This fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasizing computational fluency and the…

Looking away from an interlocutor's face during demanding cognitive activity can help adults and children answer challenging mental arithmetic and verbal-reasoning questions (Glenberg, Schroeder, & Robertson, 1998; Phelps, Doherty-Sneddon, & Warnock, 2006). While such "gaze aversion" (GA) is used far less by 5-year-old school children, its use…

At the heart of the debate about the place of standard arithmetic algorithms is the practice of teaching subtraction through decomposition. One welcome feature of the national numeracy strategy in both its initial and current incarnations has been the introduction of a focus upon a variety of mental strategies supported by jottings. In this…

Mathematical computation consists of both written computation and mental computation. The strategies for mental computation can be used to check the reasonableness of written computations. Mental computation has two distinguishing characteristics: "it produces an exact answer, and the procedure is performed mentally, without using external…

This study examines the mental computation strategies used by pupils at the end of primary school. In 1998 a new strategy for teaching mathematics was introduced into British schools (the National Numeracy Strategy) that specifically focused on mental calculation. The first part of the study took place in 1999, one year after the implementation of…

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

Drawing upon research, theory, classroom and personal experiences, this paper focuses on the development of primary-aged children's computational fluency. It emphasises the critical links between number sense and a child's ability to perform mental and written computation. The case of multi-digit multiplication is used to illustrate these…

This arithmetic textbook aims to teach the reading of figures so as to train the mind to instantly catch the idea that any combination of figures is intended to express. This is to be done by "the simple process of reading;" and the method consists: (1) in teaching the alphabet; and (2) in teaching the combinations of the alphabet, which…

Use of an ancient method of mental calculation with aliquot parts is illustrated. Other tips for helping children reason are also included. (MNS)

Estimation of measurements is discussed, with a definition, rationale, strategies, teaching suggestions, and several references. (MNS)

This article focuses on the aspect of mental arithmetic that uses thinking strategies that are effective with large numbers as well as basic facts. Two activities are suggested for lack of the four operations. (MK)

Discusses the importance of mental mathematics beyond the middle school. Presents sample objectives for different courses or strands, and teaching ideas to make mental mathematics an important, ongoing goal in secondary mathematics instruction and beyond. (KHR)

What mental computation and estimation are, what is known from research about each process, and what can help students develop these skills are discussed. (MNS)

Using factoring as an aid to mental multiplication is illustrated. Other suggestions for teaching mental computation are also included. (MNS)

Four ways of knowing about numbers are listed, with direct estimation emphasized. Using perceptual anchors is described, with several teaching tips on their use in estimation. (MNS)