Discusses the implications of a research study of more than 2000 students aged 11 to 15 that explored why the students interpret algebra in certain ways. Recommends strategies that can help teachers deal with prior knowledge that students may bring to their study of algebra. (DDR)

Proposes activities that promote students' awareness of the structure of the information involved in their everyday activities, and builds the concept of function from students' mental representations of phenomena. Recommends the use of spreadsheets to provide external representations of these functions. (DDR)

Describes an investigation-based, lecture-free first-year algebra course in which students are responsible for compiling their own textbooks. Discusses the purpose and procedures of the activity. Includes student worksheets. (KHR)

This article provides a rationale for using graphic organizers based on the fact that students with language disorders often struggle with traditional instruction that places large demands on language skills. Effective features of graphic organizers are identified and examples of direct instruction in secondary algebra using graphic organizers are…

Discusses Einstein's special relativity theory and some of the developmental mathematics involved. Presents motivational classroom materials used in discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations. (KHR)

This study compares algebra performance tested under timed and extended-time conditions of 88 community college students with and without learning disabilities (LD). With extended time, the LD students' performance did not differ significantly from the timed or extended-time scores of the students without learning disabilities. (Author/DB)

Describes the habits of mind that would be most desirable for students to develop. In high school for example, content-specific habits would include geometric habits of mind that support the mathematical approaches, and algebraic ways of thinking that complement the geometric approaches. (AIM)

Addresses the early stages of children's introduction to the use of variables in formal algebraic notation. Describes a teaching approach that aims to situate the use of formal notation in meaningful contexts. Presents a study of a teaching sequence based on children working with this approach using graphical feedback in problem solutions. (AIM)

Describes a study that examined block scheduling's effects on student and teacher performance and attitudes at a large Texas high school. While the 2-hour Algebra I block had a higher failure rate than the traditional 50-minute algebra class, the block classes were comprised of students who have traditionally struggled in mathematics. Maximizing…

Describes a project incorporating movies, literature, games, and other resources into mathematics instruction. Focuses on cultural differences. (Contains 10 references.) (YDS)

Describes an approach to the design of learning environments around a computer algebra kernel. Presents two environments to help students learn precalculus. Provides students with symbolic, graphic, and numeric tools as well as functionalities to help them build proofs. (Author/KHR)

Describes how a measure of problem difficulty (problem complexity) can be developed. Explores factors that may affect the difficulty of mathematics problems by focusing on ninth-grade student test responses (n=125), mathematics teacher questionnaire responses (n=29) in Hong Kong (China), and using a computer. Identifies four problem difficulty…

Nine freshmen in a ninth-grade accelerated algebra class were asked to solve five nonroutine combinatorial problems. The four mathematically gifted students were successful in discovering and verbalizing the generality that characterized the solutions to the five problems, whereas the five nongifted students were unable to discover the hidden…

Research findings concerning student learning difficulties in algebra are discussed. A teaching approach which takes into consideration these findings is suggested. Encouraging students to see patterns and to develop flexibility in their thinking are stressed. (CW)

Discussed is the use of magic squares as examples in a first year course in linear algebra. Four examples are presented with each including the proposition, the procedure, and a proof. (KR)