DENSITY: AN APPLIED CONCEPTUAL MATHEMATICS AND SCIENCE
CURRICULUM FOR MIDDLE SCHOOL GRADES
By Nickoleen Margaret Smith
Spring 1999
The purpose of this project was to develop a middle school curricular unit which
utilized integration of conceptual content and constructive teaching strategies to
significantly improve student comprehension of identified mathematics and scientific
concepts and subconcepts. The unit developed for this purpose focused on the concept of
density. The project utilized 12 hands-on laboratory investigations which maximized
student involvement.
The unit introduced mathematical and scientific concepts and subconcepts
progressively, spiraling previous data to aid in the sense making of new and more
challenging information. The integration of a mathematical strand of measurement and
calculation, necessary for the interpretation of the scientific data generated by the
laboratory experiments, also led students to realize the essential role mathematics plays in
conceptual understanding. Embedded, often informal, daily assessment allowed early
identification of misconceptions, giving rise in turn to extensions and opportunities to
remediation.
A field test of the unit was conducted with three eighth grade classes and one
seventh grade class. Prior to, and immediately following, the field test, pretests and
posttests of mathematical and scientific concepts and subconcepts, were administered.
Of the two science tests administered, one was an informal evaluation which consisted of
group definitions and illustrations of density and its subconcepts, as well as volume,
mass, and measurement. The second science test consisted of a 10-question essay
evaluation which required students to define and explain terms and concepts. A 30question math test, based upon measurement and the utilization of scientific measurement
tools, density calculations, and the interpretation of graphic data, was administered and
evaluated.
The data generated by the pretests and posttests were analyzed statistically.
Academic growth and understanding, as evidenced in the analysis, were significant. This
information supports the efficacy of constructive methods of education coupled with
integrated, conceptual, curriculum. The application and generalization of the
mathematical and scientific concepts covered in this curriculum show evidence of lateral
transfer in laboratory experiences dealing with convection of the Earth’s crust and
dispersal of airborne pollutants.