A SPECIAL COURSE DESIGNED TO MEET THE NEEDS OF STUDENTS WHO ENTER HIGH SCHOOL WITH ACHIEVEMENT IN MATHEMATICS BELOW THE SIXTH-GRADE LEVEL IS PRESENTED. AFTER COMPLETION, THE STUDENTS WILL BE QUALIFIED TO TAKE THE ESSENTIAL MATHEMATICS COURSE DESIGNED FOR STUDENTS WHO ARE NOT PLANNING TO ENTER COLLEGE. THE BASIC CONCEPTS, UNDERSTANDINGS, AND SKILLS…

CUISENAIRE RODS ARE COLORED, RECTANGULAR PIECES OF WOOD ONE UNIT WIDE AND ANY NUMBER OF UNITS LONG. THE COLOR OF THE ROD DEPENDS UPON ITS LENGTH. RODS CAN BE USED IN KINDERGARTEN THROUGH HIGH SCHOOL, BUT ARE PARTICULARILY HELPFUL IN THE EARLY GRADES. THE RODS CAN BE USED TO TEACH CHILDREN SUCH CONCEPTS AS…

To test whether the process of learning mathematics involves the effect of a hierarchical concept (as opposed to a "snowball" effect, in which one set of concepts becomes the basis for a new set), a matrix of correlations of progress test scores from a self-instructional high school algebra course was analyzed. The form of the matrix did not…

This report describes the results of preliminary work by the Human Resources Research Organization to develop a comprehensive theory for structuring subject matter. The report focuses on the first three of five components that any comprehensive model of instruction should include: (1) a representation of the subject matter to be taught; (2) a…

Investigated was the feasibility of presenting proof materials to college-capable sixth-grade students. A unit on mathematical proof was developed using an iterative procedure. Formative evaluation procedures were used to improve various components of the unit. Included in the unit are terminal student behaviors, cartoon stories, and several…

This status study provides evidence supporting the feasibility of teaching certain probability concepts to fifth and sixth grade students. The study employed an interview technique to analyze the status of three basic concepts of probability--sample space, probability of an event, choosing the most likely of two events. The effects of visual aids…

Reported is the development and testing of a program designed to encourage individual creative mathematical activity in first grade students. Initially some characteristics of the creative process and creative thinking were examined and six criteria describing certain aspects of mathematical creativity were identified and validated. An instrument…

Reported is research involving the development and testing or a program designed to encourage individual creative mathematical activity in first grade students. Initially, some characteristics of the creative process and creative thinking were examined and six criteria describing certain aspects of mathematical creativity were identified and…

Reported are the results of a study designed to determine the most efficient learning sequence appropriate for preschoolers in learning three set relations. The efficiency of a particular ordering of the relations, equivalence (E), greater than (G), less than (L)) was evaluated in terms of time required to reach criterion, and amount of transfer.…

Provided is an introduction to the properties of continued fractions for the intellectually curious high school student. Among the topics included are (1) Expansion of Rational Numbers into Simple Continued Fractions, (2) Convergents, (3) Continued Fractions and Linear Diophantine Equations of the Type am + bn = c, (4) Continued Fractions and…

This paper presents a method of encoding geometric line-drawings in a way which allows sets of such drawings to be interpreted as formal languages. A characterization of certain geometric predicates in terms of their properties as languages is obtained, and techniques usually associated with generative grammars and formal automata are then applied…

Curves are considered to have the same shape when they are related by a similarity transformation of a certain kind. This paper extends earlier work on parallel curves to curves with the same shape. Some examples are given more or less explicitly. A generalization is used to show that the theory is ordinal and to show how the theory may be applied…

Reported are the results of an investigation of the child's acquisition of the concept of area measure. To measure this acquisition, four axioms were developed to define the concept of area. A task was developed for each axiom to test operational understanding of the axiom. A test of vocabulary and a conservation of area task were administered to…

The three parts of Vancouver's survey test in mathematics--computation, concepts, and problems--for grade 6 are presented. The parts contain 36, 24, and 12 items respectively. (For related document, see TM 002 473.) (KM)