Recent research suggests that humans and other animals have sophisticated abilities to extract both statistical dependencies and rule-based regularities from sequences. Most of this research stresses the flexibility and generality of such processes. Here the authors take up an equally important project, namely, to explore the limits of such…

We investigated the common difficulties that students have with concepts related to rotational and rolling motion covered in the introductory physics courses. We compared the performance of calculus- and algebra-based introductory physics students with physics juniors who had learned rotational and rolling motion concepts in an intermediate level…

Mathematics majors' study of abstract algebra should provide these students with opportunities to connect what they are learning to their prior experiences with algebra in high school. This paper illustrates how such connections can be used to motivate the notion of binary operation and the axioms for a group.

Perimeter and area are important real-world concepts in their own right, and their relationship certainly is no less important. This relationship can be intuitively challenging for both children and adults. In this article, the author explores the relationship between perimeter and area with students from grades 4 to 6. The study of perimeter-area…

This article describes a unit of instruction designed to promote algebraic thinking in second graders. Students examined second- and fourth-grade students' ages and heights on a table and graph and described the patterns that they observed in the data.

In 2 experiments with 74 high school students, subjects studied worked examples while learning how to translate English expressions into algebraic equations. Those using worked examples outperformed the control group on posttests, made fewer errors, completed work more rapidly, and required less assistance from the teacher. (SLD)

The "I CAN Learn[R] Mathematics Curriculum" is designed to help ethnically diverse, inner-city students in grades 7 through 10 achieve parity in mathematics and problem-solving skills. It uses an interactive software program to teach pre-algebra and algebra. The "I CAN Learn[R] Algebra 1" course, which was used in all of the…

This general achievement trends profile includes information that the Center on Education Policy (CEP) and the Human Resources Research Organization (HumRRO) obtained from states from fall 2008 through April 2009. Included herein are: (1) Bullet points summarizing key findings about achievement trends in that state at three performance…

This study examined practices of teachers in Wake County Public Schools' (WCPSS) middle school Algebra I classes. Regression analyses of standardized state testing results allowed for identification of the most effective and least effective Algebra I teachers. The study used surveys, observations, and focus group interviews to compare and contrast…

In this study we explored the effectiveness of individualizing instruction using a system that diagnosed students' knowledge gaps in pre-algebra and provided individualized instruction and practice. One hundred middle school students participated, and received either no instruction or individualized computer-based instruction. Diagnosis of…

This descriptive study was aimed at looking into how Primary 5 pupils solve pre-algebra problems concerning patterns and unknown quantities. Specifically, objectives of this study were to describe Primary 5 pupils' solution strategies, modes of representations and justifications in: (a) discovering, describing and using numerical and geometrical…

Experiences in designing and teaching a reformed abstract algebra course are described. This effort was partially a result of a five year statewide National Science Foundation (NSF) grant entitled the Rocky Mountain Teacher Enhancement Collaborative. The major thrust of this grant was to implement reform in core mathematics courses that would…

The purpose of this study was to determine the effectiveness of a typical California community college Intermediate Algebra course in preparing students for success in the transfer level mathematics courses for which Intermediate Algebra was the prerequisite. The subsequent mathematics course taken by each of the 986 students who received a grade…

The aim of this study is to investigate the effectiveness of computer-based/assisted teaching method using ISETL [Interactive SET Language] programming language on students' understanding of subgroup and group concepts. The data was collected from a group of students by means of written assessments and clinical interviews. Analysis of student's…

This article describes how two middle school teachers incorporated algebraic thinking into their textbook-based geometry lessons. One teacher embedded algebraic concepts within an existing textbook lesson while the other teacher elicited algebraic thinking by extending a textbook lesson. (Contains 5 figures.)