Mathematics

Problems Solving Part 1: More than Key Words

by Bob Shields

Countless well-intentioned teachers of mathematics instruct their students to find and circle the key words in a word problem. We look for the words sum, join, altogether, difference, or possibly phrases such as ‘in all’ or ‘twice as many’ to guide us to the operation that we will choose to use. While this plan of attack will sometimes work in the larger mathematical world in which we live, this situational rule will not always hold true. Consider the following:

EXAMPLE: Kelly made $42 and Mary made $37. How much money did they make IN ALL? COUNTER EXAMPLE: Kelly and Mary made $79 IN ALL. If Kelly made $42, how much money did Mary make?
OR
EXAMPLE: Bill had 9 cookies. His sister TOOK AWAY 4 cookies. How many cookies does Bill have now? COUNTER EXAMPLE: Bill had a bag of cookies and his sister TOOK AWAY 4 of them. Now Bill has 5 cookies. How many cookies did he start out with in his bag?

In these examples, we can see that training our students to find key words that are directly tied to specific operations is problematic and leads to neither the correct answer, nor an understanding of the structure of the mathematical problem. “In all” does not always indicate addition, similarly, “twice as many” does not always indicate that we should find the number closest to the key word/phrase, and multiply it by two. This strategy is void of having student understand the question being asked and consider the structure of the problem being posed. By training our students to use keywords to decide the operation, we are instilling temporary rules that are not mathematically valid.

Instead of emphasizing Key Words, you can teach students self-regulation strategies that will help them decode word problems. One of these strategies is the use of mnemonics. There are a variety of mnemonics that can be used, one of them being UPS Check.

Understand – Read carefully, identify the question
Plan – Record the necessary information, draw a picture or diagram, choose a strategy or tool
Solve – Write an appropriate equation, use your plan to solve, label with units
Check – Check your math, ensure you answered the identified question, and your answer is reasonable.

Other possible mnemonics are RIDGES, RICE or STARS.
Read the problem Read and Record the problem Stop and read the problem carefully
I know statement Illustrate your thinking Think about your plan and the strategy to use
Draw a picture Compute Act – follow your plan and solve
Goal statement Explain your thinking Review your work and check your answer
Equation development
Solve the equation

In the interest of continuity for all of the mathematical learners in your building and district, it is best practice to have an agreed upon and consistently used mnemonic across all grade levels. Common language helps students transition between previously learned content and new content presented in subsequent grades and mathematics courses.
The PaTTAN Mathematics Initiative does training on this and additional content regarding supports for all students struggling in mathematics. Check the PaTTAN training calendar for available trainings.

Resources:
Dr. Paul Riccomini has presentations archived on the PaTTAN website and co-authored Chapter 3 Developing Mathematical Problem Solving through Strategic Instruction: Much More Than a Keyword as part of the Book Series: Advances in Learning and Behavioral Disabilities.
Dr. Sarah Powell at www.sarahpowellphd.com has resources and presentations on Evidence-Based Practices Related to Problem Solving

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