A few years ago, my students tanked a word problem situations assessment. When talking with my principal at the time, he said, “If we improve students’ reading abilities, then their word problem understanding will improve also.”
Intrigued by this thought, I looked at the scores on this assessment focusing on at level readers. The assumption is that if students struggle to read, then they will struggle with word problems as well. Before I tell you what the data showed, let’s take a little quiz:
Guess what the data actually showed? Of the students that were at level readers, only 3 of them passed the assessment. 70% of my at level readers had failed the test. So the claim that if we focus on improving reading in order to increase math scores was false from my own personal experience.
What was the problem then? If students could solve the same types of problems when presented to them from a procedural standpoint, but failed when the same type of operation was required in a word problem situation, the issue was related to the way I was teaching word problems in the first place, not reading comprehension.
How do we teach word problem situations?
My first year teaching, I remember sitting in another teacher’s classroom during a professional development.
Hanging on the wall was a set of steps for solving word problems. At the time, I thought this was a novel idea, so I snapped a picture so that I could make my own version of it in my classroom. I made it and used it for a few years. Let me tell you right now, word problem situation success DID NOT improve.
Being in the classroom for over 10 years, and being an avid user of Pinterest and Instagram, I found that this model, known as CUBES, was not novel.
The idea is that we want to make word problems as simple as possible for your students. So, we use a set of repeatable steps and simplify the process. We think our students will be more successful because we have simplified word problem situations. However, circling numbers, boxing keywords, and underlining the question does little for our students.
Boxing keywords and placing a bulletin board doesn’t improve student success. Neither does a keyword bulletin board. It does lead to a lack of understanding when it comes to solving word problem situations. It was shown that students who rely on keyword identification strategies, rather than comprehending word problems as the stories that they are, are MORE often incorrect.
Word problems are stories. When we teach reading, we teach our students to identify story elements like characters, setting, and plot. This allows them to check their understanding. We encourage them to visualize the story. The same strategies work with story problems also. Word problem situation instruction needs to be more than just a reduced formula of circle, box, and underline.
Genres of Word Problem Situations:
Just as stories come in a variety of genres, word problems come in a variety of types. At the elementary level, there are eight different types of word problem situations commonly encountered:
Brain science, specifically cognitive load theory, states that by building familiarity with lower level concepts, more brain power can be devoted to higher level thinking skills.
Deciding what operations should be used to solve a problem is a higher level thinking skill. A similar study focused on how experts approach new types of physics problems.
The shorthand version of this research showed that experts relied on previous problems they encountered, the associated equations and operations they used to solve those problems, and decided if those same solutions were useful with this new type of problem.
They were MORE accurate than novices at approaching these same problems.. The freshman physics students who lacked the experience with these problem types and the associated equations to solve were MORE often wrong as they relied on keywords to help decide what to do.
As math teachers this means that we need to give our students opportunities to work with word problem situations. They need experiences in solving them. This will broaden their depth of knowledge for future problem solving situations.
Word Problem Situation Sorts:
How do we do this? Word Problem Sorts are a fantastic way to help students develop their understanding of word problem situations. The best part is, you probably have a number of examples of word problems that you can use already at your fingertips.
You have access to your:
- School adopted curriculum
- Task cards for different word problem situations
My favorite type of word problem sorts are those that involve numberless word problems.
When we remove the numbers from word problems, we are focusing student attention NOT on actually solving the problem, but the context of the situation. Instead of having students solve the problems, asking students to think about what kind of problems these are and classify them accordingly is more meaningful in developing their understanding of word problem situations.
How do you do a word problem situations sort:
Keep it simple:
- Decide if you are going to focus on ALL eight types of word problems, or one or two types.
- Deciding to use ALL eight types is a great beginning and end of the year activity. Why? This is a wonderful time to get to know your students, their thoughts, feelings and experiences with word problems. Furthermore, it gives you a baseline of understanding to track student progress over the year.
- Even if you choose one word problem type, within it there are three different types of situations that arise. Take for example ADD TO PROBLEMS. You have the starting amount, the difference, and the RESULT. This means, depending on what information you do or do not have, you can have problems that have the TOTAL (result), the STARTING amount, or that have the DIFFERENCE. In this one problem type, your students will have to discuss if they would need to ADD to find the solution, or subtract.
- Choosing two or three different problem types may be beneficial on a unit about MULTIPLICATION. Situations that call for multiplication include AREA PROBLEMS, ARRAY PROBLEMS, and EQUAL GROUP PROBLEMS. Having students sort problems based on the type of word problem situation is a great way to focus students on context clues when deciding the types of word problems they are working on.
Split students into groups
- In order to increase participation and support learning in a large group setting, having students work in pairs, or triads at the most, gives students more opportunities to engage in the learning process. Quiet students feel more comfortable talking in a small group setting. It is important to consider the equity of experiences and opportunities for students to engage with word problems. Small groups increase access to content, and help reluctant students to participate more.
Give student groups either the SAME set of cards with the same problems, or split situations up among the WHOLE class.
Either of these methods will give students opportunities to discuss, listen to other groups, and discuss whether or not they agree with their classmates.
If you are using a small set of cards with each small group getting one card, display the types of word problems or situations that the class has. For example, you could tell the class that some word problems require one of the four operations, and that there are ONLY 2 of each operation in the entire class.
Student groups can then make their case for which operation they believe their situation calls for in order to solve and why. With either approach, your students are going to be talking, discussing, and thinking at a higher level during your math block time.
Keep it a mystery
Instead of justifying student responses as correct or incorrect, leave it till the end. Hold out the reveal, allowing for lively debate and drama in your math class. Imagine if there were only two situation cards that called for MULTIPLICATION, but 3 groups claimed that their word problem called for this operation? You have created drama and left students in a state of dilemma, a time of TRUE mathematical growth according to Joan Boaler in her book Mathematical Mindsets.
To conclude, and to help you get started with a word problem sort, I have a set of 8 word problems for you to try in your classroom.
These problems are NUMBERLESS, so they can be used in any upper elementary classroom. I invite you to try them with your students and focus not on solving these problems, but in sparking lively debate and discussion in your math classroom.
Don’t forget to come back and share in the comments how it went.
Want to learn more? I have created a course on PopPD ALL about word problems. I walk you through my three step approach to building confident word problem solvers. Check it out!