ABSTRACT
It was fairly evident in Chapter 5 that Lorraine’s grip on certain mathematical processes and concepts was quite tenuous. When given individual help she could achieve some success, but, left to her own devices, she floundered. The vast majority of primary schools, according to the Cockcroft Report (1983) spend a good deal of time on maths teaching, but what actually occurs during that time is clearly of greater significance. Lorna Ridgway (1976) outlines her criteria for good maths teaching and good maths learning and, with her kind permission, I should like to quote the nine points she makes.
Since the ultimate capacity to think abstractly does not originate in abstract teaching but depends upon the learner’s own interaction with the external world in thought-provoking situations, the teacher’s responsibility is to provide for the appropriate mathematical activity in breadth and in depth.
Children proceed along a broad front; a variety of numerical and mathematical ideas at approximately the same level is provided.
All pupils need not necessarily go through all processes in the same order.
The programme is so arranged that learners return frequently to the same aspect of mathematics to renew their grasp and deepen understanding.
Recording of number and mathematical experience often takes forms other than the numerical. Young children grasp and use number ideas expressed in pictures, diagrams, charts, graphs, histograms, mapping and three dimensional structures and use them more effectively than they did the former purely computational ‘sums’.
Apparatus, text-books and task assignments are used flexibly as learning aids; at any level their use may be modified, dispensed with or prolonged as necessary.
Mechanical mastery dependent upon rote-learning has a very limited place: it is not usually undertaken unless the process it represents is fully understood: but the terms required to express mathematical ideas are memorized through constant use and this memorization may occasionally be tested.
Individual interest is highly valued: children may prolong their work in an area that interests them even if other aspects or subjects are temporarily neglected.
Much help is available to the teacher. Commercially produced equipment abounds, from beads and bricks to the structural materials of Cuisenaire rods, Stern or Dienes blocks, Logiblocs, metrication kits, Poleidoblocs and calculators and computers. The literature is rich, ranging from theoretical studies … to practical guidance.
Commercial assignment-card kits make individual work comparatively easy, although there is often need to use them selectively.
