Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's…

The way mathematics teaching and learning activities are presented to learners can make them hate or like the subject. The question of accomplishing the mathematics education of the learner from primary to post-secondary school levels is one which necessarily tasks, not only the teacher's stock of mathematical knowledge but also his skill, his…

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…

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…

Math fluency, which refers to the ability to solve single digit arithmetic problems quickly and accurately, is a foundational mathematical skill. Recent research has examined the role of phonological processing, executive control, and number sense in explaining differences in math fluency performance in school-aged children. Identifying the links…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

Mathematical knowledge in classrooms is mediated through the use of both technical and informal language. This paper is a report of a study of the language use of teachers as they examine students' work and discuss teaching for the topic of fraction operations. This provides a window on their pedagogical content knowledge and also on the way in…

The problem of sex bias in mathematics word problems is discussed, with references to the appropriate literature. Word problems are assessed via cognitive science analysis of word problem solving. It has been suggested that five basic semantic relations are adequate to classify nearly all story problems, namely, change, combine, compare, vary, and…

Ongoing work toward developing a learning environment that will perform real-time diagnoses of students' difficulties in solving mathematical word problems is described. The learning environment designed consists of a microworld and expert modules. The microworld (or toolbox) is a collection of mouse-driven interfaces that facilitate a transition…

The article details a process to develop and test an instructional program designed to teach learning disabled students the procedural, process, and task specific knowledge necessary to solve four kinds of arithmetic story problems. Single subject and group research designs were used to evaluate the problem solving unit. (Author/DB)

This article summarizes research on how students who are bilingual or learning English use two languages and examines how this research is relevant to mathematics classrooms. It is easy to notice that bilingual students sometimes use two languages. It is more difficult to know whether this practice might be significant to learning mathematics.…

Evaluation of the ability of 77 students who are moderately to profoundly deaf to solve arithmetic word problems found that students who are deaf experienced delays in successful work problem performance. Results support the idea that the delayed language acquisition of this population affects their capacity to solve arithmetic word problems.…

This special section on cognition and mathematics contains an introduction and 13 articles on advances in the psychology of mathematics learning. The articles focus on how students learn to solve mathematics problems, including arithmetic computation problems, arithmetic word problems, and computer programing problems. (SLD)