Home PublicationsL&LIssuesVolume 26 (1998-1999) February (No. 5)

In the Curriculum
Math, Science, and Technology

The Heat Is On

Using the Calculator-Based Laboratory to Integrate Math, Science and Technology

By Joanne Caniglia

Graphing calculators and data-gathering devices help elementary and middle school students connect ideas in math and science and relate them to real-world phenomena.

Teachers are always searching for methods and materials that provide opportunities for students to make connections among subject areas and to engage in real-world problem solving. Collecting data, questioning results, consulting resources, exchanging ideas, and reaching conclusions are core activities in both science and mathematics. Technology can tie these disciplines together by aiding in the collection and analysis of data.

Figure 1. CBL and TI-82 set-up. Photo courtesy of Texas Instruments. Although meaningful learning experiences can be created without the use of technology, using instrumentation such as the Calculator-Based Laboratory (CBL) from Texas Instruments heightens student interest and promotes active learning. Until the advent of the CBL, it has been difficult to collect data in actual locations. The CBL is an inexpensive and portable device that allows students to use technology while they gain an appreciation of the scientific process.

What Is the CBL?

The CBL is a handheld battery-operated unit used to collect real-world data. The unit can be connected to a TI-82, TI-83, TI-85, TI-86, or TI-92 graphing calculator for students to retrieve and analyze that data. Data and graphs can then be printed from a computer using the TI-Graph Link, a versatile software and cable package that allows graphing calculator users to transfer files between the calculator and the computer.

Using the CBL system, students can simultaneously measure and graph such physical quantities as position, velocity, acceleration, force, temperature, light, and sound. CBL's advantage over traditional labs is its capacity to quickly and frequently gather and graphically display data, allowing students to conduct many experiments in the same amount of time that one traditional experiment would require. A strong link is created between real-life events and the graph that exists as an abstract representation of the events.

Texas Instruments provides three probes with the CBL unit: a temperature probe, a light sensor, and a voltage probe. The focus of this article will be on three labs using the temperature probe. The program HEAT for the TI-82 (Bellman, Antione, Brueningsen, Krawiec, & Randall, 1994) assists students in collecting data by controlling the temperature probes and recording data at specified time intervals.

The following three activities were developed by groups of elementary and middle school teachers in a course about using calculators and computers in the elementary classroom. The teachers later tried the ideas in their classrooms, where new possibilities evolved; the results are described in the following sections. Sample worksheets for each of the experiments can be downloaded. To avoid wasting time during these experiments, teach students how to use the CBL, graphing calculator, and other data-gathering devices before you begin. This ensures that most of students' time completing these activities is spent on task.

Which Cup Is Best?

When coffee is poured in a cup, it generally cools off rather quickly, eventually reaching room temperature. For this investigation, students placed a temperature probe in styrofoam, ceramic, and paper cups full of hot water for approximately five minutes. Students then determined which type of cup retained heat the longest (see Figure 1). The program graphed the relationship between the temperature (T) of the water and the time (t) in seconds, where t = 0 when the water is initially poured into the cup.

Instead of generating graphs on their own, students used the CBL and TI-82 to create immediate graphic displays. This allowed them to investigate other scenarios such as covering the cups, using different amounts of water, and using different types of liquid. Figure 2 shows a graphical representation of the data they collected.

Figure 2. Graphs of various insulators for the "Which Cup Is Best?" activity.

Data collection and analysis are essential, yet they represent only two parts of the scientific process. The exchange of ideas and results is equally important. Students didn't just look for patterns in their graphs. They also discussed inconsistencies, drew conclusions, and made connections to the physical processes involved in cooling and heating. They found that the best insulators were the worst conductors of heat. For example, air is a poor conductor of heat but the best types of insulating materials trap air. Other examples of everyday insulators include the following:

• Wood used as handles on cooking pans.
• Fiberglass placed between walls, above ceilings, as well as in water heater covers.
• Styrofoam used in picnic coolers and cups.
• Cloth used as a covering for windows.

Which Melts Faster: Ice Cream or Sherbet?

After completing the previous experiment, students questioned whether a material's composition had an effect on its rate of cooling. Their discussions led them to consider which frozen dessert melts faster. Students enjoyed consuming the data sources and were more than willing to repeat the experiment, testing for such variables as different flavors and contents (cookies, fruits, nuts, etc.).

Scoops of ice cream and sherbet were placed in each of three dishes. Because of the wide variety of these products on the market, students controlled the brand names, contents, and flavors. Again, they inserted the temperature probe into the experimental substance. After collecting the data, students transferred them to a desktop computer for organization, analysis, and reporting. Students can then use statistical programs to manipulate the data (see Figure 3), and they can copy and paste screen shots, programs, and data directly into word processing files.
Figure 3. Graph of the melting rates of ice cream and sherbet.

This activity allowed students to sample and record the temperatures of varying amounts of frozen desserts in dishes of varying sizes. They found that the size and volume of an object affects its ability to retain and radiate heat. When the frozen dessert was not packed well--that is, it had more surface area--students found that the dessert melted faster. They also discovered that the more of any frozen dessert they had, the less it melted. Students used these observations to conclude that size is a natural insulator for many animals. Larger animals live in colder weather, whereas smaller animals inhabit the desert. Because they have less volume, smaller animals need more warmth from the environment.

Stovetop or Microwave?

Which retains heat longer, water boiled on a stovetop or water boiled in a microwave oven? The previous experiment controlled the initial temperature by removing the ice cream and sherbet from the same freezer at the same time. This experiment didn't control the heat source, giving students the opportunity to investigate more variables. The key question for students was not only which method of boiling water approached room temperature first, but also which method produced the greatest rate of change in heat emission.

To control for extraneous variables, students conducted this experiment within the same kitchen area using the same cookware. Once the water came to a full boil, students removed the water from the heat source and began the measurement process. With one probe in each cup, the CBL and graphing calculator created a graph for students to compare (see Figure 4). After both graphs were plotted, students found the average rate of change in temperature. Students developed a greater appreciation for the concepts of instantaneous and average rate of change after completing this experiment. They saw a reason for their mathematics--their calculations became meaningful.
Figure 4. Graph of the cooling rates of water boiled by different means.

This experiment helped students understand that microwave heat is generated within the food rather than from an outside source such as a gas flame or electric element. They investigated the microwave heating process and found that microwaves are moving 2.5 billion cycles a second. This movement causes the molecules within the food to rotate 2.5 billion times per second. As a result, the molecules vibrate next to each other, causing friction, which produces heat. Microwaves penetrate about 1.5 inches into the food and cook from the inside out. Students then concluded that if the food is thicker than 3 inches in diameter, the center will cook by conduction of heat rather than microwave-related heat.

How the CBL Enhances the Classroom Experience

Both teachers and students enjoy these experiments, and these activities enable them to experience and understand more fully the scientific process. A middle school teacher involved in this experimental implementation expressed her excitement when she exclaimed: "This is cool! I am using my math to do science."

The CBL and graphing calculators offer exciting opportunities for students to collect and analyze real-world data while making connections between mathematics and science. The National Council of Teachers of Mathematics (1989) discusses the value of such modeling problems:

Students who are able to apply and translate among different representations of the same problem situation or of the same mathematical concept will have at once a powerful, flexible set of tools for solving problems and a deeper appreciation of the consistency and beauty of mathematics (p. 146).

Joanne Caniglia, Eastern Michigan University, Room 504f Pray Harrold, Ypsilanti, MI 48197; mth_caniglia@emuvax.emich.edu

References

Bellman, A., Antione, L., Brueningsen, C., Krawiec, W., & Randall, J. (1994). CBL system: Experiment workbook. Dallas, TX: Texas Instruments.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

Resources

Texas Instruments offers many graphing calculators, accessories, and support materials, including TI-Graph Link and the CBL. Call 800/TI-CARES or visit their Web site at www.ti.com for product and ordering information. Many retailers offer educational discounts on TI products.

Margaret Niess is the editor of the Mathematics column in L&L. You can contact her at Oregon State University, Department of Science and Mathematics, Corvallis, OR 97331; niessm@ucs.orst.edu.

By Bob Albrecht and George Firedrake

Visit these Web sites mentioned in Bob & George’s Power Tools for Math & Science column.

	Acculab Products: Microcomputer-based lab (MBL) www.sensornet.com
	LOGAL Software, Inc.: Data Loggers www.logal.com
	Onset Computer Corporation: Data Loggers www.onsetcomp.com
	Team Labs Corporation: Microcomputer-based lab (MBL) www.teamlabs.com
	Texas Instruments: Calculator Based lab (CBL) www.ti.com/calc/docs/cbl.htm
	Texas Instruments: Calculator Based Ranger (CBR) www.ti.com/calc/docs/cbr.htm
	Vernier Software: Microcomputer-based lab (MBL) www.vernier.com
	Alta Vista http://altavista.digital.com
	How Hot Is That Color? http://acept.la.asu.edu/products/summer97/mods/exp7/ Exp7Instructor.html
	How Fast Can You Cool It? http://acept.la.asu.edu/products/summer97/mods/exp8/ Exp8instruct.html
	Your Mother Told You Never To Do This! http://risdwww1.richardson.k12.tx.us/ntmac/phs/Academics/ Physics/honorsbulbtemp.html
	Shivering Isn't Enough: Heat Conservation in Homeotherms www.gene.com/ae/21st/TE/PW/EXP/HEAT/tch.html
	Spreadsheets Using the TI Calculator and CBL http://jwilson.coe.uga.edu/EMT668/EMT668.Folders.F97/ Norton/Anderson.html
	Temperature Experiments www.baylink.org/lessons/tempexp_right.html
	Cooling www.ti.com/calc/docs/act/stan4.htm
	Newton's Law of Cooling www.southwestern.edu/`richards/cool.html

Bob Albrecht and George Firedrake, dragonfun@aol.com

Copyright © 1999, ISTE (International Society for Technology in Education). All rights reserved.