August 23, 2023
Do you dread giving your students word problems? It’s no secret that story problems are challenging. The complexity of story problems can leave students confused and frustrated. There are so many strategies for solving math word problems – it’s hard to know which to use.
As educators, we understand the importance of cultivating problem-solving and critical thinking skills. But the path to fostering these abilities can be unclear.
The challenges with word problems
Students struggle with math word problems for many reasons. But most of them fall under the umbrella of comprehension.
“This is one of the biggest challenges in word problem-solving, educators and researchers agree – getting students to understand that the written story on the page represents a math story, and that the math story can be translated into an equation.
Making this connection is a key part of early mathematical sense making. It helps students begin to understand that math isn’t just about numbers on a page, but a way of representing relationships in the world. And it’s one of the ways that kids learn to unite conceptual understanding of problems with the procedures they will need to solve them.” (Edweek, 2023)
A breakdown of 4 common strategies for solving math word problems
As a math coach and education consultant, I’ve worked with teachers across many grade levels. They’ve tried it all. Some have found bits and pieces that work, but not for every child and not for every problem type. I’ll break down some common approaches, from least to more effective. Let’s look at 4 strategies for solving math word problems.
Keywords
Words such as “in all”, “take away”, and “more” are categorized by operation. Students are taught to find the keyword in a story problem and use the associated operation to solve it.
Advantages: n/a
Pitfalls:
- Encourages short cuts
- Not all problems have keywords
- Perceived “success” with beginning word problems
- Students don’t have to think critically or make sense of a problem
- Words can be misleading (example: “more” could mean add or subtract depending on the context)
“Key words encourage students to take a shortcut instead of making sense of a situation. If students think about what makes sense, they don’t need shortcuts or key words. They don’t need to worry about what happens when there aren’t any key words or when there are multiple keywords in a story.” (Nicora Placa)
Example of when a keyword is misleading: Bananas come 5 to a bunch. Deidre buys 3 bags. How many bananas does she have in all?
“In all” would lead a student to add, when the correct operation is multiplication.
CUBES
This procedure uses 5 steps to solve word problems. There are many problem-solving acronyms out there. Even those that attempt to include a comprehension component are rote and don’t provide strategies to support understanding or sense-making.
C – Circle the numbers
U – Underline the question
B – Box the key words
E – Eliminate what you don’t need
S – Solve and check
Advantages: n/a
Pitfalls:
- Students can go through the steps without understanding the situation or context
- Students haven’t made sense of the problem and can’t check for reasonableness
- Only works if students already understand what the problem is asking
- Students don’t even have to read the problem to apply these steps
- It’s a quick fix that gives teachers and students false confidence
- Doesn’t work for multi-step problems
- Relies on keywords
As David Wees noted, “It might be helpful (sometimes) but it’s almost certainly not sufficient.” (The Reflective Educator, 2016)
Numberless Word Problems
With this approach, the numbers (and sometimes the question at the end) are removed from the problem. The teacher leads students through discussion and multiple reads of the problem to make sense of what the problem is asking.
Advantages:
- Encourages sense-making
- Students have to read and make sense of the problem
- The focus is on understanding, not arriving at an answer
- Focuses on the situation and context of the story problem
- No opportunity for students to pluck out the numbers
- Encourages visualization
Pitfalls:
- Students are not modeling with mathematics
- Can be challenging with some fraction or geometry problems
I’m a fan of numberless word problems, especially over keywords or word problem acronyms. But even though they encourage sense-making and understanding, there are some limitations.
Bar Models
Also known as tape diagrams, bar models are pictorial representations of story problems. They help students visualize known and unknown quantities.
Advantages:
- Focuses on quantities and relationships
- Students have to use critical thinking and problem-solving skills
- Uses a model to help students visualize the situation in the math story
- Provides a structure to help students determine which operation to use
- Systematic approach that students can build upon and apply to different types of word problems
Pitfalls:
- It’s possible for a student to draw a bar diagram and still not completely understand the relationships in a story
Example:
Image from Singapore Math Learning Center
Conclusion about strategies for solving math word problems
In conclusion, solving math word problems is undeniably challenging, and students often struggle with comprehension. We’ve explored four common strategies used by teachers to address this difficulty, each with its own set of advantages and pitfalls. While keywords and CUBES offer quick fixes, they may not foster true understanding. Numberless word problems encourage sense-making, but they might not work for all types of problems. Bar models help students visualize relationships, but they may not fully grasp the complexities of certain situations.
Stay tuned for next week. I’m excited to introduce you to a systematic, conceptual approach to solving word problems. It has the advantages of both numberless word problems and bar models without the limitations.
