The acquisition of basic quantitative reasoning skills during adolescence: Learning or development?

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Abstract
Five items requiring use of proportional, probabilistic, and correlational reasoning were administered to students in grades 6, 8, 10, and 12. Proportions are taught in the school district in grades 7 and 8, probability in grade 10, and correlations are not taught. Based on the hypothesis that successful performance is due to classroom instruction, improvements on the proportions item were predicted between grades 6 and 10 and improvements on the probability items were predicted between grades 10 and 12. Actual gradewise improvements did not correspond well with predictions. Yet performance did correlate significantly with enrollment in classes such as chemistry, physics, and trigonometry. It is argued that successful qualitative reasoning arises as a consequence of the process of equilibration, and influences one's selection of course work. Specific instruction may initiate the equilibration process.

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