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# MTMS Blog

### Bringing in the Real World

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.

1. 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.
2. 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.
3. 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?
4. 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.

 Some blogging friends and I have a monthly blog link up where we encourage people to link up with "Math in real life" examples! We are hoping it grows...Posted by: Meg_2 at 7/28/2014 2:20 PM

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