The intention of this investigation was to diagnose the retention of some basic skills in some topics in algebra and geometry and to reveal difficult steps in the learning processes in these topics. (MP)

Solutions to difficult equations are illustrated with numerical techniques that can be used easily on calculators. Flowcharts and programs for computers and calculators are included. (MP)

Tree diagrams with numbers in a given pattern generate questions related to pattern recognition and number concepts such as binary numbers and exponentials. (MP)

A method for solving certain types of problems is illustrated by problems related to Fibonacci's triangle. The method involves pattern recognition, generalizing, algebraic manipulation, and mathematical induction. (MP)

A questionnaire was given to 129 high school students taking college-prep mathematics and to 63 college students taking a pre-calculus course. Students were to identify sentences as axioms, postulates, facts, definitions, or theorems. Findings showed students did not have the formalist point-of-view about the structure of mathematics. (DT)

Definitions of giftedness, the identification of gifted students, appropriate learning materials, research, teacher education, public relations, and the role of state and local groups in the education of the gifted are discussed. (DT)

Cellular partitioning of space is discussed. Directions are given for making geometric models of cells. (DT)

Mathematics as a multicultural activity is discussed, with emphasis on contributions by Hindu and Muslim mathematicians. (DT)

Methods of incorporating the history of mathematics into secondary school mathematics lessons are discussed. (DT)

Using a staircase to introduce the concept of slope is discussed. (DT)

These worksheets provide students an experience with a geometry in which distance is not assigned in the usual Euclidean fashion. (DT)

After students learn that it is impossible to trisect an angle using compass and straight-edge, students are introduced to the trisectrix curve which accomplishes the trisection. (SD)

Discussed is the distinction between weight and mass, and the need to distinguish these concepts in a successful metrication program. (SD)

The famous birthday problem is discussed and activities which can be used with it as an introduction to probability are examined. (SD)

Eighty tenth-graders studied a two-day unit on quadratic inequalities presented in one of four programmed-booklet forms: analytic treatment with advance organizer, analytic treatment plus introductory overview, graphical treatment with advance organizer and graphical treatment with introductory overview. No differences were found between groups on…