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…

A teacher describes her experiences using "mathematics across the curriculum" problem solving activities with 12- and 13-year-old students with moderate to severe learning difficulties. She concludes that the experience of real problem solving is an approach that has great potential for use with special need students. (PK)

How min-max problems can be solved with trigonometry and without calculus is described. (MNS)

This second booklet of a two-part publication, designed as an in-service tool for teachers of grades K-9, concerns the teaching and curriculum aspects of problem solving. It is a digest of selected topics integral to successful problem-solving instruction. The resource is organized into independent units for individual reference or group…

A calculator solution of a simple computational problem is discussed with emphasis on its ramifications for the understanding of some fundamental theorems of pure mathematics and techniques of computing. (Author/MK)

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 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)

Mathematical activities suitable for reproduction as worksheets are suggested. These activities are adaptations of the classic tower puzzle and are intended to help students discover patterns, make generalizations, and use the strategy of solving simpler problems in order to solve a more difficult one. (MK)

This introductory book of a two-part publication, designed as an in-service tool for teachers of grades K-9, is based on the postulate that a teacher should become a better problem solver in order to teach problem solving more effectively to students. This booklet provides an overview of problem solving as a process used daily by all individuals…

A diagrammatic approach to invariants of knots is the focus. Connections with graph theory, physics, and other topics are included, along with an explanation of how proofs of some old conjectures about alternating knots emerge from this work. (MNS)

Knot theory has been inspirational to algebraic and geometric topology. The principal problem has been to ascertain whether two links are equivalent. New methods have been discovered which are effective and simple. Considered are background information; the oriented polynomial; the Jones polynomial; the semioriented polynomial; and calculations,…

Two posters that can be used to provide experience in recognizing patterns in sequences of numbers are provided. Suggested number sequences for different grade levels are given. (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)