Nathan Grawe, Economics

Nathan Grawe is an associate professor of Economics at Carleton College, a private 4-year liberal arts institution. Information for this case study was obtained from an interview conducted on August 26, 2013. This page is part of a collection of profiles about a variety of techniques for integrating Quantitative Reasoning (QR) across the curriculum.

Jump down to Design and Implementation of QR Goals | Key QR Assignment of the Course | Challenges | Advice | Documents

Overview and Context

About the Course

Principles of Microeconomics is an introductory course that is required for economics majors and is a prerequisite for almost all of the other courses in the department. I have taught this class for 14 years, and have modified it over time to incorporate more quantitative reasoning and quantitative writing.

The audience includes many students who are not economics majors, including some who take the course because it satisfies a distribution requirement at Carleton called, "Social Inquiry." In addition, students in interdisciplinary programs such as environmental studies majors take the course as a pre-requisite for upper level courses in our department that have an environmental component. This course also satisfies Carleton's Quantitative Reasoning Encounter (QRE) requirement. The course size is usually around 30 students.

Syllabus for Principles of Microeconomics (Microsoft Word 61kB Aug26 13)

Key QR Assignment Description (links to section in this page)

How Quantitative Reasoning (QR) and Literacy are Approached

Quantitative reasoning is a continuum within which students can deepen their sophistication over time. No matter what we know, we can always know more. I prefer the term quantitative reasoning over quantitative literacy in order to avoid confusion with analogies to verbal literacy, in which people often talk about achievement of a static level of proficiency.

When I think about how quantitative reasoning is approached in this course, my objective is to make sure that my QR and course goals align. I don't want the quantitative reasoning to be left sitting on the side. I want it to be integrated with my substantive goals for the course. By teaching quantitative reasoning, I believe that my students will be better prepared for the major, will have a better understanding about economic theory, and ultimately will become better economists.

Design and Implementation of QR Goals

Motivation to integrate QR

My motivation stemmed from involvement in several campus-wide initiatives at Carleton College: Writing Across the Curriculum and Quantitative Reasoning Inquiry and Knowledge (QuIRK).

I first became involved with the Writing Across the Curriculum project because I was not satisfied with the quality of my students' writing. I recognized that there were broader general education goals that, frankly, were more important at some level than my economics goals. While teaching economics is very important, only a few of my students were going to earn doctorate degrees in economics. Writing seemed to be a very important general education goal, so I started adding writing assignments to the class. However, there was a tension at that time between the content I needed to cover to accomplish the course goals and the time it took for the writing assignments.

Some time later, an information literacy grant started on campus in conjunction with the librarians, and our department chose to work on creating information literacy assignments involving data. At that point, everything began to make more sense. The writing wasn't going to be just writing; it was going to be quantitative writing.

Soon thereafter, the Quantitative Reasoning Inquiry and Knowledge (QuIRK) initiative started at Carleton. The emphasis was on quantitative reasoning in the context of argument. This initiative solidified the connections in my mind about what I wanted my students to do: I wanted them to be able to argue about economic theory, informed by quantitative evidence. That meant that the writing and the quantitative reasoning were now serving the goals of the course; they were serving to help students better understand the theory so that there would no longer be a tension between accomplishing the course goals as defined by the department and introducing quantitative writing.

QR goals

I view goals for quantitative reasoning goals in light of my goals for learning economics. Certainly students need to be prepared for continuing on into upper level courses in the major. For those who will never take another economics class, my goal is to give them a taste of how economists think and what economic theory is about.

I want my students to be comfortable with pursuing quantitative questions. I want them to have confidence in their critical thinking about what quantitative information means.

Students should be well prepared to interrogate quantitative texts. I want them to ask questions like, "Controlling for what?" or "What other variables have been accounted for in the analysis?" Many students don't initially feel comfortable playing with data or they're easily browbeaten by the sense that quantitative evidence holds an unquestionable authority. They don't tend to question numerical claims and don't approach them with the same level of skepticism as they would with qualitative claims. My goal is for students to become comfortable and capable when confronting quantitative claims.

Immigration example of how QR goals mesh with course goals
I align my QR and course goals by using real quantities to study economic theories. In helping students to understand a problem like immigration reform, we can state in theory what we think would happen to the supply and demand curve if we adopt some portion or all of immigration reform as it is being debated. But in making predictions about whether the effect will largely be played out in price or quantity, the real question is regarding the slopes of these two lines. As the two move, where does the intersection point go? A lot depends on the elasticity of the supply curve, and the same for the demand curve.

Problems involving economic predictions can be understood by studying basic, easily accessible quantities. I ask my students to go and explore how many illegal immigrants there are or factors like what fraction of output is accounted for by labor. This raw data helps them better understand how to use the supply and demand model. It ceases to be a conflict between course time for theory and course time for quantitative reasoning. Instead, quantitative reasoning instruction helps me improve what I already wanted to do.

Pedagogic approaches used

I would like to emphasize that there is a broad continuum of pedagogic options that can be followed. There are longer assignments and there are shorter ones; I will illustrate how the more modest assignments can still have a big impact.

If you assign three writing assignments that require students to write 2-5 pages, there is going to be a fair amount of grading time. If I were teaching hundreds of students at one time, even with a staff of TA's, I am not sure that this would be feasible.

I have found that there are many opportunities to make very small changes to how I teach that can--especially if you call attention to what you're doing--reinforce for students quantitative reasoning elements in a shorter time frame.

Small interventions involve being consistent in modeling the behavior we want, and not modeling behavior we don't want. For example, we don't want students to use abstract phrases like "lots and lots" in their writing to describe a quantity that has easily findable real values. To model the behavior we want, one pedagogical approach is to work through a short estimation exercise in class that determines real numbers in order to illustrate a theory or concept. By giving students opportunities for short in-class activities like the estimation routine described in the example below, we can make some pretty big impacts.

The following example occurred while I was teaching about the Diamond-Water Paradox.

Example of using small QR interventions: the Diamond-Water Paradox
The Diamond-Water Paradox, identified by Adam Smith, deals with the difference between value and price.

The key observation that Smith made was that the value of something is in essence the area underneath a demand curve. The first unit might have a lot of value, but the price of something is related to the last unit consumed. It might be that the price--the value of the last unit consumed--might be quite low, and yet the aggregate value is quite high.

For instance, because water is a relatively plentiful resource consumers pay a low price despite their willingness to pay dearly for the first quart or gallon. By contrast, diamonds, despite being less essential to life than water, have a very high price because of their scarcity.

In modern textbooks, this idea is often presented as the NFL player/K-12 teacher paradox: "Why do NFL players get paid so much even though K-12 teachers are arguably so much more valuable?" The answer is the same: it's about scarcity. There aren't that many people with the skill set to play in the NFL. As I was teaching this, the little gray box in the text presented it this way.

So I asked the students, "How many NFL teams are there? There are just over 30. And there are a little over 50 players on a team, so there are about 1,500, maybe 2,000 people at any point in time with the skill set to play at that level in the United States. How many teachers are there?" And I almost said, "There are lots and lots of teachers." And then I realized that's exactly the kind of thing I don't want my students doing in their writing, saying, "lots and lots" when there's a number out there that's easily findable.

I invited students to work in small groups to estimate how many teachers there are. I said, "There are about 300 million people in the U.S. population, so how many K-12 teachers are there?" They spent a couple minutes working on that estimation problem while I turned on the computer and went to the Statistical Abstract of the U.S. where the number sits.

When I got to the Statistical Abstract, I asked them for their answers. In literally about two minutes time I was able to get them to do some estimation. They all did a fairly good job. However, they were all off by half and underestimated the actual number. Every group said that there were about half as many teachers as there actually are. I was able to show them where they could get the data, and explain a little bit about the Statistical Abstract. They could see that it was readily accessible to them.

Then we got to talk about why their estimates were off. All of the students used a similar algorithm. At some point, they inserted class size. The average class size to them was about 30 kids per class. But in the United States, the average pupil-to-teacher ratio is 15 due to factors like smaller class sizes in special education. My question was, "Where did you get 30?" And the answer was that it came from their experience, but none of the students had experience with special education.

That was an "aha!" moment for the students because they recognized that there are disparate experiences. My experience might be the mode, but it's not the mean because there are other classes with sizes of one or two. I don't know quite how we resolve these kinds of problems of bias because we don't know what we don't know. But at least if we recognize that our own personal experiences can then influence our thinking about what is normal or what is common, it can help us with our analysis. All of this got packed into just two or three minutes, where in the past I would have just said, "There are lots and lots of teachers."

Knowing the course is successful

With a small class size of 30, I do not expect to assess and find that there's a statistically significant difference between the group that I didn't treat and the group that I did treat. I know from anecdotal evidence based on grading rubrics. My grading rubrics include components of economics content, writing, and quantitative reasoning.

I don't expect my introductory students to be experts. This is way too soon to expect that kind of level. Getting all students at or above the novice level, and maybe getting half the students to a level beyond novice is reasonable.

We don't have to get everything done with this one course. These students are going to go on and take many other courses from other faculty, putting what they have learned into different contexts, and in Carleton's case, many courses will have quantitative reasoning in mind. I am just one part of their educational experience. This is helpful to keep in mind because it gives me a little more freedom to design my interventions within the context of the course content.

The more nuanced use of quantitative information is going to be hard to see in the time-frame of one course. There are all sorts of learning experiences where you have a number of experiences before you reach some critical threshold, and then you have your "aha!" moment. If you look before you hit the threshold, you will see no learning going on. Of course we can't run that argument without at some point checking to find out that the "aha!" moment does happen.

Key QR Assignment of the Course

This assignment is a series of three papers that culminate in a white paper brief written to a policymaker. The final paper assignment, Data Rich Economic Policy Brief, requires students to use economic models to analyze a public policy debate.

The key QR assignment of my Principles of Microeconomics course is a series of three papers that students write over the course of the semester. While the students experience the assignments as three different writing moments and I give them grades at each step, from my perspective, this is really one assignment.

The papers are spaced strategically throughout the semester in such a way that students have sufficient content knowledge to do each one. The first two papers are 2 pages each and the last paper is about 5-7 pages.

The first paper is simply getting the lay of the land in terms of quantitative evidence. Students must find data from the Statistical Abstract of the U.S. that will demonstrate the size and importance of a public policy debate, for instance, immigration reform. They need to demonstrate that it is a big issue. They can define the size any way they want, but they cannot argue that it is unimportant or insignificant. In the immigration reform example, the data they find will presumably have something to do with the number of undocumented citizens, the flow of undocumented citizens across the border, how many people are in the American low-skilled labor force, or their wages.

The second assignment asks students to use the supply and demand model to predict the direction of an effect of one of the elements of a public policy decision. The second paper says without arguing one way or the other, pick some element of, for example, immigration reform, and use the supply and demand model to predict the effect on pricing and quantity in some market.

The final paper asks them to write a policy brief, and if they do it correctly, this paper will draw heavily on the first two papers. This final assignment, Data Rich Economic Policy Brief, requires students to use economic models to analyze a public policy debate. An example topic for the final paper might be, "Analysis of the effect of adopting immigration reform using the supply and demand model."

Instructions to the students for the third paper include, "You are working for a senator who has to cast a vote, and they ask you for a white paper brief informing him/her on the effects of the immigration reform." We talk a little bit about audience and the fact that senators don't usually like being told what to do. Their role is to provide information, and not to give an opinion about how to vote. Students then use the information on the size of the issue from the first paper and information on supply and demand and predicting effects from paper two, in order to explore the consequences of various policies.

I don't tell students that they should draw upon the two papers that they have already done. There are some students who manage not to recognize that they should use some of the data they collected for earlier papers to write the final paper. Preparation for the last paper is provided by scaffolding the work so that when they get to the final assignment, at least if they've taken advantage of the opportunities, they've been equipped to write the final paper successfully.


  • Integrating QR within the context of course. Until I was willing to think hard about how quantitative reasoning serves the content, I was continually bumping up against the challenge that the syllabus was already packed. It is important to think about how the QR goals serve the course goals ahead of time.
  • Student push-back. Sometimes there is a bit of resistance from students because this is not the kind of assignment they expect or are used to doing. They think of it as busy work because it is a practically-oriented task where they have to go to a source and find a number or do some computations, as opposed to think critically. In anticipation of this problem, I've tried to work into the assignments and to the syllabus explicit articulations for why I'm doing what I'm doing and to keep open lines of communication with the class. With institutional commitment to QR, students have come to recognize that this is a legitimate part of their learning.


  • Be explicit about course goals in the quantitative reasoning area. In order to reduce student resistance, I talk about QR in the course goals and in the assignment goals. I make it clear that this isn't something that only I am doing, but rather that it is institution-wide because Carleton has a quantitative reasoning requirement and this course satisfies that requirement.
  • Don't reinvent the wheel. The SERC resources are a great place to start. When you look at similar sites, keep in mind that you might not find an assignment that you can use verbatim. You might, but more often when I use these resources I find the seed of an idea. That seed can come from a classics course. It could come from a geology course. What is important is sharing resources and not reinventing the wheel.
  • Collaborate and join a network. Get involved with a network somehow. If there are other people on your campus involved in quantitative reasoning, maybe there's an opportunity to meet with them once a term to discuss what they do. It is ideal if these conversations happen on your campus because these faculty are working with students who are similar to your students. They know the level of preparation and the strengths and the weaknesses of your particular student body. But if you can't network with faculty on your own campus, then join a group like the National Numeracy Network and tap into meetings and resources there. Get ideas from other people about what they've tried and what has worked.
  • Honor the many different ways that the integration of QR plays out across a variety courses. For those who are responsible for moving forward the QR conversation on their campuses, it is helpful to realize that there will be diverse approaches, perspectives, and needs.
    • The kinds of methods that are used and the skill sets that are emphasized differ from department to department and discipline to discipline. Sometimes there is a temptation to emphasize the differences. But if we really want to be successful, we need to emphasize the commonalities.
    • Institutionally, I have found that it is helpful not to stay too long on the question of how to define QR. That conversation can get divisive after a point as people start to say, "This is in and that's out." Reaching agreement about quantitative reasoning requirements can be harder because of diversity across disciplines, but I think it's stronger because of that diversity as well.


Assignment description: Data Rich Economic Policy Brief. Part of the National Numeracy Network collection of teaching activities (the list of activities may be refined to social science fields by clicking on the discipline headings to the right in the blue box.)

Syllabus for Principles of Microeconomics (Microsoft Word 61kB Aug26 13)

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