In this article, Garcia and Davis describe problem analysis as the process of examining a given mathematics exercise to find ways in which the problem can be modified and extended to create a richer learning opportunity for students. Students are often reluctant to attempt what they perceive to be higher-order thinking problems, but problem…

Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

Pattern blocks are inexpensive wooden, foam, or plastic manipulatives developed in the 1960s to help students build an understanding of shapes, proportions, equivalence, and fractions (EDC 1968). The colorful collection of basic shapes in classic pattern block kits affords opportunities for amazing puzzle-like problem-solving tasks and for…

Generalizing--along with conjecturing, representing, justifying, and refuting--are forms of mathematical reasoning important in all branches of mathematics (Lannin, Ellis, and Elliott 2011). Increasingly, however, generalizing is recognized as the essence of thinking in algebra (Mason, Graham, and Johnston-Wilder 2010; Kaput, Carraher, and Blanton…

An historical case is presented in which extra-mathematical certainties lead to invalid mathematics reasonings, and this is compared to a similar case that arose in the area of virtual education. A theoretical-methodological instrument is proposed for analysis of certainties. The article suggests the need for teachers to be aware that certainties…

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the "analytical derivation" game. This game involves deriving an…

The focus of the present synthesis reflects the research on programs, practices, and policies intended to improve mathematics outcomes funded through the Institute of Education Sciences' (IES's) National Center for Education Research (NCER) and National Center for Special Education Research (NCSER). The authors were asked to review those published…

This study aims to investigate the effectiveness of the Emporium instructional method in a course of college algebra and trigonometry by comparing to the traditional lecture method. The math emporium method is a nontraditional instructional method of learning math that has been implemented at several universities with much success and has been…

This paper describes a model for building cognition-and-instruction-based goal trajectories (GT) in the context of a study that examines the validity of curriculum-embedded assessments. The model consists of six design processes and two constraints. The GT is constructed from curriculum-specified learning goals as well as developmental…

Many integrals require two successive applications of integration by parts. During the process, another integral of similar type is often invoked. We propose a method which can integrate these two integrals simultaneously. All we need is to solve a linear system of equations.

Problem solving in the field of quantitative composition of solutions (QCS), expressed as mass share and molar concentration, is essential for chemistry students. Since successful chemistry education is based on different mathematical contents, it is important to be proficient in both mathematical and chemistry concepts as well as interconnections…

Students' attitudes and approaches to physics problem solving can impact how well they learn physics and how successful they are in solving physics problems. Prior research in the U.S. using a validated Attitude and Approaches to Problem Solving (AAPS) survey suggests that there are major differences between students in introductory physics and…

The data for this study were gathered from an assignment consisting of 10 number sense related mathematics problems completed in an algebra course at developmental level. The results of the study suggest that a majority of developmental mathematics students use routine algorithmic procedures rather than mathematical reasoning to solve problems.…

Linear algebra is a basic mathematical subject taught in mathematics and science depar-tments of universities. The teaching and learning of this course has always been difficult. This study aims to contribute to the research in linear algebra education, focusing on linear dependence and independence concepts. This was done by introducing…