I have been writing
about how to use real-world contexts in the mathematics classroom. What are
some practical ways to do this? Let’s consider three examples that explore how
to integrate diversity, connect to students’ lives, and analyze social issues (three
reasons for teaching mathematics).

McCoy, Buckner,
and Munley describe how they used games from a diverse group of cultures to
introduce probability concepts. Each lesson started with students learning
about the game, “including the history and background.” Next, the students
played the games and then were introduced to a relevant probability concept.
The games and cultures could just be used as a superficial context, but if they
are explored in greater depth, perhaps as part of a social studies lesson, then
this form of mathematics could allow students to learn about other cultures. It
also shows these students how mathematics, when viewed from a game format, can
provide a new way of looking at and understanding something familiar.

Leonard and Guha
explore how they allowed students to take photos of their neighborhood that were
then used by students to write word problems, such as calculating the number of
light posts along the road or the age of a local church. Although some of these
problems might not qualify as “authentic” (based on my last
post), they have the potential to be more
engaging because they come from students’ environments and because the students
wrote them. This scenario also engages students in *posing* problems. The real world is
messy, and figuring out how to ask mathematical questions that provide insight
into these contexts is a central part of mathematical
modeling.

I
have also explored income inequality with prospective and practicing
teachers. I fill 20 Baggies™ with blocks, with each block representing $1,000 of
annual income. I set up the Baggies to mimic the distribution
of income in the United States. Everyone gets a Baggie (students can either
pair up or we can pretend if the class is much larger or smaller than 20), and we
line up from poorest to richest and break into quintiles (5 equal groups, so
that there are 4 Baggies in each group). If I have enough time, I take a
hands-off approach and allow the teachers to decide how to analyze the data.
This can be particularly powerful because it allows teachers to think about *how* to analyze the data, which is at
least as important as learning specific procedures (like calculating the mean
or creating bar graphs). If I have less time, I take a stronger lead and guide
the investigation in directions that are productive both mathematically and for
understanding the context. I ask questions like those below. The first two
questions introduce **mean** as a fair
share, and I make connections between the standard algorithm and equally
sharing the blocks. In my experience, this is a powerful way to introduce mean
and median because it is set in a context that teachers understand.

- If every household at
your table (quintile) made the same amount, how much would they make? Show how
you can determine this amount by using your blocks.
- If every household in
the class made the same amount, how much would they make? Explain how we could
find this amount by using the blocks.
- Compare the median
income with the mean income. Why are these numbers so different? Which do you
think is a better measure of “typical” in this context? Why?
- Create bar graphs and
circle graphs that show each quintile’s share of the total income in the United
States.

How have you integrated
real-world contexts into your mathematics teaching? Are there ideas from this
post that you are planning to use in your classroom?

Mathew Felton is an assistant
professor of mathematics education in the department of mathematics at the
University of Arizona and will be starting in the department of teacher education
at Ohio University this fall. He is a coauthor of *Connecting the NCTM Process Standards and the CCSSM Practices*. His
research focuses on supporting current and future teachers in connecting
mathematics to real-world contexts and on teachers’ views of issues of equity,
diversity, and social justice in mathematics education.