“Mathematical thinking is when students have opportunities to doubt, understand, conceive, affirm and deny, will and refuse, imagine, and perceive.”
(Dan Finkel, Five Principles of Extraordinary Math Teaching)
Problem solving is central to doing mathematics. By learning to solve problems and learning through problem-solving, students are given, and create, numerous opportunities to connect mathematical ideas and to develop conceptual understanding.
Problem-solving forms the basis of an effective mathematics program that places all students’ experiences and wonderings at the centre. Problem-solving is foundational to mathematical instruction. It is considered an essential process through which all students are able to achieve the expectations in mathematics and is an integral part of the Ontario mathematics curriculum.
To encourage students to engage in problem-solving, ask questions! You may want to try questions, where there may be more than one answer. We call these “open questions”, the focus is on the opportunity to engage, think and play with the math.
The questions asked should be thought-provoking to engage students in problem-solving, as problems with quick and easy answers offer minimal thinking opportunities. If you don’t know the solution, use this as an opportunity to explore the thinking together.
Encourage communication by asking promoting questions:
- "Can you walk me through how you solved this? What steps did you take?"
- "Why did you choose this method to solve the problem? Were there other methods you considered?"
- "What did you find challenging about this problem, and how did you overcome those challenges?"
Above all else, play. Enjoy playing with math.
Resources to support problem-solving at home.
Would You Rather Math engages students in critical thinking and mathematical reasoning. It presents students with mathematical problems, prompting them to compare and analyze options. It encourages problem-solving and provides opportunities for students to connect and justify mathematical ideas in a fun and engaging way.
Consider the wide variety of Would You Rather? situations that come up in everyday life: when deciding which line to join at the supermarket; selecting the “best” route to a destination; or choosing whether to buy a large amount of cheaper items or a small amount of more expensive items. These are great opportunities to encourage your child to see how mathematical problem solving is everywhere!