SCALE Scale and Scaling: How Big is a Nanometer?

On Being The Right Size

Space – the final frontier. This Star Trek slogan could apply not only to space in a large, cosmological sense, but also to the frontier of very small spatial dimensions. The frontier of the small is currently being opened by advances in the field of nanoscience. Almost 400 years ago, the invention of the telescope opened up the possibility to explore vast distances beyond our normal human perception, whereas the microscope similarly opened up whole new worlds for study. In this case the very tiny. As reflected in the following quote by a high school student in one of our earlier research studies related to scale conceptions, scientific investigations focused on distance scalesbeyond everyday human scale continue to intrigue people, much as it did in the early 1600s.

"It's strange the way you can learn about how things can be tiny, tiny, and huge"
-a high school student

The development of these two scientific instruments and their many successors has led to gigantic scientific advances, and such advances continue unabated even today. As humans have developed the ability to extend their sensory perceptions into previously unimaginably large (cosmic) and small (nanoscale) realms, they have also had to develop ways to conceptualize these very different scales.

Scale: A Theme Across the Science Domains

Scaling conceptions are one of four recommended unifying themes in the AAAS Project 2061 Benchmarks for Science Literacy (1993). Understandings of unifying themes such as scaling may serve as a solid framework for students to anchor further learning in a variety of disciplines and allow students to make cross-curricular connections between seemingly disparate topics.

Research: Teaching and Learning Scale and Scaling Effects

With support from the National Science Foundation we are researching how students learn scale and scaling effects. We are examining what students at different levels know and how they learned concepts about size and scale.

“The distance from the sun to the nearest star is close because there are stars all around it [the sun]. The distance from the sun to the nearest star is the same as the thickness of a staple.” (Fifth grade student)

“The quarter and the blood cell are the same size because I don’t know the size of the blood cell, but I've seen pictures in my book of the cell and they [cells] looked a little bigger than a quarter.” (Middle School Student)

Our studies are examining:

• What existing cognitive frameworks do students and teachers have with respect to conceptualizations of scale and scaling effects

• How do individual and sociocultural factors such as ethnic background (e.g., African American, European American, Hispanic American), mathematical ability, or gender influence students’ scale conceptualization’s framework?

• How do educational experiences influence students’ conceptual ecology of scale?

• How do adults in a variety of professions conceptualize and apply scale and scaling effects?

Scale and Scaling Effects on the Web.

http://www.vendian.org/envelope/dir1/scaling_to_desktop.html
Scaling the Universe to your Desktop -- Jumps by three orders of magnitude to develop a sense of relative scale within those three orders of magnitude, then links from one jump to the next larger or smaller. “Rooms” each contain objects spanning 3 orders of magnitude within them.

http://www.vendian.org/envelope/dir0/scales.html
Starting point for “Back of the Envelope” web site related to scale and scaling. Great links to other websites.

http://www.vendian.org/mncharity/cosmicview/pages/page35.html
Has “Cosmic view: The universe in 40 jumps”

http://www.powersoften.com/
Powers of Ten -- From the “Time” portion of the website (at 10 ^19 seconds), LINKS BETWEEN LARGE AND SMALL 10+19 seconds is 300 billion years or 100 times the age of the Moon--a time period far beyond our realm.

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html
Another version of a powers of ten jump (java applet with either automatic or manual mode)

http://invsee.asu.edu/Modules/size&scale/unit3/unit3.htm
Good scale charts (logarithmic with images of objects and which microscopes function at which scale). Has figure captioned “Scale of our material world: from galaxies to atoms.” Also has diagram “overview of the history of microscopes” including chart of when developed and scale of use.

http://cern.web.cern.ch/CERN/Microcosm/P10/english/P-2.html
An interesting site where you can jump powers of ten

http://www.miamisci.org/ph/hextend1.html
Relates pH to powers of 10 (an example of a logarithmic scale)

http://acept.la.asu.edu/PiN/rdg/powers/powers.shtml
Basic Math, Scientific Notation, and Astronomical Dimensions, Dealing with Numbers Great and Small

http://science.nasa.gov/headlines/y2002/15jan_nano.htm
Voyage of the Nano-Surgeons -NASA-funded scientists are crafting microscopic vessels that can venture into the human body and repair problems – one cell at a time.

http://www.nano.org.uk/images.htm
Institute of nanotechnology. Lots of great nanoscale images.

http://www.foresight.org/Nanomedicine/Gallery/Captions/index.html
Lots of cool nanoscale images from the nanomedicine art gallery. Most are biology-related, but not all.

http://home.nc.rr.com/enloephysics/enloephysics/Scaling/Page_1x.html
Liz Woolard’s “Physics of Scaling” page (Enloe HS)

http://hep.ucsb.edu/courses/ph6b_99/0111299sci-scaling.html
Of Mice and Elephants: A Matter of Scale -- Good overview of the development of scaling laws in the 1980s and 1990s, including an extension from the animal world into the plant world. Nice discussion of the universality of these laws revealing underlying pattern and structure.

The link From the Small to the Huge, how body size and energy consumption differ on this site goes to a picture of a log-log graph and elephant comparing the metabolic rates of mammals which shows that bigger mammals are more efficient in energy consumption.

The link Like an Ant, Only Bigger?, strength vs. proportion on this site goes to a picture of Superman and an explanation from DC Comics that Superman’s strength comes from different scaling laws on his home planet of Krypton.

http://school.discovery.com/lessonplans/programs/sizeandscale/
Discovery Channel school web site with lesson plans (mostly involving scale models of the solar system). Has suggestions for a variety of books related to scale and scaling effects along with discussion questions related to the lesson that look promising. Also has a link to a video “Size and Scale – Skyscrapers.”

http://www.amnh.org/education/resources/rfl/web/earthmag/peek/pages/clock.htm
This link portrays geologic time on a 24 hour clock = 4.5 billion years of Earth's existence, but maybe same thing could be done with size scale.

http://www.amnh.org/rose/scales.html
Hayden Planetarium scale exhibits

http://www.ucmp.berkeley.edu/education/explotime.html
Has explorations through time including “Understanding Geologic Time.”

http://www.concord.org/newsletter/2001spring/zoomin.html
Molecular Workbench project. Describes software that allows students to enter the atomic-scale world and see what the results of their experimentation in the macroworld, such as increased salinity, has on the atomic-scale world.

http://micro.magnet.fsu.edu/optics/activities/perspectives.html
Examines Powers of 10 and tools scientists use to objects of different sizes.
Includes a link to a “Power of 10” type java interactive tutorial where students soar through space, and a second link to a “Virtual Scanning Electron Microscope” java interactive tutorial where students explore the microscopic world.

http://www.wehi.edu.au/education/wehi-tv/illustrations.html
Cool illustrations and movie animations of biomolecular processes (DNA, nerve cells, white blood cells, malaria, etc.) Some animations include jiggle to simulate Brownian motion at that scale.

http://www.intuitor.com/moviephysics/
Site that discusses “Insultingly Stupid Movie Physics” in a humorous manner. It's an old movie gimmick; a misguided scientist, radioactive fallout, pollution, or some other folly of mankind abnormally shrinks or expands someone or some creature. While we must admit to being entertained by such gimmicks, the physics are another matter.

http://www.kokogiak.com/megapenny/default.asp
The MegaPenny Project aims to help by taking one small everyday item, the U.S. penny, and building on that to answer the question: "What would a billion (or a trillion) pennies look like?" Site provides a nice concrete anchor for students’ conceptions of quantity.

http://www.msa.microscopy.com/ProjectMicro/PMBooks.html
MICROSCOPY, Project MICRO (Microscopy In Curriculum - Research Outreach). MICRO’s goal is to put MSA members, teaching materials, and microscopes in middle school classrooms nationwide.

http://micro.magnet.fsu.edu/primer/virtual/virtual.html
Molecular Expressions Virtual Microscopy Website includes an interactive Java-powered virtual microscopes that we have constructed. These virtual microscopes explore specimen focus, illumination intensity, magnification, and translation---operating essentially in a manner that is identical to real-life microscopes.

Read more About Scale and Scaling

American Association for the Advancement of Science (AAAS). (1993). Benchmarks for science literacy. New York: Oxford University Press, Inc.

Anderson, P. W. (1972). More is different. Science, 177, 393-396.

Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1-42.

Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83-120.

Falvo, M. R., & Superfine, R. (2000). Mechanics and friction at the nanometer scale. Journal of Nanoparticle Research, 2(3), 237-248.

Gallegher, R., & Appenzeller, T. Eds., (1999). Special issue on Complex Systems. Science, 284, 79-109.

Golledge, R. G., & Stimson, R. J. (1997). Spatial behavior: A geographic perspective. New York: Guilford Press.

Jones, M. G., Andre, T., Kubsko, D., Bokinsky, A., Tretter, T., Negishi, A., Taylor, R., & Superfine, R. (in press b). Remote Atomic Force Microscopy of microscopic organisms: Technological innovations for hands-on science with middle and high school students. Science Education.

Jones, M.G., Andre, T., Superfine, R., Taylor, R. (2003). Learning at the nanoscale: The impact of students’ use of remote microscopy on concepts of viruses, scale, and microscopy. Journal of Research in Science Teaching, 40, (3).

Jones, M. G., Bokinsky, A., Andre, T., Kubasko, D., Negishi, A., Taylor, R., and Superfine, R. (2002). NanoManipulator applications in education: The impact of haptic experiences on students’ attitudes and concepts. Proceedings of the IEEE Computer Science Haptics 2002 Symposium, (pp. 295-298). Orlando, Florida: IEEE Computer Society.

Jones,M. G., Bokinsky, A., Tretter, T., Negishi, A., Kubasko, D., Superfine, R., Taylor, R. (in press a). Atomic force microscopy with touch: Educational applications. Science, technology and education of microscopy: An overview, vol. II, (pp. 776-686). A. Mendez-Vilas, (Ed.). Madrid, Spain: Formatex.

Kunzig, R. (1997). A head for numbers. Discover, 18(7), 108-115.

Lawson, A. E. (1978). The development and validation of a classroom test of formal reasoning. Journal of Research in Science Teaching, 15(1), 11-24.

National Research Council. (1996). National science education standards. Washington, DC: National Academy Press.

Myers, R., Oldham, K., Tocci, S. (2000). Chemistry visualizing matter. NY: Holt, Rinehart, & Winston.

Stevens, P. S. (1976). Patterns in nature. New York: Penguin Books.

Thompson, D.’A. W. (1961). On growth and form. J. T. Bonner (Ed.), London: Cambridge University Press. (Original work published 1917)

Trend, R. D. (2001). Deep time framework: A preliminary study of U. K. primary teachers’ conceptions of geological time and perceptions of geoscience. Journal of Research in Science Teaching, 38(2), 191-221.

Tretter, T., & Jones, M. G. (2003). A sense of scale: The importance of size. Science Teacher, 70 (1), 22-25.

Wolpert, J. (1964). The decision process in a spatial context. Annuals of the Association of American Geographers, 54, 537-558.

© 2004 NanoScale Science Education Research Group
URL: http://ced.ncsu.edu/nanoscale/scale.htm
last updated 9/11/07

In Partnership with UNC-Chapel Hill & University of Louisville