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Why Metacognition in mathematics? Where did my interest in metacognition? First of all, metacognition is essential to self-regulation and self-knowledge. In mathematics, students are required to use metacognition but it is not directly embedded in the mathematics curriculum but it is rather implied through math process expectations, such as communication, connection, problem-solving, reflection.

The problem solving model provided by the curriculum documents is the one developed by Polya in 1945 and presented in his book, “How to Solve It”. The steps for problem solving are: Understand the Problem, Devise a plan, Carry out the plan and Revise/Extend.

Like any teacher I have tried to create anchor charts explaining the steps, modelling them and expecting students to use the steps. This seems like a great recipe for success in problem solving if it were a linear process. Soon, I realized that there is a lot of work involved in the teaching of problem solving skills and that this is more related to teaching reading comprehension than doing math. The latter cannot be done without the former. This problem solving method works for students who know what to do to understand the problem.  It works for those who know what devising a plan means.  In fact, it means devising a few plans or strategies, and, through close monitoring and continuos assessment of their effectiveness in relationship with the problem, going back to the problem, review the understanding of this problem and try a new strategy. It is a redundant , circular process that good problem solvers do it unaware of the many times they re-read the problem, wondered whether a prelimiray result makes sense, whether they are on the right track.

Too many times I have to tell the students, “This would work if you were solving this type of problem.” Or: ” Given this information, you were actually solving a different problem.” It is because there is so much work involved in the understanding of the problem that depends on what one knows about mathematics ( math knowledge) about that content or similar ones ( ability to build on prior knowledge, apply or make connections), what one knows about himself as a problem solver( self- knowledge and critical self knowledge), the previous experiences ( failures or successes) with similar problems. In other words, a lot of thinking about themselves and a lot of skills that play a major part, I believe, in the students’ ability to do well in mathematics.

COLLECTING DATA:  A PROSPECTIVE AND RETROSPECTIVE METACOGNITIVE QUESTIONNAIRE

During the summer of 2012 I began my research for my project. I focused on ways to collect data at that time.  I discovered this Belgian research paper, published in the Journal of Research in Educational Psychology, that focused on assessing metacognition, Evaluating and Improving the Teaching-Learning Through Metacognition ( 2007). It contains two types of questionnaires used for metacognitive practices: one for children and one for the teacher’s observation habits. It also includes descriptors for “think aloud metacognitive behaviour”. I used this as my source for creating my questionnaire.

I administered the questionnaire to two grade 6 classes and the following behaviours scored consistently among the student population in both classes. Additionally, these answers were in line with my initial diagnostic assessment using the ONAP testing, journal entries, as well as observations taken in class during problem-solving sessions. The behaviours included in the questionnaire are prospective ( before ) and retrospective ( after) solving the problem.

1. Knowing in advance whether you will be successful or not

2. Underlining the relevant information needed to solve the problem

3. Checking the answer with the estimated result

4. Reflecting on how a task was solved

5. Thinking whether the solution or the answer would make sense in reality.

After analyzing the results and evidence, it was clear to me that this is an area of need and I needed my entire program to be designed in such a way that metacognitive behaviours are taught explicitly and reinforces continuously until they become habits.