Mathematics exercises involving the number of electoral votes, the apportionment of representatives, and population data are described in detail, with solutions given. (DT)

Interprets Salinas' use of geometric figures for depicting concepts of time and infinity, and for portraying idealism and realism (the vertical line is idealism, perfection; the circle stands for reality and imperfection). (DS)

The author lists and discusses each of six stages of mathematical learning. The stages are: (1) interaction, (2) rule construction and manipulation, (3) isomorphisms, (4) representations, (5) symbolization, and (6) formalization. Examples from geometry are used to demonstrate the learning processes. (JG)

The predicted and actual achievement in college calculus is compared for students who had studied two semesters of calculus in high school. The regression equation used for prediction was calculated from the performance data of similar students who had not had high school calculus. (CT)

This material shows how to use basic techniques, principles of counting, and geometry to count squares on geoboards. The methods are elementary in that the proofs are easily conceptualized. A discussion of other approaches illustrates that easily stated problems may lead to very difficult and sophisticated methods. (MP)

Three examples are presented which involve constructions employing a compass, a centimeter ruler, and a calculator. Employing mathematical tools to support understanding and discovery of mathematical principles is viewed as being clearly a desire of mathematics educators, but it is felt such tools are not frequently used to their fullest. (MP)