In order to solve word problems, students need to be able not just to read the words but comprehend what they mean. Paul Swan discusses three tiers of vocabulary that need to be included in the pedagogy of mathematics lessons and strategies for classroom practice.

Problems are part of our lives. It causes stress, tension, emotional instability, and physical strain to us. It is very essential to deal with our problems before they deal with our happiness. Problem solving skill is an irreplaceable life skill and it is cognitive or thinking activity essential to our day-to-day lives. In order to lead a…

Identifying mathematical interventions that practitioners can implement to improve the mathematical problem solving (PS) of students is a need for the field. Literature on the PS performance of students with disabilities has grown; recently, schema instruction (SI) has been suggested as an evidence-based practice. The purpose of this study was to…

This article reports on a "post hoc" study using a randomised controlled trial with 31,842 students in the Netherlands and an instrument consisting of 21 paired problems. The trial showed a variability in the differences of students' results in solving contextual mathematical problems with either a descriptive or a depictive…

In this article, the authors describe the Japanese term "bansho," which refers to the intentional use of board space for facilitating student learning. Bansho offers a structure for sequencing mathematics visually on the board. By purposefully organizing the board space alongside the lesson, teachers can provide students with a framework…

The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…

The purpose of this study was to introduce a rubric named "Rubric for the Assessment of Modeling Skills" for assessing cognitive modeling skills and explaining the rubric's development process. The dimensions of the rubric are understanding the problem, simplifying, mathematizing, working mathematically, interpreting and validating.…

This longitudinal study aimed to identify specific executive function (EF) profiles in 5-year-old children and to examine the association between these profiles and later math achievement. Six EF measures were administered to 175 children who were then tested in Grades 1 and 3 on math tasks. Using a cluster analysis, four EF profiles were…

A presentation on the Budapest Seminars in Mathematics Education website, inspired the author to try a new approach while teaching a unit on quadrilaterals in his Geometry for K-8 Teachers course, a class primarily composed of undergraduate students interested in teaching at the elementary or middle school level. The author designed a lesson that…

Originally intended as a replication study, this study discusses differences in problem solving performance among different domains caused by the same instructional intervention. The learning sciences acknowledges similarities in the learners' cognitive architecture that allow interventions to apply across domains, but it also argues that each…

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…

Ratio and proportional relationships, along with the interrelated topics of fractions,decimals, and percent, provide a critical foundation for algebra (National Mathematics Advisory Panel, 2008). Proportional reasoning, which not only requires understanding the concept of ratios and that two or more ratios are equal, also requires the ability to…

The adoption of the Common Core State Standards has necessitated a change in the instructional practices used by many mathematics teachers. The new standards encourage problem solving and the development of conceptual understanding rather than rote memorization of formulas and rules. Researchers have demonstrated that formative assessment is a…

This dissertation reports the research methodology and findings of three studies focused on mathematical modeling as a structured problem-solving process where the student translates relevant details from a situation, event, or phenomena in daily life into mathematical language with mathematically-defined structures and operations, which form the…

Despite recommendations to incorporate mathematical problem solving into the practice of primary teachers there is little evidence of the widespread acceptance of such advice by Early Years teachers. Understanding teachers' perceptions of the obstacles they encounter when incorporating mathematical problem solving into their teaching can shed…