The Inquiry Process
The inquiry process is the method through which students intuitively approach problems. Generally, the inquiry process involves the following four steps:
This four step process directly correlates to the 3-part lesson plan implemented by teachers as they employ the problem-solving approach to teaching mathematics. To read more about the 3-part math lesson, click here
Teaching the Four-Step Problem-Solving Model
Rather than explicitly teaching problem-solving methods, it is encouraged to teach a problem-solving model. According to the Guide to Effective Instruction: Problem Solving, by, “Grade 3, the teacher can present the problem-solving model more explicitly, building on students’ prior experiences in the previous grades.”
The most commonly used problem-solving model is Polya’s four-step model which is: understand the problem, make a plan, carry out the plan, and look back to check the results (Polya, 1945).
When using this model, children should be given flexibility to use a strategy of their choice or creation during the make a plan and carry out a plan section. Sharing at the end of this process will expose children to the strategies used by their peers. As stated by Lucy West, "as our students become better listeners, they will retain this information and see value in these peer discussions".
- Understand the problem
- Make a plan
- Carry out the plan
- Look back and reflect
This four step process directly correlates to the 3-part lesson plan implemented by teachers as they employ the problem-solving approach to teaching mathematics. To read more about the 3-part math lesson, click here
Teaching the Four-Step Problem-Solving Model
Rather than explicitly teaching problem-solving methods, it is encouraged to teach a problem-solving model. According to the Guide to Effective Instruction: Problem Solving, by, “Grade 3, the teacher can present the problem-solving model more explicitly, building on students’ prior experiences in the previous grades.”
The most commonly used problem-solving model is Polya’s four-step model which is: understand the problem, make a plan, carry out the plan, and look back to check the results (Polya, 1945).
When using this model, children should be given flexibility to use a strategy of their choice or creation during the make a plan and carry out a plan section. Sharing at the end of this process will expose children to the strategies used by their peers. As stated by Lucy West, "as our students become better listeners, they will retain this information and see value in these peer discussions".
Is it the best approach?
YES! All current research leads to the same conclusions – the problem solving approach to teaching mathematics is the most effective method to implement in the classroom and this is supported by the Ontario Elementary Mathematics Curriculum.
Utilizing this approach to teach math has numerous benefits for students and teachers alike. Through a detailed analysis of numerous case studies (see references) which compare methods of direct instruction to the problem-solving technique, it is evident that the latter is the most effective. This approach should be central to mathematics instruction as it teaches conceptual understanding, promotes academic excellence and fosters critical thinking. While all students, regardless of learning method, can succeed in mathematics, research proves that those who learn through problem solving consistently outperform their peers. There are significant differences in student achievement versus those taught through direct instruction.
Teaching through the problem-solving approach is also beneficial because it:
Utilizing this approach to teach math has numerous benefits for students and teachers alike. Through a detailed analysis of numerous case studies (see references) which compare methods of direct instruction to the problem-solving technique, it is evident that the latter is the most effective. This approach should be central to mathematics instruction as it teaches conceptual understanding, promotes academic excellence and fosters critical thinking. While all students, regardless of learning method, can succeed in mathematics, research proves that those who learn through problem solving consistently outperform their peers. There are significant differences in student achievement versus those taught through direct instruction.
Teaching through the problem-solving approach is also beneficial because it:
- Allows for differentiation – problems can be easily manipulated to suit the unique needs of all students
- Promotes cooperative learning by creating an environment which fosters math talk in the classroom and stimulates meaningful conversations
- Increases student engagement and sense of responsibility over their own learning
- Improves confidence and stimulates students’ interest in mathematics
- Helps students to develop math schemas and activate prior knowledge (both formal and intuitive)
- Requires students to experience real-life, multifaceted problems and employ a sense of reasonableness to solve
- Has cross-curricular links
- Creates an opportunities for peer-evaluations and constructive feedback