We sought to create a visualization-based methodology which would allow undergraduate students to become involved in experimental design. By experimental design we mean collecting, organizing, analyzing, and interpreting numerical data obtained from a constructed model. Once developed, our experimental design methodology became metaphorically known as "Candle in a Box." The methodology is here briefly outlined. Students placed digital temperature probes into a cardboard box to determine where a heat source was located within the closed box. The temperature data were output as three-dimensional volume visualizations which could be animated through time. Many different experimental situations can be simulated through modification of the box’s volume. This quantitative methodology allows students rapidly to explore many different kinds of problems.
In an ideal lab learning situation students employ interactive methodologies built around the scientific method. Upon analysis the student-collected numerical data provide a deeper understanding about some process or principle of science. The design of such a learning situation places two burdens upon the instructor: 1) the creation of a viable student-centered laboratory experiment with several testable hypotheses and 2) the creation of a learning environment which can be assessed at several levels. To these ends we found that digital temperature recording produced numerical databases very rapidly. With proper visualization software these databases can be expressed as three-dimensional volumes. By using a large cardboard box students can create controlled environments in which variables can be explored. With student-constructed models based on these elements, students can then use mathematical concepts such as interpolation to investigate the temperature data. The resultant series of exercises based on the candle in a box metaphor has students building testable physical models which quickly reveal the level of student understanding.
Cost-efficiency, digital interfaces, and broad student involvement were additional considerations in the development of the methodology. Clearly the use of computers in modern research has become ubiquitous. Digital-based modeling and simulation drive engineering design and increasingly the same is true for "traditional" scientific research. Today’s students should have access to digital modeling and simulation experiences. Expense, lack of numerical skills by students, and instructor inexperience with modeling approaches have hindered students’ learning opportunities. Recognizing that most learning environments have temperature-measuring equipment and computers with spreadsheets, we used this technology in developing the candle in a box metaphor.
The initial experimental concept is simple: how would one find a lighted candle in a closed box? A 2 by 1.5 by 1.5 foot cardboard box provides a convenient 4.5 cubic foot space to explore. An electric light provides a safe alternative to the metaphorical candle. We used eight direct-coupled digital temperature probes distributed by Vernier Software of Portland, Oregon to sample the box space. The two long, continuous sides of the cardboard box were pierced with four holes each and the temperature probes inserted with their recording tips spaced to define a centered, one foot cube inside the box. Two probes each were connected to a serial interface box (A to D converter) and the interface box to a computer (Macintosh). Please see Figure 1. Using Data Logger 4.5.9 software (provided by Vernier Software), temperatures were recorded every six seconds and simultaneously graphed on each of the four computers. Four teams of students were involved with each team responsible for two probes and two data sets. Students had to consider how to calibrate the multiple recording devices. It would be possible to record the temperature with standard bulb thermometers instead of digital probes.
Figure 1: Left Image - the open
2x1.5x1.5 foot box with temperature probes defining a one
cubic foot volume outlined in red. Right Image - the open box
with a heat source and connected to the computer.
At a recording rate of 10 times a minute for 10 minutes, each temperature probe produced 100 data points. With eight probes, the lab students collected 800 pieces of information which needed to be compiled into a spreadsheet. An immediate question arose: was the sampling rate appropriate for the questions being asked; no trivial matter. A related question evolved: do eight sampling points adequately describe the volume for the question being asked; or again, do the data resolve the question? With all the data in one spreadsheet, a standard coordinate graph of the eight sampling sites can be drawn and examined for obvious indications of the placement of the heat source. Please see Figure 2. The students quickly learn that data can be arrayed in different ways to reveal different aspects of the exercise; for example, displaying the temperature difference by time increment. Quickly the spreadsheet can grow to include thousands of information bits. Learning to organize the data becomes an important part of the exercise.
The experiment evolved the following protocol: 1) at time zero minutes, begin temperature recording by all eight probes; 2) at one minute recording, establish the base line temperature; 3) at one minute recording, turn on the heat source; 4) at five minutes recording, turn off the heat source; and 5) at ten minutes recording, end the temperature recording. The recording interval exhibits three discrete periods: no load, heat load, and cool down. With these data, students can learn and practice interpolation and extrapolation. They also have the means to verify their calculations by rerunning the experiment and varying the sampling rate or the length of recording time. For example, they can extrapolate when the box temperature would return to the base line value and then verify the accuracy of the prediction by recording temperatures for the calculated period.
Figure 2: Left Image - a traditional coordinate graph
plotting the temperatures and time for eight recording
probes. Right Image - the interpolated temperature volume
visualization performed with Noesys Suite software.
We decided to enhance the analysis and interpretation aspect of the exercise by introducing volume visualization software. Using the Noesys software suite (Fortner Software, Sterling, Virginia), temperature data can be entered into a three- or four-dimensional spreadsheet and visualized as a volume or a volume through time. The software can also interpolate the volume as well as provide animations. The volume data visualization can prove challenging for some students who still confuse the selection of axes for dependent and independent variables on two-dimensional graphs. The T3D feature of Noesys can visualize the shape of an interpolated temperature volume because the software can surface render selected temperature range data. Volume visualizations provide students with interpretability prospects not easily performed with traditional graphing. Please see Figure 2.
Once students gained experience with the methodology and analysis, they and the instructors proposed experimental variations. Some of the ideas included the following: 1) opening one side of the box and installing a fan, 2) placing tubing, with either chilled or heated water pumped through it, into the box, and 3) using dry ice rather than a heat source. These modifications were all based on the original, regular one cubic foot sampling arrangement. It was at this point that the idea of different contours for the box volume was introduced. By using styrofoam, newspaper, and cut cardboard, the box volume could be given other shapes. Further, the placement of the recording probes could describe positions other than that of a cube within the box. At this time students were asked to model "real world" situations. For example, using the existing equipment, could the temperature volume of a lake be simulated? Not only would the students try to model a hypothetical lake, but they would have to do library research to determine what is known about lake temperature distributions. Having created a "virtual" lake, the students could model the following hypothetical situation: what would happen to lake temperatures if an electric plant were built along the shore and it used lake waters for cooling? Other ideas were proposed such as finding a tumor in the human body or locating fish in the ocean. The candle in the box metaphor had grown well beyond its original intention.
Many educational issues are addressed by the candle in a box methodology. Perhaps the most important is the concept of layering; the process in which a student revisits a topic in successive layers. Too frequently a semester of lab experiences has students perform a variety of techniques superficially and explore certain topics only once. This is similar to an athlete working on a sport a week: football, baseball, dance, and archery. With each repetition, the temperature measurements become more complex as do their interpretations. With each repetition, the experimental design prospects grow. At first the disciplinary approach to the exercise appears to be a cross between physics and engineering. However, as the metaphor grows other disciplines enter the picture: biology, geology, and mathematics. Students learn first hand from the modeling experiences that the practice of science is multidisciplinary. Students also have to work in teams in order to explore ideas and solve problems. The box as a modeling environment does something that computer-based virtual reality models do not: the students have a real physical object to relate to, the box. In this design, the students learn to compare the simple experiment to the complex visualization of data.
The candle in a box exercise offers some real challenges and possibilities. The most challenging question concerns where this experience belongs in the curriculum; which department or program should claim it? In terms of possibilities the metaphor offers a strong sense of abstraction: using temperature gradients in air as representations for water. One idea actively being discussed is whether air temperature measurment in the box can be used as a model for measuring glucose concentration differences within the liver. Another idea is to examine how to incorporate this methodology as a central piece for a scientific visualization course. The model, sample data, and various exercises will be presented at the meeting session. This work is supported by NSF CCD 95-54855.