Function Probe is a multi-representational software for Apple Macintosh computers. It was designed to allow students to approach problems in different ways and/or use different representations. This case study describes a 16-year-old student as he creates a path among a variety of representations of transformations of functions while using the…

Over the past 10 years, national conferences and committees investigating the state of American mathematics education have advocated an increased emphasis on problem solving and mathematical modeling situations in the secondary school curriculum. However, little effort has been made to prepare secondary school teachers to use mathematical modeling…

This booklet is a collection of 45 problems that have appeared in the Problem Department of the journal "School Science and Mathematics." The booklet is divided into four parts. The first part presents 20 cryptarithms, puzzles in which letters or symbols are substituted for the digits in an arithmetical calculation, that require knowledge of…

The 52 tests cited in this bibliography are geared to students in grade 7 and above. This bibliography also includes descriptions of item banks and test batteries in which algebra is one of several subjects being assessed. Although grades 1 through 12 are represented, the tests are primarily designed for grades 7 and above, including adult-level.…

This study examines the effectiveness of multiple methods of soliciting attributions. The Attributional Style Questionnaire, specific attributions, and causal dimensions are used to predict the grades and feelings of frustration of college algebra students. The results show that, contrary to current theoretical work, both specific attributions and…

This review guide, prepared as an aid to teachers of Course III, starts with a pre-test review of Course II topics found again in Course III. The five units of Course III, as outlined in the New York State Syllabus, are then separated into nine smaller units. These include: real numbers; complex numbers; functions; logarithms; trigonometry;…

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

This study tested the benefits of matching field dependent (FD) learners to an algorithmic method and field independent (FI) learners to a discovery method relative to mathematics achievement. It also attempted to discover if FD learners reacted more positively to computer experience than did FI learners. A total of 126 college algebra students…

This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. Intended for administration in January 1987, it is available in both English and French. It contains 52 multiple-choice questions and 3 written-response problems, with 2.5 hours allowed for completion. Approved calculators may be…

The effect on algebra achievement of college students of using a specific study method, algebra notecards, was examined. Whether achievement differed for adult learners and traditional college students, and the interaction between the study method and the status of the learner were also investigated. The research was conducted at the University of…

This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. Intended for administration in June 1986, it is available in both English and French. It contains 52 multiple-choice questions and five written-response problems, with two-and-one-half hours allowed for completion. Approved…

The use of new extension of standard Item Response Theory (IRT) modeling of dichotomous items to include external variables is proposed. External variables may appear both as categorical grouping variables and as continuous variables; this requires the formulation of a model for the relationships between the external variables and the response…

Described is the notion of multiple alternative representations of mathematical reasoning, particularly as they relate to algebraic notation and the potential of computers to change representations. Features of a desirable notation for algebraic problem solving are described. This is followed by a description of the RAND Corporation's intelligent…

The New Jersey College Basic Skills Placement Test (NJCBSPT) is designed to measure certain basic language and mathematics skills of students entering New Jersey colleges. The primary purpose of the two mathematics sections is to determine whether students are prepared to begin certain college-level work without a handicap in computation or…

This study explored the relationship between students' high school mathematics courses and grades; the affective variables--mathematics anxiety, effectance motivation, and attitude toward success; and performance in the first quarter developmental studies algebra course. The study reports significant differences between males and females on…