Abstract:

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 that could be animated through time. Many different experimental situations can be simulated through modification of the box’s volume. This quantitative methodology allows students to query and explore varied data images. Working cooperatively with the students, we continue to expand this lab experiment as an interactive lab exercise and Web site.

Introduction

In an ideal lab learning situation students employ interactive methodologies built around the scientific method. When students collect and analyze numerical data, they gain 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 series of exercises derived from 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 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, student lack of numerical skills 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 model.

The Students’ Experiment

Methods

The initial experimental concept is simple: how would one find a lighted candle in a closed box? A 2 x 1.5 x 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). (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 2 x 1.5 x 1.5 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? This is 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. (See Figure 2, left image). 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 would show the rate of change of the temperature of each probe. Just a few minutes of computer-driven data collection can create a spreadsheet with thousands of information bits. Learning to organize the data becomes an important part of the exercise.

Results

The experiment evolved the following protocol: 1) at time zero minutes, begin temperature recording by all eight probes; 2) at time one minute, establish the base line temperature and turn on the heat source; 3) at time five minutes, turn off the heat source; and 4) at time ten minutes, end the temperature recording. The recording interval exhibits three discrete periods: no load, heat load, and cool down or anticipated return to equilibrium. With these data, students can determine values of parameters in mathematical models, validate mathematical models representing physical or biological phenomena or principles, and 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 versus time for eight recording probes. Right Image &emdash; visualization of the interpolated temperature volume over time from two of the probes performed with Noesys suite software.

We enhanced the analysis and interpretation aspect of the exercise by introducing volume visualization software. Using the Noesys suite software (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 (see Figure 2, right image). The software can also interpolate the volume and provide animations to aid the students’ understanding of the phenomenon or principle being studied. The T3D feature of Noesys is used to render and visualize isometric surfaces from the interpolated data. Using the software to slice the rendered solid in different planes, the students then can determine visually the location of the heat source. These volume visualizations, interpolations, and slices provide students with interpretability prospects not easily performed with traditional graphing.

The Faculty’s Experiment

Introduction

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 in a semester of lab experiences, 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. In our case, 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 model develops it becomes clear that other disciplines such as biology, geology, and mathematics can utilize the model. Students learn first hand from the modeling experiences that the practice of science is both multidisciplinary and collaborative. 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.

Methods

We had several goals with this project: 1) to create a lab experiment that would focus on experimental design, mathematics and data collection for biology students, 2) to create a lab experiment that would focus on experimental origin of data and applications for mathematics students, 3) to create a method for students to learn to work with experimental design and with each other, 4) to create a lab exercise with a simple foundation and with increasingly sophisticated layers of data-processing, 5) to create a flexible teaching and learning methodology which would allow for improvements and ease of evaluation, and 6) to encourage instructors to design laboratories that would incorporate more innovative features including, inquiry-based learning, student journal-keeping in addition to the traditional lab book notes, and frequent student feedback.

Discussion

We thought that student involvement in and "ownership" of the experiment was critical to the success of student learning in this lab exercise. We encouraged this ownership in four areas. First, we placed primary emphasis on asking for, listening to, and incorporating student ideas and comments. For example, we originally had designed and created a much more complex experimental format involving a sampling matrix with 27 probe points, filling much of a laboratory room. Students suggested a simpler model, one they could work with more easily for design purposes: a box instead of a room.

Second, students were encouraged to take charge and take responsibility for the experiment as much as possible. For example, we asked students to seek alternative ways to analyze the data and to experiment with the Noesys software for effective and creative processing.

Third, students were asked to design an experiment using the basic model. 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.

Fourth, to work with applications of the model, 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 also they would have to do library research to determine what is known about lake temperature distributions. If they created a "virtual" lake, the students could model the following hypothetical situation: what would happen to lake temperatures if an electric power 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 model had found applications beyond its original intention.

Summary

The Candle in a Box exercise offers some real challenges and possibilities. Learning how to use the software was a challenge to both the instructors and the students. The significant difference in the screen coordinate system and the typical mathematical coordinate system proved to be a challenge for many of the students. Pacing the exercise and allowing sufficient time for the completion of the collaborative work proved to be a challenge for the instructors. The difference in the students capabilities made it difficult to get students to engage in the experiment and to evaluate the learning.

One of the successes involved the interaction between mathematics and biology. Getting the students to engage in a discussion with the instructors about the interface of mathematics with biology was a highlight of the exercise. This metaphor is a starting point for experimental design for many different problems and offers to the student a strong sense of abstraction. Another problem faced by the faculty was how to incorporate this methodology as a central piece for a scientific visualization course that spans the sciences and mathematics. A web page has been developed as an on-line laboratory manual for the experiment. It includes such things as the calibration of the temperature probes, the use of the Data Logger software, the placement of the probes, and the recording of the data into the Noesys spreadsheet. Numerical and graphical results of the students’ analyses could be placed on the web page, then the students could compare their analyses with those of other students. In this manner the page becomes a teaching tool for the current class and can be used by other classes in the future.

Acknowledgments

We gratefully acknowledge the help of the students in the Fall 1998 section of the Biological Imaging and Visualization course at Trinity University, our very capable student assistant Julie Stephens, and our web consultant Seven Bohannon.

The authors’ efforts are being funded through an NSF CCD grant(95-54805) where synergistic relations between statistics and biology education are being sought.

References

Coleman, G.J., & Dewar, D. (1977). The Addison-Wesley Science Handbook. Don Mills, Ontario: Addison-Wesley Publishers.

Graham, I.S. (1997). HTML Stylesheet Sourcebook. New York: John Wiley & Sons, Inc.

Greenberg, L.H. (1975, 2nd ed.). Discoveries in Physics for Scientists and Engineers. Philadelphia: W.B. Saunders, Co.

Tobias, S. (1992). Revitalizing Undergraduate Science: Why Some Things Work and Most Don’t. Tucson, Arizona: Research Corporation.

Williams, J.E., Metcalfe, H.C., Trinklein, F.E., Lefler, R.W. (1968). Laboratory Experiments in Physics. New York: Holt, Rinehart & Winston, Inc.

(software) Data Logger (Macintosh Version) vers. 4.5. (1990-1994). Tufts University, distributed by Vernier Software, Portland, OR.

(software) Noesys Suite, T3D, Plot and Transform (1997). Sterling, VA: Fortner Software

---