August 2013: Improving Reading to Improve Math

​​Glenberg, A., Willford, J., Gibson, B., Goldberg, A., & Zhu, X. (2012). Improving reading to improve math. Scientific Studies of Reading, 16, 316–340.

Summary by Dr. Marcia Barnes

Reading is an important medium through which learning across many subjects is acquired. In order to “read to learn,” the reader must understand what the words and sentences of a text mean and apply their understanding to the task at hand. In the study reviewed here, Glenberg and his colleagues applied their Moved by Reading intervention, a general reading comprehension strategy, to solving math word problems.

The Moved by Reading approach helps children make sense of what they read. The idea is that comprehension arises from mapping words and phrases onto our real-world experiences and that to understand text, skilled comprehenders create integrated mental simulations of what words and sentences stand for in the real world.

The intervention was first used to encourage beginning readers to treat reading as an opportunity for understanding, rather than as a decoding exercise. In this earlier study (Glenberg, Gutierrez, Levin, Japuntich, & Kaschak, 2004), children were first taught to move figures and objects to capture the meaning of what they were reading; this phase is called physical manipulation (PM). Then, students were taught to mentally simulate, or imagine, doing the same actions while they read; this phase is called imagined manipulation (IM). For example, a child is given a printed sentence, such as: “The horse jumped over the fence and ran behind the barn.” In the PM phase, the child manipulates toy objects while reading—first jumping a horse over a fence and then moving the horse behind a barn. In the IM phase, the child imagines the same events while reading. Children who participated in the Moved by Reading intervention remembered more and better understood texts than children who simply reread the sentences.

Although other interventions include imagery, an important component of the Moved by Reading approach is the focus on real movement by the reader in the PM phase and then similar imagined movement in the IM phase. This approach can be contrasted with static imagery and “imagined moving picture” methods, which do not involve actual movement on the part of the reader.

Applying the Moved by Reading Approach to Math Word Problems

The authors asked whether this general comprehension strategy might be helpful for understanding text in areas other than English language arts, such as mathematics. It has been observed that children often suspend story “sense-making” while solving math word problems. Quite often, children come up with answers that make no sense, given the situation the word problem describes. Specifically, the researchers asked whether the Moved by Reading approach would help children make sense of math story problems by helping children focus on relevant numerical information and ignore irrelevant information.

The study used 97 third- and fourth-graders and approximately equal numbers of boys and girls. More than half of the children were Hispanic, about a quarter were African American, 16% were White, 8% were Native American, and 2% were Asian American. This study used both PM and IM, but the PM component was computerized, so that children used a mouse to move objects on the right side of the screen as they read the story problems, one sentence at a time, on the left side of the screen. For children in the intervention group, a green dot after a sentence was the cue to manipulate the pictures on the right side of the screen. During the IM component, only the word problem text was displayed, and students were instructed to imagine pressing the buttons and using the mouse to move the objects on the screen. Children in the comparison condition (those who did not receive the intervention) were told that the green dots indicated important sentences, to which they should pay attention.

The study took place over 3 days. For the intervention group, the first day included instructions in PM, using the computer while reading. In this first session, four stories from two different scenarios (one about a about boy and his uncle and the other about a humanoid robot called ASIMO) were read and terminology such as telekinesis and levitate was explained. The intervention children were instructed on how to use the computer to move objects according to what the text said—for example, using the cursor to drag and drop objects. When a picture was correctly placed, the next sentence to be read appeared on the computer screen. Only sentences with green dots after them needed to be manipulated in this way. On day 1, students answered questions about what they read but did not have to solve the math story problems.

On day 2, the intervention students were instructed in how to imagine (IM) using the mouse to drag and drop pictures for the sentences with the green dots. They then read four new stories, using PM instructions for two and using IM instructions for the other two. On day 2, instead of answering comprehension questions, students were asked to answer the math question at the end of the story and to show their work on a worksheet.

On day 3, the intervention group was reminded of the IM strategy and given four new story problems to solve. The children in the comparison group were given the same stories, but without any instructions about PM and IM. Although students were told that the sentences with a green dot were important, they did not manipulate any pictures on the computer screen. Students also got the same comprehension questions as on day 1 and answered the same math questions on days 2 and 3, showing all of their work. An example of a story problem adapted from Glenberg and colleagues is presented below.

Uncle Robert is not good at putting dishes away after they are washed. He often does not put his clean dishes away in the cupboard.
His nephew John will help him put the dishes in the cupboard.
Using his telekinesis, John first put 10 dinner plates on the top shelf of the cupboard. 
He then moves 14 salad plates onto the bottom shelf. 
Finally, he moves 7 dessert plates onto the second shelf. 
8 of the dishes are white.
How many dishes are now in the cupboard?
Show all your work.

Study Findings

The answers to the story problems from days 2 and 3 were compared across groups. Correct solutions were investigated, as were algorithms that were correct but that included an error in arithmetic. The inclusion of irrelevant number information from the word problem (e.g., the number 8 from the problem above) was also recorded. Children in the Moved by Reading condition correctly solved more problems and used more correct arithmetic procedures, even if they made an error in adding or subtracting. Their problem solutions also contained less irrelevant number information; children in the comparison condition included irrelevant number information in their solutions 59% of the time, compared to about 39% of the time for children in the intervention condition. Effect sizes were moderate, which is of interest, given that the “training,” or intervention, took place in only a few sessions.

The researchers interpreted their findings as suggesting that their intervention helps children to make sense of math word problems by anchoring those problems in the real world, rather than relying on more abstract words and numbers with no reference to what they apply. In other words, the intervention seems to ground mathematical symbols in real-world experience. The researchers consider Moved by Reading to be a fundamental comprehension strategy that could be applied across a variety of academic content domains and text genres. They note that there was nothing specifically mathematical about the instructions, and yet students’ math problem solving improved.

Conclusions and Caveats

  1. Although the findings show some promise for improving math word problem solving, this study is the first to use the Moved by Reading approach, and relatively few children were studied. This approach requires further research and replication before making definitive statements about its usability and effectiveness in improving children’s ability to solve math word problems.  
  2. This approach should be seen as a supplement to best instructional practices in teaching math word problem solving. That is, the approach is not meant to replace skills-specific instruction in math word problem solving, but in combination with skills-specific instruction, the strategy might provide additional benefit.  
  3. Although the authors report some promising findings for math story problem solving, the long-term benefits of this approach are unknown. In other words, would the effects hold true for solving math word problems that children encounter in class, their textbooks, and on high-stakes testing?  
  4. Future studies might specifically investigate for whom and when this type of instruction would be most helpful—for example, for English language learners, children with mild versus significant difficulties in reading comprehension and mathematics, and children in early elementary school versus secondary students who have struggled for many years with math word problem solving.

In conclusion, this general reading comprehension strategy, which uses physical and imagined manipulation, shows some promise for supplementing and enriching current instruction in math word problem solving. However, the findings are preliminary and require replication and extension.


Glenberg, A. M., Gutierrez, T., Levin, J. R., Japuntich, S., & Kaschak, M. P. (2004). Activity and imagined activity can enhance young children’s reading comprehension. Journal of Educational Psychology, 96, 424–436.