Review of Reading Strategies for Solving Math Word Problems
Different content teachers use different types of strategies applicable to their specific content. There is no right or wrong strategy that a teacher has to use in their given content. Math is no different. An internet search of “teaching strategies” provides an abundance of suggestions. Nonetheless, this section will focus on research based strategies for solving math word problems. These are options that can be used in the unit and/or everyday teaching in the math classroom.
An article entitled Reading Coaching for Math Word Problems presents some meaningful strategies and viewpoints for reading comprehension in math word problems and the role of literacy/math coaches. The article is from The Literacy Coaching Clearinghouse, which is a website that “offers an array of policy and practice briefs and coaching tools for literacy coaches, teachers, administrators, and researchers”. In the article, the three authors Sharon A. Edwards, Robert W. Maloy, and Gordon Anderson draw from their collective experiences teaching and working on the elementary and collegiate level, as well as the computer science field. They used the fourth grade questions from the Massachusetts Comprehensive Assessment System (MCAS) test to identify seven specific word and math language comprehension challenges4. The seven strategies they discuss are as follow:
- Unfamiliar Vocabulary
- Proper Names
- Sentence Structure and Syntax
- Math Terminology
- Multiple Math Operations
- Words and Numbers
- Visual Displays of Information
The Seven Strategies
1: Unfamiliar Vocabulary
The authors discuss the challenges for students to solve math word problems because of unfamiliar vocabulary. They give examples of different words on the MCAS that students may not have experience with, such as “bow” and “depositing.” Obviously there are many more words that students are not familiar with on this state exam, as well as any other state exam across the country. This is a common problem shared with all math teachers regardless of their location. They use a word problem (below) from MCAS to provide some strategies.
Haley swam 22 laps each day for 18 days. Then she swam 25 laps each day for 10 days What was the total number of laps she swam over the 28 days?(Massachusetts Department of Education, 2006)
They suggest ignoring the words in the problems that are not familiar and those that are confusing to students. In the Haley question, a youngster can read the problem while ignoring the words swam and laps. The reader can learn to recognize that Haley did something 22 times each of 18 days and then 25 times each of 10 days. Multiplying 22 x 18 and 25 x 10 and then adding those two totals will produce a correct solution without the student needing to understand what it was that Haley did5.
2: Proper Names
The article states that there were 29 proper names in 39 questions. As a middle school teacher, I took the strategy of looking for proper names for granted in my classroom. Because I teach middle school students, I often assumed they would not get confused by proper names. However, this is very noteworthy point because those struggling readers on the middle school level may be on a third or fourth grade reading level. The strategy they suggest using is having students make the names familiar. Replacing the name in the word problem with its first letter, or with their own name or a more meaningful name, could help connect students to the problem.
3: Sentence Structure and Syntax
The article makes another valid point about the way in which tests and textbooks are written. Those texts “are written in compositional, not conversational English.” As such, they are not easy for some young readers to interpret. Consider the following problems:
Mr. Thomas walks every day. The distance that he walks each day is between 4 miles and 8 miles. Which of the following could be the total number of miles Mr. Thomas will walk in 30 days (Massachusetts Department of Education, 2006)
The article suggests using a strategy from a mathematician named George Polya for the aforementioned word problem. Polya created a four step approach to solve word problems. Polya’s book “How to Solve It” is a viable resource that identifies a four step method for problem solving: Understand the problem, Devise a plan, carry out the plan, and look back.
In Polya’s framework, a problem solver first understands what type of problem is being posed, then clarifies what is being asked for, investigates the problem to see what information is already given, formulates a plan for solving the problem, and checks the computational work for any missteps or errors before finalizing an answer6.
The article points out that Polya’s approach addresses math and reading strategies. They also state that the first three steps in Poyla’s approach/chart are very reading comprehension specific.
4: Math Terminology
The researchers state that math terminology “is a comprehension as well as decoding challenge.” This challenge is further complicated for students with disabilities who struggle with comprehension and decoding. Obviously the various “math terms” that represent the different four basic math operations (addition, subtraction, multiplication, and division) are complex for students. In addition, equations, inequalities, and expressions are also problematic for students. Another word problem the authors analyze from the MCAS is:
Last month, 3801 people ate at Tony’s Pizza. This month, 2765 people ate at Tony’s Pizza. How many more people ate at Tony’s Pizza last month than this month? (Massachusetts Department of Education, 2007)
The strategy they propose may seem obvious, which is to teach math vocabulary. The research proves their point. Their second strategy of having students “create their own informational placements and posters as memory guides to math terminologies and memory guides” can lend itself to more buy-in and ownership because the students are the one’s creating the “math vocab.”
“How many more” suggests adding to find a total, but “more” in the question above requires subtracting the smaller number from the larger to find the correct answer. I feel that understanding of issues like this is best achieved by class discussions involving reading and interpretation of word problems, and these discussions will be an important feature of my unit.
5: Multiple Math Operations
Word problems and math problems in general that require the use of multiple steps to solve can pose challenges. The authors refer back to the “Haley Swimming problem” to make their point and offer strategies for dealing with multiple math operations:
Haley swam 22 laps each day for 18 days. Then she swam 25 laps each day for 10 days what was the total number of laps she swam over the 28 days?(Massachusetts Department of Education, 2006)
As they point out, the mistake that many students will make is to add throughout the problem instead of multiplying then adding. The tendency for some students may be to add the 22 laps + 18 days + 25 laps + 10 days and believe the sum is their answer, as opposed to adding the two products from (22 x 18) and (25 x 10).
A possible strategy that is stated for this type of problem is to have students change the “context” of the problem, without changing the numbers. For example, they state that instead of “Haley” (or any person) swimming laps it could “Haley” shooting basketballs at a goal. The basketball fans in the class will relate to the idea of making 22 baskets for 18 days followed by making 25 baskets for 10 days more easily than swimming laps. In this way, those children will recognize that more than one math operation is needed to answer the problem7.
6: Words and Numbers
In math word problems that combine words and numbers, the article states that the blending of words and numbers is problematic. The following example is used to demonstrate the challenges:
Mr. Jordon is buying 3 CDs. Each CD costs $18.99 including tax. Which is the best estimate of the cost of the 3 CDs?” (Massachusetts Department of Education, 2001)
It is observed that the numbers 3 and $18.99 are embedded within sentences that appear straightforward, yet the two words including tax are easily missed8.
Their strategy for dealing with this is to have students “compose their own math word problems, math comics, and math stories as another way to understand how writers blend words and numbers together to pose questions9.
7: Visual Displays of Information
Even though a picture may be worth a thousand words visual displays may actually present challenges for students. To read and interpret charts, graphs, pictures, and other visual displays of information. These visual displays can be confusing even to adult readers (Tufte, 2001)10. The confusions, as the authors point out, can be from an inability to correctly interpret words and numbers not in a “normal” sentence, but spread throughout the visual graphic designs. The authors’ strategies are straightforward—design visual displays that have meaning and ownership to the students. By creating stimulating visual displays (charts, tables, graphs) that peak students’ interest and/or curiosity, it may lead to them discussing their displays with friends and family.
The article concludes with a very important point—“Math word problems have been a relatively understudied component of math and literacy learning (Powell, Fuchs, Fuchs, Cirino & Fletcher, 2009)11. I found this research helpful in designing certain aspects of this unit, and overall a great resource. I also applaud the recommendation of having literacy coaches use more math word problems to help address deficits in reading and math. Literacy coaches and teachers need wide-ranging strategies in order to support children as they improve their skills in reading and mathematics12. My experience with math coaches has been that they focus primarily on math procedures and computation aspects, and much less on the literacy aspects of math (e.g. comprehension, decoding, and fluency) in math word problems.
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