This article presents a story of Robert Andrew's mental engagement with mathematics. It has been jointly written by Robert, who is a Y8 student, and his father, Paul Andrews, who is a mathematics educator. It starts with Robert who presents the context for the story and is followed by Paul's commentary which draws on what Robert has written.…

"Cognitive Tutor[R] Algebra I," a full year course, delivers instruction in single variable data, simplifying linear expressions, mathematical modeling, solving systems with linear equations, problem solving using proportional reasoning, and powers and exponents. Students work at their own pace to develop problem-solving skills. The…

A study is conducted to prove Kaprekar's conjecture with the help of mathematical concepts such as iteration, fixed points, limit cycles, equivalence cases and basic number theory. The experimental approaches, the different ways in which they reduced the problem to a simpler form and the use of tables and graphs to visualize the problem are…

This book includes two main sections: a discussion of problem solving and a section on computation with whole numbers. A primary theme of the text is that problem solving sets the stage for meaning and conceptual development with respect to numbers. The section on problem solving includes numerous problem-solving activities that have a dual…

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third…

David Schwartz's classic book "How Much Is a Million?" can be the catalyst for sparking many interesting mathematical investigations. This article describes five episodes in which children in grades 2-5 all heard this familiar story read aloud to them. At each grade level, they were encouraged to think of their own way to explore the concept of…

"Focus in Grade 1: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 1 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate…

The title of this mathematics text for preservice elementary teachers is intended to suggest the book's theme of mathematics as an abstraction from human experience with sticks (lines, segments), stones (sets, counting) and other objects. An introductory chapter which describes the objectives of the author and discusses learning and attitudes…

The Pythagorean Theorem, arguably one of the best-known results in mathematics, states that a triangle is a right triangle if and only if the sum of the squares of the lengths of two of its sides equals the square of the length of its third side. Closely associated with the Pythagorean Theorem is the concept of Pythagorean triples. A "Pythagorean…

The mathematical performance of 182 third and fourth graders in 8 different areas of mathematics was examined. The children belonged to 4 achievement groups: children with mathematic difficulties (MD only), children with both mathematic and reading difficulties (MD-RD), children with reading difficulties (RD only), and normally achieving children…

Prediction is a great skill to have in any walk of life: it can, in fact, save lives at times. While the two investigations posed in this column may not be that dramatic, they might just increase one's appreciation of some important connections between grids and rectangles and the divisors of numbers that appear in the dimensions of those…

This report describes an investigation in England of some of the problems children experience with fractions. In particular, the restricted view that some children have of fractions is investigated. The methodology involved a large number of interviews with secondary school children (aged 12-14). The results of these interviews led to the design…

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

More work with fractions needs to be done in the elementary school, with emphasis on concepts rather than computational algorithms. (MP)

This is a reprint of an address given at the Christmas National Council of Teachers of Mathematics (NCTM) meeting in 1958. It provides a critique of elementary instruction and discusses the changes necessary. It calls for fundamental change in the concept of mathematics teaching. (PDD)