Problem Solving
Problem solving is central to doing mathematics. By learning to solve problems and by 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 effective mathematics programs that place all students’ experiences and queries at the centre. Thus, problem solving should be the mainstay of 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.
(Ontario Elementary Math Curriculum, 2020)
Instructional Strategies
collaborate with students, asking questions or thinking aloud when a student or a group of students is not making progress
scaffold based on knowledge and skills of individual students
provide resources and time for students to gather data, detect patterns, make and justify conjectures.
ask probing questions if data or strategy seems to be unconnected or inappropriate to the inquiry.
guide students as they apply their chosen strategy.
facilitate the purposeful sharing of different problem solving strategies for the same problem.
direct students to use multiple strategies when appropriate
recognize, encourage, and applaud perseverance.
validate different approaches to the same problem
use cross-curricular connections to demonstrate the usefulness of mathematics.
support and encourage risk taking, and applaud creative approaches.
encourage independence
Prompting Questions
How does this problem remind you of a problem you have solved before?
What are the connections between this problem and other problems we have solved?
How would you state this problem in your own words?
What problem-solving strategies have you tried?
What strategy will you try next?
Which strategies can you combine to help you solve this problem?
What factors make this a difficult problem?