# Progress Among the Treatment Students

Children receiving the Inquiry Project curriculum made clear progress in both grade 3 and grade 4 on multiple aspects of conceptual understanding of matter, weight, volume, and density, although they are not yet at ceiling on most measures. These changes provide evidence that they are engaged in a productive but long-drawn process of reconceptualizing their matter network.

### MAJOR CHANGES BY THE END OF GRADE 3

By the end of grade 3 Treatment children made great progress on multiple items probing their understanding of weight and materials. Some (limited) progress was also made in understanding of volume, “heaviness of materials,” and matter, although in these cases the majority of students did not yet achieve a canonical understanding. The fact that children’s understanding of materials and weight leads their understanding of volume, density, and matter is consistent with the emphasis of the curriculum and the assumption that weight and material are productive entry points for further learning.

More specifically, by the end of third grade, children were virtually at ceiling on understanding that grinding did not change materials (91%) as well as understanding that reshaping clay did not change heft, weight measured with a balance scale, or amount of material (84%). Children also made progress in weight measurement, with the majority able to use a set of gram weights to measure the weight of an object.

Children made dramatic progress in their understanding that tiny things both have weight and take up space (from 10% in the pretest to 60% in the posttest), typically justifying their choice by arguing “Everything must weigh something.” Some further explained, “although I can’t feel it, I could detect the weight of the piece with a ‘sensitive scale’”. As evidence that this is a watershed idea, two-thirds of the students who understood that the tiny (visible) piece had weight were also willing to infer that even (invisible) pieces of clay—pieces too tiny to see—would have weight and take up space as well.

Finally, there was also dramatic progress both in their knowledge of specific material kind terms and their use of material kind differences in explaining why larger objects are not always heavier. Indeed, the majority (76%, up from 27% at pretest) were considering that differences in the kinds of things the cylinders were made of could explain why some were heavier than others, with half started to talk about differences in the “heaviness of the kind of material” and considering specific materials the cylinders might be made of. Lagging behind was an understanding that reshaping did not change the amount of space the clay took up (38%). We know from the pretest that these children had a very poor understanding of volume, and were much more likely to compare the sizes of objects in terms of the areas they occupy. The difference in area occupied by the clay ball and the clay pancake was very salient; moreover, fewer lessons in the 3rd grade curriculum were devoted to volume.

Also lagging behind was children’s ability to attend to the invariant of the volume of the blocks in the volume measurement task and to systematically distinguish heaviness of kind of material from weight (in the judgments about the cylinders). Although children made clear progress in their patterns on these tasks, less than a third of the students had achieved the target understandings by the end of grade 3. In addition, children made no significant progress on volume displacement (a topic not yet investigated in the curriculum) nor in using stacking of cubes to make inferences about the kind of material the mystery cylinders were made of.

### MAJOR CHANGES BY THE END OF GRADE 4

By the end of grade 4, Treatment students had maintained many of their understandings of weight and materials and continued to improve on the challenging volume and density tasks. In many ways, their understanding of volume and density, which had begun to develop in third grade, seemed to “catch up” with their understanding of weight.

More specifically, students continued to improve on the volume measurement task. Forty percent of students focused on volume, rather than length or area in this task. Students also improved dramatically in realizing that the size of an object, not its weight, predicts water displacement (58% of students, as opposed to 7% in the pretest and 18% at the end of grade 3). The task could be solved successfully by simply comparing the heights of the cylinders, which had the same cross section, but it did call for reconceptualizing that spatial extent, not weight, is relevant to water displacement. Of course, students did explicitly address this topic in the curriculum, but it is also a notoriously difficult topic for students to learn, so we take this progress to be encouraging and a sign that the curriculum was effective in fostering the development of a concept of volume as “occupied space” stable enough to integrated into a new account of water displacement.

Students also continued to improve in developing precursors to a formal density concept. When asked which of two objects was made of a heavier kind of material, half the students were able to systematically relate weight and size, rather than base (at least some of) their answers on weight only. In addition, and quite impressively, half the students were able to use a sophisticated stacking strategy in order to correctly infer what material two small covered cylinders were made of. (That is, they stacked three of the same small covered cylinders together to make them the same size as the uncovered cylinders of known materials, and then compared the weight of the stack to each of the uncovered cylinders their strategy for inferring material.) Recall that, in third grade, most had directly compared the weight of one small covered cylinder to the weight of the uncovered cylinders, ignoring the difference in size.

We take progress on both these tasks as strong signs that students are developing meaningful precursors of density. Further, we note that although the curriculum discussed “heavy for size”, students were never asked to use weight information to infer what a mystery material was; so this kind of task represents a novel extension of their class work. Overall, 44% of the students did distinguish heaviness of kind of material from weight in the judgment task and used the stacking strategy in the other; 67% of the students showed insight in at least one of these two demanding tasks.