By Leslie Smith
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Extra resources for Piaget, Vygotsky and Beyond
The problem of hierarchy and progression was therefore addressed by starting with the National Curriculum (1991 version), analysing the Statements of Attainment (SoA) as to whether, broadly, they required mature concrete (2B), concrete generalisation (2B*), early formal (3A) or mature formal (3B) thinking. The result of this analysis is shown in Figure 12. Hence nine broad strands were picked out, containing five more central strands. The thirty Thinking Maths activities were then designed in terms of a progression up the five central strands starting from Level 4, with contexts chosen in addition as far as possible from Ma4 (Space) and Ma5 (Data-handling).
The data for the schools that had used the CASE intervention were entered separately on the same graphs, and can be seen for the most part to lie above and outside the limits of sampling variation of the control schools. For Science and Mathematics the regression line lies above the national average, so the effects for the CASE schools may be slightly underestimated. In the case of the English results there was much more variability, both for control and CASE schools, and this is attributed to the poor reliability of the English test.
Mathematical activity at the secondary school level is only sketchily addressed in the Genevan research, although clearly proportional and probabilistic thinking are widely used. The problem of hierarchy and progression was therefore addressed by starting with the National Curriculum (1991 version), analysing the Statements of Attainment (SoA) as to whether, broadly, they required mature concrete (2B), concrete generalisation (2B*), early formal (3A) or mature formal (3B) thinking. The result of this analysis is shown in Figure 12.