1. Metacognition and its effects on teaching and learning of mathematics
Mustapha Nadmi,
Mathematics Department

2. Purpose
The purpose of teaching mathematics is to empower learners to “make sense of society (DOE, 2003, p. 9). Students often struggle when solving mathematical problems on tests, especially when confronted with problems that they have never seen before. Therefore, they need to be equipped with the knowledge to solve problems successfully.
As teachers, it is our job to help students improve their learning by teaching them how to become more independent learners when they plan, monitor, apply, and evaluate their own learning processes. Therefore to facilitate student learning, we need to teach metacognition in our classroom to equip students with the tools necessary to monitor their own learning. Metacognition is defined most simply as “thinking about thinking”.
In other words cognition refers to our thinking and reasoning. Metacognition means going beyond our thinking

3. Why teach metacognition?
Metacognition has been shown to lead to deeper, more durable, and more transferable learning (Bransford, Brown, & Cocking, 2000)
Metacognition is important in learning and is a strong predictor of academic success (Dunning, Johnson, Ehrlinger and Kruger, 2003; Kruger and Dunning, 1999).
Metacognition can increase engagement. Metacognition “has the potential to empower students to take charge of their own learning and to increase the meaningfulness of students’ learning.” Gama, 2007
Metacognitive awareness allows students to regulate their learning strategies and to revise them when a breakdown in learning occurs. One significant factor in developing metacognitive awareness of learning is allowing students to become more self- regulate and less teacher-directed in completing learning tasks. Self-regulation is viewed as synonymous to metacognitive strategies (Boekaerts& Simons, 1995, p. 85).

4. Metacognitive strategies refer to the conscious monitoring of one’s cognitive strategies to achieve specific goals.
Metacognitive strategies can be viewed as the decisions learners make before, during and after the process of learning.( Boekaerts and Simons 1995, p.91).
These strategies include the ability to plan, check, monitor, evaluate, and revise learning strategies in reference to the task, learning characteristics, available strategies, and the type of material assigned (Brown et aI., 1981).

5. A more “metacognitive” teacher believes that the students’ difficulty may not be with the skills, rather it might indicate a lacking in self-regulation of the problem solving process.
As teachers, “we can significantly increase student’s ability to learn by teaching them the learning process and provide specific strategies; avoid judging student performance on initial performance; encourage students to persist in the face of initial failure; and encourage students to use metacognitive tools to help them succeed” (McGuire, 2013).
Implementing metacognitive strategies in the classroom will help students transition from being passive to actively engaged learners who can impact their own learning both in and out of classroom.

6. Below are strategies we can implement in our teaching that can make an immediate impact on students’ learning to help them think about their thinking:
To be effective, we need to build a learning environment where students as well as those with low mathematics performance are more likely to feel emotionally secure and confident that they can succeed rather than on authority and “always the right answers only.”
Talking about thinking is important because students need a thinking vocabulary. During planning and problem-solving situations, as teachers; we must think aloud so that students can follow demonstrated thinking processes. Modeling and discussion develop the vocabulary students need for thinking and talking about their own thinking.
We should write down the steps one at a time on board with explanation. Not only this gives some time for the students to digest what we are saying but also allow us to modify the solution as the explanation progresses. After showing the solution, we should ask the students what other methods could be used. This shows the students that there are different paths to the answers.

7. When showing students a worked example, we have to change “This is the way to do this.” with “This problem could be solved in this way”. “This could be ……” encourages multiple interpretations and solutions, whereas “This is ……” will close off creative thinking.
Practicing, monitoring, and evaluating in small groups with our support help students to monitor their own thinking learning both in and out of classroom.
Assign problems that require higher order thinking skills to students to solve in small groups and encourage them to discuss different approaches to the same problem. While walking around to check, ask the following questions:
What are you doing?
Why are you doing it this way?
What is next step?
How does this help you?

8. Create learning goals for our students through the use of a journal or learning log allow students to think about their own progress in class and ask them to complete a “thinking checklist” at the end of each topic by engaging each student in metacognitive thinking through the following questions.
What did I try to accomplish?
What skills did I need to complete the task?
What new ideas and skills have I mastered?
Which of these skills are my strengths?
What were the difficulties with this topic?
What did I do to try to overcome these difficulties?
What specific learning strategies did l use?
Did I reach my goal?
Show students how to use graphic note taking strategies (KWL) for solving a problem such as:
What I Know
What I Want to learn
What I have Learned

9. New City College of Technology/ CUNY
Thank you very much.
Mustapha Nadmi,
New City College of Technology/ CUNY
October 27/ 2016