Why “keywords” might be holding you back in math
Remember learning math and being told that certain “keywords” always meant the same thing? Words like “total” meant add, and “difference” meant subtract? This approach is pretty common in math education, where keywords are often taught as a shortcut to solve word problems.
But what if relying on those keywords is actually hurting your ability to truly understand math? It might be preventing you from developing solid problem-solving skills.
This article explores why relying solely on “keywords in mathematics” can be a problem and offers some alternative strategies for teaching real mathematical reasoning and problem-solving skills.
What Are Keywords and Why Are They Problematic?
In the world of math word problems, “keywords” are those little words or phrases that seem to point you toward a particular operation. For instance, “more” and “total” might suggest you need to add, while “less” and “difference” might signal subtraction. A lot of teachers introduce keywords as a way to help students decode word problems.
But here’s the thing: While keywords might seem like a helpful shortcut, they can actually lead students astray.
Why? Because:
- Keywords send the wrong message about doing mathematics. They encourage memorization rather than real understanding. Instead of thinking about what the problem is asking, students might just hunt for keywords.
- Keywords are misleading. The same word can mean different things depending on how it’s used. “More than,” for example, can mean addition, but it can also be used to compare two things.
- Many problems don’t have keywords at all. What happens when a student encounters a problem like this: “There are 12 apples on the table. 4 are red, and the rest are green. How many green apples are there?” There aren’t any obvious keywords there, so a student who relies on them might get stuck.
- Keywords don’t work with more complicated problems. Two-step problems and other difficult scenarios are too complex for simple keyword matching.
Bottom line: Keywords are too simplistic and can lead to errors, especially as problems get more challenging.
Why Keywords Can Be Bad News
While keywords might seem helpful on the surface, research shows they can actually hinder your understanding of math.
It gets in the way of thinking mathematically.
When you focus on keywords, you don’t truly engage with the problem. Instead, you’re skipping straight to the answer, ignoring the need to analyze and understand the underlying mathematical ideas. This keeps you from “making sense of problems and persevering in solving them.”
It stops you from visualizing or modeling.
Keywords give you a shortcut, so you don’t have to picture the problem or create a model to represent it. These are important tools for understanding more complex concepts.
It tricks you into thinking you understand.
You might feel good about your answer just because you spotted a keyword, even if you got the problem wrong. This false sense of confidence can make it harder to learn from your mistakes.
Alternative Strategies: Fostering Mathematical Thinking
Instead of fixating on keywords, try these strategies to help your students develop a deeper understanding of mathematical concepts:
Focus on Conceptual Understanding
Make sure your students understand what the different operations mean. Don’t just tell them that “total” means addition. Teach them that addition means combining quantities.
Use visual aids and manipulatives to help them see and feel the concepts. For instance, you might use blocks to show how addition works or draw diagrams to explain fractions.
Hands-On Learning and Real-World Connections
Turn word problems into hands-on activities. If the problem involves apples and oranges, bring in some apples and oranges! Let your students physically represent the problem.
Also, be sure to use real-world examples that are relevant to your students’ lives. Make the situations culturally relevant, so they can picture themselves in the story. If you’re teaching about money, use examples of things they might actually want to buy.
Encourage Problem Creation and Exploration
Have your students create their own word problems. This will force them to think about the math concepts and how they’re expressed in words. What kind of situation would require division? What would a graph of that situation look like?
You can also present word problems without questions. Use the “I notice/I wonder” strategy. Have students analyze the information and come up with their own questions about the problem. What do they notice? What are they curious about?
Numberless Word Problems
Try using numberless word problems. Present the context of the problem first, without any numbers. For example, instead of “John has 5 apples and Mary has 3 apples. How many apples do they have in all?” try “John and Mary have some apples.”
This allows students to focus on understanding the situation before they get bogged down in the calculations. Remove the expectation to solve, and focus on understanding the problem and identifying the relevant information.
Activities and Examples
So, how do you teach mathematical concepts without relying on keywords?
- Concept-Based Activities: Instead of focusing on keywords, have students group problems by the mathematical operation they require. This encourages them to understand the underlying concepts rather than just looking for trigger words.
- Real-World Problem-Solving: Give students real-life situations where they need to use math. For example, planning a party budget or figuring out the best deal on groceries. This helps them see how math applies to everyday life.
- Collaborative Problem-Solving: Have students work together to solve problems. Encourage them to talk about their thinking and strategies. This helps them learn from each other and develop a deeper understanding.
- Numberless Word Problems: Present problems without numbers. For example: “Maria had some candies. She gave some to her friend.” Ask students what they notice and what questions they could ask. This encourages them to think about the situation before jumping to calculations.
Final Thoughts
It’s time to move away from relying on keywords to teach math. While it might seem like a shortcut, keyword-based instruction actually prevents kids from developing crucial critical thinking and problem-solving abilities.
The alternative strategies we’ve discussed—focusing on conceptual understanding and real-world application—promote deeper learning, greater engagement, and increased confidence in math. When students truly understand the “why” behind the math, they’re better equipped to tackle complex problems and apply their knowledge in new situations.
I encourage educators and parents to adopt a more holistic approach to math education. Let’s empower our children to become confident and capable mathematicians, not just keyword memorizers.