This talk is, above all, a talk about synergies -- in a bumper sticker, the synergies between bits and atoms -- but, more thoughtfully, the synergies between traditional kinds of teaching and learning and newer technology-intensive kinds of teaching and learning. The two links below lead to a pdf file and a Postscript file that can be used to print some atom-based equipment that we will use as an example and a metaphor.
If you have Adobe Acrobat Reader and a Postscript laser printer then click on the pdf file and print two copies of the file you obtain, one on ordinary paper and one on transparency film. The Adobe Acrobat pdf reader is available directly from the Adobe Web site at no cost. Click on the yellow "Get Adobe Acrobat Reader" button below to obtain it if you do not already have it. If you have a utility for printing Postscript files, you can use the Postscript file above rather than the pdf file. The results should be the same whichever file you use.
Either file will print six copies of the pattern below. For a hands-on experience, use one copy printed on transparency file and one printed on plain paper. Either pattern by itself is OK but not particularly striking. If you put the transparency file pattern exactly on top of the plain paper pattern, you won't see anything new. However, if you slide the transparency pattern around so that it no longer matches the plain paper pattern exactly then you will see some interesting new patterns -- the results of the synergies between the two patterns rather than using one to duplicate or replace the other.
This metaphor drives home the power of synergy -- two or more things in combination producing something quite different than either produces by itself. Technology is often viewed as either a different way to do the same things that were formerly done by other means or as displacing more traditional science and mathematics. The real power of technology, however, results from the synergies between technology and traditional science and mathematics. We give an extended example later that illustrates the kinds of synergies we have in mind.
This talk begins with a discussion about a National Digital Library for Science Education. Such a library could provide an infrastructure to support exciting new kinds of science, mathematics, engineering, and technology (SMET) education and to help the very best SMET education reach all students. The PowerPoint style "slides" below outline the points made in the presentation at James Madison University.
The World Wide Web has already demonstrated enormous potential for education. Its resources, however, are of uneven quality and its best resources are often difficult to find and, when found, are often difficult to use. One of a National Digital Library for Science Education's most important goals is helping students and teachers find the best quality resources and making it easy to use those resources in the best ways. A number of mechanisms will aid in this quest.
By providing recognition comparable to the recognition associated with publication in prestigious research publictions, selective portals and collections will stimulate faculty to create high quality resources and make them available in the library.
combining
The two graphs above point out the biggest source of problems in using the World Wide Web. The red graph, on the left, shows the exponential growth of all things technological -- the power of our desktop and notebook computers, the speed of our network connections, the number of pages on the Web. The blue graph, on the right, shows the growth of all things human -- my personal reading speed, the number of hours in the day, and the number of days in the week. Putting millions of books on the Web does not give us the time to read them all. We need tools to help us find high quality and appropriate resources and when we do find them they must be easy-to-use, reliable, and stable.
The URLs below lead to additional information about a National Digital Library for Science Education and other information related to this talk.
http://www.math.montana.edu/~frankw/ccp/home.htm
http://umastr1.math.umass.edu/~frankw/ccp/home.htm
Duke site
http://www.math.duke.edu/modules/
Cal Poly site
http://grandmac.calpoly.edu/
http://www.math.montana.edu/~frankw/ccp/modeling/topic.htm
http://umastr1.math.umass.edu/~frankw/ccp/modeling/topic.htm
http://www.math.montana.edu/~frankw/ccp/talks/PKAL-JMU/index.htm
http://umastr1.math.umass.edu/~frankw/ccp/talks/PKAL-JMU/index.htm
The
WebPhysics Project
The Journal of Chemical Education
at the Institute for Chemical Education.
This example is intended to illustrate several different ideas, all involving synergies in ways that can dramatically improve teaching and learning in science, mathematics, engineering, and technology.
This example contains material that can be used at many different levels from middle school algebra and geometry through undergraduate courses in mathematical modeling.
You will need some hands-on equipment to get the most from this section -- an inexpensive laser pointer, patterns obtained over the Web from this site and then printed on plain paper and on transparency film (one of the patterns is the same one used as a metaphor earlier), and a light source you can use to project images on a wall.
The links below lead to the patterns to be printed on plain paper and on transparency paper. Each one prints several copies on the same sheet of paper to save money. Each one is available in either Adobe Acrobat pdf format or Postscript format. The first pattern -- "Ripple tank transparencies" -- is the same one used earlier as a metaphor for synergy. The second one is new and is used with a laser pointer to produce diffraction patterns. This pattern works but is fairly crude. Much better diffraction patterns can be produced using slides that are available at very low cost from the Journal of Chemical Education at the Institute for Chemical Education (ICE). In particular, excellent materials on the discovery of the structure of DNA using diffraction are available from that site.
We begin by looking at "ordinary" projection -- the kinds of images produced by light shining through a slide or past an object onto a wall or movie screen. The figure below shows a slide taken at Capitol Reef National Park as it might be projected using an ordinary slide projector with an ordinary light source or projection lamp.
Your students are probably familiar with these kinds of images but it is worthwhile to experiment a bit in any case. Have your students draw simple pictures on transparency film and project their pictures onto a light wall using an ordinary light source. A small light source will produce sharper images than a larger light source.
Ask your students to answer the questions below.
Now we are ready to talk about a mental "model" of what is going on. We can't actually see light going from the light source through the slide and hitting the wall but we do have a mental "image" or model. Whatever light is, we probably picture it as traveling in straight lines. The figure below shows one such picture. The black dot at the right side of the figure represents the light source. The vertical gray line in the middle of the figure represents the slide with three marked points -- blue, red, and magenta. The vertical gray line at the left of the figure represents the wall with three marked points -- blue, red, and magenta -- representing the images produced by the corresponding points on the slide. The three colored lines -- blue, red, and magenta -- represent the paths traveled by light as it goes from the light source; through the slide; and hits the wall.
This is a live figure. You can click and drag the light source to see the effect that moving the light source has on the image.
It is worthwhile summarizing some observations we can make from experimentation with a real slide and from playing with this model.
Now we look at another situation involving light, slides, and images on walls. This time we use an ordinary laser pointer and slides with very fine patterns. You may have already obtained the necessary slides as described above. If not, you should do so now.
The picture above shows the pattern produced on a wall by shining a laser pointer through a slide printed from the .pdf file (or Postscript file) available above. The slides you can obtain from the Institute for Chemical Education produce even better results. The slide obtained from the .pdf (or Postscript) file looks something like this.
It has both very thinly spaced and even more thinly spaced lines. You and your students can experiment with the images produced in this situation. In particular, investigate the following questions.
You and your students may be surprised by the results. Moving the laser pointer closer to the slide or further away has no effect on the magnification of the image. More closely spaced lines produce images with more widely spaced patterns. The model we used to help understand ordinary slides and ordinary light sources doesn't help at all in this situation. We can begin to understand what is going on by looking at waves.
We are all familiar with waves -- in bathtubs, lakes, oceans, and puddles. Water waves are everywhere. You can also see waves in other "media." For example, if two people each hold one end of a clothes line so that the line sags a little bit between them and one person shakes his or her end once you will see a wave travel down the clothes line toward the other person.
Both sound and light are produced by waves. It took a long time for these two facts to be discovered because, unlike water waves, we can't see light waves or sound waves. We will see some of the evidence that lead to the discovery of the wave nature of sound and light. We begin by looking at a Java applet that can help us visualize waves. Click on either of the two links below for a Java applet "ripple tank" -- an applet that simulates waves in a water tank.
Click to load Frank's ripple tank applet in a new window.
Click to load WebPhysics' ripple tank applet in a new window.
Arrange your windows so that they overlap and you can move back-and-forth between them by clicking on the inactive window to make it active. Watch whichever applet you open for a while, giving it time to generate a series of pictures that make up an animation, or movie, showing what happens when there are two sources of waves in a ripple tank. Either applet requires some computing time before the animation runs smoothly. After you've watched the animation for a bit return to this window below.
The figure above shows one frame from a ripple tank animation. This particular applet (Frank's applet) shows three ripple tanks. The first two each show waves emanating from single source. You see a familiar pattern of circular waves similar to the waves you see when you drop a pebble in a puddle. The only difference between these first two ripple tanks is the point at which the wave source is located.
The third ripple tank shows what happens when the waves from the two different sources are combined and interact, or interfere, with each other. We see light and dark bands. In some of the bands the two sets of waves reinforce each other, producing waves that are higher than either source produces by itself. This is called constructive interference. In other bands the waves cancel each other out. This is called destructive interference.
The two ripple tank applets allow you to experiment by moving the sources.
Notice that when the sources are further apart there are more and thinner bands of constructive and destructive interference than when the sources are closer together. This phenonenon is reminiscent of what happened with the laser pointer and finely-ruled slides. The closer the lines on the slide the further apart their "images" on the wall. The phenomenon we observed with the laser pointer is called diffraction and is closely related to interference. The laser light acts like waves. When it hits the slide the waves spread out in circular patterns from each clear spot in the slide. These circular patterns interfere with each other, producing the the "image" on the wall. When the clear spots are closer together the pattern in the image spreads out in the same way that the interference patterns produced by two close sources is more spread out than the pattern produced by two sources that are further apart. The size of the image on the wall is determined by the spacing of the clear spots on the slide.
The image on the wall is not simply a magnified or reduced copy of the pattern on the slide. In fact, it is an interesting proiblem to determine the original pattern on the slide from its image on the wall. This is exactly the problem that was involved in determining the double helix structure of DNA.
This example shows how we can build upon each others' work. In this case on the work of Arthur Ellis, Wolfgang Christian, and Gregor Novak.
Copyright c 1999 by
Frank Wattenberg, Department of Mathematics, Montana State University,
Bozeman, MT 59717