Presents research on students' use and understanding of algorithms in Poland. Concludes that there are detrimental side effects that stem from the teaching and learning of standard written algorithms. (ASK)

Presents an approach for illustrating, on an intuitive level, the significance of loop invariants for algorithm design and analysis. The illustration is based on mathematical games that require the exploration of regularities via problem-solving heuristics. (Author/MM)

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 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)

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…

The study's purpose was to investigate the differential effects on the achievement of second-grade students that could be attributed to three instructional sequences for the learning of the addition and subtraction algorithms. One sequence presented the addition algorithm first (AS), the second presented the subtraction algorithm first (SA), and…

Investigated was the development of a diagnostic and individualized remedial program for prospective elementary teachers in the area of mathematical skills. Subjects were 120 students in the pre-methods course on number systems during the Winter and Spring 1971 terms at the Ogontz Campus, Pennsylvania State University. All subjects were given a…

A comparison of four methods of finding the maturity value of the principal is presented. The four methods are: table, period-by-period iterative calculation, formula, and Binomial Theorem. (MP)

The long division algorithm approached as repeated subtractions is explained. (DT)

Shows that the rules of thumb for propagating significant figures through arithmetic calculations frequently yield misleading results. Also describes two procedures for performing this propagation more reliably than the rules of thumb. However, both require considerably more calculational effort than do the rules. (JN)

An algorithm is given for computing the cube root of any real number on a calculator. (DT)

The purpose of this conference sponsored by the French Commission of the Methods of Teaching was to give deep reflection as to the place of algorithms in the teaching curriculum and learning of mathematics. Devoted to the concept of new teaching methods at levels 1-4 of compulsory school education, the debates of this seminar were an occasion for…

Using negative digits in writing numerals and in calculation is explained. This is the second article in the series; for the first, see Vol. 1, No. 7, Nov., 1972, pp. 8-9. (DT)