The purpose of this study was to identify common problems students that experience in proof writing. Toward this end, the authors videotaped groups of students in a bridge course as they worked to construct mathematical proofs. They report on their observations and offer suggestions as to how teachers of transition courses might enhance the…

"The Price is Right" ("TPIR") is a rich source of examples of applied probability, combinatorics, and game theory. While some of the games played on stage by individual contestants stress a knowledge of pricing, many are also heavily based on probability. "TPIR" stage games are a treasury of interesting modules that can be effective learning tools…

In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

Groups of first-grade (mean age = 82 months), third-grade (mean age = 107 months), and fifth-grade (mean age = 131 months) children with a learning disability in mathematics (MD, n=58) and their normally achieving peers (n = 91) were administered tasks that assessed their knowledge of counting principles, working memory, and the strategies used to…

The Third International Mathematics and Science Study (TIMSS) 1999 Video Study examined eighth-grade mathematics teaching in the United States and six higher-achieving countries. A range of teaching systems were found across higher-achieving countries that balanced attention to challenging content, procedural skill, and conceptual understanding in…

Research suggests component skill performance has a strong positive relationship with composite skill performance. This study examined the association between accuracy and fluency for the component-composite relationship within multiplication. One hundred and fifty-seven fifth-graders did one-minute assessments for single-digit, and multi-digit…

Factors affecting performance on base-10 tasks were investigated in a series of four studies with a total of 453 children aged 5-7 years. Training in counting-on was found to enhance child performance on base-10 tasks (Studies 2, 3, and 4), while prior knowledge of counting-on (Study 1), trading (Studies 1 and 3), and partitioning (Studies 1 and…

One hundred eight preschool children and their teachers participated in a cross-sectional study of the socio-emotional correlates of mathematics skills. Children's strengths and difficulties were considered as possible correlates of skills. Initiative, self-control, and attachment were all related to better math skills. Overall behavior problems,…

A series of 13 survey questions based on a 50-50 spinner is used to explore school students' understanding of statistical variation in a chance setting. Five questions set the context by assessing the understanding of theoretical expectation and representation of repeated trials in a stacked dot (line) plot. Four questions provide opportunity to…

The New Zealand Ministry of Education has introduced a Numeracy Project for students aged 5-14 years in selected schools. The project encourages the adoption of flexible strategies for solving numerical problems, and discourages reliance on standard computational algorithms. One potential benefit of the project is that the methods students acquire…

The traditional order in which science courses are taught in U.S. high schools is biology, chemistry, physics. The physics course usually is regarded as very difficult because it requires both high-level mathematical skills and high-level thinking skills; it is taught in the final year of high school to provide time for students to develop the…

This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of…

Previous research suggested that Incremental Rehearsal (IR; Tucker, 1989) led to better retention than other drill practices models. However, little research exists in the literature regarding drill models for mathematics and no studies were found that used IR to practice multiplication facts. Therefore, the current study used IR as an…

A subcategory of computer-assisted instruction (CAI), games have additional attributes such as motivation, reward, interactivity, score, and challenge. This study used a quasi-experimental design to determine if previous findings generalize to non simulation-based game designs. Researchers observed significant improvement in the overall population…

In this article, the authors explain how curriculum-based measurement (CBM) differs from other forms of classroom-based assessment. The development of CBM is traced from computation to concepts and applications to real-life problem solving, with examples of the assessments and illustrations of research to document technical features and utility…