What happens when a student's mental models do not agree with her observations, such as when a phenomenon observed in one situation fails to repeat itself on a larger scale? Does that mean all models are wrong, or are they just too simple to describe the complex situations that students face on a daily basis? To study this question, our Data and Models project is purposefully creating such conflicts for students in order to look at the interplay of theory and experiment and to develop strategies for dealing with it.

Using state-of-the-art wireless data collection, simulation, and visualization technology (see article, page 7), we are guiding students at the Fowler Middle School in Maynard, Mass., through the study of heat transfer. By doing experiments that involve the variation (both temporal and spatial) of temperature in solids, liquids, and gases, students form models to describe what they see, and extend and revise those models in the face of conflicting evidence gained from experiments and observation. When they encounter discrepancies they use this information to revise their model or improve their experiment, an iterative process that mirrors the real scientific method much more closely than the simplistic hypothesis-experiment-conclusion sequence that permeates the pre-college curriculum.

Student Preconceptions
At the beginning of the study we administered to approximately 250 sixth and seventh graders a quiz designed to identify students' preconceptions regarding heat and temperature. Many of the questions drew on experiences related to situations familiar to the students' physical world, such as roasting marshmallows with metal coat hangers or wooden sticks, describing methods for cooling a hot bowl of oatmeal, and comparing the boiling rates of different amounts of water on a stove. The interviews allowed us to ask the students to elaborate on their initial answers, and many of their responses provided unique and sometimes conflicting theories. One student proclaimed that blowing on a bowl of oatmeal cools it down because "cool energy blocks the heat energy," yet he continued to explain that "heat energy moves faster than cool energy . . . so it [heat energy] can push it [cool energy] away." Conflicts continued to surface when their explanations seemed to contradict their real world experiences. The classic case that a "metal [coat hanger] is cold" and a wooden "stick is warm" caused visible confusion when a student was asked to explain why she thought the coat hanger was hotter in the fire compared to the wooden stick. The student started with the classic statement that "metal is cold, the stick is warmer" and then paused and said after some thought that "metal is made differently than wood and it warms faster."

We subsequently selected 13 students whose answers to the quiz needed more explanation or were contradictory to other answers provided on the quiz.

Conflicting Models
Through our literature survey and knowledge of the domain, we were able to identify two possible sources of confusion that might make it difficult for students to understand heat and temperature. Our initial curriculum development was aimed at those areas. First, we recognized that it is not so much the concept of temperature that is foreign to students as that of temperature gradient - i.e., the change in temperature over spatial separations. We imagined students were familiar with the concept of the temperature of an object but were likely confused by the idea of an object having more than one temperature. As a result, our early activities centered on the notion of measuring temperature gradients along metal blocks and formulating a mental model about the role of heat flow in establishing thermal equilibrium in the absence of external energy sources or sinks.

Our second intuition was that student models about temperature are affected greatly by the fact that the students are themselves temperature detectors and heat engines. As mammals, all students maintain a relatively constant internal temperature that is usually significantly higher than that of their surroundings. All students are familiar with the method of estimating the temperature of something by touching it. Since their finger is in contact with a heat bath (blood) at a nominal 98.6oF, it does not cool down to the temperature of the object it is touching, but generally reaches equilibrium at some higher temperature. The apparent temperature of the external object has more to do with its thermal diffusivity - its ability to conduct heat away from the hot finger - than with its actual temperature.

This confusion can lead to a conflict between a student's mental model and his observations. Take, for example, the student who learns that "hot things cool off and cold things warm up" - in other words, objects in thermal contact with their environment tend to take on the temperature of that environment.

On a cold winter day, take such a student outdoors, show her a tree, and ask her whether it is the same temperature as, say, the school's metal flagpole. Following her newly acquired mental model, she may be tempted to say the two objects, having come to equilibrium with their shared environment, are at the same temperature. But if she touches them both with her ungloved hand she is bound to realize that the flagpole feels a lot colder than the tree. Her abstract mental model concerning temperature gradients, heat flows, and the inevitable approach to thermal equilibrium (the essence of the Second Law of Thermodynamics) is in direct conflict with her everyday experience that metal objects feel colder than wooden ones at the same temperature.

To help resolve the conflict, we designed some preliminary activities involving human body temperature versus room temperature and tried them out on some students. This spring we will try the activity again with fast-response temperature probes (see article, page 7) that will enable the students to quickly compare the higher temperature data of their body first hand to that of their surroundings.

By confronting students' mental models with the evidence of real time data, we have watched the students adjust their theories. For example, during past and recent testing, the students made the statement that "heat cannot move around corners." After heating metal bars embedded with temperature probes in different configurations, the students quickly realized that heat can travel through the metal no matter what the alignment of the bars. Yet, they still hold to some of their original theories: although heat moves around the corners it "moves more slowly." In future work with the students, we plan to challenge this misconception with side-by side set-ups with different metal bar configurations, careful analysis of the graphs, and a stopwatch.

Real World Models
Based on our first year observations of student response to the gradient activities, our next logical step is to investigate two-dimensional systems that exhibit temperature change. Interesting new phenomena arise when we introduce fluids (liquids or gases), because now different parts of the system can move with respect to each other. As we extend our studies beyond conduction to other forms of heat transfer, such as convection and radiation, our students will be able to investigate ever larger and more complex systems. Computer technology will enable them to formulate increasingly complex models, run them as simulations and compare their behavior to experimental data. Eventually, they will be able to use this powerful technique to develop a qualitative understanding of such real world phenomena as weather patterns, seasonal variation, and global climate change.

Carolyn Staudt is the curriculum developer for the Data and Models Project carolyn@concord.org
Paul Horwitz is director of the CC Modeling Center paul@concord.org

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Last Updated: April 21, 2001
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