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…

Exploring the numerical nature of quadratic equations is the focus of this article. Small solutions, the general case, and a detailed analysis are each presented. (MNS)

A "lab method" for solving quadratic equations is presented. Suggestions for applying the method in the classroom are given. (MK)

This document, produced by a committee of teachers in mathematics, includes a program description with pertinent extracts from the school district philosopy, as well as major goals and objectives. Curricular objectives state what a student should know, demonstrate, or be able to do in this study area. The sequence of goals and objectives…

This twenty-second unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 21. For each of the chapters in Unit 21, a time allotment is suggested, the goals for that chapter are discussed, the mathematics is explained, some teaching suggestions are given, answers to exercises are provided, and sample test…

Comments on bells throughout history are noted. 'Change-ringing,' focusing on the sequence in which bells are rung, is then explored. (MNS)

How probabilities change when playing the game of craps with dice having 8, 12, or 20 faces is discussed. Five challenge questions are also included. (MNS)

Mental skills developed through the study of mathematics are identified, and ways in which this information can shape the role of teachers of algebra are suggested. (MNS)

A method used by the ancient Babylonians to solve quadratic equations is presented. Illustrations are included from one Babylonian tablet. (MNS)

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

Ways of using the calculator as a vehicle for investigating one aspect of the square root concept are illustrated. (MK)

A method for sketching functions and finding slopes and roots rising synthetic division is illustrated. (MK)

A generalized method of synthetic division where the divisor polynomial may be of any degree equal to or larger than 1, and the dividend polynomial may be of equal or larger degree than the divisor polynomial and a generalization of the familiar remainder theorem, are presented. (Author/MK)

A lesson taught by an American teacher to Chinese students is described. The lesson was a "Silent Lesson in Mathematics" (SLIM) presentation concerning the guessing of functions. (MK)

This is the teacher's guide and commentary for the SMSG textbook Algorithms, Computation and Mathematics (Algol Supplement). This teacher's commentary provides background information for the teacher, suggestions for activities found in the student's Algol Supplement, and answers to exercises and activities. The course is designed for high school…