Background/Context: Since 2002, U.S. federal funding for educational research has favored the development and rigorous testing of interventions designed to improve student outcomes. However, recent reviews suggest that a large fraction of the programs developed and rigorously tested in the past decade have shown null results on student outcomes…

Previous research has found that different presentations of the same concept can result in different patterns of transfer to isomorphic instances of that concept. Much of this work has framed these effects in terms of advantages and disadvantages of concreteness or abstractness. We note that mathematics is a richly structured field, with deeply…

This study reports errors and misconceptions about division operation in fractions made by eighth-grade students. To investigate these errors and misconceptions, the study examined students' understanding of division operation in fractions using a questionnaire and expectation table. Students' misconceptions were determined for each question and…

Although the topic of division by zero has been widely discussed in the literature, this subject is still confusing for students, pre-service teachers and teachers. Because of this, teachers at various grade levels may encounter difficulties in conveying the concept to their students. Therefore, in order to provide students with a strong…

"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…

Several studies have shown that rapid automatized naming (RAN) is a significant predictor of mathematics, but the nature of their relationship remains elusive. Thus, the purpose of this meta-analysis was to estimate the size of their relationship and determine the conditions under which they correlate. We used a random-effects model analysis 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…

Mastering the basic facts for addition, subtraction, multiplication, and division is an essential goal for all students. Most educators also agree that success at higher levels of math hinges on this fundamental skill. But what's the best way to get there? Are flash cards, drills, and timed tests the answer? If so, then why do students go into the…

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,…

Learning or doing mathematics involves approximate quantification. The purpose of this research was to improve approximate number system acuity in primary school students with low achievement in mathematics. A quasi-experimental, pre-test, post-test design with a control group was utilized. Mathematics Achievement Test (MAT), Arithmetic…

This study examines the core predictors of the covariance in reading and arithmetic fluency and the domain-general cognitive skills that explain the core predictors and covariance. Seven-year-old Finnish children (N = 200) were assessed on rapid automatized naming (RAN), phonological awareness, letter knowledge, verbal counting, number writing,…

We present the results of a research project on arithmetic-algebraic thinking that was carried out jointly by a team in Mexico and another in Quebec. The project deals with the concepts of variable and covariation between variables in the sixth grade at the elementary level and the first, second, and third years of secondary school--namely,…

The Say-All-Fast-Minute-Every-Day-Shuffled (SAFMEDS) strategy promotes fast and accurate recall. The existing literature suggests that the strategy can help learners improve academic outcomes. Through a cluster randomized controlled trial, we assessed the impact of implementation support on children's mathematics outcomes during a teacher-led…

The literature has shown that preservice elementary school teachers (PSTs) struggle to adequately attend to a number's multiplicative structure to determine divisibility. This study describes an intervention aimed at strengthening preservice and in-service teachers' procedural knowledge with respect to using a number's prime factorization to…