Teaching Mathematics in Rich, Complex, and Realistic Contexts: Part 1
Making the Case
Let’s admit it, we math instructors can be a bit touchy about defending the importance of our field. We are quick to bristle when people tell us they never use math. One of my standard replies is, “You use math all the time. You just don’t know you’re doing it.” Those of us who like math, are fond of explaining that just because you aren’t doing tasks that look like they came out of an algebra textbook, it doesn’t mean that you aren’t thinking mathematically.
So now I want to turn that around and challenge the math instructors out there: What are your examples of the ways in which people use mathematical thinking in their daily lives? Let’s think of some common examples not associated with specific jobs.
- Making decisions about financial information such as weighing different loan options, choosing investments, or planning for a large purchase or retirement.
- Interpreting and evaluating a product or idea based on quantitative information presented in advertisements, news stories, political arguments, etc.
- Making an argument based on statistics summarizing the results of a study or a poll.
This list presents a problem for math instructors. In all of these examples, the mathematics is deeply embedded in complex context, which is mostly communicated through text. Even when quantitative information is presented graphically, the graphs contain text that has to be interpreted. Most math instructors love, and are most comfortable teaching, math in its “purist” form—abstract symbols stripped of context. After all, this is an essential and critical characteristic of the nature of mathematics: It is abstract and generalizable; it transcends context.
But the nature of pure mathematics is at odds with how math is used most commonly. Most people not only prefer mathematics in context; they have a desperate need to learn to use math in context. You might be wondering what the big deal is. We have included “application” problems in our math courses for years. Indeed, we have textbooks full of short, artificially simple, contrived problems. They are carefully constructed to be clear and not lead to any misinterpretation—in other words, the exact opposite of how information in the real world is often presented. And because of this, they fail to develop the critical thinking skills that are necessary for the kinds of tasks listed above.
There are a number of reasons we have generally avoided teaching mathematics in rich, complex, and realistic contexts. One reason is that these contexts are “messy.” The quantitative information is presented in poorly written articles, graphics meant to be eye-catching rather than informative, or in advertisements deliberately designed to mislead. This requires that we help students develop literacy skills so they can interpret, evaluate, use, and communicate about quantitative information in authentic situations. Generally, math instructors have been reluctant to do this.
This is not to say that math instruction has completely ignored integration of reading and writing. “Writing across the curriculum” is a widely used model that has led to practices like math journals and writing explanations for problem solving strategies. These are excellent learning activities that support problem solving, deepen understanding, and help students retain learning. Yet these practices typically do not help students develop skills to use quantitative information and mathematical thinking in complex and realistic contexts.
Here are a few examples of authentic tasks that are often surprisingly difficult both in terms of understanding the context and exploring the mathematical concepts.
Using a credit card disclosure form to explain how monthly payments are calculated and how the interest rates are affected by credit scores.
Using information in a prescription drug advertisement to make a health care decision.
Forming an argument for or against a local bond issue based on information from news articles and campaign materials.
Almost everyone agrees these types of literacy skills are important. The point of contention is how these skills should be taught and by whom. Math faculty often say, “I’m not trained to teach reading or writing.” This is a valid concern. In this age of self-proclaimed experts, it is good to know that there are people who respect the need for education and training. But the question remains, if we do not fill the need, who will?
One response might be that these skills should be taught in reading and writing courses. We have a problem there as well. Language arts instructors often feel equally unprepared to tackle text with quantitative information. The result is that these skills fall into a no-man’s land between disciplines.
A second common concern is that many students in entry-level college mathematics courses have poor reading and writing skills. This often leads to the conclusion that it is not possible to integrate complex context into lower level mathematics courses.
Some colleges choose another strategy: Restrict the math courses to students with higher reading skills. This, in effect, delays or denies access to the population of students with the greatest need to complete their math courses in a timely fashion.
We abdicate our responsibility when we deny students the opportunity to develop these critical skills by artificially lowering the complexity of the material or by denying access. This has real consequences. As noted in the sidebar, these students are usually from populations that most need strong quantitative literacy and reasoning skills.
There is another option. We can meet the students where they are and help them develop skills over time. Our students can rise to this challenge if we give them the right support. Next week in part 2 of this series, we will discuss strategies for delivering that support. In the meantime, please share your own ideas about how you have integrated complex contexts and/or literacy skills into your mathematics courses.
About the Author
Amy Getz is the Strategic Implementation Lead for the Higher Education Team at the Charles A. Dana Center. Her work focuses on the reform of developmental and gateway mathematics programs at community colleges and four-year institutions through working with state and regional systems. Amy led the team that developed and implemented the New Mathways Project in Texas and is currently leading work to expand the NMP to new states. Amy also led the development of the Quantway™ curriculum in partnership with the Carnegie Foundation for the Advancement of Teaching. Before joining the Dana Center, she taught mathematics for 20 years in high school and college. As the founding director of the Freshman Mathematics Program at Fort Lewis College in Durango, Colorado, Amy taught developmental and freshman-level math and led curriculum redesign that resulted in significant improvements in student success in both developmental and college-level math courses. She also led initiatives to provide professional learning services to K–12 math educators.