Carrie S Cutler
As advocates of problem solving point out, we can learn operations and problem-solving skills simultaneously by working on word problems (Verschaffel, Schukajlow, Star, & Van Dooren, 2020). Embedding the operations within a meaningful context (such as those found in word problems) helps us grasp the meaning of the operation.
So, don’t feel like you have to save word problems until after you have developed fluency with the operations. Jump in to problem solving and watch your fluency with number, flexibility with strategies, and problem-solving confidence grow!
Did you know it’s okay to talk to yourself? Yep! The best problem solvers have conversations with themselves that take them through the logical steps they follow as they work toward a solution.
This requires self-assessment, reasoning about mathematics, and metacognition (thinking about our own thinking). Most of all, it requires practice.
Here are some prompts you can use while working to solve math problems.
+ What can I ask myself to help me understand the problem?
- How can I say the problem in my own words?
- What are the facts?
- What is the question?
- Are there hidden questions that need to be answered first?
- What additional information do I need to know?
+ What can I ask myself as I make a plan?
- Can I draw a picture of the situation and look for patterns?
- Can I organize the data in a list, table, or graph and look for patterns?
- Can I find other examples of this type of problem and look for patterns?
- Would it help to work backward?
+ What can I ask myself as I carry out the plan?
- Have I worked on a similar problem?
- If yes, how did I solve it?
- Would using smaller numbers make the problem easier?
- Would a systematic guess-and-check approach allow me to eliminate possibilities and close in on the solution?
- Is the plan working, or do I need to try something else?
- Am I getting closer to the answer?
- Do I need to separate the problem into smaller parts?
+ Look back.
- Did I answer the original question?
- Is my answer reasonable?
- Does my answer meet all the conditions of the problem?
- Can I solve the problem using a different approach and get the same result?
