The maturation of multiplicative thinking is key to student progress in middle school as rational number, ratio, and proportion concepts are encountered. But many students arrive from the intermediate grades and falter in developing this essential disposition. Elementary students have historically learned multiplication and division as operation…

Presents a study in which 13 fifth-grade students were given an assignment to invent their own numeration systems following a unit on bases and a look at early events in the history of numbers. Offers an assessment of student understanding of numeration provided by analyses of the patterns embedded in their invented systems. Contains 13…

This six month study investigated the similarities and differences between 137 fourth graders' understanding of and reasoning about multiplication, division, and proportion tasks. All students were administered a pretest mid-year and a posttest at the end of year. A sample of 18 students was interviewed individually on tasks involving reasoning…

Several experiences with palindrome numbers are given, each leading to the "Law of 11." Conjectures for the reader to consider are included. (MNS)

Examines the effects of a teaching strategy in which fifth-grade students evaluated the strengths or weaknesses of solution methods to pattern finding problems, including an experimental and control group each consisting of 34 elementary students, in Japan. The experimental group showed a significantly better performance on the retention test…

Suggestions for using a computer disc containing unprotected programs are given. The Fibonacci sequence, prime factorization, sum puzzlers, and other examples are described. (MNS)

This book provides dozens of carefully prepared letters for parents in English and Spanish that teachers can send home weekly. Each of the 40 letters focuses on direct and easy-to-implement mathematics activities that can be incorporated regularly into a family's daily routine without turning the home into a school away from school. The letters…

A teacher of deaf fifth graders recounts the use of math logs to help students to write about their math experiences and thus generate, comprehend, and express mathematical ideas and knowledge. The process also helped the teacher pinpoint math problem areas and assess and monitor students' understanding of math concepts. (DB)

Defines number sense and gives suggestions and activities for teachers to use in helping students develop number sense, including using process questions, using writing assignments, encouraging invented methods, using appropriate calculation tools, helping students establish benchmarks, and promoting internal questioning. (MKR)

Describes a mathematics activity using square pads of notepaper and sticky notes to do simple paper folding in order to increase students' understanding of fractions. (ASK)

Defining better implicit models of children's actions in a series of situations is of paramount importance to understanding how knowledge is constructed. The objective of this study was to analyze the implicit mental models used by children in complex change problems to understand the stability of the models and their evolution with the child's…

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 4-6, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, whole numbers, number theory, fractions, decimals, geometry, ratio, proportion, percent, probability, sets, and…

Presents an activity using base-10 blocks and the TI Explorer calculator to help fifth and sixth graders represent their ages in different numerical bases to appear older or younger than their real age. (MKR)

Activities with balance beams were used to motivate students and help them to learn basic mathematical principles. Illustrations are included. (MNS)

The view of the researcher is that students in the upper elementary to middle school range need to increase their problem-solving skills by making logical deductions and organizing and structuring their thoughts through the use of word problems. Giving children a daily word problem challenged and introduced them to the lesson. This activity…