Mary Savina, Geology
Overview and Context
About the course
In most years, I teach Introduction to Environmental Geology to about 30 students. The course is a mix of undergraduates, some proto-geology majors and most who take the course to fulfill a lab science requirement. The course is one of a few introductory course options for students entering the geoscience major. These students must take just one introductory course. I have taught the class for more than 12 years.
The course also satisfies Carleton's Quantitative Reasoning Experience (QRE) requirement, of which students need 3. The QRE requirement was adopted in 2010. When I added the QRE credit to the course, I didn't change the curriculum of the course; the course was already satisfying the new QRE requirements.
Key QR Assignment Description (links to section in this page)
How Quantitative Reasoning (QR) and Literacy are approached
I address QR with the following statement that is used by some of the QR committees and projects at Carleton College: "it's not complicated math applied to simple problems. It's simple math applied to complicated problems." I try to emphasize to students that it's about deciding whether the numbers that are being presented as part of an argument are correct or not, and how to use numerical information and quantitative information to strengthen arguments.
Motivation to integrate QR
It was very natural for me to use QR in my class because I felt like I had been talking about it with colleagues for years. I have been involved with Carleton's QR committee discussing quantitative reasoning at Carleton from the start. After "writing across the curriculum", "QR across the curriculum" is the second big cross-disciplinary skill that we've worked on at Carleton.
The QR goals of Introduction to Environmental Geology are really two-fold.
One is for students to come out of the class knowing something about how geologists think. Geologists think with quantitative tools. A map is a quantitative tool. A graph in a textbook is a quantitative tool. Thinking quantitatively is not the sum of thinking like a geologist, but it is part of it.
The other purpose is to help students understand how geology can contribute to understanding global problems that are of concern to them and society. One way I do this is to put students on the spot about their own contributions to problems like energy use because students have a tendency to want to blame other people or other generations and not think about their own contributions. I turn this into a class activity and have them analyze an energy bill from home.
Pedagogic approaches used
I attempt to show students how to reason quantitatively without necessarily telling them that it's "quantitative reasoning" until the end. For instance, it's important to me that students have some understanding about how systems work. When I start to teach about systems, I hand out a bunch of sheets of newsprint and markers and give each group a particular kind of system behavior. One group be asked to draw a system that increases linearly through time. Another group will get a system that has periodic changes between high points and low points. Another group will get a system that experiences an exponential increase. I ask students to draw a graph representing that system behavior and come up with an example from science and from their personal life that fits the description of that system behavior.
One of the examples of periodic systems the students come up with is to say that there's a periodic relationship between family weekends, which come once a term at Carleton, and their perception of the quality of the food in the dining halls. Sleep habits tend to be something that the random system group comes up with to explain their system behavior.
This activity results in a series of oversized graphs that then we hang around the room. Then I can pick up on concepts throughout the term from their reading or that they're working on and ask students which graph and example relates to that concept. To me that's quantitative reasoning. But, in this case, I call it "system behavior" rather than "quantitative reasoning."
In general, I use a lot of small group work and discussion in my classes because I prefer to listen to the students talk. For a number of years now I've noticed my students don't take many notes. On top of that, the educational research says that only some very small fraction of what somebody says to you is going to be retained, so I try to engage the students in different ways as much as possible.
Knowing the course is successful
If I'm successful integrating quantitative reasoning into this introductory geology course, I expect to see that:
- without prompting, students use quantitative terms (for instance, for system behavior) when they speak and in their written work.
- in their work, students interpret quantitative data and their analysis techniques correctly (for instance, the extent and duration of drought and the running average technique they used to analyze the climate record).
- in their work, students contextualize the numbers they provide.
I'm working to develop ways (including rubrics to give to students) to determine how well and how many students meet these goals. In general, I think student do show gains, particularly when I allow them to revise their work.
I have an assignment that is key to reaching my QR goals that involves students working in groups to analyze climate data. The activity requires a mix of quantitative literacy and reasoning components. In the assignment, students find and analyze data to try to answer one of two questions:
- Was the climate anomaly during the Dust Bowl years really unique in space and time?
- Has global temperature in fact risen uniformly across the globe? If not, why not?
To answer those overarching questions students must find and analyze data. Specifically, students learn where to find the data, how to get the data into a spreadsheet and some simple statistical tools that can used to analyze the data. Students need to locate and use climate data spanning a large time range beginning in about 1880 when climate data began to be collected widely. Global temperature and precipitation data included polar, temperate and equatorial regions, though not all areas are equally represented or have the same lengths of record. For the Dust Bowl problem, different groups are assigned to different location, both within the "classic" Dust Bowl area and in other stations in North America. Each group of students presents data and interpretations in a four-slide PowerPoint which is archived to be available to all the students.
For the Dust Bowl problem, students then produce a thesis-driven paper about what caused the Dust Bowl. We have a class session about what constitutes a thesis and I give them some short readings by people who have different opinions of what caused the Dust Bowl. Students also have to find some sources from the period that they can incorporate into their argument for what caused the Dust Bowl.
This assignment takes students 3-4 weeks to complete involving a combination of time in class and out of class. We usually start the data collection in a lab one day, we have one class session in the library, one session in class where they present their four-slide PowerPoint presentations and one class session to discuss what a thesis entails.
- To me, one of the biggest challenges in teaching (QR and other things) is being intentional and articulating to students what the purpose of a given lesson is (something I know, but they probably don't). I often operate by instinct and it's hard for me to remember to verbalize, for example, "this assignment is intended to give you direct experience working with large data sets–and scientists use these data". I don't mean telling them "this is a quantitative reasoning project" but rather saying "these are the datasets and tools we use to analyze climate change". Students do need some insight to follow what you're doing, especially in the beginning.
- Another challenge is thinking about things that I do naturally and reminding myself that they are quantitative. For example, introductory geoscience students put together a stratigraphic section from three field sites we visit during lab. To do this, they have to measure thickness of different layers of rock, note the elevation of each site and use the numbers to generate a correlation diagram. Before doing this exercise we talk about maps, but I think I could do a much better job emphasizing the importance of using the numbers. This would reinforce the quantitative reasoning component of the exercise, which is important for me.
- I still haven't completely figured out how to help students understand that numbers have to have context. When students try to frame an issue or topic that they're writing about, they tend to use numbers that are out of context. Students start papers by writing 'Since time began humans have been...', or 'Thousands and thousands of people are at risk if sea level rises' or 'The population of the U.S. that's within 50 miles of the coastline is X million'. Well, if you don't know the length of time or what proportion of the population that is, then you don't know the context and the number is meaningless. Even putting in a precise number is not enough. The number must have context.
I think my biggest piece of advice would be to look in the direction of statistics for inspiration on where to add a QR component to a geoscience course. Look for something (like climate records or energy use) that can be statistically understood. In part, that's because statistics is a more universal language that students are likely to run into in life as compared to some of the advanced math problems that I have students do in upper level classes or some of the analytical problems that at their root are differential equations. A grounding in statistics will help prepare them for the future and provides relevance for what they're learning.
I truly think that in many cases, faculty can fairly easily come up with a way to address quantitative reasoning in their class. I think a lot of QR integration can be done just by tweaking the approach to the subject matter that is already embedded in the course. Rather than presenting data to students and telling them what it means, you could add QR to a course by having students:
- Compare one number to another
- Analyze the data you present
- Calculate the means from a dataset and have students tell you what information can be drawn from those means
- Get students to collect and analyze their own data. That helps students come to understand how good and how bad those numbers really are.
- Mary's climate activity can be viewed in two pieces. One page focuses on the data collection and analysis with a second part focusing on the Dust Bowl writing component.
- Mary's activity for students to analyze an energy bill from home.