Saturday, August 20, 2011

The Density Dunk: Using Inquiry & Problem-Based Learning to Teach the Density Concept

Density is an important concept in the physical and life sciences. Density carries a significant physical meaning that relates the amount of mass an object possesses to the volume it occupies. Yet this unique property of matter is often separated from its physical meaning to instead focus on the calculation of quantities associated with density. Students do not develop a strong conceptual sense of density, despite the fact that many students can perform density calculations. Students' reasoning should not be sequestered from the calculations they perform (Reif, 1995); however, often through the use of algorithmic teaching methods, the learning that is displayed and is not a true indication of conceptual attainment learning that has taken place. Students "fake it to make it," which is to say they can perform the calculations without having any sense of what it all physically means. This later leads to learning that cannot be transferred to other contexts outside of the original learned algorithm or typical practice problems (Darling-Hammond, Low, Rossbach, & Nelson (2003).

When density is presented with only minimal attention on the concept itself, students lose sight of the physical implications of density and become imbued with a sense that density is just another equation they have to memorize and use. This is very poignantly illustrated with the use of the "density triangle" or any variation thereof (see right.) Knowledge of how to use this triangle algorithm is easily acquired by most students, but this method is a gross decontextualization from the physical meaning of density, mass or volume. Furthermore, students who use the density equation to solve problems and perform calculations, or those who use the triangle algorithm, are usually just shown to do so by their teacher through some form direct instruction. This further obfuscates the density concept and students' construct of a physical meaning for the equation. 

In an effort to implement research-based practices to elucidate important concepts, two adjustments to the teaching methodology associated with the density concept are suggested: 1) the learning should be active and cooperative (Marzano, 2004); and 2) the physical meaning of the density concept and related equation must be constructed with students before calculations can be performed.

Using an inquiry based approach to teach the relationship between mass and volume can help to develop the mathematical model for density as well as a conceptual sense of that relationship. This resulting equation, which should then have a physical meaning, can be used to solve problems and further develop students understanding of the density concept. The suggested instructional strategy that will be the focus here to achieve the desired learning of the density concept will be Problem-Based Learning (PBL) and will be used in sequence with the inquiry method. 

Ultimately, teachers want students to be able to use the density concept to do something, e.g., uniquely identify unknown substances, compare how fluids or solutions may interact when mixed, or to determine whether or not an object might float when put into water. These example tasks require more than a mere calculation to be successful. The PBL strategy and inquiry approach, when properly used in sequence, will allow students to construct a sense of density, derive the density equation, and solidify their knowledge as they stretch the density concept further by solving a novel problem: determining the density of a person--the density dunk tank experiment
Measurement is a very important skill in any science; similarly, the ability to interpret and compare data is essential to experimentation. Creating the opportunity for students to be actively involved in the development of those skills is an invaluable part of the scientific experience. The inquiry process, cooperative learning, and PBL each create the conditions that foster this type of learning. Each step in the sequence of this unit on density deals with problems and solutions to those problems. All steps are student-centered and constructivist. Cooperative learning groups will be explained and should be employed throughout the sequence. Steps are as follows for teaching the density concept:

Step 1.         Relationship Between Mass and Volume of Regularly Shaped Objects
Step 2.        Mass vs. Volume of Water
Step 3.         Water-Displacement for Measuring Volume of Irregularly Shaped Objects
Step 4.        Density Dunk

   Cooperative Learning (CL) Groups
All activities and experiments in this sequence should be done using cooperative learning groups. Student lab groups should be assigned to be heterogeneous, where each member of the group has a specified role. This facilitates their working together and prevents dominating lab partners from getting all of the value out of the activity. The class as a whole will serve as one cooperative learning group, but individual lab groups should be selected ahead of time (unless you have an established lab group protocol that you cannot give up.) More information on CL groups in the resources below. 

The detailed handout explaining how to conduct each of the steps in this learning progression of the density unit, and including the full lab for the density dunk, can be found here on the ChemEd handout page of my website.
The dunker goes under in the dunk tank as classmates are poised to determine their volume through water displacement

Containers of known volumes full of displaced water. The more variety of containers, the more unit conversions students will have to do
Students fill containers of known volumes with displaced water to determine the volume of the dunker
Danny, a dunk tank volunteer, is completely submerged to obtain his total body volume
Students collect the displaced water, using measuring cups, funnels, and containers of known volumes to determine the volume of the student in the dunk tank

  1. The Harvard Education VisibleThinking Project
  2. Arizona State University Modeling Instruction Program in Chemistry
  3. Modeling Chemistry Instruction Curriculum Framework Materials
  4. Problem-Based Learning, a Study Guide
  5. Cooperative Learning Groups
  6. If you are not yet ready to completely move away from direct instruction as part of your instructional sequence, you can consider integrating this Density PowerPoint

·   Collins, A., Brown, J. S., & Holum, A. (1991). Cognitive apprenticeship: Making thinking visible. American Educator, 15(3), 6-11, 38-46. 
·   Darling-Hammond, L., Low, B., Rossbach, B., & Nelson, J. (2003). The learning classroom. S. Burlington, VT: Mort Crim Communications, Inc. 
·   Levine, M. (2002). A mind at a time. New York: Simon & Schuster. 
·   Marzano, R. (2004). Classroom instruction that works: Research-based strategies for increasing student achievement. New Jersey: Prentice Hall. 
·   Reif, F. (1995). Understanding and teaching important scientific thought processes. Am. J. Phys. 63(1), 17-32.

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