DIFFERENTIATING MASS FROM DENSITY:
THE EFFECT OF MODELING AND STUDENT DIALOGUE
IN A SIXTH-GRADE CLASSROOM
Martha L. (Molly) Shaw
The concept of density can be difficult to learn. In the middle grades, students characteristically conflate mass and density, and even after instruction many students do not distinguish them consistently (Smith, Maclin, Grosslight, & Davis, 1997). Few develop a conceptualization of density that accounts for the implications of changing mass, volume, temperature, and/or state. My work looks specifically at how students make sense of the relationship between mass and volume as they refine their understanding of density.
The concept of density is challenging to teach. Traditional methods of teaching density in middle-school classrooms typically involve either the measurement of an object’s mass and volume and the subsequent calculation of the ratio of the two quantities, or the observation of different materials in water to learn about their buoyancy. Unfortunately, as Carol Smith and her colleagues have documented (1985, 1992, 1997), these approaches leave many students stuck in their “commonsense frameworks” that merge mass and density into one concept. Teachers need better ways to teach density.
Hence I designed an intervention to study the effects of some possibly more effective ways to teach density. I developed and taught a complex intervention (Brown, 1992) featuring student modeling, extensive student dialogue on data and data analyses, formative assessments, the substitution of hands-on inquiry for mathematical problem sets, and multiple thought experiments. The hallmarks of the intervention were modeling and student dialogue, and the research question I posed was: Does classroom practice that encourages modeling with open-ended discourse help students differentiate between the concepts of mass and density?
I patterned my research on a Smith study of density instruction in eighth grade (Smith, Maclin, Grosslight, & Davis, 1997), which had a quasiexperimental research design that compared the results of teaching density differently in two classrooms. I selected an intervention class and a comparison class from those I was teaching. The core of the density curriculum was similar in both classes. Instead of the intervention, though, the comparison class closely followed the lesson sequences provided by the classroom textbook, which tended to focus on formal and formulaic density instruction. I modified Smith’s assessments for sixth graders. After teaching one class the intervention curriculum and the other the textbook-based curriculum, I evaluated and compared the progress of research participants in both classrooms by means of a pre- and post-instruction clinical interview, a pre- and post-instruction written test, and the end-of-chapter test from the textbook used in the comparison classroom.
The results of my study were consistent: the intervention students outperformed and showed greater improvement on all assessments compared to the comparison students. In this study, modeling and student discourse were more effective ways to teach density than a standard textbook-based lesson sequence. The intervention helped students start to disrupt the conflation of mass and density, fostering both the comprehension of volume as a variable property of matter, and a nuanced understanding of density beyond formulaic reasoning.
This dissertation is a report of my study for two audiences—academics and science educators. For the latter, I include recommendations for improving density instruction that are informed by my research.