Sustaining engagement with a mathematics task is not a novel suggestion for effective mathematics teaching. "Principles and Standards for School Mathematics" (2000) specified that "students need to know that a challenging problem will take some time and that perseverance is an important aspect of the problem-solving process and of…

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of…

Every day, 27,000 trees are used to make bathroom tissue. Americans use an average of 23.6 rolls per person per year, and more than 7 billion rolls of toilet paper are sold yearly in the United States alone. Perhaps the amount of bathroom tissue used can be reduced by changing the dimensions of the paper or the core. This brief article presents…

This study explores talent-development trajectories of early-career chemical engineers to identify key components for success in the field using the talent development megamodel as a theoretical framework. Interviews with 12 recent PhD graduates reveal a trajectory across four developmental stages: (a) math ability and science ability, (b)…

This research investigates the impact of mathematical problems created with Scratch on the problem-solving skills of 8th-grade middle school students. The research was based on the descriptive design of mixed research approaches. In this direction, the research model was single-group pretest-posttest design, which is a weak experimental design…

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.

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…

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…

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 mathematics test is the most difficult test in the GED (General Education Development) Test battery, largely due to the presence of story problems. Raising performance levels of story problem-solving would have a significant effect on GED Test passage rates. The subject of this formative research study is Ms. Stephens' Categorization Practice…

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…

We investigated how pre-service teachers (PSTs) interpret their calculations in proportional tasks. A written questionnaire was administrated to 199 PSTs and an inductive content analysis approach used for data analysis. We found that one item that asked PSTs to interpret the meaning of their results had unusually low success; open coding on the…