This report describes a research project that investigated how to design instruction to help children take the step to generalizing and formalizing their knowledge into powerful abstract systems for representing and operating mathematical ideas. The studies build on existing research on cognitively guided instruction (CGI). The goal of this paper…

This guide provides students with practice for all the major types of graphs they are likely to encounter. It includes information on graphs of various families of algebraic functions; bar, line, and circle graphs; the creation, reading, and interpretation of graphs; and the use of graphing calculators. (MVL)

This paper describes an intensive 3-year classroom- and district-based study of the process of integrating the development of algebraic reasoning into elementary school mathematics in an educationally underachieving school district based on a year-long pilot effort in 1997-98 with two 5th grade teachers and one 6th grade teacher. In 1998-99, the…

This report describes a program for increasing students' ability to simplify square roots. The targeted population consisted of high school students in a rural community in a midwestern plains state. The problem of the ability to understand the abstract algebraic process of simplifying square roots was documented through teacher-made tests,…

This volume presents a full high-school course in elementary algebra and contains all the topics given in the standard year-and-a-half courses. It is adapted to the prevailing practice of teaching elementary algebra in two courses--a full-year course followed by a half-year course. The first 23 chapters contain all the work required in any…

The busy teacher of high-school algebra often finds that limitations of time forbid the actual working out of all the exercises and problems in a text. This teachers' edition is designed to meet such a condition. In its plan it is brief and schematic rather than complete and detailed. Many exercises are so simple that the answers only are given in…

The busy teacher of high-school algebra often finds that limitations of time forbid the actual working out of all the exercises and problems in a text. This teachers' edition is designed to meet such a condition. In its plan it is brief and schematic rather than complete and detailed. Less time should be required to prepare a lesson from this…

Three examples of the use of intuitive geometrical ideas in clarifying analytical results. (MM)