Teaching and Learning Through Problem Solving

Teaching and learning mathematics today looks very different than the way it was 20 or even 10 years ago. In the past, teachers used the “I Do-You Do” approach to teaching, where basically they showed students how to solve a problem, making sure to follow specific steps and rules, and students were expected to copy the exact procedure and solve similar problems. Sometimes pages, and pages, of the exact same type of problems, just different digits. There were no opportunities for approaching the problem in a different way.

That is how I learned math, and unfortunately that is how I taught math when I started teaching 30 years ago.

The math content has not changed much. In grade 5, students learn about fractions and decimals, that is still the same. It is our approach to teaching & learning fractions and decimals that has changed. Using algorithms to solve problems with fractions and decimals is one strategy, but it’s not the only strategy.

There is a lot of research that helps us understand that students learn best when they can:

  • Visualize the math needed (tool or strategy)
  • Make Sense of the problem to choose an approach
  • Make connections between math concepts
  • Explain how they solved a problem
  • This sounds great, and all of us want to be better math teachers, but what are some steps and tools we can use in our classroom to make sure we provide students with opportunities to learn math through problem solving?

    Use a Student Centered Approach

    The first step is to let your students be the center of their learning. In other words, let students drive the learning in your math class. Instead of using the “I Do-You Do” approach, let students come up with their own problem-solving strategies.

    Once the first problem solving strategy to comes up, start an anchor chart for your class!

    Be intentional about the type of problem you choose that day, perhaps one that could be solved using more than one strategy. Here is an example:

    This is one strategy to solve this problem.

    Dan is handing out candy. He gives Susan 8 pieces, but she says she doesn’t need that many, so she gives him 3 pieces back. He gives Mandy 7 pieces, and lastly, he gives James 5 pieces. After doing this, Dan has 4 pieces left for himself. Based on all the information, can you find out how many pieces of candy Dan started out with?

    *If you want to find problems that can be solved in a variety of strategies, check out the Low Floor-High Ceiling Tasks. (some ideas here)

    Start a Problem Solving Chart

    After a student shares an efficient strategy to solve a problem, start the chart. Consider letting your students create the chart. Encourage students to add some pictures or key words to describe the strategy.

    This cumulative chart stays displayed in your room waiting for the next problem-solving strategy to be added and come alive!

    These are some examples of Problem-Solving Charts for different grade levels:

    KG-1st grade Notice there are still empty spots for new strategies.
    4th/ 5th grade Sample


    There is still so much to learn about how kids learn best. I am glad I am not the teacher I was 30 years ago; today I know how much I still need to learn about teaching.

    Most importantly, I don’t believe I have to “tell” students what to learn. My job is to provide opportunities for them to discover why math works, and how it works, so they can have many “A-ha!’ moments in my class.

    References and Ideas:

    SEEING AS UNDERSTANDING: The Importance of Visual Mathematics
    for our Brain and Learning. By Professor Jo Boaler, Standford University.

    Youcubed mathematical tasks.

    Empowered Problem Solving online workshop by Robert Kaplinsky.

    Numberless Word Problems Using a Student Centered Approach blog by Caty Romero

    Problem of the Month by Insidemathematics.org

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