These instructional objectives have been selected from materials submitted to the Curriculum Laboratory of the Graduate School of Education at UCLA. Arranged by major course goals, these objectives are offered simply as samples that may be used where they correspond to the skills, abilities, and attitudes instructors want their students to…

This article sketches the historical development of arithmetic and algebraic symbols. (SD)

Presented is an activity for teaching linear algebra to grade 7 or grade 8 students. The activity is taken from the "Victorian Secondary Reality in Maths Education" (RIME) Pack. The activity called "Backtracking" builds on intuitions and understandings that students already possess. (RH)

Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)

Linear ciphers, substitution ciphers, public-key cryptosystems, and trapdoor knapsacks are each discussed. (MNS)

The organization and contents of a linear algebra course for chemical engineers are described. The course, which emphasizes both abstraction and application, meets twice a week for two hours and runs largely as a lecture, although active student participation is encouraged by frequent questions from the instructor. (JN)

An interesting graphical interpretation of complex roots is presented, since it is probably unfamiliar to many mathematics teachers. (MNS)

Two methods for solving matrix equations are discussed. Both operate entirely on a matrix level. (MNS)

The history of the study of dynamical systems is traced, examples are given, and the contribution of Birkhoff and Smale are described. (DT)

In this paper, we describe instruction designed to teach students about exponents and logarithms and report a pilot study to test the effectiveness of this instruction. Based on the theoretical work of Dubinsky and Sfard, we postulate a set of mental constructions that a student could make to understand the concepts of exponents and logarithms. We…

This collection of activities is designed to show how graphics display calculators can be used to foster algebraic thinking in middle school students. The collection consists of five activities addressing such topics as functions, estimation and scatterplots, and patterns. Blackline masters for the activities are included. (MM)

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,…