Checking up Guides

The Nuffield Mathematics Project Check-up Guides were intended to provide information on the students' progress. As traditional tests were difficult to administer in the new atmosphere of individual discovery it was the intention of the authors to replace these by individual check-ups for individual students.

The first of the Checking Up guides, Checking up 1, from Nuffield is complementary to Mathematics Begins to which there are numerous references. It is strongly recommended that this guide is not used independently.

This guide focuses on the various concepts leading to the idea of number and to the operations on numbers. The word concept is used to describe ideas which are abstracted from experiences, such as addition, sorting, ordering. In this sense of the word, a concept cannot be taught - it is acquired through the student’s activity.

The concepts and pathways of development are mapped out diagrammatically and are supplemented by comprehensive notes listing required apparatus, teacher questions and typical replies. Included is one-to-one correspondence and conservation, one-to-one correspondence and transitivity, comparisons, sorting and union and intersection of sets.

Checking Up 2 from the Nuffield Project deals with 'shape and size' concepts for children of roughly ages five to eight or nine, although some of the 'summary' check ups at the end would extend to older children. An important emphasis in this part of the work is on measurement, with its necessarily approximate nature.

Checking Up 3 is a continuation of both Checking Up 1 (towards number) and Checking Up 2 (towards space and invariance). The first two chapters, on Speed and Time and Logic, cover topics which are not on the concept map as it is impossible to pin-point them. The check-ups concerned cover a wide age-range, as does the chapter on Probability.

The remaining chapters cut across the concept map. Three investigate geometrical ideas, Chapter 7 deals with invariances of weight and volume, and the last chapters are concerned principally with underlying ideas of arithmetic.

The guides re-emphasised that the check-ups were flexible and only for the guidance of the teacher. They were not intended to be intelligence tests but milestones that would allow teachers to judge where a student was in their normal development. The aim of the check-ups was to show that students acquire concepts gradually and point to the difficulties they could encounter. Materials could be adapted and students should only be given a check-up when the teacher felt it was valuable.