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Supervising High-Quality Math Instruction
By Cathy Buyrn, M.Ed.
Click image to go to the
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Word Problems? No Problem!
A Conversation With Dr. Sarah Powell
By Cami Williams, M.Ed. and LaShauna Britt, M.Ed.
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Problem #1:
A store had a total of 6,721 customers on Friday, Saturday, and Sunday. This store had exactly:
- 2,704 customers on Saturday
- 288 more customers on Sunday than on Saturday
Exactly how many customers did the store have on Friday?
Taken from 2019 4th-grade SOL released test (SOL 4.4d)
(Virginia Department of Education, n.d.)
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Problem #2:
Jeremy ran 1.4 miles each day for eight days. Amelia ran 2.1 miles each day for eight days. What is the difference in the total distance Amelia and Jeremy ran in these eight days?
Taken from 2019 5th-grade SOL released test (SOL 5.5b)
(Virginia Department of Education, n.d.)
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Consider Problems #1 and #2. First, think of strategies you would use to teach your students how to solve these or similar problems for their grade level. Next, ask yourself the following questions:
- Would I start by telling students that we will be working on a particular operation that day (e.g., “We will be working on addition and subtraction problems today.”)?
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Would I have students link key words to specific operations (e.g., total and more means add, each means multiply, difference means subtract)?
Now think about mistakes you anticipate your students might make when trying to solve one or both of these problems. In Problem #1, would they subtract 2,704 and 288 from 6,721? In Problem #2, would they subtract 1.4 from 2.1? Finally, have you found a method that works effectively when instructing students on how to reason through various word problems they are faced with throughout their math experience?
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Many educators teach students how to recognize key words in a word problem, to identify mathematical operations that should be applied for the solution, and to group problems based on an operation. However, this method of teaching “… discourages mathematical reasoning and frequently produces incorrect answers” (Powell & Fuchs, p. 31).
Schema-based math instruction can be a more effective approach to helping all students (including students who struggle with math) learn how to reason and solve word problems. Dr. Sarah Powell, an associate professor in the Department of Special Education at the University of Texas at Austin, is a highly respected educator who has conducted extensive research on schema-based problem-solving. In the video linked below, she shares why schemas work, what this instructional approach should look like in elementary and middle school classrooms, and effective strategies for successful implementation.
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Shifting to instruction that teaches a schema-based method for solving word problems takes time, practice and, most important, preparation. Although more than half of the school year is behind us, it is not too late to introduce schema-based instruction to students. As Dr. Powell notes in the video, first it is important to select an attack strategy. Not sure, which one to choose? Dr. Powell explains several attack strategies in the video Word-Problem Instruction: Attack Strategies.
Attack strategies can be introduced at any time. The key to successful implementation of an attack strategy is proper modeling and consistency of use. Model the use of the attack strategy with each lesson – after all, it is an approach for solving problems, not just word problems. If that seems overwhelming, try using the attack strategy as a way to structure intervention for a smaller group of students who need remediation.
Dr. Powell further recommends that one attack strategy be used across grade levels, or even an entire school, so that students get layers of exposure and consistent, prolonged experience reasoning through problems using it. Before choosing an attack strategy, discuss this idea with your department.
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Resources
For more support with implementing schema-based instruction for problem-solving, please visit the following resources:
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Guide from the Virginia Department of Education, Section V, dedicated to problem-solving strategies, including guidance on schema instruction. |
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The VDOE provides essential characteristics of problem-solving strategies that teachers are encouraged to use when instructing students with disabilities to solve word problems. |
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VDOE-sponsored resource that includes problem solving with schema instruction as well as examples. |
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Three research-based instructional strategies for intervention with fact fluency, problem solving, and motivation. |
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Teacher materials for use in individual and small-group word-problem intervention. |
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Evidence-based mathematics resources for educators. |
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Recorded sessions sponsored by TTAC William & Mary on schema-based problem solving for the elementary grades by Dr. Stephanie Morano, assistant professor of Special Education at the University of Virginia, and for middle grades by Dr. Sarah Powell. |
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Powell, S. R., & Fuchs, L. S. (2018). Effective word-problem instruction: Using schemas to facilitate mathematics. Teaching Exceptional Children, 51(1), 31-42. https://doi.org/101177/0040059918777250
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