Three forms of a problem-solving test were given randomly to 322 tenth graders. Performance on the form containing accurate pictorial representations of items was significantly higher than on the form with only prose descriptions, which was in turn significantly higher than on the form with distorted pictorial representations. (DT)

Discussed are specific methods of teaching computational and manipulative skills in mathematics in a meaningful way. (CT)

Described is a study concerned with the mode of presentation of printed mathematical word problems. Tenth grade students were given twenty word problems to solve, presented in one of three ways: (1) prose only, (2) prose with an accurate picture included, or (3) prose with a distorted picture. Experimental results showed that the group with an…

Solutions are given to the problem of determining the number of regions obtained by connecting points on the circumference of a circle; implications are drawn for teaching problem solving to students. (DT)

Modular arithmetic is used to show that there is at least one Friday the 13th in every year. A case-by-case proof is outlined and a proof of the general case is given. (DT)

A discussion of the use of mathematics problems containing erroneous statements and the use of mutual consultation by students on the solution of mathematics problems. Critical questioning ability of students is enhanced through the utilization of both these procedures, according to the author. (JG)

Discussion is focused on standard teaching procedures that contain the elements of modern mathematics. Of the various methods which have been tested, it is concluded that the solving of problems remains the most effective basic activity. A sample collection of problems is presented to indicate relationships and the principles they illustrate. (RP)

Student errors led to this exploration of the conditions under which log of x base a = x. The discussion requires only techniques contained in a first-year calculus course. (MP)

Discussed is the problem of finding the volume common to two intersecting right circular cylinders. (MP)

The teacher's guide for Unit 10 of this SMSG series covers the chapter on problem solving and the chapter on solution sets of mathematical sentences. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives…