Many professors assigned to teach introductory science classes have some experience, or considerable experience, teaching introductory courses for majors. If you are one of those few lucky scientists who are assigned to teach the general survey course for non-majors, you need to know that you’re starting out a disadvantage. Many of the important skills you’ve perfected teaching science to science-majors are well-poised to interfere with the best of teaching intentions—particularly those related to solving numerical problems with a calculator.
I propose that there are at least two distinct places where you’re going to have to consider making major changes in order to be successful: (i) working numerical problems and (ii) international systems of units. Let’s first talk about working problems in class before going to the thornier problem of selecting the appropriate unit system to use in teaching introductory sciences long-steeped in mathematics–like, physics, chemistry, and astronomy.
Teaching with Numerical Problems
We can all readily agree that all science is a quantitative science at its core. We can also agree that many science courses are taught within the context of a College of Science, including Mathematics Departments. Moreover, many of your colleagues will perceive your class to be more rigorous if students are frequently reaching for their scientific calculators, like their majoring students do. Given these three facts, it seems only natural that all science courses could be taught with the successful techniques of a majors-course course. Unfortunately, adopting this perspective is a guaranteed way to earn low teaching evaluations.
You might be asking yourself, what am I supposed to do during class time if it isn’t work example numerical problems on the board? Or, you might be saying to yourself, what will exams look like if I’m not grading their ability to solve numerical word problems? These are reasonable questions. Again, we’ll implore you to digest the rest of the ideas presented here: By the end, we’ll think you’ll wonder how you’ll have time to do all the classroom things you want to do rather than endlessly work example problems on the board.
As an interim suggestion for now, we suggest that you adopt as read-alert, all-engines-stop, warning that things in your class aren’t going well anytime a student reaches for a calculator. Really. Instead, your task is to spend your energy finding ways—many of which are here elsewhere on this blog—for your students to engage in juicy, high-level mathematical reasoning in science. The goal is to do mathematics with your students by eliminating boring and perhaps pointless plug-and-chug arithmetic from your class—think graph interpretation!
Selecting Units of Measurement
Much of science is concerned with systematically solving the mysteries of how big and how far. You can’t escape using numbers to describe how many planets in the solar system, how big is the Sun, and how far are we from the center of the Milky Way. We’re not suggesting that you don’t use numbers, far from it. Instead, I’m warning you upfront that you should be compassionately sensitive to how non-science majoring students can viscerally respond when they encounter long tables of large numbers laced with unfamiliar units.
For Centuries, science teaching professors, among others, have helped their students see intrinsic value the metric system. The benefits of a 10-based measurement system are undeniable, especially when contrasted with the archaic system used in the United States. A problem-solving strategy that involves converting any numbers in an end-of-chapter word problem into the meter-kilogram-seconds paradigm is a time-tested problem-solving strategy leading to success. Taken together, a professor might naturally assume that all science courses should be taught using metric units, since it is inherently easier.
A long-standing debate in the teaching of general science at the college level 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 college 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. This seems like an issue closed to debate.
If you didn’t grow up in the United States, you might not know that the question of which system of units to teach under has been a raging debate for decades, at least. The United States’ historical efforts to go-metric have been a complete failure and are relatively well-known. We don’t have space here—in any unit system—to delve deeply into the US’s metrification attempts, such as unfruitful efforts to change all US highway road signs to metric, which I believe only still exist south of Tucson.
Rigorous education research shows that people—and even some scientists—conceptualize sizes and scales based on benchmark landmarks and mental reference points from their experiences. Most college students naturally tend to think of the world in terms of objects that are: small, person-sized, room-sized, field-sized, shopping mall-sized and college campus-sized objects, big and really big. The greatest impacts on how people develop these benchmarks are outside-the-classroom experiences involving measuring movement—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 college students use various measurement scales.
For us teaching science, we use our extensive experience as scientists in quantifying the world to automatically and often unawareingly change between scales. For example, when measuring the distance between Earth and Neptune, astronomers automatically know if we should describe it in meters, astronomical units, or light-travel-time, depending on why an astronomer would want to describe such a distance. For experts, using meters, AU, and light-years is readily interchangeable whereas for most college students, these are three totally separate determinations. This potential disconnect between you and your students requires your careful attention.
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 science 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 available to be able to do this. The bottom line here is that astronomy students rarely have a well-developed sense of scales going beyond their human-body size and experience with movement from one place to another.
If you’re still following this TL;DR discussion, what we’re saying here is when some astronomy professor, for example, 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, subsequently, then inadvertently miss what you really wanted them to know, or they have to ignore any and all 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.
Education research points to using relative sizes as being more fruitful for helping students learn than absolute, numerical sizes. Expert teachers try to rely on things students are most familiar with and then help students to use simple, whole number ratios. For example, experienced science teachers on North America is about three Texas’ wide, the Moon is about one North America, our planet Earth is about four Moon’s, the star Betelgeuse is 1,000 times larger than the Sun, and …. Notice we don’t have to type very many of these ratios before you yourself start skimming to the end of this paragraph: That’s the same experience your students too often have. Fortunately, many modern science textbooks now give planet sizes in Earth-radii, just like we have long given solar system distances in astronomical-unit Earth-orbit sizes. 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?
Across the domain of science, there are countless scientific ideas with which I want my students to engage. I propose that you adopt the position that you help your students deeply engage in physical processes and causality of astronomy, stimulated by wonder and curiosity. To do this, you’ll need to choose to give up on allocating the time necessary to fully teach the metric system and focus all of your available efforts on teaching things in terms of relative sizes and avoid using a self-defeating calculator-task whenever possible.
To say again for emphasis sake: Experienced, master high-school 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 science, despite our desires for it to be otherwise.
Tim Slater, University of Wyoming, Tim@CAPERteam.com
Suggested citation: Slater, T. F. (2019, January). How much math should I use in my Science 101 course? Society of College Science Teachers Blog, 4(6), https://www.scst.org/blog
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