This article reports on the main experiences gained from a 2-year study which incorporated A.L.E.X., an educational puzzle game available on iPad or Android tablet devices, within the primary school mathematics curriculum. The study took place in a public primary school, located in a rural area of Cyprus. The majority of its students come from low…

Of the "big four", division is likely to regarded by many learners as "the odd one out", "the difficult one", "the one that is complicated", or "the scary one". It seems to have been that way "for ever", in the perception of many who have trodden the learning pathways through the world of…

In order to give insights into cross-national differences in schooling, this study analyzed the development of multiplication and division of fractions in two curricula: "Everyday Mathematics" (EM) from the USA and the 7th Korean mathematics curriculum (KM). Analyses of both the content and problems in the textbooks indicate that…

"Achieving Fluency" presents the understandings that all teachers need to play a role in the education of students who struggle: those with disabilities and those who simply lack essential foundational knowledge. This book serves teachers and supervisors by sharing increasingly intensive instructional interventions for struggling students on…

The present study examines the effect of three different structured methods, traditional, independent and problem-solving, of teaching children arithmetic in the beginning of 7th grade in Sweden, age 13 years. The progress made by these students is presented by measures of their arithmetic ability, calculation and quantitative concept, as well as…

Analyzes and refutes the arguments made by "back-to-basics" proponents against the use of calculators and for traditional instruction in the algorithms of pencil-and-paper arithmetic. Argues for the value of mental arithmetic in achieving all the aims and more of the traditional curriculum. (Author/ASK)

Efforts to develop a mathematics curriculum that meets the needs of a modern society are reflected in reform recommendations across the developed world. A common requirement is for students to understand the calculation procedures they are taught and to develop "number sense". This paper will analyse students' strategies for calculating…

Calculators have made the arithmetic curriculum obsolete in both scope and sequence. Calculators can perform each operation as easily as any other. We should be asking if there is ever a time when we should trust paper-and-pencil computation. (MNS)

A description is given of a calculator-oriented arithmetic course given at a community college. Problem solving was the primary objective of the course. (MK)

This paper discusses an approach to the study of algorithms which values students' construction of nonstandard algorithms but also emphasizes the essential roles of the teacher and instructional activities in supporting the development of students' numerical reasoning. Episodes are presented from a 3rd grade classroom in which a 9-week teaching…

Discusses a counting system and number operations. Suggests six distinct areas in a "number" subject: one-to-one correspondences; simple counting process; complicated counting process; addition and multiplication; algorithms for the operations; and the decimal system. (YP)

A range of estimation techniques are described, and a series of mental computation procedures based on concepts of measurement and real numbers are presented in detail. (MP)

This study compared intact beginning fifth grade classes in one of the districts in Shanghai, People's Republic of China to American Norms on the KeyMath-Revised: A Diagnostic Inventory of Essential Mathematics (KeyMath-R) and the Wide Range Achievement Test (WRAT-3). The review of literature contrasted the two cultures with regard to students,…

This book was written to help teachers to plan and implement an effective multiplication-division basic fact program. When it is determined that children have gained an adequate concept for an operation, the next long-range goal is fact memorization. Children need to respond quickly and correctly to number facts and retain this learning over time.…

This article explains how this method is done, examines some reasons for including it as a topic in mathematics curricula, and uses modular arithmetic to explore its mathematical basis and its generalizability to computations in bases other than 10. (CW)