Scale and Scaling

Size and Scale..Being the Right Size

Scale (n.) A progressive classification, as of size, amount, importance, or rank
American Heritage Dictionary of the English Language – Fourth Edition


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 scales beyond 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, very tiny, and also 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.


Benchmarks for Science Literacy

What students should know by the end of:

• Grade 2: Things have very different sizes, weights, ages, and speeds.
• Grade 5: Things have limits on how big or small it can be.
• Grade 5: The biggest and smallest values are as revealing as the usual value.
• Grade 8: Properties that depend on volume change out of proportion to those that depend on area.
• Grade 8: As the complexity of a system increases, summaries and typical examples are increasingly important.
• Grade 12: Representing large and small numbers in powers of ten makes it easier to think about and compare things.


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



Scale and Scaling Research:

We are conducting a series of studies that cross ages and levels of experience to document the learning trajectory for size and scale. Research studies include examining the following:

•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?



Scaling on the Web

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. Link to Site

Starting point for “Back of the Envelope” web site related to scale and scaling. Link to Site

Has “Cosmic view: The universe in 40 jumps”. Link to Site

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. Link to Site

Another version of a powers of ten jump (java applet with either automatic or manual mode). Link to Site

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. Link to Site

An interesting site where you can jump powers of ten. Link to Site

Relates pH to powers of 10 (an example of a logarithmic scale). Link to Site

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. Link to Site

Institute of nanotechnology. Lots of great nanoscale images. Link to Site

Lots of cool nanoscale images from the nanomedicine art gallery. Most are biology-related, but not all. Link to Site

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. Link to Site

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.” Link to Site

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. Link to Site

Hayden Planetarium scale exhibits. Link to Site

Has explorations through time including “Understanding Geologic Time.” Link to Site

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. Link to Site

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. Link to Site

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.Link to Site