This report presents results of several extensive empirical studies. Prior to these studies it was believed that errors in procedural skills such as multi-digit subtraction could be accurately modelled with two mechanisms: bugs ("competence" phenomena reflecting mistaken beliefs about subtraction which are stable over time) and slips…

Two methods for solving problems are presented, designed to help people overcome difficulties that often occur in the problem-solving process. One difficulty people have is in using their knowledge to reach the decisive solution idea. The proposed "method of description" for eliminating this difficulty is based on a directed enrichment of the…

A new potential for using microcomputers to help secondary school students learn mathematics through self-diagnosis and self-remediation is contrasted with current uses of computers for diagnosis and remediation. Research findings and software are cited in the discussion. (MNS)

Ways to combine the strengths of teacher and computer are suggested. Multiplication concepts and an algorithm for multiplication are taught in the same lessons. The computer is used as an electronic chalkboard to teach at a semiconcrete level. The computer program is included. (MNS)

An application of functions and their inverses is described--the coding and decoding of messages, or cryptographs. The helpfulness of computers is noted, with two programs listed. (MNS)

Presented are two problems that can be solved using a computer simulation by students who have completed Algebra II. The distance and bisector formulas and the various forms of the equations of a circle and straight line are the topics. Computer program listings are included. (MNS)

Numerical inaccuracies, which occur in many ordinary computations, can create serious problems and render answers meaningless. Cancellation and accumulation errors are described, and suggestions for experimentation are discussed. (MNS)

A computer program that can be easily modified to offer individualized drill, practice, or remediation is presented. How the program operates is described, and how to modify it for numerical order, number sequences, number words, inequalities, basic operations, percents, decimals, fractions, and measurement is noted. (MNS)

Stressed is a conceptual approach to absolute value, based on the visualization of the graphs of absolute-value equations. An important by-product is predicting a graph on the basis of certain constraints. Four worksheets plus teacher comments are included. (MNS)

Presents a set of classroom activities and a computer program that have been used to help students intuitively grasp, in a minimum of instructional time, such fundamental concepts as hypothesis testing, random sampling, statistical inference and p-values. The lesson shows students how statistical thinking and microcomputers can be used in…

Suggested is the presentation of problems for which student teams are to write computer programs which will reveal the results of guesses at the answer by users of the program. Illustrative problems and programs are included. (MNS)

An approach to help teachers understand the elementary constructs of the BASIC programing language and to begin writing simple programs is described. Short programs that illustrate educationally sound uses of computers in the classroom are used. A lesson scenario is given, with 10 program listings. (MNS)

Included in this section are brief articles on an algebraic puzzler, periodic decimal fractions with computers, and the arrow method of teaching logarithms. (MNS)

Describes the principles underlying computer programs designed to improve undergraduate calculus instruction. The programs were produced for teacher use on a single microcomputer for when there are not enough microcomputers available to allow students to have access to them. (JN)

An environment for investigating vector-valued functions in two- and three-dimensional space using Logo is described. The language is presented, followed by use of the environment. Appended are Logo primitives and procedures. (MNS)