Conceptions of Treatment Students on the Grade 3 Pre-Interview

Our interviews revealed that at the start of third grade, our treatment children’s initial understandings of material, weight, and size were grounded in perceptual experiences with objects and materials rather than tightly inter-related in an explicit model of matter. Further, they did not yet conceptualize physical quantities as dense linear dimensions for which a metric supports additive and multiplicative relationships, had almost no conceptual understanding of fractions as numbers, and little conceptual understanding of measurement. A distinct concept of volume (i.e., a concept of volume differentiated from length, area, shape, and weight) is almost totally absent, as is a concept of density differentiated from weight. Thus the conceptual relations in these students’ knowledge network were very different from the relations observed among experts. Overall, they also lacked a coherent concept of matter as something that includes solids, liquids, and gases, and as something that takes up space and has weight and did not think of materials as varying in density.