical word problems of grades four to six learners in Kang-iras Elementary School. It attempted to establish a relationship between the learners' level of comprehension and solving skills. This research…

This study's purpose was to investigate effects of 3 intervention approaches for building working memory (WM) and improving word-problem solving (WPS). Children with mathematics difficulties (n = 240; 7.51 years [SD = 0.33]) were randomized to 4 conditions: a control group, general WM training with contiguous math practice, WPS intervention…

It is aimed to determine the strategies used by the fourth-grade elementary students during the operational estimations in this research which is designed by using basic qualitative analysis. The study group consists of 26 fourth-grade students selected through convenience sampling method and attending at a state school which was located in the…

Mental models are representations of students' minds concepts to explain a situation or an on-going process. The purpose of this study is to describe students' mental model in solving mathematical patterns of generalization problem. Subjects in this study were the VII grade students of junior high school in Situbondo, East Java, Indonesia. This…

The article is dedicated to solving extrema problems in teaching mathematics, without using calculus. We present and discuss a wide variety of mathematical extrema tasks where the extrema are obtained and find their solutions without resorting to differential. Particular attention is paid to the role of arithmetic and geometric means inequality in…