The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

Described are a discrete group of isometries that fix a line but do not stabilize a point. Each type is accompanied by an example of their representation in concrete form which served as material on which young children could operate. Pupil responses to each situation are provided. (CW)

Seriation, or serial ordering, is a type of classification involving the arrangement of items according to how much of a specific property they possess. Presents several activities for teaching seriation to preschool and kindergarten children. (PR)

This month's investigations deal with patterns and the importance of looking at data from more than a single perspective. The investigations focus upon ordering animals in some way. Includes reproducible student worksheets. (MKR)

Quantifies and confirms subjective impressions of similarity and differences in musical monophonic scores. Adapts concepts from sequence comparison theory and uses algorithms to define distances between any two melodies created by tone and rhythmic structure. Presents and applies a generalized algorithm for identifying locally similar portions in…

Discusses opportunities to use nursery rhymes to aid in the mathematical development of young children. Considers rhymes that involve patterns, ordering, and problem solving. (MKR)

Well-known questioning strategies, built on question classification systems, are examined. Types of question classification systems are identified as: "hierarchical," which are sequential and cumulative; "non-hierarchical," which are based on elements which should not be rank ordered; systems which are "context-bound" to specifics; and…

A method for helping students to find formulas involving symmetry under various conditions is explained. Necklace symmetries, orbit counting, tetrahedra and cubes, relationship patterns, and finding patterns are discussed. (CW)

Expresses the opinion that education has overemphasized the written word and needs to move back to the oral tradition. Warns that Americans are trained to use the left brain whereas much of engineering needs right brain processing. Gives perspectives to improve engineering education. (MVL)

Noticing relationships between similar things and developing rules for treating things the same or differently, based on characteristics like color, size, shape, and texture provides the basis of beginning mathematics learning. Based on the view that teachers and parents of young children should provide children with age-appropriate words,…