The ability of students to sort cards based on surface features and deep patterns is investigated. The effect of the presence of variables and what makes a pattern difficult or easy for students to recognize are discussed. Study revealed that students are unsuccessful at making connections between expressions, sentences, and sequences which share…

Hierarchical (adaptive) and linear methods of testlet construction were compared. The performance of 2,080 ninth and tenth graders on a 4-item testlet was used to predict performance on the entire test. The adaptive test was slightly superior as a predictor, but the cost of obtaining that superiority was considerable. (SLD)

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

Discusses a classroom presentation using a Tonka toy truck's forward and backward motion that (1) develops a graphical representation of the truck's one-dimensional motion; (2) creates graphs representing constant velocity; (3) leads students to a definition of average velocity; and (4) introduces the concept of instantaneous velocity. (MDH)

This paper describes an accelerative instructional program in algebra provided to a sixth-grade boy, highly able in mathematics, by parental home tutoring. The boy's high intrinsic motivation and teaching sensitive to his needs and abilities led to successful achievement. (DB)

Discussed is an application of the computer software package, "Mathematica," to solve typical optimization problems from freshman calculus. An example of the use of this method is provided. (CW)

This study investigated questions asked during tutoring by 27 college students about research methods and by 13 seventh graders about algebra. Student achievement was positively correlated with the quality of questions after students had some experience and training in tutoring, but the frequency of questions was not. (SLD)

Stresses recognition and application of the identity property of 1 across the mathematics curriculum to help students overcome difficulties. (MKR)

Explores algebraic thinking as children search for patterns while collecting, organizing, and graphing data and as they derive equations describing relationships found in the data. (ASK)

Discusses the application of the theory of contingent tutoring to the design of a computer-based system for algebra. Considers help seeking and analyzes interactions between secondary school students and the computer-based tutoring system to explore the relations between individual differences in learner-tutor interaction, learner's prior…

Middle school and high school algebra students (n=2,369) taught in a manner consistent with the National Council of Teachers of Mathematics (NCTM) Standards took three standardized algebra assessments. Middle school students seemed to benefit from the approach, and high school students were neither hindered nor helped. (SLD)

Presents a brief definition and examples of residue designs while sharing some of the algebraic thought that a student used to form generalizations about the patterns discovered during the investigations of residue designs. (ASK)

Details a study in which grade 9 females were assigned to either an all-female or mixed-sex algebra class. Findings indicate that the all-female intervention group demonstrated a greater gain in math scores between grades 8-11 than the nonintervention group. Contains 41 references. (DDR)

Reports that students entering an urban state college still had high remedial placement rates even though they successfully completed college preparatory math and English courses in high school. Discusses the "chain of blame" and concerns regarding the rigor of high school programs. (Contains 45 references.) (AUTH/NB)

Describes changes that are being made in mathematics teachers' subject studies in order to provide students with sufficiently deep knowledge of mathematics and science and with present-day expertise in their profession as teachers. Provides an abstract algebra course as the ultimate example of a pedagogical experiment where co-operative learning…