Original Proposal | Final Exhibit Components

Mathematics may be the language of science, but many Americans feel intimated by mathematics and anxious at even the prospect of performing simple calculations. Indeed, many middle-school American students, especially girls, express intimidation with mathematics (1995 Harris Poll). At the same time, our everyday lives are filled with mathematics, from the simple (but onerous) math associated with family finances to reports on the statistical significance of various public opinion polls.

Mathematical information is presented, often in graphs or as probabilities, in news reports almost every day. As citizens and consumers, we need to know how information is collected, organized, used, and misused so that we can make better decisions, solve problems more effectively, and gain a deeper understanding of the world around us. But there are many instances when mathematical information, such as the probability of rain, health risk factors, or economic trends, may be inaccurately presented or understood. For example, is a sharp price increase shown on a graph due to a distorted scale?

This exhibition is designed to help families become more aware of how we make measurements, interpret the results, assess how accurate the results are, and use mathematics to model things that vary. In our everyday lives, we carry out some of these activities without realizing it, such as reading the temperature (measuring), deciding when (estimating), seeing a chart in the newspaper (graphing), hearing about a 4% margin of error on a survey (uncertainty), and comparing monthly heating bills over a year (modeling things that vary). By recognizing that they are already doing many of the things scientists do, families will begin to make the connection that math and science are really a way of thinking and approaching problems, rather than a body of facts.

REVIEW OF RELATED EXHIBITIONS AND APPROACH

We have reviewed the science center field for related exhibitions on mathematics. The classic IBM-sponsored exhibition on mathematics, which can be found at the Franklin Institute and several other museums is beautiful, but is acknowledged by museum exhibit designers as being ineffective with most visitors. The Franklin Institute and the Maryland Science Center have both designed exhibitions which present activities derived from recent developments in mathematical theory. For example, Maryland has activities on mapping, efficient routing, and many other areas. TEAMS member Ann Arbor Hands On Museum has developed a traveling exhibition on geometry. These exhibitions are welcome additions to the limited number of mathematics activities in science centers and all present activities which do not directly involve numbers. We believe that our proposed exhibition will add to the growing inventory of mathematics exhibitions and fill a gap by providing interactive exhibits that deal directly with counting and the use of counting and measurements in graphing and making predictions.

EDUCATIONAL GOALS

After participating in the exhibition, families will be more aware that:

• Mathematics plays an important role in our everyday lives and that we already use mathematics daily without knowing it.
  
• Mathematics is a subject accessible to everyone.
  
• Many every day events can be quantified and graphed.
  
• Quantitative information should not always be taken at face value, but should be interpreted.
  
• Quantitative information presented in the media should not be taken at face value, but interpreted.

THE EXHIBITION

An arched gateway invites families to come in and explore the exhibition. The arch is parabolic and made of clear 100 mm diameter tubing. Short bursts of colored water shoot from one base of the arch through the tubing to the other base, triggered by approaching families and providing a memorable entry point that is also related to the Making Models theme area described below. Once inside, families see four adjacent areas of free-standing exhibits on counter-tops supported by kiosks, each colored according to the four themes of the exhibition:

I. For Good Measure. Most numerical information begins as a measurement or estimate. Why measure things? When can we get by with an estimate? What are different ways to measure? We often measure things such as temperature, height, or volumes of liquid, but we seldom make the connection with science. In this area, families have direct experiences in measurement and estimation, with the results directly linked to graphing.

Check Yourself Out By measuring their height, weight, and grip strength at separate stations and entering the data in a computer database, families can make the connection between measurement and graphing. A colorful cartoon youth character will greets families and encourage them to take the measurements, then enter them in a multimedia program. They will find their measurements displayed on percentile graphs similar to those given parents by pediatricians. The program stores and displays previous measurements by each visitor, so that families can compare how they've grown or changed since their last visit. A prototype of the exhibit has shown clearly that parents enjoy helping their children understand how their measurements compare with others and that children leave the exhibit with a better understanding of how to interpret graphs.

Is Your Guess as Good As Mine!

By guessing the number of jelly beans in a large jar, the weight of a hockey puck, or the length of a shoe, families become more aware of estimation as a mathematical tool. A 100 mm rod and 100 g mass are provided for reference. Using a technique successfully prototyped, families record their estimates by slipping a rubber washer onto a peg behind a screen. By flipping down the screen, they can compare their "guesstimate" with those of other families.

Wait A Minute!

Families try their hand at estimating time by pressing a button for one minute. When they think a minute is up, families release the button, and a large LED display shows the actual elapsed time. A kiosk with four carrels creates separate corner environments that include: no sound, a fast-paced Elvis song, and a boring speech. In a fourth carrel, a short audio message with related graphics describes the history of time measurement from earliest methods through the current cesium standard clock. A space shuttle photograph and diagram describe how critical timing is for atmospheric reentry.

II. Picture it with Numbers.

Once we have information, how can we visualize it best? What is a graph? How can graphs make numbers and measurements easier to understand? Most people can visualize information better when it is shown graphically. In this area, families create their own graphs (e.g., histograms, X-Y graphs).

Watch Your Language:

After looking at a large and colorful world map, with clear tubes and flags in front, each representing a country, families place pennies in the tubes representing the countries of their ancestors, creating a histogram. Because most children do not know about their ancestors, the exhibit encourages interaction between adults and children. A prototype has shown this format to be highly engaging, and parents and children enjoy discussing the map, their forebears, and the meaning of the resulting histogram. Placing the tubes at the right height prevents children under five from randomly dumping in pennies.

Picture Your Height:

Families stand against a growth chart on a large panel and record their height with a colored dot sticker. Since age is the horizontal axis, a full-size (by height) graph results. Children observe the dispersion of measurements and see that there is a relationship between height and age.

The Eyes Have It

Families compare their eye color to 10 different eye colors in a mirror. Families then place a penny in a clear tube according to color and discuss the resulting histogram.

How Long is a Beetle?

Families experience the importance of standard units of measurement by using their own feet as a ruler to measure the length of a VW Beetle colorfully painted on a large panel, recording their own measurements by dropping a penny into a one of several clear plastic tubes to create a histogram of length measurements. A prototype of this exhibit has indicated that families enjoy making the measurements and comparing their results. Families can repeat the activity using a set of standard feet provided; the activity shows that standard units reduce uncertainty.

III. Can You Be Sure?

How good are measurement and estimates? In what ways can numbers be uncertain? How can we describe things we don't know exactly? All measurements and estimates are subject to errors and other forms of uncertainty. How do errors affect our decisions? This area challenges families to experiment with uncertainty and to recognize that we always need to be aware of experimental error.

Super Bowl

Families learn about dispersion by taking aim with a sliding puck at the center of a row of hanging bowling pins. Each pin has a column of lights above it to indicate how many times that pin has been hit; each hit lights another light. Families will be challenged to hit the target pin, and the width of the resulting histogram will indicate the relative precision ­ a narrow curve indicates better aim. An audio message and graphics will relate this spread to measurement precision.

Try it Out or In!

In everyday life, measurements can often be rough, but in science and industry, precision can be important. Families experiment with steel dowels and drilled blocks of three materials to see how different levels of precision are needed in different applications. Blocks of steel, wood, and rubber have marked holes exactly 10 mm in diameter. Steel dowels with large old-fashioned key handles are provided with diameters of 9.00, 9.90, 9.99, 10.00, 10.01, 10.10, and 11 mm. By trying to fit the keys (which look almost the same) into the holes, families experience that the steel block requires considerably more precision than the rubber block, and that close enough is relative.

IV. Making Models

This area invites families to make associations between things that vary, and to experience different ways things can be related to each other (proportionally, exponentially, etc.). Most things vary with time, distance, or some other factor. How can we show relationships between things that change or depend on each other? How can we describe shapes with numbers? Families are encouraged to experience curves and learn their names as a first step toward seeing that curves describe relationships between things that vary.

Get In Shape

is a set of four multi-media computer games that introduce relationships between phenomenon that vary and mathematical curves that represent this variation. A version has already been successfully prototyped for the Sciencenter by Abacus Systems, Inc., a firm that won first place in Microsoft's 1995 International Windows Programming competition. The games are introduced by a cartoon character on a skate board, who challenges families to relate shapes, their names, and the variables that control them. The games include:

• The simplest game Name That Curve is a math-readiness exercise that challenges families to match curves with their names. Correct answers are rewarded by applause and a congratulation screen, while incorrect answers are accompanied by a hint and the encouragement to try again. Audio instructions appear at all points.
  
• Mystery Match Levels I and II are intermediate games in which families use joysticks to adjust various equation parameters to match an equation and associated curve with a randomly-generated fixed curve.
  
• Equation Detective requires a middle-school level of math and lets families use joysticks and push buttons to create equations that solve specific problems. (Pizzas cost $5 plus $1 per topping ­ what is the general equation for pizza cost?) Preliminary testing has shown that families enjoy the challenges and are able to find one that matches their ability level. Even 6-year-olds can play the simplest game and learn about curves. Photographs of curve application (water fountain - parabola; kitchen table - circle; planet orbit - ellipse; cooling tower - hyperbola, etc.) are displayed with the curves to show some of their applications.

The King and the Pauper:

Families are provided a chessboard with bins and are challenged to put 1, 2, 4, 8, ... grains of rice in successive squares, as far as they can, to experience exponential growth. An audio recording tells the story of a king who agreed to pay a debt to a pauper in rice. Starting with one grain, the clever pauper asked that for as many days as there are squares on a chessboard, the king would double the number of grains. The king did not realize that by the end, he would owe 100 billion tons/day ­ enough to fill more than a million ships. Families will likewise discover it is an impossible task.

Logging Your Activity:

Families learn the hard way how logarithmic relationships really work. Logarithms (sometimes referred to as the powers of two, ten, etc.) are used for many common scales (Richter magnitude, pH, sound dB levels, etc.). In this exhibit, families press a start button and pump as fast as they can for one minute on foot pedals connected to a binary counter. Each time the number of strokes doubles (1, 2, 4, 8, ...), another light in a column goes on and a higher tone sounds. Families experience that it takes increasingly more units on a linear scale (the number of pedal strokes) to make one unit on a log scale (the lights). Pictures and labels relate log scales to earthquake magnitude (graphic damage photos from earthquakes having different Richter magnitudes) and sound dB levels (pictures of various noise-creating objects and their dB levels: e.g., flute, car, jackhammer).

Additional panels contain measuring devices, photos, explanatory text, historical poster displays of women and minority mathematicians, and objects related to the four themes. A kid-sized podium holds a loose-leaf math bloopers notebook with various examples of mis-represented mathematical information from the media (distorted graphs, ridiculous claims, etc.).