This document shows a different way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss?s method to check it.

Theon's ladder is an ancient algorithm for calculating rational approximations for the square root of 2. It features two columns of integers (called a ladder), in which the ratio of the two numbers in each row is an approximation to the square root of 2. It is remarkable for its simplicity. This algorithm can easily be generalized to find rational…

This research investigated the relationship between the magnitude or scope of a stimulus and its subjective value by contrasting 2 psychological processes that may be used to construct preferences: valuation by feeling and valuation by calculation. The results show that when people rely on feeling, they are sensitive to the presence or absence of…

This article illustrates how the arithmetic series 1 + 2 + 3 + ... + n is pervasive in mathematical contexts as a powerful problem-solving tool.

The Schools and Staffing Survey (SASS) is conducted by the National Center for Education Statistics (NCES) on behalf of the United States Department of Education in order to collect extensive data on American public and private elementary and secondary schools. SASS provides data on the characteristics and qualifications of teachers and…

This book, written by participants of a joint Japan-United States seminar, drawing upon years of classroom and research experience, examines how computation applies in basic and far-reaching ways, starting in early childhood and continuing throughout individuals' lives. The book presents both the Japanese and American views of computational…

This case study examined the performance of a 13-year-old highly skilled mental calculator on mental multiplication tasks. She solved difficult tasks by using various ingenious calculation methods, including distributing, factoring, and recalling the product directly. Implications for instruction are reported. (Author/RH)

Studied for three years were eight Swedish classes with pupils aged 10-12 using calculators whenever they could be of use, along with experimental textbooks. The experimental classes were as competent as control classes in mental arithmetic and calculations with simple algorithms, and had better understanding of numbers and problem solving. (MNS)

This report consists of two volumes, the first takes an in-depth look at the various graduation indicators, with a description of the computational formulas, the data required for each indicator, the assumptions underlying each formula, the strengths and weaknesses of each indicator, and a consideration of the conditions under which each indicator…

Included in this section are brief articles outlining an approach to teaching mental computation, an inductive approach to algebra, and using football to teach probability. (MNS)

Focuses on mental strategies for computing in the middle grades. Describes what they are and why they are important. Refers to relevant research and presents some teaching ideas for developing these strategies beyond the primary grades. Includes a discussion of the role of mental calculation in everyday life both past and future. Contains 27…

The hypothesis that a task that increases in complexity (increasing its correlation with a central measure of intelligence) does so by increasing its dimensionality by tapping individual differences or another variable was supported by findings from 46 adults aged 20-70 years performing a mental counting task. (SLD)

Examines the use of mental, written, and calculator strategies of numerical computation by 56 upper primary students. Finds that students introduced to a "calculator-aware" curriculum make greater use of mental computation, particularly multiplication strategies based on distribution and compensation. Notes implications for models of…

Computation activities focusing on speed and accuracy do not provide children with the opportunity to learn or develop their own mental computation strategies. Sets out some goals and ideas for teaching mental computation and introduces a card game for helping children compute mentally. (ASK)

The Williams Review (Dept. for Children, Schools and Families, 2008) is significantly important to all early years and primary educationalists, including those who are involved in teaching mathematics to the next generation of primary school teachers. The report, compiled as a result of this review, sets out the ways that children in primary…