The author shares 12 problems he has found effective in stimulating the imagination of students. (MNS)

The nature of cooperation between mathematics and science departments at the secondary school level is based on a survey of this issue. There was no situation found where there was a formal, continuing integration thoughout a school, but evidence of several types of cooperation was detailed. (MP)

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…

A modification to the ancient game of NIM is promoted which can provide a set of games seen as suitable for promoting practice in subtraction and simple strategy formation for a range of pupils in both the primary and secondary grades. The game versions noted are normally for two players. (MP)

Geometrical probability deals with probability on infinite sample spaces where each outcome of an experiment is equally likely to occur. Geometry which identifies sample space regions and event subregions leads to a method of finding a desired probability. A collection of problems with solutions is presented. (MP)

The material is designed to help students build a cone model, visualize how its dimensions change as its shape changes, estimate maximum volume position, and develop problem-solving skills. Worksheets designed for duplication for classroom use are included. Part of the activity involves student analysis of a BASIC program. (MP)

The problem involves randomly breaking a stick into three pieces and using the pieces to form a triangle. The probability of getting a triangle is calculated using four different solution methods. Two unique problem interpretations are noted, and one solution method involves a BASIC program. (MP)

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)

The proof is given that, if three equilateral triangles are constructed on the sides of a right triangle, then the sum of the areas on the sides equals the area on the hypotenuse. This is based on one of the hundreds of proofs that exist for the Pythogorean theorem. (MP)

Case studies of two schools that demonstrate approaches to a liaison between mathematics and science are presented. The establishment of a combined mathematics-science faculty is the most obvious factor that tends to lead to a school's success in achieving a liaison. Additional factors are also considered. (MP)

Some functions on digits of positive integers are presented as possible sources for useful investigations by students, particularly through the use of calculators and computers or in the writing of small proofs. The material is designed to encourage students to conduct their own investigations. (MP)

Students' misconceptions in mathematics and how teaching may be directed to diagnose and eliminate these misconceptions are discussed. Four main types of misconceptions during problem-solving are noted. It is also noted that the basic mathematical processes of generalizing, representing, and explaining are used in selected student self-help…

Estimates of the criterion-related validity for the National Teacher Examinations (NTE) in mathematics and science were determined empirically. Results suggest that the science tests are not as useful as the mathematics tests as indicators of subject knowledge. (GK)

A test of logic was given to 862 students in their first, second, and fourth years in Lesotho secondary schools. Results supported the contention that while difficulty in understanding English contributes to difficulty with the logical grammar necessary for mathematics, there are factors other than second language interference to consider. (MP)