This paper reports on results of a targeted and extended (two school terms) program for building Grade 3 and Grade 4 students' facility with number facts and application for mental computation. As part of a larger project, this paper reports results from two schools. Results indicated strong gains in number fact recall and mental computation for…

This article sets out to evaluate the English Early Years Foundation Stage Goal for Numbers, in relation to research evidence. The Goal, which sets out to provide "a good foundation in mathematics", has greater breadth of content and higher levels of difficulty than previous versions. Research suggests that the additional expectations…

Mental abacus (MA) is a technique of performing fast, accurate arithmetic using a mental image of an abacus; experts exhibit astonishing calculation abilities. Over 3 years, 204 elementary school students (age range at outset: 5-7 years old) participated in a randomized, controlled trial to test whether MA expertise (a) can be acquired in standard…

How this teacher develops composition of ten with second graders was dramatically reshaped by the 2006 release of NCTM's "Curriculum Focal Points." The release of "Curriculum Focal Points"--particularly the suggestion that number sense and computation be focal areas in the second-grade mathematics curriculum--resulted in positive changes in this…

Cantor's diagonal proof that the set of real numbers is uncountable is one of the most famous arguments in modern mathematics. Mathematics students usually see this proof somewhere in their undergraduate experience, but it is rarely a part of the mathematical curriculum of students of the fine arts or humanities. This note describes contexts that…

This yearbook responds to the growing recognition among mathematics educators of the importance of teaching and learning estimation. It makes a strong case for the importance of estimation in such domains as numerosity, computation, and measurement. An important theme is the interdependency between the process of estimating in a particular domain…

What students need to know in a world where most computations are done by machine is discussed. Needed changes in the mathematics curriculum are then detailed in relation to mental arithmetic, numeration, decimals and fractions, paper-and-pencil computation, order of operations, problem solving, and instruction on calculator use. (MNS)

The author suggests that the efficient use of mathematics in everyday life means translating situations into mathematical contexts, using a calculator and mental methods of calculation. Suggestions for teaching these concepts are included. (PK)

The author argues that the idea of canonical elements provides a coherent relationship between equivalence relations, the basis of modern approaches to too many mathematical topics, and the traditional aspect of computation. Examples of equivalent relations, canonical elements, and their calculations are given. (MK)

Masters of worksheets designed to generate interest in mathematics and provide mathematical experiences that lead to the introduction of the concept of a variable are presented. (MK)

Curricular placement of and emphasis on common and decimal fractions are discussed. Suggestions include: retaining common fractions in the curriculum, teaching decimal concepts and notation earlier, reducing fraction computation complexity, and moving fraction computation upward in the curriculum. (MK)

Presents three methods invented by fourth graders for obtaining the arithmetic mean. This presentation is in support of the idea that encouraging children to invent their own mathematical processes is a good way for them to clarify the idea of representativeness and consequently the teacher can facilitate the students' construction of higher…

An experimental program using the calculator in third, fourth, and fifth grades is described. Three example lessons are included, on (1) subtraction with regrouping, (2) estimation, and (3) number theory: Quadratics. (MK)

Some benefits of helping learners think in prime numbers are detailed. Reasons for the decay of this ability are described, with short division presented as one activity which should be reintroduced in schools. (MNS)

This report on mathematics education in Soviet elementary schools was prepared by a writer for the Novosti Press Agency in Moscow. It notes that mathematics is taught by subject specialists beginning in grade 4 and provides details on both curriculum and instructional practices. (MNS)