Problem-Solving Strategies in the Math Classroom
Promoting a positive experience in the classroom of problem-solving processes as well as the acquisition of problem-solving strategies is crucial for students to become independent critical thinkers in the 21st Century. My ultimate goal is to foster in students positive habits towards problem solving.
“Don’t take the problem solving out of problem solving” (p. 34). Rather, teach through problem solving, and teach students to solve problems with effective processes and strategies. Find tasks that encourage students to practice a particular problem solving strategy. As students’ grapple with the math, and discuss their ideas about their solutions, they develop skills and learn to organize their thinking (Van de Walle, Karp & Bay-Williams, 2013).
Here is an article that allows you to explore what’s happening in your classroom. It guides you through some aspects to consider, and forces you to reflect on your classroom culture. This is a great place to start if you are curious about developing a classroom culture that supports a problem-solving approach to mathematics. It is full of rich resources!
“As teachers we can support our students to develop the skills they need to tackle problems by the classroom culture we create. It needs to be one where questioning and deep thinking are valued, mistakes are seen as useful, all students contribute and their suggestions are valued, being stuck is seen as honorable and students learn from shared discussion with the teacher, Teaching Assistant (if present) and peers.”
U-P-S Check is one of my favorite problem-solving strategies. Check out the video below to see the structure in action!
Here is a helpful template you can use with your students to try the UPS Check method.
Here is another video of a 4th grade teacher demonstrating how to solve a word problem using the UPS Check method.
Here’s another article about teaching mathematics through problem-solving. It includes illustrations and examples with practical teaching scenarios where students are given the opportunity to persevere through problem solving.
The common instructional model of “I do, we do, you do,” increases student dependence on the teacher and decreases students’ inclination to persevere. How, then, can teachers develop perseverance in problem solving in their students?
One important factor in creating a classroom culture that supports a problem-solving approach to mathematics is finding authentic tasks that allow for students to work together, persevere, and use different strategies. In the following video, Dan Meyer suggests that problems with too much guidance stifles thinking. By stripping away all the excess information, we can allow our students to think critically and solve real-life problems.
Dan Meyer has created a free spreadsheet on which he lists several of his “three-act” tasks. Act One is usually a video or image that sparks a question that can be solved mathematically. Act Two gives more information that can help answer the question. Finally, Act Three shows a video or image that answers the question.
Finally, this a book by George Polya that shows how problem-solving in mathematics can help attack ANY problem.
“One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.”
