Problem-solving is a powerful approach for teaching students to develop mathematical concepts and skills. This methodology is not about teaching a specific problem-solving skill to students; it’s about students using problem-solving and collaboration skills to develop their mathematical skills and solidify their identities as capable problem-solvers.
Problem-solving is an instructional approach used widely in other countries and is currently helping to inform the instructional approaches many educators are developing to meet the demands of rigorous state math standards. Problem-solving is designed to create interest in mathematics and stimulate creative mathematical activity while supporting student collaboration in the classroom. A typical lesson starts with a problem, then might progress as follows:
• First, students work individually to solve a problem using their own mathematical knowledge.
• Then, students discuss various approaches and solutions with each other while the teacher listens closely to the strategies being used.
• Lastly, the teacher facilitates a whole-class discussion to compare student approaches and solutions in a progression leading toward grade-level standards.
According to Dr. Akihiko Takahashi from DePaul University, “The whole-class activity provides students with opportunities to develop their mathematical abilities including conceptual and procedural understanding.” Over time, students also develop critical qualities, such as perseverance and independence.
In this Exploration, you will design a lesson that provides students with the opportunities to understand mathematical content while supporting them to become independent learners and problem-solvers.
• In the Plan/Prepare section, you will select a math problem for students to solve and plan a lesson using the problem-solving approach.
• In the Teach/Assess section, you will refine your lesson plan and include ways to assess the effectiveness of the content objective and the learning process.
• In the Analyze/Reflect section, you will evaluate what worked and identify any challenges you may have encountered. You’ll also reflect on the next steps of how you can continue to build upon what you’ve learned.
Through the Discussion Group for this Exploration, you’ll share questions, reflections, and resources with other teachers who are teaching math through problem-solving.
Successful completion of this Exploration includes:
• Regular weekly participation during the 8 weeks.
• Posting in the Plan/Prepare, Teach/Assess, and Analyze/Reflect discussions in the Exploration Discussion Community.
• Submitting the Exploration Self-Assessment and Survey within the allotted time frame.