Applying metacognitive skills in the Math classroom is important just so students understand what they are doing, instead of solving problems mechanically. Math teachers can also beneﬁt from it when they prepare, conduct and reﬂect back on their lessons.
Have you ever stopped to consider why you always use a certain approach to solve a Math problem? Do you use it because it is the best, or because you are so used to it? Are you aware of the alternatives?
This is what metacognition is. In essence, it is “thinking about thinking” and being aware of the ability to control one’s thinking process (Ministry of Education, 2012).
Developing metacognition has been an aim of Math education since the conceptualization of the Math curriculum framework in the 1990s. But even now, some teachers are still not confident that they can develop it in their students.
Recognizing that this is an important 21st century competency, Mdm Wong Lai Fong, a Lead Teacher in Anderson Secondary School, agreed to join Professor Berinderjeet Kaur from the Mathematics and Mathematics Education Academic Group at NIE in a project to enhance Math teachers’ pedagogy for developing metacognition in their students.
After drawing up the framework with Anderson Secondary, Prof Kaur spoke to their Cluster Superintendent to involve a few schools nearby. Then, selected Math teachers from these schools convened weekly to design tasks to be used in the classroom.
Giving students the opportunity to solve non-routine and open-ended problems is the first part in helping them develop metacognitive awareness. For example, students have studied the topic of percentage in primary school – so teachers should ensure that students are not just answering questions mechanically and not understanding what they are doing.
“Instead of reinventing the wheel, we encouraged teachers to use existing questions and improve on them by changing performative tasks into knowledge-building ones.”
“For example, when I ask, ‘If I give you 20% of what I have in exchange for 10% for what you have, do you want to take that offer?’, they have to think deeper about what percentage is and, hence, understand it,” Lai Fong adds. “This makes them visualize their working backwards instead of doing it in the usual forward manner without thinking!”
Also important in developing metacognition is allowing the students to vocalize their thoughts. “Verbalizing is very powerful,” Lai Fong says. “When students have to discuss or speak out, they have to reflect on what they are doing and think about what to say out loud.”
Furthermore, by listening to how students support their answers, teachers will know if the students have understood the topic and can truly “make mathematical sense”. This is a way of measuring if the students have indeed developed metacognition.
Practising “Teacher Noticing”
Verbalizing is very powerful. When students have to discuss or speak out, they have to reflect on what they are doing and think about what to say out loud.
– Wong Lai Fong, Anderson Secondary School
Students are not the only ones sharpening their metacognition in this project – teachers do, too! After preparing the questions, the teachers in this project continue with meetings in their own schools, sharing the tasks with their own colleagues.
But while putting them to practice, how do the teachers know if the pedagogy is actually working? “It’s difficult for any teacher to teach, carry the task out and observe students’ reactions and behaviour at the same time!” Lai Fong shares. “But we, too, have to have some form of metacognition and somehow reflect on our own lessons.”
At Prof Kaur’s suggestion, the teachers video-recorded their lessons and watched it afterwards. With so many things to look out for, Prof Kaur introduced the concept of “teacher noticing” to help teachers focus on specific and crucial elements of the lesson.
Lai Fong explains: “When we look back at our lessons, we observe it through four lenses: the teacher lens, student lens, task lens and climate lens. For example, with the teacher lens, we look at how the teacher asked the questions and carried out the tasks, while for the student lens, we look at their behaviour and reaction towards the said tasks.”
“This is useful not only for the project, but also for any peer observations with my colleagues. We know now to focus on these various things and see how they can be improved on.
Encouraging Math Communication
Every classroom – not just a Math one – should have norms. What kinds of behaviour would the teacher want to promote in the students? Which are specific to Math?
Lai Fong points out that emphasizing on Math communication and literacy, which is being promoted in the new syllabus, is actually part of metacognition. It is important that students and teachers alike use the correct Math language.
“There are times when the teachers are teaching reducing of fractions, and instead of explaining that it’s a process to divide both parts by a common term, they just say ‘cancel’ the numerator or ‘strike’ the denominator,” Lai Fong shares.
“That’s where students don’t understand – whenever they see the same numbers, they will just strike them out even though it cannot be done! We want to eliminate that kind of wrong language and encourage the right Math classroom norm.”
Putting It All Together
Lai Fong notes that initially, her students were not used to the teachers asking so many questions. It was difficult to get them to talk more, and even harder to talk more mathematically.
“But the students got comfortable quickly! We want them to speak up and justify their solutions with mathematical reasons, and we are seeing more of that happening in class,” Lai Fong enthuses.
She adds, “The teacher has to ask the right questions, and probe students to explain why they chose a particular operation instead of describing the operation. And when the students answer, the teacher has to listen and know what the students are really thinking.”
While this might seem overwhelming for some teachers, Lai Fong advises teachers to start small and keep in mind how this paradigm shift will help students learn deeper.
“Time is always a factor when you’re a teacher, but work within your means,” she says. “You don’t need a nice piece of worksheet – it can be just one question, done in one class. Most importantly, it helps to work with a group. When you have the support of your colleagues and management, you have shared resources and you can learn from one another.”