The Assessment Of A New Approach To Learning Number To Achieve Arithmetical Automaticity Based On The Use Of Dedicated Manipulatives

Abstract

The original aim of this research was to determine whether or not a new approach to learning the basic processes of arithmetic, based on the use of dedicated manipulatives, would produce statistically significant improvements in automaticity – the instant and accurate recall without any conscious mental effort of previously memorised number facts. However, it was found that memorising number facts was no longer being emphasised in the participating schools of Co. Durham or Edinburgh.

The reasons identified were:

• A strongly established preference for teaching analogous procedures to calculate number facts, based on understandings of first principles.
• A general conviction that good literacy confers greater long-term benefit than good numeracy does.
• A general lack of appreciation of the potential contribution of good automaticity in improving number attainments.
• Insufficient time for memory work in overloaded curricula.

However, the new approach to learning arithmetic, using physical manipulatives, produced highly significant gains (at the 99% level) in Mental Arithmetic and General Maths, as measured using the InCAS computer adaptive programme for five to 11 years old pupils over their early years of formal number learning.

Five schools in Co. Durham and seven in Edinburgh were involved at some stage with 545 children being assessed initially, while 299 started in the Empirical Study. They attended six schools, being three each in Co. Durham and Edinburgh. Comparisons by location and also by gender were made as secondary questions.

Two Swiss schools, with a total of 23 children, were similarly assessed. Their results were not included in the Study, but they were used in terms of contextualising understandings.

The case for automaticity was made throughout the Study in the participating schools. The need for more research into the effectiveness of manipulatives in improving number attainments was identified in the literature.