Pre- and posttests of prerequisite vocabulary terms were given to (n=162) intermediate and (n=178) college algebra students to determine their word knowledge and differences between the intermediate and college algebra students. (11 references) (MKR)

Examines students' understanding of the quantitative relationships, operations, and properties of relationships and operations that are introduced in arithmetic and beginning algebra courses. Develops alternative approaches to the teaching of structure such as the structural-to-computational model and the procedural-to-structural model. Concludes…

Examines advanced students' course taking procedures and their senior year mathematics participation. Concludes that students who took early algebra demonstrated a substantially higher participation rate in advanced mathematics in the later grades of high school than students who did not. (Contains 25 references.) (ASK)

Presents a teaching experiment to turn students from external observers into active participants in a game of algebra learning where students use graphs to build meaning for equivalence of algebraic expressions. Concludes that the graphic-functional approach seems to make the introduction to algebra much more meaningful for the learner. (ASK)

Reported is a study of types of errors exhibited by students of intermediate algebra at the college level and the effect the time of day instruction has on students' performance. Results indicated that two types of errors, conceptual and prerequisite, and that student performance is better in the morning. (MDH)

An algebra test administered to (n=18) first-year college students found a disregard for negative numbers, ineffective use of counterexamples, misapplication of rules, and a lack of a good grasp of relevant mathematical terminology. (12 references) (MKR)

Using computers to provide diagnosis and remediation in mathematics is emphasized. Some essential features of technology-supported learning environments are discussed, as well as features that facilitate their use. Illustrated is a computer environment for learning algebra. (MNS)

Several intuitive proofs for evaluating specific infinite expressions are given. Observations on intuition and errors in mathematics are included. (MNS)

Discusses a technique for graphically composing functions. Describes three-step composition procedures in two- and three-dimensional rectangular coordinate systems. Provides three examples. (YP)

Describes learning difficulties students may have with the basic notions of linear algebra and three phases of abstraction. Discusses results of a program based on the abstraction process. (YP)

Assessed was the level of thinking of 140 students who had been placed in developmental algebra as entering college freshmen. Scores on the Group Assessment of Logical Thinking, Scholastic Aptitude Tests, college placement tests; high school grade point average, and developmental algebra final grade were analyzed. Group characteristics are…

A collection of student distortions, represented by student-invented variations of theorems, are presented. They were drawn from examination papers of 17-year-old students in Israel. (MNS)

Illustrated first is the case in which a wrong procedure (with fractions) leads to a correct result. Trying to justify why it works in this case and looking for similar patterns involved interesting algebraic considerations as well as use of computers. (MNS)

Reports on a study to determine if having students write about the work required in doing three types of exercises from elementary algebraic fractions would affect the students' error patterns on quizzes. The study involved six developmental studies in elementary algebra classes. (PK)

Tests of (n=105) ninth-grade algebra students involving the addition and multiplication of monomials found that common, systematic errors made when multiplying monomials were related logically to the symbolism used and the algebraic convention of using an implicit 1 as an exponent. (16 references) (MKR)