"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

It is difficult for students to unlearn misconceptions that have been unknowingly reinforced by teachers. The examples "multiplication makes bigger,""pi equals 22/7," and the use of counter examples to demonstrate the numerical property of closure are discussed as potential areas where misconceptions are fostered. (MDH)

What is meant by meaningful instruction is discussed in terms of interest and relevance, pseudo-real problems, unconscious reinforcement, stories for symbols, and mathematical mirrors. That mathematics must be talked about with and by children is emphasized. (MNS)

Discusses research findings that relate to teaching fractions for conceptual understanding. Gives teacher/student dialogues that illustrate the thought processes of students as they form part-whole and improper fraction concepts. (MDH)

Discussed is why students have the tendency to apply an "add the numerators and add the denominators" approach to adding fractions. Suggested is providing examples exemplifying this intuitive approach from ratio, concentration, and distance problems to demonstrate under what conditions it is applicable in contrast to the addition algorithm. (MDH)

This guide contains a collection of alternative techniques for teaching arithmetic that have proved useful in teaching both children and adults with various learning problems. Discussed first are several underlying principles of instructing individuals with learning disabilities, problems, and differences and special accommodations for…

A survey study asked Australian experienced teachers during workshops to rate what they believed to be the most difficult aspects of mathematics in grades seven and eight. Problem solving, number sense, and rational numbers were rated as most difficult. The research question provided a catalyst for action in professional development programs. (MDH)

The author analyzes his 11-year-old daughter's investigation of patterns in multiplication. In an investigation initiated herself, Becca generates hypotheses, discovers patterns, asks questions, and discards procedures that do not produce desired results. Providing a classroom environment that values questioning is a key recommendation. (MLN)

Describes an activity that demonstrates a teaching-learning model in which students ask yes or no questions to determine an unknown number on a number line. Provides a sequence of five steps to carry out the activity and suggestions for extending and expanding the activity for different grade levels. (MDH)

Presents two spreadsheets for middle school students applying Polya's heuristic to help develop number sense, reasoning abilities, and problem-solving skills. Spreadsheet 1, "the coin problem," allows students to vary coin quantities to total $8.32. Spreadsheet 2, "ratios," develops number relationships while finding 3 3-digit…

This guide presents math-focused learning projects and accompanying inquiry activities to help students pass the math portion of the GED 2002. It is Volume 2 of a proposed four-volume series; Volume 1 describing the concept of the GED as project is also available. Section 1 relates GED as project to the math portion of the GED and explains how…