This is the from PERC (Physics Education Research Conference). This talk was by Andrea diSessa (Berkeley), who developed the theory of phenomenological primitives (or p-prims).
diSessa’s recent work is looking at how students’ intuitive ideas help them construct meaning. For example, Newton’s Law of cooling says that the rate of change of temperature of something is proportional to the difference in temperature between the thing and its surrounding. That means that liquids cool off quickly at first. One of the students in the high school class that he studied explained that “so when one is way off they kind of freak out” and then they “calm down” when they get closer to equilibrium.
Going back to 1993, in his writings on p-prims he developed some ideas of ideas that people bring to problems such as these. Eg., “more effort begets more result”, a p-prim of “agency.” “Abstract balance” is a p-prim indicating that in certain situations things must balance out. Abstract imbalance is the idea that things can be “out of balance.” Equilibration is a “return to balance” that can involve either overshooting equlibration or slowing equlibration.
“I think that the liquids like to be in equilibrium [abstract balance], so when one is way off they sort of freak out and work harder to reach equilibration [abstract balance, where “agency” is defined as “freaking out” and “working harder”] and when it’s closer to equilibrium they’re more calm [lower agency]. So they sort of drift slowly [lower effort begets lower rate of change].
So, this person has introduced agency (“freaking out”) in an area that is usually not seen as having agency. The amount of agency is controlled by the temperature differency, and “more effot begets more change” is invoked to explain the rate of heating and cooling. The net result is that the student has created a causal chain in his understanding of heating and cooling. These are very useful ideas! Temperature difference is what drives the rate of heating and cooling in this student’s mind, which is exactly right!
What about how the glass reaches equilibration…. does it slow down and approach equlibration, or does it “overshoot” it and then come back? Here is one student explanation: “The hot water is like shocked.. but the colder water that you put it into… causes it to cool down really quickly. but once it’s at a lesser temperature, it starts to slow down as it reaches equilibrium.” Like the word “freaking out”, “shocked” invokes an idea of agency. “Once the really cold water gets put into the much warmer water, it experiences like a shock because they’re so drastically different. So it gets closer to that temperature faster in the beginning and stops freaking out and calms down as it approaches equilibrium.” Again, this student is bringing up the idea of temperature difference being important.
Eventually, though the students start translating their ideas into math. A few days later, a student asks why the cooling graph for a hot object is steeper than that for acold object the student says “because the hot one is further away from equilibrium than the cold one.” She’s dropped the anthropomorphism and ideas of agency.
So, these intuitive ideas help students make sense of something, and move towards a more abstract formal understanding. Note that this is like the ideas in one of my first posts this week, where we discussed how to use students’ informal understanding of some event to build up a more mathematical description.
He emphasized that social interaction, like how these kids figured out their ideas of heating and cooling, is an important part of how we know.