This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

This paper presents tips, activities, resources, and games that parents can use to help their children become more proficient in math. Some helpful tips offered are: (1) Be positive; (2) Play family games; (3) Avoid stereotypes; (4) Choose gifts that develop problem solving skills; (5) Expand your children's horizons; (6) Buy or borrow library…

Using license plates and telephone numbers for teaching probability ideas involving counting rules is suggested. How each is useful is illustrated in some detail. (MNS)

An example is noted in which a given problem is reformulated and extended. The problem solving includes discussion and dispute, plus the recognition that different approaches are both possible and desirable, is thus demonstrated. (MNS)

A traveling salesman problem is used to illustrate the key idea in a general proof of a reduction technique. It is reduced to a problem in propositional calculus. (MNS)

Using a proportions approach to solving the three types of percent problems is discussed, with a drawing of a comparison scale. (MNS)

A letter from a parent about a homework assignment involving much repetition (and time) is used as the vehicle to discuss the problem. (MNS)

The article presents and discusses an optimization problem concerned with observing objects from a moving car. (MK)

A discussion of what constitutes proof is given. Methods of teaching proof in a more intuitive and informal way than is usually done are suggested. (MK)

The focus is on how line graphs can be used to approximate solutions to rate problems and to suggest equations that offer exact algebraic solutions to the problem. Four problems requiring progressively greater graphing sophistication are presented plus four exercises. (MNS)

The Australian Mathematics Competition was designed around the content of common school mathematics, and thus is intended for almost all mathematics students, not just exceptional ones. The competition's conceptual and organizational basis and the three levels of competition papers are described. Sample questions are included. (MNS)

A new version of a standard old problem is presented. Ways of solving, extending, and continuing the problem that make it applicable to many grade levels are discussed. (MK)

Approaches to teaching verbal problems that are interesting and useful are reviewed. Four basic difficulties in teaching problem solving are also covered. (MP)

This monograph provides teachers with a wide range of articles on the teaching of problem solving in the mathematics classroom. The first section, on Understanding the Problem, includes articles which provide a sense of the "problem" of teaching problem solving. The second section, on Devising a Plan, provides suggested plans for…

When the words "problem" and "answers" are used in connection with computational exercises, students think they are solving problems. Distinguishing between computational forms and problems is illustrated with a variety of topics. (MNS)