Produces algebraic solutions by reducing the problems to equations and arithmetic solutions that do not use variables. Investigates how the arithmetic solution helps students better understand the problem before they approach it algebraically and how logic used in solving the problem arithmetically can be directly linked to the algebraic…

Presents and investigates a theoretical perspective on the development of understandings of mathematical operations with a particular focus on addition. Presents a case study on the development of a young boy and concludes that his attainment of aspects of operation sense supported transitions into algebraic ways of thinking. Contains 46…

Reports the results of research conducted to investigate the relationship between involvement in learning mathematics and achievement as measured by test scores and course grades. Finds that attendance is the one measure of effort most closely related to success in developmental mathematics. Indicates that academic autonomy was consistently…

Presents the story of a mathematics teacher's transformation that resulted from her engagement in collaborative action research. Discusses issues related to the broader study of collaborative action research in the mathematics classroom that are connected to teachers' transformation. (Contains 31 references.) (Author/ASK)

To allow variable amounts of time for students to complete Algebra I, a gateway course, schools must address four issues: curriculum, instructional methods, assessment, and scheduling. The Algebra I curriculum should be divided into four parts; assessments should be designed to measure students' mastery of each part. Also, a two-period block of…

Describes an approach to algebraic thinking based on an extension of the problem-solving tasks typically investigated by elementary and middle school students. Demonstrates how elements of algebraic thinking may be developed in a systematic and coherent way through problem-solving experiences. States that students' pattern-building capabilities…

Describes an experiment using applications and projects to motivate students in college algebra. Provides a few illustrative examples of the applications/projects used and shares some student comments. (Author/ASK)

Interviews students majoring in mathematics who had passed a required introductory course on algebraic structures on students' difficulties with basic concepts in group theory as part of a research project. Reports data concerning cyclic groups. (ASK)

Presents findings from a study of students enrolled in college algebra. Concludes that the predicted success of students is related to explanatory variables using a linear model. Recommends advising cut-off scores in terms of student success rated as well as the mission statement and philosophy of the university. Contains 12 references.…

Used national survey data to examine the impact of high school algebra on students who differed in mathematics skills before entering high school. Regression analysis with over 12,500 students indicates that all students benefit from taking algebra, although benefits are smaller for those with very low prior achievement. (SLD)

Used data from groups of 376 and 273 algebra teachers to study the reliability of the Stages of Concern Questionnaire (G. Hall and S. Loucks, 1978) and explore changing it to a five-stage questionnaire rather than the seven current stages. Results confirm a lack of reliability but do not support a change to five stages. (SLD)

Gives concrete examples of examinations in which Computer Algebra Systems (CAS) can be used. Discusses the need to link the construction of the examination and evaluation of the exam scripts in terms of an existing classification scheme for mathematical tasks, the MATH Taxonomy. (Author/MM)

The effect of optional retesting on the achievement of 1,314 college students in an individualized algebra course was studied. A performance improvement was found for about 90% of students who had earned a "B" or lower. Optional retesting appears to affect initial mastery, but not cumulative mastery. (SLD)

Presents and discusses examples that can be used to develop the concept of slope as a rate of change through three modes of learning: (1) visualization, (2) verbalization, and (3) symbolization. (ASK)

Computer algebra systems have great potential uses, but learning the basic concepts of algebra is itself a mathematical activity. Explores theoretical concepts that may be seen as essential enabling skills for computer algebra systems users. (Author/ASK)