Lesson: Conceptualizing and measuring democracy 

Course: “Government and Politics in Global Perspective”

Professor: Clarisa Pérez-Armendáriz, Associate Professor of Politics

What is democracy? And how do we measure how democratic a country is? 

Democracy is a “foundational, fundamental concept” in political science as well as day-to-day life, says Associate Professor of Politics Clarisa Pérez-Armendáriz, yet researchers can spend their entire careers trying to measure it — assigning to individual countries labels or numbers that can influence real-life foreign policy decisions. 

“There’s no agreement on what democracy even means, and yet we’re claiming we can measure it from one to seven or even ‘yes’ or ‘no,’” she says. 

To show how tricky defining and measuring an abstract concept like democracy can be, Pérez-Armendáriz has her students do exactly that. 

Associate Professor of Politics Clarisa Pérez-Armendáriz meets with David Quintero ’20 of Oxnard, Calif. (Phyllis Graber Jensen/�ֲ���ý College)

Over the course of two or three class sessions and the intervening homework, her students divide into groups and choose a specific country. They come up with questions that would indicate how democratic a country is: How are elections set up? How robust are individual rights, civil liberties, and media freedom? How effective are checks and balances? 

Once they’ve tried to answer those questions, they classify their country based on an existing measure, such as ; or the same organization’s scale of one to seven. 

Students quickly realize that measuring democracy, or even coming up with a good method, is as fraught as can be. 

“In the classroom you can’t teach everything, but you can teach students to become aware of what they don’t know.”

For example, what do analysts miss if they only read English-language sources? How would, say, an American scholar’s evaluation of Russia differ from a Russian’s? How do you figure out if a country’s constitution actually reflects what’s happening on the ground? What if the laws promise free and fair elections, but opposition party leaders are being jailed? 

“There was definitely real awareness of sources and bias, and some humility,” Pérez-Armendáriz says. “It’s nice to say, ‘Wow, I really need to be an expert.’ There’s even some question of, ‘When do you become an expert?’” 

Associate Professor of Politics Clarisa Pérez-Armendáriz says she’s noticed a fundamental change in how students define democracy. (Phyllis Graber Jensen/�ֲ���ý College)

It can take a professional analyst months or years, of course, to come up with and implement a democracy measure, whereas �ֲ���ý students only have a couple of days. Pérez-Armendáriz therefore grades the assignment primarily based on the quality of the questions students come up with and critiques of existing indicators, rather than the results they present. 

“In the classroom you can’t teach everything, but you can teach students to become aware of what they don’t know,” she says.  

Pérez-Armendáriz, who joined the �ֲ���ý faculty in 2009, has noticed a marked shift in how her students conceive of democracy, which she attributes to generational changes in students’ values.

“If you asked a student to put it concretely, 10 years ago they were more likely to say that democracy is a system of government where people choose their leaders through elections,” she says. 

“Today, they’re more likely to say, ‘Democracy is a governing system where people’s rights are protected.’ They talk a lot more about equality and outcome-oriented things as opposed to process-oriented things.” 

This perspective could have implications down the road, especially for a college whose mission statement promises “informed civic action” among its graduates. That’s why it’s important for students to think in the classroom about deceptively basic concepts like democracy, and to reflect on how those concepts impact their own lives. 

“If [the traditional definition of democracy] isn’t good enough for you, that’s okay,” Pérez-Armendáriz says. “Trust in yourself, and be really rigorous and critical.”  

Lesson: Sine curves and daylight  

Class: “Mathematics Across the Sciences” 

Professor: Meredith Greer, Associate Professor of Mathematics and Chair of the Program in Digital and Computational Studies 

It’s an eternal question for generations of math students: How am I going to use this in the real world? 

At �ֲ���ý, Meredith Greer answers that question with an entire course, “Mathematics Across the Sciences.” It’s designed for both students who want to major in the natural sciences and need a strong math foundation, and those who need to fill a general education requirement. 

Students spend the course applying mathematics principles to real-life examples: They illustrate exponential growth by studying bacteria populations, measure earthquakes with logarithms, and use straight line equations to calculate the speed of human recall. 

“It gives them a sense of all the ways math really is used,” says Greer, an associate professor of mathematics and chair of the Digital and Computational Studies program. “It’s not just a separate area of study alone, but it’s really relevant.” 

Greer has taught “Mathematics Across the Sciences” in both fall and winter semesters, but it’s during the fall when she sees a special opportunity to make trigonometry click. 

Toward the end of the semester, when temperatures are dropping and the sun sets depressingly close to 4 p.m., Greer explains trigonometric functions like sine and cosine. 

Then, over the course of a class session or two, she has students collect data on the number of minutes of daylight Lewiston receives on days throughout the year. They do the same for Miami, then plot the data for both cities in an Excel chart. 

The chart’s regularly occurring peaks (the highest amount of daylight a city gets in the summer) and valleys (the lowest in the winter) constitute a classic example of a sine curve, or oscillation.  

Two results stand out. First, Lewiston’s curves from summer to winter and winter to summer are steeper than Miami’s. In other words, it’s true that when it gets darker in the fall, it gets darker �ڲ����ٱ��.��

Now here’s the cool part. We all know that Lewiston hurts for daylight in the winter. The chart bears this out, showing lower valleys at the winter solstice for Lewiston (nearly nine hours of daylight) than for Miami (10.5 hours). In mathematical terms, the sine curve representing Lewiston has a greater amplitude.

The reverse is true in the summer: Lewiston’s peaks are higher than Miami’s; the northern city gets about 15.5 hours of daylight, compared to Miami’s nearly 14. 

“What a lot of folks haven’t thought through is that if you get to the summer, they peak at this much lower level, and we peak much higher,” Greer says. “We have a lot more daylight in the summer.” 

Why? It has to do with the tilt of the earth’s axis. The farther north or south you go, the more widely the amount of daylight varies. It’s why the poles have six-month alternating periods of daylight and dark. 

For students, Greer says, working with daylight data at the end of the semester is one of the more immediate examples of the ways math can explain the world around us. 

“A logarithmic function, a sine or cosine function, e^x, 2^x — they’re not just developed and done in math class and nowhere else,” she says. “They’re intrinsically related to nature. There’s a reason they were developed, and they mean something still.”