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Understanding Metacognition and its Role in Mathematics

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Metacognition is “thinking about thinking.” It is the ability to recognise, analyse and reflect on our own cognitive processes. Believed to be unique to humans, metacognition enables us to think about what we do know, what we need to know and what strategies we can apply to solve a problem. Metacognitive processes allow us to learn from prior experiences, and then apply those learned strategies to new situations. This provides invaluable opportunities to learners, especially in mathematics.

At Reflective Learning, metacognition is the educational cornerstone that provides a crucial shift in focus from schooling to actual learning.

We provide a learning catch-up intervention for maths based on a metacognitive model, and our framework offers a new approach for teachers to deliver targeted, personalised catch-up materials. We identify learning gaps in mathematics across 81 threshold concepts and deliver learning material designed to fast-track student learning.

With our framework, students have the ability to catch up four to six grades in mathematics in less than a single year!

We have created this guide to assist you in better understanding metacognition and its immensely valuable role when it comes to teaching mathematics.

The language of metacognition

Before we begin, here are some helpful definitions when using this guide:

Learning 

The integrating of new knowledge with prior knowledge in order to increase understanding and abstract deeper meaning. (Learning is dependent on cognition.)

Cognition 

The mental processes involved in gaining knowledge, comprehension and understanding. These processes include paying attention, perceiving, thinking, knowing, remembering, evaluating, communicating and problem-solving.

Metacognitive awareness 

Recognising the limit of your knowledge and figuring out how to expand that knowledge. (This includes metacognitive knowledge and metacognitive regulation.)

Metacognitive knowledge 

This refers to knowing what you know and what you don’t know. It includes understanding how you learn and how to apply relevant strategies to increase your understanding.

Metacognitive regulation/expertise 

This is managing and improving your learning through planning, implementing, monitoring, and evaluating learning strategies with self-reflection to order to increase cognition.

Metacognitive strategies 

These are the actions you take to monitor, direct, and optimise your learning experiences.

The history of metacognition

The term ‘metacognition’ was coined by American developmental psychologist John H. Flavell in the early 1970s to describe what he called “cognition about cognition.”

A more helpful definition, in the context of education, was given by Cornford (2002) who says that metacognition is the learners’ knowledge of themselves as learners. It encompasses their knowledge of their strengths, challenges, needs, course context and tasks, as well as their ability to select relevant learning strategies and resources. It also includes the learners’ evaluations of their thinking strategies in order to expand their knowledge and extend their abilities.

In Metacognition: A Bridge between Cognitive Psychology and Educational Practice, Kuhn & Dean (2004), the claim is made that both critical thinking and metacognition can be defined as “awareness of one’s own thinking and reflection on the thinking of self and others as an object of cognition” (p. 270). The value of critical thinking is undisputed, and its similarity with metacognition makes them both to be worthwhile goals of classroom practice.

Some interesting findings regarding metacognition.

  • While some people are naturally more metacognitive than others, everyone can be metacognitive. Children as young as three years old can demonstrate metacognitive behaviour.
    (Whitebread & Coltman, 2010; Bernard, Proust, & Clement, 2015)
  • Metacognition can be intentionally taught.
    (Schraw, 1998; Tanner, 2012)
  • Metacognition and self-regulation” are considered a high impact, low cost approach to improving learner attainment backed by an extensive and “strong body of research from psychology and education.”
    (EEF, 2018)
  • Pupils using metacognitive strategies are “the most effective learners.”
    (Tomlinson & McTighe, 2006)
  • Metacognitive approaches to learning produce greater retention of knowledge and understanding. There is significant evidence indicating that people with greater metacognitive abilities are better problem solvers.
    (Mevarech & Kramarski, 2003)
  • Metacognitive approaches to learning reduce the educational disadvantage of low-achieving students while simultaneously being greatly beneficial for high-achieving students.
    (White & Frederiksen, 1998)
  • Metacognitive awareness initiates the student to take charge of their own learning experiences.
    (Hacker, 2009)
  • Metacognition gives students greater control over their learning which leads to greater understanding of content.
    (Baird & White, 1984)
  • A review of over 50 international studies conducted over the past 20 years (to explore the effects of teaching metacognition in classrooms) shows the consistent and significant impact of a metacognition focus, adding eight months of learning progress to learners’ grade-level outcomes.
    (Perry, Lundie & Golder, 2019)
  • With a metacognitive approach to learning, learners can catch up four to six grades of knowledge in Mathematics in a single year.
    (Butchart, 2017)

The importance of metacognition for mathematics

Metacognition offers a new approach to learning mathematics. Metacognitive students are aware of gaps in their understanding and are willing to fill these gaps. Consequently, metacognition builds motivation and influences student behaviour.

Metacognition teaches students how to think about how they think and how they approach learning. This has the potential to transform a student’s trajectory because the internal dialogue goes from “I can’t” to “How can I?”

Reflective Learning provides a framework to teach and advance metacognitive skills to a high level in mathematics. Learners are first guided through a 4-step process that identifies learning gaps across 81 threshold concepts. Catch-up courses are then assigned to each learner based on their individual needs. Metacognitive activities are embedded in these courses, and they include formative feedback and continuous assessment.

Embedding metacognition in the learning of mathematics produces:

Higher achievement

More engagement

Improved behaviour

Greater motivation

Independent and self-directed learning

A positive attitude to learning

An accurate ability to analyse and evaluate one’s own knowledge and understanding

Increased resilience

Emotional and social growth

Research by Paris and Winograd (1990) concludes that “metacognition helps students to develop intellectual curiosity and persistence, to be inventive in their pursuits of knowledge, and to be strategic in their problem-solving behaviour” (p. 10).

How to teach metacognitive skills in the classroom

Metacognitive activities unlock greater learning potential. A metacognitive learner notices when they don’t understand something and then they can do something about it. Metacognition becomes an internal guide that equips the learner for autonomous, self-sustaining, successful learning.

Here are some practical ways that you can teach metacognitive skills to your learners:

Formative diagnostic assessments 

Conduct formative diagnostic assessments when introducing a subject, topic or concept. These assessments must include the students in the marking, analysis and subsequent discussion to ensure that each student can identify what they already know and what they still need to know in order to understand their knowledge gaps.

Pre-test self-estimations 

Use pre-test self-estimations and guide students in comparing these with their post-test results to improve their understanding of their strengths, challenges, and what they can and cannot do just yet.

Metacognitive questions 

Create and maintain a supportive environment in which students can ask and answer metacognitive questions presented by both their teachers and their peers.

Structure knowledge 

Assist students to structure knowledge. To do this, you can use visuals such as thinking maps, mind maps, concept maps, and learning pathways to show the links and dependencies of the important concepts that underpin the understanding students need to acquire.

Thinking-aloud

Model ‘thinking-aloud’ when presenting and demonstrating: This involves making explicit what you do implicitly and making visible the expertise that is often invisible to the novice learner.

Varied visualisations and multiple strategies 

Present varied visualisations and multiple strategies for learning and guide students to explain and justify their choice of a particular method of working or solving problems.

Self-analyses 

Use self-analyses to clearly articulate what mastery of a topic or concept means and guide students to evaluate their own understanding when concluding the topic or concept.

Self-reflection 

Use self-reflection to guide students in thinking about how they learn. For example, what do they need from others? How can they successfully learn on their own?

Learning goals

Model and guide students in how to set attainable learning goals and then monitor their progress in achieving them.

Learning is what most adults will do for a living in the 21st century – Alfred Edward Perlman

The one really competitive skill is the skill of being able to learn – Seymour Papert

How Reflective Learning is driving innovation

In 2020, Reflective Learning was placed 4th in the world at the Global Edtech Startup Awards. While we are grateful for this achievement, it is nothing compared to the pride that we feel when we see our students becoming empowered learners with a new-found confidence in their own abilities and their dramatically improved mathematics results.

At Reflective Learning, we use seven learning journeys that intentionally cut across the years of education to build and strengthen the threshold concepts necessary for success in mathematics. Students take part in mathematics activities that are personalised, fun, and highly motivational.

As a teacher, you can use our software to fast-track grade-level learning in mathematics. Our software provides formative feedback so that students can understand their learning and can develop personal metacognitive skills.

The purpose of the Reflective Learning intervention design is to enable students, as well as their teachers and parents, to identify learning backlogs and then to catch up these backlogs.

By using Reflective Learning for student catch-up, you can close specific gaps in maths learning with a solution backed by decades of research. You can help your students identify their knowledge gaps and catch them up within a year.

Creating lifelong learners

The metacognitive pedagogical model provides the added benefit of advancing students’ metacognitive skills so that they can use these to become agents of their own learning. This is the core business of a teacher!

After all, successful teaching results in self-sustaining, successful learners who are able to understand their learning process and its requirements and can access and utilise the resources they need (human or otherwise) to create their own knowledge and understanding.

In the future, this will increase the opportunities for learners entering uncertain job markets and ensure their value as contributors in their communities and countries.

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