This study, based on individual interviews with 100 students (aged 16 to 22 years), was designed to investigate understanding of elementary calculus (particularly integration and differentiation). Results indicated that items related to understanding integration as the limit of a sum were difficult even for good students. (Author/MP)

The material focuses on the power and usefulness of the number three and is presented as though the number was being interviewed. Among the issues covered in the presentation is the impossibility of dividing an angle into three equal parts using just a straight edge and a compass. (Author/MP)

The material presents an alternative method for arranging proofs, which arranges development in levels. The method is described as triggered by recent ideas from computer science and is intended to increase the comprehensibility of mathematical presentations while retaining their rigor. Several examples using this approach are presented.…

An attempt is made to show that algebra is rarely obvious, and merely expecting children to learn rules is an oversimplification. Sections cover: (1) The Non-visual Nature of Algebra; (2) The Apparently Arbitrary Nature of Algebra; (3) The Relationship Between Symbolism, System and Question; (4) The Complex Nature of Algebra; and (5) Some…

Language arts (oral and written communication), physical education (communication with motor skills), and mathematics (communication with words and symbols), are seen to present the most natural environment for instruction on spatial relations. Activities are suggested which can combine these areas and provide pupils with an enjoyable learning…

The harmonic mean is defined, and examples of problems viewed suitable for classroom exploration are presented. Such exercises provide many opportunities for students to engage in interesting nontrivial problem-solving activities and practice on many algebraic skills. Class discussion of the arithmetic, geometric, and harmonic means is suggested.…

The trick focuses on a theorem that the sum of the digits of the difference between any natural number and the sum of its digits is divisible by nine. Two conditions of using the trick are noted. The reason that the theorem works is established through a proof. (MP)

A scheme for diagnostic teaching is discussed, and aspects of the approach are illustrated from three teaching experiments. Instruction that aims towards free and relaxed discussion of single points of difficulty or conflicts and towards pupils seeking to learn how a particular system works is promoted. (MP)

A program written in PASCAL designed to find the number of binary trees possible for a given number of nodes is presented. The problem was found to be highly motivating and exciting for the group of introductory computer science students with whom it was used. (MP)

Utilizes 42 second-grade rural students to determine if using multiembodiments rather than a single embodiment of concepts related to three-digit numbers would result in greater understanding of selected place value concepts. Reveals no significant differences on the group main effect or group-by-time interactions. (AH)

The following five steps are designed to help teach a directed mathematics lesson: (1) introducing, (2) presenting, (3) analyzing, (4) practicing, and (5) applying. It is noted that teaching a directed lesson means to help students master specific mathematical skills, as well as to formulate concepts and understand principles. (MP)

Problems designed to show the meaningful use of logarithms in the age of calculators are presented. The emphasis is placed on viewing a logarithm as an inverse operation to raising to a power. (MP)

A science fiction approach is used to explore some unusual properties associated with the concept of infinity. (MP)

This article, written by a high school junior, shows that there can never be more than two isosceles triangles having the same perimeter and area. (MK)

The way that fractions are taught to fourth-grade pupils at the Village Community School in New York City is detailed. The approach is thought to make the often frightening symbols of fractions into something that even beginning students find meaningful. Meaning rather than computational technique is emphasized. (MP)