causal pattern → causality & misconceptions → view student ideas → density examples

Relational Causality involves holding two variables in mind at once and considering their relationship. This is hard and students often lapse back to reasoning about the variables separately. The relationship between mass and volume determines density. Adding to the difficulty, mass and volume are obvious variables that can be directly perceived while density is non-obvious and cannot be directly perceived. This student reverts to focusing on mass, rather than mass in relation to volume even though he uses the word density and refers to different types of materials.

Students often think that there is air between the particles in a material. In some cases, there is (such as between the styrene in Styrofoam). But with pure substances, there is space between the molecules or atoms, not air. Often "air molecules" wouldn't fit in those spaces. This idea can keep students from focusing on the relational causality that defines density. This student does realize that air takes up space so fewer particles of the material would fit in the given space, but many students miss this finer distinction.

As we see here, many students think that breaking a pure substance in half means that the density will be half. The mass will be half and the volume will be half, but the density stays the same—it is an intensive property of the material. Students who understand the inherent relational causality are more likely to realize this. Here, the student has difficulty holding both sides of the relationship in mind at once. Instead, he holds mass constant and realizes that the volume would be half.

As we see here in these three examples, many students think that heavier things sink and lighter things float. They focus on the object as the direct cause of the outcome in a simple linear way instead of focusing on the relational causality involved—between the density of the object and liquid (or between the density of two liquids). Labeling objects as "sinkers" or "floaters" can exacerbate students' difficulties. In the everyday world, using a simpler model of weight to predict what happens is often reinforced, because in many cases it leads to correct predictions. However, it doesn't explain all cases and misses the relational causality involved.

Students sometimes say that the type of liquid doesn't matter for whether an object sinks or floats. This reflects an object-focused, simple linear model rather than a relational model that takes into account the densities of the object and liquid or two liquids. This student refers to the liquid's viscosity and thinks that the type of fluid makes something sink faster or slower but that it doesn't affect the ultimate outcome.

Students often learn density as a given number for a given material. Unless they realize that these two numbers are under standard conditions of temperature and pressure, it can lead to the view that density is static. To quote a science text, "Every substance has a density that can be measured. The density of a substance is always the same." This student reveals good understanding of the motion of particles at different temperatures, but does not realize that density can change. In relational causality, changes to either variable in the relationship affects the outcome. Realizing that density can change is key to many understandings—changing weather patterns, atmospheric layers, why ice floats in water and so on.