“Children need models more than they need critics.” -Joseph Joubert

It’s the beginning of a new school year. The students are ready to begin working on one of the most exciting mathematical concepts they’ll encounter this year…drum roll, please…WORD PROBLEMS! And, another drum roll, please…as your grade level increases, so do the number of steps in the word problems.

How do I teach word problems? How do I help my students complete word problems correctly? How do I get my students to try to solve word problems? These are common questions asked by teachers at all grade levels. I’m going to describe the most effective tool I’ve ever used for helping students understand and successfully solve word problems, but I have to give you some background information first.

For me, the challenge of teaching word problems really began back when I was in the 4th grade. My teacher asked the class to complete some word problems about Mr. Smith, Mr. Jones, and their driving. You know the problem:

“Mr. Smith drives from Smithville to Jonestown going 50 miles per hour. Mr. Jones drives from Jonestown to Smithville going 45 miles per hour. If the Smithville and Jonestown are 150 miles apart, when will the two cars intersect on the highway?”

As soon as I read that problem my 9-year-old brain began to think all kinds of things. Unfortunately, none of the things I was thinking had to do with solving the math problems. Here’s what I was thinking,

“I simply DON’T care when Mr. Smith and Mr. Jones get in their cars. I don’t care how fast they drive. And, I don’t care when their cars cross paths.”

I can’t remember any teacher, any textbook, or any situation making story problems engaging enough for me to want to work the problem. I was probably an overachiever type and worked the problem anyway so that I made a good grade. But most of the students with whom I have worked over the last two decades aren’t overachievers. However, these students will need to solve word problems for the rest of their lives so it’s my job to help them. More importantly, it’s my job to figure out how to excite them and engage them in the solving of word problems.

HOW DO I ENGAGE THE STUDENTS IN A MEANINGFUL, PURPOSEFUL WAY SO THAT THE TASK BECOMES ITS OWN REWARD?

When I taught 4th grade and my students were encountering word problems similar to one about Mr. Smith and Mr. Jones I approached it in such a way that my students couldn’t wait to solve more problems like it. Here’s how I did it.

First of all, I thought about the comprehension strategies I had been using in our balanced literacy block. [For more about these, read Harvey & Goudvis book, ”Strategies That Work.”] One of the key strategies for comprehending what you read is to have a text-to-self connection. If a learner can “connect” to what he is reading, then he’s more likely to comprehend and understand what he’s read. If this works for literacy, then it’s certainly going to work for mathematical word problems since the problem is one that is read. (I hope there are a lot of light bulbs going off in teachers’ heads right now as you’re making the connection from literacy to math.)

Part of the challenge of the Smith/Jones problem is that my students weren’t connecting to it. They aren’t car drivers and most of them are playing hand-held video games or listening to MP3 players, not calculating the times that their vehicle is crossing another vehicle’s path.

To help my students make this connection to the word problems I had to create a simulation. We went out into the newly waxed hallway and marked off 100 feet. To make everything as consistent as possible, we used the same car at each end and the same type of launch pad or ramp. There were student/police detectives all along the route of the two cars. The detectives were to determine where the two cars intersected paths and report this to the rest of the class.

The students took turns launching the cars, gathering data of the intersection of the cars, measuring the exact distances, and hypothesizing about the velocity of the model cars. The most exciting portion of our experiment was when the two cars not only intersected, but crashed into each other. The students LOVED it!

If you’re a science and math teacher, then you’re already seeing the connection from literacy to math to science. Interdisciplinary problem solving is real-world problem solving. The world doesn’t hand you a challenge and tell you to calculate the math in it and then hand it off to someone else to read it and then someone else to do the experimenting and finally to someone to spell the words correctly. (My speech about spelling lists that have no connection attached to them will have to be shared another day.)

This learning experience may seem like “fluff” to some people or like too much “play” to others. It is basing your students’ educational experiences on what is important to them. It’s the essence of how the brain learns. Educators such as Steven Webb, superintendent of Vancouver Public Schools, assert that play is essential. In his article, “Educating Children in the New Millennium: Child’s Play,” Steven says,

“…our daughter is constructing mental “maps” based on her experiences. Jean Piaget, the child psychologist, described this early-childhood development stage as “pre-operational.” He theorized that a child’s mental models, or cognitive structures, are based on the child’s activities; engagement makes meaning. Free, unstructured play is healthy and, in fact, essential for helping children reach important social, emotional, and cognitive developmental milestones. Piaget’s theory is based on the idea that the developing child builds cognitive structures known as mental maps or schemes for understanding and responding to physical experiences.

What is known as constructivism postulates that by reflecting on our experiences, we develop our own understanding of the world. Each of us generates our own mental models to make sense of our experiences. Learning, therefore, is the process of adjusting our mental models to accommodate new experiences. Constructivist teaching focuses on creating experiential and engaging activities for students, such as participating in a science fair. This kind of learning also involves an element of play.

Imagine what is possible when a community focuses its development efforts on attracting the creative class and building the creative economy.”

After cultivating the curiosity in my students, arranging time for them to “play” with the mathematical concepts, and helping them gather the data needed to solve the problem, we went to a story map to help us understand what we were trying to solve. In our small-group guided reading instruction we had already used a story map for the story of Goldilocks and the three bears [Goldilocks & the Three Bears: An Analyzing Perspectives Task]. We read several different versions of the story and created a story map for each. We also made a Venn Diagram comparison of our favorite versions [Venn Diagram with Characteristics]. Now we were about the use all those effective strategies to help us solve our story problem.

Together, we completed the Story Problem Map for one of the story problems for which we had already participated in a scenario with our model cars. I was amazed, but not surprised that the students were able to complete the story map and talk about the essential portions of the word problem. The problem wasn’t abstract anymore. The students were ENGAGED, CONNECTED, and ready to SOLVE!

Every time I have used the Story Problem Map I have had incredible success—especially if I have helped the students make a connection to the story problem. Let me know how it works for you.

“There are children playing in the street who could solve some of my top problems in physics, because they have modes of sensory perception that I lost long ago.” -J. Robert Oppenheimer