Number Choice Matters
By Corey Drake,
posted May 8, 2017 —
the previous two posts on this blog, authors have written about the importance
of the context of word problems—focusing
specifically on the use of food as a context and representations of gender in word problems. In this post, I shift the
discussion to a focus on the mathematics of word problems and, specifically,
the numbers used in word problems.
often, we as teachers take the numbers in a word problem for granted and think
that one number choice will work just as well as another. But researchers and
practitioners alike (e.g, Carpenter et al. 2014; Land 2017; Land et al. 2014) have
found that is not the case—number choice matters for both the accessibility and
productivity of problems. Additionally, number choice can be used to meet
specific learning goals, differentiate instruction, and build relational
thinking (Land 2017) in each and every learner.
are four considerations for you to keep in mind when you are choosing numbers for
a word problem.
I often tell the teacher candidates with whom I work, there is no single right
or perfect number choice for a given problem. And, as Land and her colleagues
note, the best way to learn about how number choices work is to “try different
numbers and see what happens,” (2014, p. 8). Many resources are available to
help you do that, including those cited here. The more purposeful you can be in
your choices of numbers and contexts, the more you will be able to facilitate
productive engagement with mathematics for all your students.
Thomas P., Elizabeth Fennema, Megan Loef Franke, Linda Levi, and Susan B.
Empson. 2014. Children’s Mathematics:
Cognitively Guided Instruction. 2nd
Ed. Portsmouth, NH: Heinemann.
Common Core State Standards Initiative (CCSSI). 2010.
Common Core State Standards for Mathematics (CCSSM). Washington, DC: National
Governors Association Center for Best Practices and the Council of Chief State
School Officers. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf
Tonia J. 2017. “Teacher Attention to Number Choice in Problem Posing.” Journal of Mathematical Behavior 45
(March): 35–46. doi:10.1016/j.jmathb.2016.12.001
Tonia J., Corey Drake, Molly Sweeney, Natalie Franke, and Jennifer M. Johnson.
2014. Transforming the Task with Number
Choice, Grades K–3. Reston, VA:
National Council of Teachers of Mathematics.
Drake is an associate
professor of teacher education and Director of Teacher Preparation at Michigan
State University. She teaches elementary school mathematics methods courses,
and her research interests include teachers learning from and about curriculum
materials as well as the roles of policy, curriculum, and teacher preparation
in supporting teachers’ capacity to teach diverse groups of students.