Consider the Context

  • Consider the Context

    By Maureen D. Neumann, posted April 10, 2017 —

    Problem-solving tasks are one way to motivate student learning and build a rich mathematical understanding. The context, culture, choices, and language used to create mathematical tasks can activate problem-solving strategies that enable students to make mathematical connections and learn mathematics (Carpenter et al. 2015; NCTM 2014; Schwartz 2013; Van de Walle, Karp, and Bay-Williams 2016). These next four blog posts will focus on different aspects of problem-solving tasks:

    • Using food as a context
    • Hidden cultural messages within tasks
    • Teachers’ choices about number and language while implementing mathematical tasks
    • Designing tasks that matter

    Let’s start by discussing the first on the list, food as a context. Food can be a helpful context for mathematical tasks because of the immediate relevance in our students’ lives. We use food to find fractional amounts (with brownies, cookies, pizzas, ice cream, etc.); to compare measurement amounts (using rice, cereal, soda, etc.); or to count or solve operation problems (by dividing a set of cupcakes, counting M&M’s®, etc.).

    Although food is a familiar context for solving mathematical problems and building conceptual understanding, here are two suggestions to consider:

    1. Be sensitive to the millions of people with food insecurity when using food as a manipulative, and
    2. Choose healthier food options rather than unhealthier ones when using food within the context of a word problem.

    Years ago when I was teaching middle school mathematics, during a professional development workshop, I shared that I had students use rice to learn that the volume of a cylinder is three times the volume of a cone with the same base and same height. A colleague pointed out that I was using someone’s food for the day as a plaything. Until that moment, I had never thought of it that way. I felt terrible, and it is a lesson I have never forgotten. Millions of children go hungry every day. Within the United States, the Department of Agriculture estimates that in 2015, 13.1 million children (20 percent) live in food-insecure households (USDA 2016). Using a small granular substance to compare volume amounts does provide a visual hands-on activity for students, but using food as a mathematical tool sends an unintended message that food can be wasted and ignores the personal plight of hungry children. Now I use birdseed that we feed to the birds after the activity is completed. If you do choose to use food as a manipulative, make sure it is something children can eat afterward.

    Many food-based word problems center around unhealthy snacks. For example, “Four children are sharing three candy bars. If the children share equally, how much can each child have?” With childhood obesity at an all time high in the United States (20 percent of school-age children are obese), we need to be mindful of the food we are promoting (CDC 2017). Consider using healthier alternatives, such as apples, oranges, or sandwiches, to share equally.

    In the end, we need to consider more closely the context in which mathematics is discussed and framed, particularly when it comes to food. The problems we choose to use as real-life examples say something about who we are and what we value.

    Your turn

    Instead of food, what authentic, real-world examples do you use as context for mathematical tasks? We want to hear from you. Post your ideas in the comments below or share your thoughts on Twitter @TCM_at_NCTM using #TCMtalk.

    Join us April 24, 2017, for the second blog post in this series, when we examine hidden cultural messages in word problems.

    References

    Carpenter, Thomas P., Elizabeth Fennema, Megan Loef Franke, Linda Levi, and Susan B. Empson. 2015. Children’s Mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann.

    Centers for Disease Control (CDC). 2017. “Healthy Schools: Childhood Obesity Facts.”
    Washington, DC: U.S. Department of Health and Human Services. Retrieved from https://www.cdc.gov/healthyschools/obesity/facts.htm

    Coleman-Jensen, Alisha, Matthew P. Rabbitt, Christian A. Gregory, and Anita Singh. Household Food Security in the United States in 2015, ERR-215, U.S. Department of Agriculture, Economic Research Service, September 2016. http://www.ers.usda.gov

    National Council of Teachers of Mathematics (NCTM). 2014. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.

    Schwartz, Sydney. 2013. Implementing the Common Core State Standards through Mathematical Problem Solving, Kindergarten–Grade 2. Reston, VA: National Council of Teachers of Mathematics.

    Van De Walle, John A., Karen A. Karp, and Jennifer M. Bay-Williams. 2016. Elementary and Middle School Mathematics: Teaching Developmentally. 9th ed. Boston, MA: Pearson.


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    Maureen D. Neumann, mneumann@uvm.edu, teaches mathematics education courses for preservice and in-service teachers at the University of Vermont–Burlington. She is interested in helping teachers understand issues of equity when teaching mathematics.

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