By
Maureen
D. Neumann, posted April 10, 2017 —
Problemsolving
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 problemsolving strategies that enable students to make mathematical
connections and learn mathematics (Carpenter et al. 2015; NCTM 2014; Schwartz
2013; Van de Walle, Karp, and BayWilliams 2016). These next four blog posts will
focus on different aspects of problemsolving 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:

Be sensitive to the millions of people with food
insecurity when using food as a manipulative, and
 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
foodinsecure households (USDA 2016). Using a small granular substance to compare
volume amounts does provide a visual handson 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
foodbased 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 schoolage 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 reallife examples say something about who we are and what we value.
Your turn
Instead of
food, what authentic, realworld 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
ColemanJensen, Alisha, Matthew P. Rabbitt, Christian
A. Gregory, and Anita Singh. Household
Food Security in the United States in 2015, ERR215, 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. BayWilliams. 2016. Elementary and Middle
School Mathematics: Teaching Developmentally. 9th ed. Boston, MA: Pearson.
Maureen D. Neumann, mneumann@uvm.edu, teaches mathematics education courses for preservice and
inservice teachers at the University of Vermont–Burlington. She is interested
in helping teachers understand issues of equity when teaching mathematics.