They know the math but they can’t do word problems.
They can do all the problems on the page correctly, but they skip the word problems at the end.
It’s a reading comprehension problem. They don’t understand what they are reading.
The dreaded word problem. In many classes I taught, students weren’t used to being asked to read in math class and they certainly weren’t used to thinking about what they were supposed to do. Math was about following a set of procedures and getting the right answer. Math wasn’t about thinking about what types of calculations might help you make sense of a situation.
Early in my career, I fell into the trap of teaching them to circle the key words. That became a problem very quickly.
Then I tried teaching them Polya’s four step model: 1. Understand the problem 2. Make a plan 3. Carry out the plan 4. Look back
This didn’t help either. If students managed to understand the problem and explain it in their own words, they didn’t know how to make a plan.
What finally worked, particularly with my struggling students, was encouraging them to use pictures. At first, students created elaborate drawings of the situations that often focused on superficial aspects of the story. Then, I guided them to use simple diagrams to represent the story– diagrams that helped organize the information given and what was missing. I found that after a bit of practice, students were able to solve a variety of word problems, including complicated multi-step ones, with a picture.
Recently, I’ve been working with teachers and students on drawing diagrams to solve word problem and I figured it would make sense to go to the research and see if there was evidence that supported my experiences. It turns out there is.
The benefits of using diagrams for story problems include:
- Reducing the memory demands
- Assisting in unpacking the situation
- Helping identify important information
- Focusing students on the quantities involved in the situation and the relationships between them
- Flexibility Diagrams can be used across grade levels and for solving both routine and non-routine problems
It is important to mention that these studies don’t encourage the use of any pictorial representation, but rather ones that highlight the structure of the problem. Bar models or part-whole diagrams are some of the representations I’ve found successful.
I’ll talk more about these particular models later, but I’d love to know about your experience with word problems. What have you found to be successful?
Want to know more? Check out:
Diezmann, C., and L. English. (2001). Promoting the use of diagrams as tools for thinking. In A.A. Cuoco and F. R. Curcio (Eds.), The role of representation in school mathematics. Reston, VA: National Council of Teachers of Mathematics, 77-89.
Yancey, A. V., C. S. Thompson, and J. S. Yancey. (1989). Children must learn to draw diagrams. Arithmetic Teacher, 36 (7), 15–23.