Fred Haise: I know why my numbers were wrong. I only figured it for two people.
Jack Swigert: Maybe I should just hold my breath.
-from the movie, “Apollo 13”

“We’ve made our Whole-Group Mini-Lesson on Fridays about problem solving. Word problems, especially multi-step ones, are really challenging for our students. Do you have any ideas that have worked for you?”

Maybe the inability to comprehend the text is what is standing in the way of of your students using their known math skills. If the student can’t comprehend what they’re reading, then they can’t complete the problem. Students need to make a “my-world-connection” to the concepts they’re studying, or there’s no place to “hook” the new knowledge in their brain. One of the ways of helping students make meaning out of word problems is to teach them to think about it as a story. I’ve posted a strategy for word problems which encouraged the use of a story map, give the problem characters, plot, setting, sequence of events, and a solution. [https://glennatabor.com/2010/08/word-problems-or-conceptual-connections/]

Many word problems infer the math skill or operation a student is to use. To help your students “read between the lines,” teach them the comprehension strategy of visualization.

What is visualization? I like the way Harvey and Goudvis describe it,

“Visualizing is like a movie in the mind. Visualizing brings joy to reading. When we visualize, we create pictures in our minds that belong to us and no one else….When we visualize, we create our own movies in our mind. We become attached to the characters we visualize. Visualizing personalizes reading, keeps us engaged, and often prevents us from abandoning a [text] prematurely.”

[from Harvey & Goudvis, from Strategies that Work, 2000, p. 97]

Why would visualizing help a student work a word problem? If the answer’s not written directly and clearly, then the student will have to use good comprehension skills to understand it. If a math teacher teaches students how to make a movie about the word problem in their head, then they can partner inferring with visualizing.

Again, I’ll let Harvey and Goudvis speak,

“Visualizing and inferring don’t occur in isolation. Strategies interweave. Inferring occurs at the intersection of questioning, connecting, and print. Visualizing strengthens our inferential thinking. When we visualize, we are in fact inferring, but with mental images rather than words or thoughts. Visualizing and inferring are first cousins, the offspring of connecting and questioning. Hand in hand, they enhance understanding.

[from Harvey & Goudvis, Strategies that Work, 2000, p. 96]

To teach students how to visualize word problems, I use the steps suggested by Wilhelm in Reading is Seeing:

1. Create mental images of observed concrete objects. Bring in interesting objects and have students handle, study, and carefully observe each object. Then have them close their eyes and imagine the most detailed version of the object that they can. Prompt them to describe the item to their classmates; other students can chime in with details they would add or change. Finally, have students open their eyes and compare their eyes and compare their mental pictures and descriptions with the actual object they were attempting to imagine, noting how their vision and the object are similar and different.
2. Create elaborate mental images of imagined concrete objects. Now ask students to visualize an absent concrete object with which they have previous experience. Next, use guided imagery prompts to have them create ever more detailed visions of this object. For example, you could ask students to imagine a car, then provide additional specific details to get students to refine their visualization. You might prompt them to see a red sports car, or a red Corvette.
3. Envision familiar objects and settings from their own experience. Next, prompt students to imagine familiar objects or scenes from home, such as the sugar jar in the kitchen, a clock, their bedroom, or a favorite place in their neighborhood.
4. Add familiar actions and events, then relationships and settings. Ask students to envision a familiar event or action, like a tea kettle whistling or to run a brief video clip they have seen back through their mind. Then ask them to build on an imagined object, such as the car described in step 2, by visualizing it in a driveway on a sunny day, then pulling out of the driveway, squealing its wheels as it peels out, and stopping at a stop sign. Visualization skills are extended when students describe the relationship of the object to other objects or characters or put the object in motion or in a situation. The more sophisticated they become at envisioning, the more their visions will move and involve these kinds of relationships.
5. Picture characters, settings, details, and events while listening to a story read or told aloud. Read aloud imagery-intense narrative and expository informational text (be sure to read both) about events, settings, processes, or ideas that are familiar to students so that they will have images from their recent experiences to draw on as a resource. Stop periodically to ask students to share their mental pictures; you might even ask them to identify what experiences they drew on to create their images.
6. Study text illustrations and use them to create internal images. Discuss text illustrations of all kinds with students as you read with them. Discuss how illustrations work in various ways to give readers a sense of setting or context, characters, concepts, mood, interactions, relationships, actions, events, and trends.
7. Create mental pictures independently. Prompt students to create mental pictures as they read on their own. It can be effective to invite students to create journal entries or drawings that respond to prompts provided at strategic points in the text.

[Reading is Seeing, Wilhelm, 2004]

After using narrative or expository texts for steps 5-7, go back and used math word problems. Use clips from movies which contain problem solving situations. Apollo 13 is a great one. The scene in which the scientists at NASA are given a bag of items and are asked to develop a way to get the square object to fit in the round hole is an excellent example of problem solving.

After watching the clip, discuss what the students saw and what math was involved. Then have everyone close their eyes and intricately describe the scene from the movie to a partner. After comparing their different mental pictures from the movie, read excerpts from the book, Apollo 13, Lost Moon, by Jim Lovell. Ask the students to create a movie in their head for each portion I’ve read.

After practicing visualizing using the book, then ask the students to work with their partner and write word problems using Apollo 13 as the context. The students practice visualizing, inferring, questioning, and connecting. Then they should practice using these comprehension strategies with word problems from their own math text. Post the the steps listed above to be used on a regular basis.

Try visualizing with your own students and SEE what happens the next time they encounter word problems!

“ Our mission was called “a successful failure,” in that we returned safely but never made it to the Moon. I sometimes catch myself looking up at the Moon, remembering the changes of fortune in our long voyage, thinking of the thousands of people who worked to bring the three of us home. I look up at the Moon and wonder, when will we be going back, and who will that be?” -Jim Lovell, from “Apollo 13”