By Susan Weaver Jones, Reading Specialist, Guest Blogger
What makes math story problems so hard for so many elementary students? Lengthwise, the story problems are considerably shorter than most of the text students are expected to read. Because of their brevity, the story problems are concise, even when they contain extra, irrelevant information.
In many cases, the vocabulary is manageable, especially when pictures accompany the text. In addition, the context in story problems provides real-world situations or scenarios that can be imagined. Despite those advantages, even one-step story problems can pose major comprehension difficulties for students. Why?
In my experience working with general education students and English Language Learners, the key issue seems to be the question. The question at the end of each story problem determines the relationship between the numbers in the problem. The question also informs the students which numbers are essential to solving the problem and which numbers are irrelevant.
Many of my students have been led astray by keywords within the question. The word more was the most misunderstood term my students encountered. They assumed they should add to get a bigger number if they read the word more in the question. They didn't realize the question of "How many more . . . ?" indicated a comparison between numbers, which meant they needed to subtract.
With few exceptions, my students could adequately decode the words in math story problems. Most could read the problems with fluency, but the majority couldn't comprehend what they were supposed to do. As a result, they usually guessed, and their guesses were often wrong. I endeavored to help my students think through one-step story problems and figure out the appropriate operations to use. To that end, I utilized reading and writing in several ways to make the problem-solving process clearer to them.
Sorts That Help Kids Answer Math Questions
To begin, I created simple, three-sentence story problems with similar wordings. With a few variations, the first sentence contained the first essential numeral, and the second sentence included the second essential numeral. The third sentence was the question, which indicated which operation to use.
Students sorted addition problems and subtraction problems, subtraction (take away) problems and subtraction (comparison) problems, and addition-only problems and repeated addition/multiplication problems. The sorts provided ample opportunities for discussion, modeling, and illustrating as the students worked through the problems with teacher guidance and discovered which problems depended on the same operations and why.
Manipulatives and Modeling to Practice Problem-Solving Skills
Because I sought to make the language of math more understandable, I focused on story problems using basic facts that could be modeled with counters and other small objects. If students could select the correct operations by working through problems with smaller numbers, they could then apply their learning to bigger numbers.
Oral Language Development Practice with Math Problems
After modeling sample problems for students, the students generated their own math story problems aloud, using the three-sentence structure. I often rolled two die or chose a domino to determine the numbers to be added or subtracted. The randomness of the numbers added interest for the students.
Benefits of Graphic Organizers
Students used T-charts to complete the sorting activities. Then, they used Venn diagrams to compare and contrast addition with subtraction, subtraction (take-away) with subtraction (comparison), and addition only with repeated addition and multiplication.
I also modified a Frayer Model graphic organizer to better support students' learning about math story problems. The four categories used to clarify each operation were description, keywords, examples, and pictures. Besides the individual graphic organizers the students completed, I created anchor charts of the same information for group reference.
I wrote several maze paragraphs, which students completed with words from word banks. The maze paragraphs served as summaries and reviews for the different operations.
Encourage Students to Write Their Own Story Problems
Finally, students wrote their own story problems, which were based on narrative texts they were reading at the time. As before, they talked through their story problems first before recording their three-sentence problems. After they recorded and solved their story problems (complete with equations), they illustrated their story problems.
Practicing Math and Fostering Creativity
My students enjoyed illustrating their original story problems, which focused on the details of the leveled books they read in class. However, their illustrations were based on several basic shapes used in the Frayer Models. The Frayer Model pictures included plane shapes, such as circles, squares, or triangles. For student-friendly information about plane shapes, check out Shapes All Around by Reagan Tunstall.
Deepening Understanding of Mathematical Operations
Depending on the grade level, my students worked with addition, subtraction (take-away and comparison), and/or multiplication. Eventually, they will also work with division and how it relates to subtraction and multiplication.
Telling Time (with increments of five) and Thermometers (with increments of two) are two nonfiction books for kids that could be helpful in looking at multiplication as repeated addition. Nonfiction text features in the books clearly show the units used, which could be useful references for students. Halves and Quarters could also assist with the concept of division and repeated subtraction.
Though the careful and close examination of mathematical story problems took some time, the results were worthwhile! At the conclusion of our extended math work, my students were much more successful in figuring out what they needed to do to solve one-step story problems and why.
Susan is an elementary educator from Orlando, Florida, who currently works as an ESL teacher in Knoxville, Tennessee. She has taught students in kindergarten through eighth grade as a Classroom Teacher, Reading Specialist, Reading Recovery Teacher, and Literacy Coach. She is also the author of several leveled readers in the Kaleidoscope Collection. If you like what you read here, be sure to read more by Susan on our blog.