One of the most interesting and important proofs in the history of mathematics is the Pythagorean school's proof of the "irrationality" of the square root of 2. After a brief look at G. H. Hardy (1941) thoughts regarding it, two versions of the classic Pythagorean proof are examined and discussed in this article, one written by an American…

This study is aimed at the mechanisms used by students with an intellectual disability in the counting process. The assessment of the counting process is carried out through experimental tests inspired by the basic principles of Gelman and Gallistel, namely one-to-one, stable order, cardinality, abstraction and order irrelevance. This is a…

This volume is a teacher's edition in a series of books that contain open-ended exploration activities and experiments. These activities allow and encourage students to set their own goals, use their own creativity and ideas, investigate the wonders of nature, learn about the workings of real businesses, and draw conclusions from their…

This book leads students through a journey of hands-on investigations of skill-based estimation. The 30 lessons in the book are grouped into four units: Holding Hands, The Real Scoop, Container Calculations, and Estimeasurements. In each unit children work with unique, real materials intended to build an awareness of number, quantity, and…

This paper explores the process by which mathematical knowledge is socially constructed. Interactional analysis of a lesson on fact families shows how one third-grade mathematics class negotiated the meanings of writing a number sentence for a picture and a fact family. In the course of classroom interactions, teacher and students shifted the…

This manual is a dictionary of some 150 errors made by students in their work in mathematics. A precise definition and examples are given for each of these errors and these, combined with a description of common causes of the error, form a background for diagnosis of student problems with arithmetic. Teaching strategies and ideas, each linked to a…

One of the major goals in mathematics education is to teach the ability to solve word problems. This study compared the word problem solving abilities of second-grade students from Taiwan (N=24) with those of American students (N=24). Two tests were used in the problem solving interviews. The comparisons between the performance of the groups on…

Stickybear's Math Splash is a CD-ROM-based software tool for teaching mathematics skills beyond simple number recognition to elementary students. The accompanying printed lesson plans are designed to complement mathematics skills with other methods and areas of emphasis including kinesthetic learning, listening skills, decision making skills, and…

Stickybear's Math Town is a CD-ROM-based software tool for teaching mathematics skills beyond simple number recognition. Accompanying printed lesson plans are designed to complement mathematics skills with other methods and areas of emphasis including kinesthetic learning, listening skills, decision making skills, and other vital tools for…

This review guide, prepared as an aid to teachers of Course III, starts with a pre-test review of Course II topics found again in Course III. The five units of Course III, as outlined in the New York State Syllabus, are then separated into nine smaller units. These include: real numbers; complex numbers; functions; logarithms; trigonometry;…

Three factors associated with arithmetical processes (sequence skills, arithmetical strategies, and information processing capacity) were measured in individual interviews with 35 first-grade pupils, aged 7.6 to 8.6, in one Finnish school. Mathematics achievement was determined from information supplied by teachers. Attitudes were assessed twice,…

Using these worksheets students explore patterns in numerical and geometric processes, and predict the outcomes when the processes are iterated further. (SD)

While repairing a sleeping bag, the author observed that the quilt stitching was unicursal. This led to development of a classroom activity relating the stitching patterns of quilts to the highest common factor of the numbers of "bumps" in each direction. (SD)

Figurate numbers based on seven geometric figures are discussed. The place of these numbers in Pascal's triangle is indicated. (SD)

The author describes two types of review activities: (1) counting exercises involving simple mental calculations, and (2) sets of five problems involving the same pair of numbers. (SD)