An illustration: Math 120 - Mathematics & Liberal Arts

Students in the general education quantitative reasoning courses I teach frequently remark on how so much of what happens in our class is connected to their other classes and their lives. One example of how critical thinking, informed by regular classroom connections to social justice, manifests itself in my mathematics students' work can be seen in their exam responses to the following problem (from a 100 point midterm exam):

The overall Consumer Price Index (CPI) in September 2002 was 185.1 and the CPI for September 2004 was 189.7. Meanwhile, the Health Care CPI for September 2002 was 308.6 and for September 2004 it was 324.0. (Source: www.bls.gov/news.release/cpi.nr0.htm).

(a) What was the overall rate of inflation from September 2002 to September 2004? (3 points).

(b) What was the rate of inflation for Health Care from September 2002 to September 2004? (3 points).

(c) Compare the rate of inflation for Health Care to the overall rate of inflation. Please write using complete sentences (6 points).

Students in other classes will answer such a question as follows:

a. 2.5%                 b. 5%                 c. Health care is double the rate of inflation.

Though my students write more than this (they will write all three responses using complete sentences) about half give similar answers. The question is mildly non-routine for my students. The class does not discuss what a Health Care CPI might be, though a brief discussion of it appears in their textbook [Bennett & Briggs, 2005]. The other half of my students give sense-making answers that frequently connect to larger mathematical or social ideas. Examples from a few students in Fall 2004:

a. The rate of inflation between September 2002 and September 2004 was about 2.5%.
b. The rate of inflation for health care between 2002 and 2004 was about 5%.
c. Since the health care inflation rate was double the overall rate (and assuming health care is part of the CPI), there must be other things that had much lower rates of inflation to balance the large increase in health care costs.

a. The overall rate of inflation from 2002 to 2004 was approximately 2.5%.
b. The rate of inflation for health care from 2002 to 2004 was approximately 5%.
c. The fact that the cost of health care rose at twice the rate of inflation means that medical care will take a larger portion of a family's income than other goods and services.

a. The overall rate of inflation over those two years was about 2.5%.
b. The rate of inflation for health care from 2002 to 2004 was about 5%.
c. Health care during those years cost more than twice what it should have, so people with lower incomes who might get a 2.5% cost of living raise would not get enough of a raise to afford the same quality of health care they could in 2001.

In addition to giving mathematically and/or socially aware responses to the question in part (c), the students' answers to (a) and (b) reflect the discussions in class about when it is appropriate to use the word ``equals'' in a mathematically laden context, and when ``approximately'' (or ``about'') are more accurate choices.

More information about this class, which I have taught nine times since coming to UNC, can be found online through my web site (see http://hopper.unco.edu/hauk ). There are links for several versions of the course, including a late-start 10-week format in Fall 2006. Links from the Math 120 - Math and Liberal Arts course web pages go to copies of the syllabus, course outline, project assignments, exams, and information for Supplemental Instruction (begun in Fall 2005).