This article explores children's responses to a task that requires them to represent square units in a grid pattern, and highlights the importance to a child's mathematical development of recognizing pattern and structure. The grid task explores children's imagery association with area measurement, and provides clear evidence of students'…

The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a "transposition" of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic…

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel…

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an…

This study explores pupils' performance and processes in tasks involving equations and inequalities of complex numbers requiring conversions from a geometric representation to an algebraic representation and conversions in the reverse direction, and also in complex numbers problem solving. Data were collected from 95 pupils of the final grade from…

"Cognitive Tutor[R]", a full-year course, covers organizing single variable data, simplifying linear expressions, mathematical modeling, solving systems with linear equations, problem-solving using proportional reasoning, and powers and exponents. Students work at their own pace to develop problem-solving skills. The duration of each…

Today's college ACCUPLACER System's Computerized Placement Test (CPT) plays a major role for determining whether post-secondary students are ready for placement into Arithmetic, Elementary Algebra, Intermediate Algebra, or College Mathematics courses. It is widely used in most college systems in the U.S. This paper discusses some of the issues to…

A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…

The name of Zoltan P. Dienes (1916- ) stands with those of Jean Piaget, Jerome Bruner, Edward Begle, and Robert Davis as a legendary figure whose work left a lasting impression on the field of mathematics education. Dienes' name is synonymous with the multibase blocks that he invented for the teaching of place value. Among numerous other things,…

The What Works Clearinghouse (WWC) looked at elementary school math curricula designed to promote math knowledge and skills among elementary school students (average ages 5 to 10 years). Curricula included in this review are replicable, materials-based instructional programs that cover one or more of the following content areas: numbers,…

The "Connected Mathematics Project" ("CMP)" is a problem-centered mathematics curriculum designed for all students in grades 6-8. Each grade level of the curriculum is a full-year program and covers numbers, algebra, geometry/measurement, probability, and statistics. The program seeks to make connections within mathematics,…

When culture is integrated into the mathematics classroom, it improves students' academic achievement, helps move classrooms towards an equitable learning environment, helps students to have positive beliefs about mathematics, and integrates mathematics with other disciplines. Moreover, if you observe today's kids, the use of video games in their…

According to the NCTM reform suggestions, when teachers are orchestrators of student interactions, students adopt a more active role in explaining and learning mathematics. This research, which mapped the nature and role of meaningful mathematical discourse, provides insights into discursive practices that lead to rich mathematical interactions.…

"Algebra for everyone" has been a popular reform, though not commonly implemented and not fully evaluated. Through investigation, one might be able to determine whether courses deemed equivalent to a traditional college preparatory algebra course provide an equitable understanding of algebra concepts and skills, while controlling for…

A long-awaited federal study of reading and math software found no significant differences in standardized-test scores between students who used the technology in their classrooms and those who used other methods. The study compared classes overseen by teachers who used the technology-based products with those of other teachers who used different…