*Tim Slater, Senior Scientist, CAPER Center for Astronomy & Physics Education Research, tslater@caperteam.com; http://www.caperteam.com*

A long-standing debate in the teaching of astronomy at the college level—and science in general—is whether to teach using metric SI units or customary US-standard units. At first glance the argument seems to be based on two juxtaposed positions. On one hand, US college students are largely unaware of the metric system and therefore need to be provided values for distance in more familiar units. On the other hand, real science is actually done in metric units and students studying in a science class should use the language conventions of science. It is this second position—authentic science uses metric units—that most college science faculty adopt. A cursory survey of most astronomy textbooks reveals that most distance values are given in metric units (with US-standard units often provided parenthetically) in the narrative sections, with data tables using metric units most frequently. Upon further reflection (or perhaps being urged to think more deeply from a learning and cognitive science perspective), one wonders if there is a more nuanced situation here and a more thoughtful approach is warranted? Cognitive science provides at least two boundary conditions to be considered in a more nuanced version of this debate: (i) issues related to novice-vs-expert learning and (ii) issues of cognitive overload.

To take a step back, we should acknowledge that the question of which system of units to teach under has been a raging debate for decades (1, 2, 3) . The United States’ historical efforts to go-metric have been a complete failure and are relatively well-known. I don’t have space here—in any unit system—to delve deeply into our metrification attempts, such as unfruitful efforts to change all US highway road signs to metric, which I believe only still exist south of Tucson). For the passionately interested reader, Phelps (4) has written about much of that history.

In recent years, however, education researchers have taken up the task of studying how learners conceptualize size and scale with the explicit goal of helping teachers teach better and helping students learn more. Much of this education research work was funded under the banner of rapidly advancing nanotechnology because educators needed to figure out how to help students learn about this new technology. Their work extends to astronomy educators because what NC State’s Gail Jones and her collaborators learned was that many students, nor K-12 teachers, fail to accurately conceptualize many distance values at all, big or small. (5-7) This is alarming because much of teaching and learning in astronomy is about “how big and how far.” (8)

Some professors have found it fruitful to use videos to help teach relative scales, using videos like *Powers of Ten*. (9- 11) Perhaps narcissistically, Jones and Tretter’s ongoing research suggests that this video works so effectively because the video starts with what people are most familiar with – the size of a human body.

Most people understand sizes and scales based on benchmark landmarks and mental reference points from their experiences. K-12 students tend to think of the world in terms of objects that are: small, person-sized, room-sized, field-sized and big. High school and college students also sometimes include shopping mall-sized and college campus-sized objects in their listings. Further, people’s out of school experiences involving measurement of movement have the greatest impacts on their sense of size and scale—walking, biking, car travel—as opposed to school experiences where they have rote memorized numbers from tables. Consistently, it is to these common experience anchors that people use various measurement scales.

For us teaching astronomy, this is where the cognitive science issue of novice-vs-expert rears its ugly head (13). Compared to a novice, an expert uses their experiences to automatically and often unawareingly change between scales. For example, when measuring the distance between Earth and Neptune, would one describe it in meters, astronomical units, or light-travel-time? The answer is, of course, it depends on why an astronomer would want to know such a distance. For an expert, using meters, AU, and ly is readily interchangeable whereas for a novice, these are three totally separate determinations. When I ask my students how far it is from where they are sitting to the front entrance of the building, or to the city with the state capital, they can usually give me a reasonably close answer using units of their *OWN* choosing, often it is time in minutes or hours, or in distances like American football field-yards or miles. If I specify the units their answers must be in, such as feet or kilometers, my college students generally have no idea. Experts are fundamentally different than students. We readily move between parsecs and light-years, whereas our novice students cannot—no matter how much we wish they could. As it turns out, if students could easily move between measurement systems, they wouldn’t be novices, they’d be experts and we teachers might be out of a job. In other words, we can’t simply tell students that a meter is about a yard, and two miles is about 3 kilometers and be done with it—if it was that easy, we’d have done that already and there would be no ongoing debate.

One might naturally think that astronomy students should be able to easily memorize a few benchmark sizes (e.g., Earth’s diameter is 12, 742 km and an astronomical unit is 1.4960 E 8 kilometers) and then they could handle almost anything by subdividing or multiplying. The problem is that the characteristic of an expert, as compared to a novice, is that experts chunk ideas more easily, allowing experts to make quick estimates. Novices have no strategies to be able to do this. Moreover, Hogan and Brezinski (14) aggressively argue that an individuals’ own spatial visualization skill level is the most important component in measurement and estimation by portioning and estimating distances. Unfortunately, these do not appear to be directly related to one’s calculation skills and teaching students to convert between units using dimensional analysis heuristics is mostly fruitless. The bottom line here is that students rarely enter the classroom with well-developed sense of scales going beyond their human-body size and experience with movement from one place to another. The cognitive science-based perspective of a novice-verses-experts teaching problem is well-poised to interfere with any instruction where students are being given sizes and scales in units with which they are highly unfamiliar.

As if this weren’t challenging enough, there is also the cognitive science-based problem of cognitive load. Cognitive load is the notion that students only have so much working mental capacity at any one time available to apply to learning new ideas. (15). That means when a professor says a comet is 10,000-m across, the Sun’s diameter is 1.4 million-km, the Virgo cluster is 16.5 Mpc, and a quasar is at a “*z* of 7”, students either have to stop being active listeners to your lecture for 30-seconds and figure out what those units mean and miss what you really wanted them to know, or they have to ignore any referenced numbers all together so that they can keep paying attention. The teaching challenge here is that I suspect the most important thing you want students to take away from a lecture about a quasar at a *z* of 7 isn’t precisely how far away it is, but instead what it tells you about the nature of the universe. The risk here is that introducing numbers and unfamiliar units gets in the way of the ideas you are most likely trying to teach.

The research alluded to earlier points to using relative sizes as being more fruitful for helping students learn than absolute, numerical sizes. I try to rely on things they are most familiar with and then help them to use simple, whole number ratios. For example, North America is about three Texas’ wide, the Moon is about one North America, Earth is about four Moon’s, Betelgeuse is 1,000 times larger than the Sun, and …. Notice I don’t have to say very many of these ratios before you starts skimming to the end of this paragraph yourself : That’s the same experience your students too often have. Fortunately, many modern astronomy textbooks now give planet sizes in Earth-radii, just like we have long given solar system distances in astronomical-unit Earth-orbit sizes (17). I think this is a really good starting place. After all, five years from now when you run into an alumni student, do you really want the one thing that they most remember about your class to be the distance to the Crab Nebula in parsecs?

As astronomy teachers focused on student learning, we seem to be left no longer with the seemingly simple question of “should I teach with metric or US-standard?”, but with the more robust question of “**do I seriously take on the semester-long task of teaching scales and measurement ***or* **do I teach using ratios using familiar distances, which vary widely from student to student in my diverse classroom?**” Re-framing the question this way is much more actionable and diminishes the less productive “science versus the rest of the world” notion. I contend that this new either-or question is much more worthy of research and debate.

Personally, I have a lot of astronomical ideas with which I want my students to engage. My personal belief is that I’d rather students deeply engage in physical processes and causality of astronomy, stimulated by wonder and curiosity. I further want them to engage in how astronomy is deeply entrenched in society and technology. To do this, I choose to give up on allocating the time necessary to fully teach the metric system and focus my efforts on teaching things in terms of relative sizes and avoid using a self-defeating calculator-task whenever possible (16). Experienced mathematics teachers will tell you that you can’t really teach the metric system with a single 15-minute lecture to novices: Teaching the metric system takes a commitment throughout the entire course. The notion that metric is easy because it is all base-10 is nonsense when it comes to teaching astronomy, despite my desire for it to be otherwise. The bottom line is that I decided that I want to teach astronomy rather than teach the metric system, and I don’t have time to teach both well.

My textbook writing solution (17) is that I provide sizes in both metric and US-standard units where it makes sense. Against the common convention, we have made the agonizing choice to include the US-standard units first (with the metric units parenthetically) so as not to unnecessarily put off neither the students who find US-standard units to be less off putting, nor the vast majority of professors who desire their science course to be characterized by the metric units characteristic of science. My eventual, downstream goal is to provide size and scale referents for as many common anchor objects as possible without overloading the students, and focus on allocating serious class-time to teaching the sizes of a few core anchor-sized objects. These anchor objects include sizes of Earth, Sun, Earth’s orbit, average distance between stars, Milky Way diameter, distance to Andromeda, and light-year, to name a few. Fortunately, teaching the distance of a light-year is not either a metric unit or a US-standard unit, and is thus elevated above the present debate no matter what your perspective.

CITATIONS

- Helgren, F. J. (1973). Schools are going metric.
*The Arithmetic Teacher*, 265-267. - Vervoort, G. (1973). Inching our way towards the metric system.
*The Arithmetic Teacher*, 275-279. - Suydam, M. N. (1974). Metric Education. Prospectus. URL: http://files.eric.ed.gov/fulltext/ED095021.pdf
- Phelps, R. P. (1996). Education system benefits of US metric conversion.
*Evaluation Review*, 20(1), 84-118. - Jones, M. G., Gardner, G. E., Taylor, A. R., Forrester, J. H., & Andre, T. (2012). Students’ accuracy of measurement estimation: Context, units, and logical thinking.
*School Science and Mathematics*,*112*(3), 171-178. - Tretter, T. R., Jones, M. G., Andre, T., Negishi, A., & Minogue, J. (2006). Conceptual boundaries and distances: Students’ and experts’ concepts of the scale of scientific phenomena.
*Journal of research in science teaching*,*43*(3), 282-319. - Jones, M. G., Tretter, T., Taylor, A., & Oppewal, T. (2008). Experienced and novice teachers’ concepts of spatial scale.
*International Journal of Science Education*,*30*(3), 409-429. - Slater, T., Adams, J. P., Brissenden, G., & Duncan, D. (2001). What topics are taught in introductory astronomy courses?.
*The Physics Teacher*,*39*(1), 52-55. - Eames, C., Peck, G., Eames, R., Demetrios, E., & Mills, S. (1977).
*Powers of ten*. Pyramid Film & Video, available on YouTube at: http://youtu.be/0fKBhvDjuy0 - Cox, D. J. (1996, January). Cosmic voyage: Scientific visualization for IMAX film. In
*ACM SIGGRAPH 96 Visual Proceedings: The art and interdisciplinary programs of SIGGRAPH’96*(p. 129). ACM. The IMAX Cosmic Voyage Video, narrated by Morgan Freeman, available on YouTube at: http://youtu.be/cMRoDyc8W2k?t=7m10s - Jones, M. G., Taylor, A., Minogue, J., Broadwell, B., Wiebe, E., & Carter, G. (2007). Understanding scale: Powers of ten.
*Journal of Science Education and Technology*,*16*(2), 191-202. - M.G. Jones (2013). Conceptualizing size and scale. In
*Quantitative reasoning in mathematics and science education: Papers from an International STEM Research Symposium WISDOMe Monograph*(Vol. 3). Available online at: http://www.uwyo.edu/wisdome/publications/monographs/ - Bransford, J. D., Brown, A. L., & Cocking, R. R. (1999).
*How people learn: Brain, mind, experience, and school*. National Academy Press. Available online at: http://www.nap.edu/catalog.php?record_id=9853 - Hogan, T. P., & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three abilities?.
*Mathematical Thinking and Learning*,*5*(4), 259-280. - Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design.
*Learning and instruction*,*4*(4), 295-312. - Slater, T., & Adams, J. (2002). Mathematical reasoning over arithmetic in introductory astronomy.
*The Physics Teacher*,*40*(5), 268-271. - Slater, T. F., & Freedman, R. (2014).
*Investigating astronomy: a conceptual view of the universe*. Macmillan-WH Freeman Higher Education. (available in the CAPER Team Book Store)

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