Reading Levels of Word Problems

I have been exploring word problems and how to use reading comprehension strategies in math class.  I have been looking at ways to address comprehension and the importance to explicit instruction in the understanding, usage and application of mathematical vocabulary.  I will discuss those areas in upcoming posts.  In this post, I would like to discuss reading levels of word problems.

Look at the problem below:

"On Monday your snail made a slime trail 2 inches long. On Tuesday the slime trail was 4 inches long. If this same progress continues, how long will the slime trail be on Friday?"

This task came from the K - 2 section from Exemplars.  When I informally surveyed a few teachers  most felt that this problem would fit into the 3 - 5 grade level span.  When you analyze the task for grade level readability you get the following results:

Generated using: http://www.online-utility.org/english/readability_test_and_improve.jsp

Looking at the "Gunning Fog" index we can say that the average child, who started school in Kindergarten, would have to be in 7th grade to easily understand the text on the first reading. The grade level ranges, according to the second set indexes, are from the middle of the 3rd grade to the first few months of the 9th grade.

So what about the students who are not on grade level or ELL students?  These students are what Phil Daro, one of the write of the Common Core State Standards for Mathematics, would call the, "canaries in the mineshaft."   They provide a spotlight on issues the "average" student is able to coverup, because he/she knows how to "do school" and get the right answers.  

Word problems can be overwhelming and require us to take the time to provide instructional support at the reading comprehension level to enable students to fully understand problem and mathematics in context.

One strategy that can be used is to understand the math story by Retelling, before looking at the question that is being asked.  Tell students to explain the story without the use of numbers.  For example, the problem cited above might be retold in the following manner:

"Some snails were sliding along leaving a trail of slime. Yuck!  They went a little way on Monday, then went a little farther on Tuesday."

Another strategy that can be used is Visualization.  In reading visualization involves taking a text line by line (sentence by sentence) or paragraph by paragraph and seeing and describing the picture that can be painted from the words.  This strategy is a precursor to making mathematical sketches.  When we visualize we see, hear, smell and feel the story as it unfolds.  We talk about what has to be present in the environment, and consequently we eliminate erroneous ideas about the context of the problem.  This is an activity that is best when done collaboratively.  

Citing the word problem above, we might see a snail.  This might lead into a conversation about what a snail looks likes and what slime looks like.  And for many students, this is a necessary step if they have never had the opportunity to observe a snail in action.  The visualization may lead to deciding if this snail was a pet in a container or free in the wild.  In this case, students might conclude that it is a pet snail, due to the fact that we had to see the same snail on Monday and Tuesday.

A word of caution...reciting or listing the events in a problem does not constitute comprehension.  A child can read a book and tell you the sequence of events, but it does not mean that they comprehend the story.  Understanding what is read is a complex task, but a doable task when students are provided the time, structure, opportunities to collaborate, appropriate scaffolds and tools to be successful.  

Below are some additional resources to help you think more this issue and how to help students understand word problems:

1. "Literacy in the Secondary Classroom" Presented by Lucy West, Susan Radley Brown, Howard Segan and Anne Burgunder
2. Phil Daro's video interview on "Against Answer-getting"
3. "Using Reading Strategies in Math" from Reading Recovery
4. From Reading to Math: How Best Practices in Literacy Can Make You a Better Math Teacher, Grades K-5
5. Comprehending Math: Adapting Reading Strategies to Teach Mathematics, K-6