Science-Technology Museum/Science Factory
The Science Factory Children's Museum & Planetarium is located in Eugene, Oregon. It is the initial home for a variety of projects being carried out by the Information Age Education organization. This article discusses some roles of science and technology museums in helping children and adults get an information age education.
There are science and technology museums located throughout the world. They vary considerably in size, financial stability, and longevity. They are unified in their goal of helping children and adults to learn. Their focus on science and technology helps to address some of the major change factors faced by people in our society and other societies located throughout the world. Most science and technology museums are financially "stressed," make extensive use of volunteers, and pay their employees only modest salaries. The Science Factory is such a labor of love.
Science and technology museums tend to make use of a combination of permanent exhibits and traveling exhibits. there is a substantial business of creating exhibits that are rented out. Usually, initial funding for such an exhibit comes of a benefactor, foundation, or government agency. These traveling exhibits tend to be of quite high quality and represent careful thinking about the needs of their renters and the visitors they serve.
Information and Communication Technology (ICT) has had a significant impact on science and technology museums. Of course, this is to be expected in terms of both the subject areas of exhibits and the exhibits themselves. ICT provides powerful aids to teaching and learning.
However, ICT also provides strong competition for the traditional science and technology museum. This competition comes in the form of wonderful television programs, computer games, and the Web. The Web is a vehicle for social networking systems, rapid access to information (including videos), computer-assisted instructional materials, and museum exhibits.
Museums throughout the world are making parts of their exhibited materials available on the Web. This is relatively easy to do with static materials such as a painting. It is more of a challenge when the exhibit is dynamic, interactive, hands-on, and perhaps designed to involve interaction among a set of visitors. Increasingly, however, modern ICT, including virtual realities, is up to the task. Thus, science and technology museums are facing completion that they have not faced in the past.
An Example—Fun: 2, 3, 4 Math Exhibit
The exhibit Fun: 2, 3, 4 Math can be described as follows:
- Whether it’s measuring, graphing or estimating, this traveling math exhibition shows visitors the fun of applying math to everyday activities. Learn how to double your allowance, count like the Aztecs, or team up with a partner to take our time challenge.
- Designed for: 5-12 year olds and their families.
- Size: 1,750 sq.ft.
- Rental Fee: $13,500/3 months
- Partners: TEAMS Collaborative; funded by NSF
- Rental managed by Sciencenter
This brief description at the Sciencenter Website includes links to an extensive description of each component of the exhibit as well as a video of children interacting with the exhibit. Notice that the construction of the exhibit was funded by the National science foundation. this suggests that it is a high quality exhibit of considerable educational value. Indeed, the exhibit comes with a substantial set of educational materials. These materials can be used by teachers in advance of bringing their students to the exhibit and after their students have toured the exhibit. A trifold brochure that can be printed and then given to visitors to the exhibit contains both a description and some references to appropriate books and Websites.
What is Missing?
My doctorate is in mathematics. I have had many years of experience in the fields of math education and computers-in -education. I have spent a lot of time learning about and thinking about how to improve education. I have served on the Board of Directors of a science and technology museum, taught lots of preservice and inservice teachers, and written a lot of educational materials for preservice and inservice teacher, parents, and other audiences.
Thus, I can analyze a set of educational materials, such as a science and technology exhibit, from the point of view of how they contribute to the overall field of teaching and learning. My first reaction to the Fun: 2, 3, 4 Math Exhibit is that it has a lot of really great "stuff" but it is somewhat weak in improving the math education of students and adults.
Here is an overall example of what I mean. Educators know that learners build new knowledge upon their existing knowledge and understanding—that is, that constructivism is an important educational theory. Thus, as I explored the exhibit materials, it occurred to me to ask the question, "What is mathematics?" What is it assumed that visitors to the exhibit already know about what is mathematics, and what increased knowledge and insight will they mentally construct?
This overview question can then be asked of each component of the exhibit. In my experience, most elementary school teachers and most adults have only a vague insight into what is mathematics. In their teaching and parenting interactions with children, they have difficulty in helping children build a solid foundational answer to what is mathematics that will serve them through out their formal and informal education in years to come.
When I expressed these ideas to the Education Committee at the Science factory, they challenged me to write a short answer to the question, " What is mathematics." Here is my first attempt to provide such an article. It has a readability level in the grades nine to ten range, and it is intended for teachers, parents, and museum guides.
What is Mathematics?
This short article is written for adults who are supervising and helping children at the Science Factory’s new Fun 2, 3, 4 math exhibit. Begin by reading material to the right of Spiderman. These quotes capture the essence of empowering the learner, responsibilities that empowerment brings, and math as problem solving.
“With great power comes great responsibility." (Peter Parker’s uncle Ben in a 2002 Spiderman movie.)
“To understand mathematics means to be able to do mathematics. And what does it mean doing mathematics? In the first place it means to be able to solve mathematical problems. For the higher aims about which I am now talking are some general tactics of problems—to have the right attitude for problems and to be able to attack all kinds of problems, not only very simple problems, which can be solved with the skills of the primary school, but more complicated problems of engineering, physics and so on, which will be further developed in the high school. But the foundations should be started in the primary school. And so I think an essential point in the primary school is to introduce the children to the tactics of problem solving. Not to solve this or that kind of problem, not to make just long divisions or some such thing, but to develop a general attitude for the solution of problems.” (George Polya, a leading mathematician and math educator of the 20th century)
Accumulated Human Knowledge
Math is part of the accumulated knowledge of the human race. Math knowledge and skills empower a person. A healthy human brain is naturally curious and has a great capacity to learn. A newborn baby’s brain has a built-in capacity to learn natural languages. It already knows a little math, and it has the capacity to learn a great deal of math.
Today’s children are born into a complex and changing world. The totality of human knowledge is huge and is growing very rapidly. This knowledge is so vast that it is divided into disciplines or specializations. Mathematics is one of these broad, deep disciplines with a huge and ever growing accumulation of knowledge. Tens of thousands of math research articles are published each year. There is a huge accumulation of how to teach math, how to learn math, the history of math, and uses of math. Mathematics is one of the great achievements of humankind, and it is usful in many different disciplines of study.
In Your Mind, What Is Math?
As an adult, you know a lot about math and you use your knowledge every day. Thus, if I ask you “What is mathematics?” you can give me an answer that fits with how you view and use math. You are empowered by your ability to use math in dealing with money, time, distance, area, weight, and other problem areas. Your insights into math and your uses of math help to guide you as you help children to learn math through their informal and formal education.
However, the chances are that your answer to the "what is math" question is different than that of many other people. In terms of educating our children, it is helpful if we can have a some agreement on what math is and what it is important for children to learn about math.
Mathematicians like to quote the famous mathematician Leopold Kronecker (1823–1891) who said: "God created the natural numbers, all else is the work of man." Long before we had written language and schools, people learned to count and make other simple uses of math.
From their early childhood caregivers, young children learn to count and how to determine the number of objects in a small set. Above that level of math understanding, knowledge, and skill, our formal math education begins to click in. For example, we have various numeral systems such as Roman numerals (I, II, III, IV, V), Hindu-Arabic numerals (1, 2, 3, 4, 5), Chinese numerals (一, 二, 三, 四, 五), and Arabic numerals (٠, ١, ٢, ٣, ٤). We have specially defined words and symbols for addition, subtraction, multiplication, division, and other operations on numbers. We have fractions and decimals. We have sub discipline of math such as algebra, geometry, statistics, probability, and calculus. We have various systems for measuring distance area, and quantity, such as the metric system and the English system.
We have developed aids to solving math problems. For example, you probably own a calculator, wristwatch, and ruler. You routinely use these as aids to doing arithmetic calculations, to determine time of day, to measure length, and so on. A car contains a speedometer and an odometer. Nowadays, it may contain a global positioning system (GPS) that can display a map and give you oral instructions as to when and where to turn to get to a specified destination.
Thus, one way to answer the question “What is mathematics?” is to name some of its sub disciplines, name some of its tools, and name some of its achievements. However, this is of limited value in talking to young children about math and helping them to develop personally useful understanding of the field. What mathematically empowers children?
A Language for Thinking About, Representing, and Solving Problems
A different way to think about math is that it empowers people who seek to represent and solve a wide range of problems in different disciplines. Math is both a special language and a special approach to representing, thinking and reasoning about, and solving certain kinds of problems. Because there has been such a large amount of research in math over the years, there is a huge accumulation of how to solve a wide variety of math problems. If a “real world” problem can be represented mathematically, this may be quite useful in solving the problem.
Here are two ideas that help to define goals of math education and empowering learners.
- Math fluency is being able to read, write, speak, listen, think, and understand communication in the language of mathematics. This is somewhat akin to developing fluency in a foreign language.
- Math maturity is being able to make effective use of the math that one has studied. It is the ability to recognize, represent, clarify, and solve math-related problems using the math one has studied. Thus, a fifth grade student can have a high or low level of math maturity relative to math that one expects a typical fifth grader to have learned.
Suggestion to Teachers, Parents, and Exhibit Guides
As an adult, you can view the Fun 2, 3, 4 math exhibit through your adult eyes and select out some ideas and information that seems important from your point of view. Then you can view the exhibit through a child’s eyes. What might the child learn that will empower the child to move toward your level of insights and math maturity? Interact with children to help make these ideas explicit and meaningful.
Analysis of Some Parts of the Exhibit
This section contains a brief description of some parts of the exhibit. For each part, I give a brief analysis from a math education point of view.
- Welcome to Fun, 2, 3, 4! Pass underneath the 8' tall wooden parabolic arch to enter the exhibition. The cabinet on the left has slots for tri-fold family guides that visitors may take with them.
My thoughts. Parabola is the name of an important mathematical function. Do we want visitors to learn the words parabola, parabolic arc, and function? Why do some curves have a name, and others do not? A function is one of the most important ideas in mathematics. Does the exhibit help to teach children what a function is? Most adults have encountered quadratic functions and quadratic equations. Many adults are familiar with the fact that a thrown stone would move in a parabolic arc if it were not for air resistance.
Quoting from the Wikipedia:
- In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). The concept of a function is fundamental to virtually every branch of mathematics and every quantitative science.
This is an "adult" type of definition, and it probably has little meaning to young children. However, it is important that young children gain some initial understanding of function. Thus, the topic is integrated into the elementary school curriculum by making use of pictures, graphs, and lots of examples.
- Have you ever noticed how useful graphing is? Ms. Measurooni asks you to measure yourself by finding your height, weight, and grip strength. When you're all finished, compare yourself on the graphs, then be sure to print your own Measurement Factory certificate to take home.
- Custom program guides visitors to measure themselves, enter their data (including gender, first name, and month and year of birth), and look at graphs to see how they compare with other people.
My thoughts. This is the first station in the exhibit. Visitors gather data, enter it into a computer, compare their data from that of other people, and receive a print out. There is a great deal of science and math illustrated in this activity. Gathering data (making precise measurements) and using a computer to store and process the data are key aspects of modern science.
There are many key ideas that might be illustrated and discussed. For example, there are possible errors in measurement, data entry, and computer processing. How does one guard against such errors, detect errors, and correct errors? Why should one believe the results of a computer printout if it can be wrong because of errors in data collection, data entry, in the compute program, or in the processing done by the computer?
Height, weight, and grip strength are variables—they can vary from person to person and they can vary for a particular person over time. A variable is one of the most important concepts in mathematics. Research in education emphasizes the value of naming the concepts or ideas that we want students to learn. What might be done in this exhibit station to better help students learn the word variable and its meaning in math and science? Quoting from the Wikipedia:
- In computer science and mathematics, a variable is a symbol denoting a quantity or symbolic representation. In mathematics, a variable often represents an unknown quantity; in computer science, it represents a place where a quantity can be stored. Variables are often contrasted with constants, which are known and unchanging.
- Planets orbit the sun in an oval shape called an ellipse. Water from a fountain forms an arch called a parabola. "Cool Curves" is a computer game that allows you to identify common shapes and curves, like the ellipse and parabola, that appear in nature.
Various curves are displayed on a screen; visitor tries to match shown curve to the six types of curves on a button board.
My thoughts. The combination of vocabulary, curves being drawn on a computer screen, and "real world" examples is very good. Children are quiet used to television and pictures being drawn on a display screen. I wonder how a typical child might explain how a parabola, circle, or other type of curve is "created" by a computer and displayed on a screen. How does this process relate to a computer drawing cartoon characters?
Ivan Sutherland's 1963 doctoral dissertation at MIT made seminal contributions to computer graphics. His doctoral work illustrated how to do things that we now all take for granted. Remember, this was state of the art, advancing the frontiers, in 1963!
A television picture is made up of a large number of horizontal lines. Within each line, there are picture elements (pixels, spots that can display a colored dot). There is a tremendous amount of "fun" math in how one goes about making curves, pictures of cartoon characters, and animated movie characters out of colored dots on a sequence of horizontal lines.
The rapid displaying of dots on a display screen by a computer is under the direction of a computer program. The program can make use of equations for line segments, circle segments, eclipse segments, parabola segments, and so on. Also, of course, it is possible to create a picture outside a computer (for example, by use of a digital camera) and store the pixels (the dots) of the picture inside a computer. Then the computer can readily display the picture on a display screen.
In summary, computer graphics is a fun and challenging field of study that draws strongly from mathematics as well as from computer and information science, art, and other disciplines.
- How special are you? Three out of four people can curl their tongue, can you? This computer exhibit has you examine six simple genetic features, then tells you how many people are like you!!
My thoughts. I remember being quite impressed when I learned that I can curl my tongue into a trough that leads from my lips into my mouth, and that some people cannot do that. Thus, visitors to this exhibit will have fun discovering whether they have or do not have certain gene-controlled traits such as tongue curling.
There is a lot known about Mendelian traits in humans. Such knowledge is part of the overall field of genetics, which is part of the overall field of biology. At the current time, genetics, nanotechnology, and computers are three of the leading change-agent fields of research and technology in our world. Two are involved in this particular exhibit, and neither is emphasized.
Probability is a very important (and challenging) component of mathematics. This display uses probability to determine what percentage of people have a particular combination of six different genetic traits. However, it really does not teach anything about probability. Thus, in my opinion, this piece of the exhibit does not come close to meeting its educational potential.
How Many is a Million?
- The goal of "How many is a million?" is to teach the concept of large numbers. You can turn a wheel to continue the Sciencenter's ongoing quest to reach one million. On the one millionth turn, a glass goblet located in the exhibit will smash.
- Entirely mechanical exhibit consisting of 7 12” diameter gears and 7 1.2” diameter gears; pair of gears attached to each of seven 5/8” diameter axles; each axle goes through a pair of pillow block bearings behind the gears. Gears are held snug with a locknut, which can be removed to reset the gears to start at zero again. Wooden wheel attached to first axle drives the nested set of gears. A glass water goblet rests on a pedestal in front of the last gear, and falls over when the wooden wheel has turned a million turns.
- Millions prop is a tube of a million candy decorations (Becker bottle available commercially for $32, placed in a stronger tube). Spin the tube to look for the one black bead amongst the million beads.
My thoughts. This exhibit station involves visitors in a process of helping to turn a wheel one million times, and it provides a physical (concrete) display of one black been in with 999,999 non-black beads.
Most people have little intuitive sense or feeling for a million, or one in a million. Since numbers of this size and probabilities of this size are relatively common in our society, the station focuses on an important topic.
However, in my opinion the station doesn't do very well in helping visitors develop mental pictures (mental models, a "feeling for" a million and for one in a millionth. Certainly young children have fun spinning the wheel. However, that is mainly just a fun physical activity. It is not at all clear that any learning about a million is occurring as the children do their thing.
What I am reminded of is the writings of Seymour Papert, one of the developers of the Logo programming language, a fantastic teacher, and a scholar working in the field of artificial intelligence. In his writings, he talks a lot about using gears as a mental model, and how this mental model helped his so much in his teaching and learning. Gears, mental models of gears, physical models of gears, and mathematical models of gears help to create a really rich area for study and understanding.
I also wonder what learning occurs with the display of one black bead in a container of a million beads. Remember, for a child the word million is just a word, with no particular meaning. It is a word that stands for a large number. What is needed is for the child to have a bunch of different and meaningful examples of this number.
For example, many of the children visiting the Fun, 2, 3, 4 exhibit will be from the Eugene-Springfield area of Oregon. The total population of this region of the state is perhaps a quarter of a million. Hmm. So, a million is four times as many as all of th people living in this region.
Children sometimes see a football or soccer stadium containing a hundred thousand people. That is a huge number of people, and it would take ten of those statiums to hold a million people.
How about money? Will a million pennies fit into a typical school room? How high is a stack of a million dollar bills? How long does it take for a typical person's heart to beat a million times?
The point is, math educators have developed lots of ways to help students gain a feeling for the size of a million.
How Many Hands High is a Horse?
- Grab a partner. Measure the height of the horse using your hands. Now compare your answer to your partner's. Are they different? Think of the confusion if everyone measured with a different "hand." That is why many countries have agreed to use one set of measures called the Metric System.
- Painted life-size mural of a horse on one side; visitors use the width of their hand to see how many of their hands it takes to go from the bottom of the horse to a line along the horse’s back.
My thoughts. I have a friend who is really into horse racing and betting on horses. If I ask him about how many hands high a horse is, he can give me an answer. Moreover, he can tell me that nowadays in the horse business, a "hand" is exactly four inches.
Well, there are more useful things to memorize. So, what might a child learn from this exhibit station? Measurement is one of the key ideas in math. They most important thing is that standards get set and that people agree to use the standards.
Thus, there needs to be greater stress on the need for and value of standards, and the history of development of such standards.
- This game allows you to make a graph. Roll a tennis ball down the lane aiming for the center of the backboard. Did you hit the center mark? How close did you come? Watch the pattern of lights that forms, showing you where your balls hit.
My thoughts. The title of this exhibit is a play on words. Users roll tennis balls down a short "bowling alley" type of arrangement, into slots at the end of the alley. The apparatus counts the displays the number of balls going into each slot.
Young visitors using this display had fun rolling the balls. I saw no evidence that they were learning anything mathematical in the process. They did gain some increased skill in aiming toward a particular slot.
There are many game and museum exhibit variations on this activity. A standard one involves having a structure that tends to produce a normal distribution of the balls into the slots. In such an exhibit, the number of balls falling into a slot (the length of the line of balls) becomes one piece of data in a bar graph.
In a school classroom setting, students might be asked to make a bar graph by repeatedly rolling a pair of dice, and marking each result as an X on a piece of paper that contains the digits 2 through 12 in either a horizontal or vertical line.
In such a school setting, students can comare their bar graphs, looking for major differences and for commonalities. The data from the individual class members can be gathered together into a whole class bar graph. Students might then note the "smoothness" of this graph as compared to their individual graphs.
Making an Elementary School Environment More Mathematical
Many students, teachers, and parents get enjoyment out of creating math types of exhibits and activities that are somewhat related to those in the exhibit Fun, 2, 3, 4: All About a Number of Things!
Over a period of time, a teacher might well collect a number of such "exhibit-like" pieces of work, and then make routine use opf them in his or her classroom.
A good exhibit engages students in a hands-on and brains-on activity. It usually has clear learning objectives, and these are clearly communicated to students. (Of course, you might want to have some exhibits where the math learning objectives are not obvious, and the goal is for students to "discover" or make up suitable learning objectives for an exhibit.
The Super Bowl exhibit given earlier in this document contains a dice throwing and graphing example that is quite useful in math education. Consider a somewhat similar example, but this time students use a spinner with the possible (equally likely) results bing 2, 3, 4, … 12. That is, both the dice tossing and the spinner generate integers in the range of 2 to 12.
However, there will likely be considerable differences between the dice results and the spinner results. This difference is a great topic for discussion and investigation.
The "standard" die is a cube with six faces. Each face is a square, and all of the squares are of the same size. Suppose one wanted to have a seven faced die, or an eight-faced die, or etc. For any particular one of these, all faces are to be the same geometric shape and size. Is it possible to construct such dice?
ASCD (October 2010). Making your field trips more meaningful. Retrieved 9/30/2010 from http://www.ascd.org/publications/newsletters/education-update/oct10/vol52/num10/Making-Your-Field-Trips-More-Meaningful.aspx. Quoting from the article:
- Lynn-Steven Engelke, director of programs for the Smithsonian Center for Education and Museum Studies, encourages educators to take advantage of the wide variety of resources museums have to offer.
- Field trips offer numerous benefits, such as student engagement, says Engelke. The best field trips allow kids to talk to curators, scientists, historians, and other professionals, she explains. Seeing adults in action, and discussing their work and research, can be an enlightening experience for students, especially those with few enrichment opportunities outside of school.
- "Kids make the connections between something someone is doing in a museum and their own personal lives," says Engelke. "It opens up a world of possibilities."
- Knowing why you are planning a field trip and what you are planning to do will help the site coordinators better meet your needs and will help ensure that students get the most out of the experience. When planning, teachers should ask, "What is [my] goal in having children go to a museum?" says Engelke. "Having fun should certainly be part of it, but how is it going to work with what you're currently teaching or as a launch for something you will be teaching?"
Author or Authors
The initial version of this document was written by David Moursund.