| Piaget took the position that before children could truly understand addition and subtraction, they had to develop conservation of number, equality and class inclusion. These foundations of understanding number were necessary for reversibility of thought to be possible. This study investigated whether there was a relationship between conservation levels and mathematical performance, and whether an intervention focused on improving logico-mathematical skills had an effect on the conservation levels or mathematical performance.;Study and control groups were each made up of nine third graders identified as low achievers mathematically. Mathematical proficiency tests and five conservation tasks were administered: one-to-one and number, equality, and three different class inclusion tasks. The majority of the students were in transition relative to most of the conservation tasks. An eight week intervention program with the study group, consisted of games and activities intended to improve logico-mathematical skills. Upon completion, conservation levels and mathematical proficiency in addition and subtraction were re-tested.;The results were analyzed qualitatively and quantitatively. Individual differences in counting, problem solving strategies and incorrectly learned algorithms were noted. Statistically, the conservation task levels correlated highly with the mathematics scores of the preliminary test (r = .84) showing a strong initial relationship between them. A repeated measures ANOVA tested the pre/post change in conservation levels for study and control groups. Significant pre/post change (F = 37.33, p < .01) and significant interaction effect (F = 4.8, p < .05) were found. A repeated measures ANOVA also tested the change, by group, of the mathematics test scores. Significant deterioration in the double-digit disembedded addition and subtraction problems was observed (F = 8.18, p < .05). Significant improvement in the part-part-whole problem solving was found (F = 4.55, p < .05). Other parts of the mathematics test showed no significant change although the means tended to drop.;This study provided evidence supporting Piaget's theory about the relationship between conservation and mathematics. The need for focusing on developing logico-mathematical skills in the early elementary years rather than memorizing algorithms was concluded. |
