arXiv | Should teachers concentrate on critical thinking, estimation, measurement, and graphing rather than college-clone algorithmic physics in grades K--12? Thus far physics education research offers little substantive guidance. Mathematics education research addressed the mathematics analogue of this question in the 1930's. Students in Manchester, New Hampshire were not subjected to arithmetic algorithms until grade 6. In earlier grades they read, invented, and discussed stories and problems; estimated lengths, heights, and areas; and enjoyed finding and interpreting numbers relevant to their lives. In grade 6, with 4 months of formal training, they caught up to the regular students in algorithmic ability, and were far ahead in general numeracy and in the verbal, semantic, and problem solving skills they had practiced for the five years before. Assessment was both qualitative -- e.g., asking 8th grade students to relate in their own words why it is `that if you have two fractions with the same numerator, the one with the smaller denominator is the larger'; and quantitative -- e.g., administration of standardized arithmetic examinations to test and control groups in the 6th grade. Is it time for a science counterpart of the Benezet/Berman Manchester experiment of the 1930's?
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