Reports on two types of unsolvability in mathematics. One is an instance of impossibility and the second is a judgment of undecidability. Presents a number of examples of undecidable propositions. (GS)

The probability integral of the multivariate normal distribution (ND) has received considerable attention since W. F. Sheppard's (1900) and K. Pearson's (1901) seminal work on the bivariate ND. This paper evaluates the formula that represents the "n x n" correlation matrix of the "chi(sub i)" and the standardized multivariate…

Success in using a computer in education as a problem-solving tool requires a change in the way of thinking or of approaching a problem. An algorithm, i.e., a finite step-by-step solution to a problem, can be designed around the data processing concepts of input, processing, and output to provide a basis for classifying problems. If educators…

Difficulty levels of 168 randomly generated multiplication problems were obtained by testing 238 fifth-graders. Variables concerning the number of operations, digits carried, and magnitude of the digits were defined, and a least-squares procedure was used to construct structural models accounting for 60-70 per cent of observed problem difficulty…

This text contains material designed for about 18 weeks of study at grades 11 or 12. Use of a computer with the course is highly recommended. Developing an understanding of the relationship between mathematics, computers, and problem solving is the main objective of this book. The following chapters are included in the book: (1) Algorithms,…

This is the student's textbook for Algorithms, Computation, and Mathematics (Algol Supplement). This computer language supplement is split off from the main text to enable a school to choose the computer language desired, and also to make it easier to modify the course as languages change. The chapters in the text are designed to add language…

This is the student's textbook for Algorithms, Computation, and Mathematics (Fortran Supplement). This computer language supplement is split off from the main text to enable a school to choose the computer language desired, and also to make it easier to modify the course as languages change. The chapters in the text are designed to add language…

Binary algorithmic logic may prove useful for teaching grammar, especially in the case of 'closed-system items.' (Text is in French.) Available from Instituut voor Toegepaste Linguistiek, Vesaliusstraat 2, B. 3000 Leuven, Belgium. (TL)

The author advocates the classroom consideration of new algorithms as a means of leading students to make original hypotheses. He discusses a multiplication algorithm based on the differences between squares. (SD)

Using macro and micro-structure analysis of large files of personal author names, this study developed retrieval techniques and algorithms to automatically correct and/or flag typographical errors in names, identify names in a database that are similar to a name entered by a user during a search, and measure similarities between names. It was…

The relative effectiveness of three methods of teaching fraction computation in the context of the community college was investigated. The use of calculators was a special focus of the study. The three methods were: (1) conventional algorithms with no calculator, (2) conventional algorithms with calculator, and (3) alternative algorithms using…

This description of the technical details required for using the HIER-GRP computer program, which was developed to group or cluster regression equations in an iterative manner so as to minimize the overall loss of predictive efficiency at each iteration, contains a discussion of the basic algorithm, an outline of the essential steps,…

This paper discusses computer simulation as a tool for teaching about phenomena characterized by a problem to be solved, a task or goal to be reached, a procedure to be learned, or an environment to be understood. Simulation is defined and characterized by an examination of both the attributes that are common to simulations, and a taxonomy…

THIS NOTE PRESENTS MODELS FOR PASSING JUDGMENT ON THE IMPORTANCE OF PROJECTS. TWO APPROACHES ARE CONSIDERED--PROJECTS WITH TWO ATTRIBUTES, PRIORITY AND DEADLINE DATES, AND PROJECTS WITH K ATTRIBUTES. THE SOLUTIONS ARE ILLUSTRATED THROUGH EXAMPLES AND BY AN ALGORITHM PRESENTED IN A COMPUTER REFERENCE LANGUAGE TO SHOW HOW ONE OF THE SOLUTIONS CAN BE…