# An analysis of the nature and function of mental computation in primary mathematics curricula

Morgan, Geoffrey Robert (1999) *An analysis of the nature and function of mental computation in primary mathematics curricula.* PhD thesis, Queensland University of Technology.

## Abstract

This study was conducted to analyse aspects of mental computation within primary school mathematics curricula and to formulate recommendations to inform future revisions to the Number strand of mathematics syllabuses for primary schools. The analyses were undertaken from past, contemporary, and futures perspectives. Although this study had syllabus development in Queensland as a prime focus, its findings and recommendations have an international applicability.

Little has been documented in relation to the nature and role of mental computation in mathematics curricula in Australia (McIntosh, Bana, & Farrell, 1995,p. 2), despite an international resurgence of interest by mathematics educators. This resurgence has arisen from a recognition that computing mentally remains a viable computational alternative in a technological age, and that the development of mental procedures contributes to the formation of powerful mathematical thinking

strategies (R. E. Reys, 1992, p. 63). The emphasis needs to be placed upon the mental processes involved, and it is this which distinguishes mental computation from mental arithmetic, as defined in this study. Traditionally, the latter has been

concerned with speed and accuracy rather than with the mental strategies used to arrive at the correct answers.

In Australia, the place of mental computation in mathematics curricula is only beginning to be seriously considered. Little attention has been given to teaching, as opposed to testing, mental computation. Additionally, such attention has

predominantly been confined to those calculations needed to be performed mentally to enable the efficient use of the conventional written algorithms. Teachers are inclined to associate mental computation with isolated facts, most commonly the basic ones, rather than with the interrelationships between numbers and the methods used to calculate. To enhance the use of mental computation and to achieve an improvement in performance levels, children need to be encouraged to value all methods of computation, and to place a priority on mental procedures. This requires that teachers be encouraged to change the way in which they view

mental computation. An outcome of this study is to provide the background and recommendations for this to occur.

The mathematics education literature of relevance to mental computation was analysed, and its nature and function, together with the approaches to teaching, under each of the Queensland mathematics syllabuses from 1860 to 1997 were documented. Three distinct time-periods were analysed: 1860-1965, 1966-1987, and post-1987. The first of these was characterised by syllabuses which included specific references to calculating mentally. To provide insights into the current status of mental computation in Queensland primary schools, a survey of a

representative sample of teachers and administrators was undertaken. The statements in the postal, self-completion opinionnaire were based on data from the literature review. This study, therefore, has significance for Queensland educational history, curriculum development, and pedagogy.

The review of mental computation research indicated that the development of flexible mental strategies is influenced by the order in which mental and written techniques are introduced. Therefore, the traditional written-mental sequence needs to be reevaluated. As a contribution to this reevaluation, this study presents a mental-written sequence for introducing each of the four operations. However,

findings from the survey of Queensland school personnel revealed that a majority disagreed with the proposition that an emphasis on written algorithms should be delayed to allow increased attention on mental computation. Hence, for this

sequence to be successfully introduced, much professional debate and experimentation needs to occur to demonstrate its efficacy to teachers.

Of significance to the development of efficient mental techniques is the way in which mental computation is taught. R. E. Reys, B. J. Reys, Nohda, and Emori (1995, p. 305) have suggested that there are two broad approaches to teaching

mental computation,,Ya behaviourist approach and a constructivist approach. The former views mental computation as a basic skill and is considered an essential prerequisite to written computation, with proficiency gained through direct teaching. In contrast, the constructivist approach contends that mental computation is a

process of higher-order thinking in which the act of generating and applying mental strategies is significant for an individual's mathematical development. Nonetheless, this study has concluded that there may be a place for the direct teaching of selected mental strategies. To support syllabus development, a sequence of mental strategies appropriate for focussed teaching for each of the four operations has

been delineated.

The implications for teachers with respect to these recommendations are discussed. Their implementation has the potential to severely threaten many teachersf sense of efficacy. To support the changed approach to developing

competence with mental computation, aspects requiring further theoretical and empirical investigation are also outlined.

Impact and interest:

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ID Code: | 16011 |
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Item Type: | QUT Thesis (PhD) |

Supervisor: | Irons, Calvin, Irons, Calvin, Cooper, Thomas, & Cooper, Thomas |

Keywords: | Arithmetic, Computation, Computational Estimation, Mathematics, Mathematics Curriculum, Mathematics Teaching, Mental Arithmetic, Mental Computation, Mental Strategies, Number, Number Sense, Queensland Educational History, Queensland Mathematics Syllabuses, Teacher Beliefs and Practices |

Department: | Faculty of Education |

Institution: | Queensland University of Technology |

Copyright Owner: | Copyright Geoffrey Robert Morgan |

Deposited On: | 03 Dec 2008 13:55 |

Last Modified: | 29 Oct 2011 05:42 |

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