Metacognition In The Classroom: 6 Tips For a Practical Approach To Teaching Math

The George Lucas Educational Foundation has been researching and writing articles regarding the importance of metacognition in the classroom for years. Here’s what some of these metacognitive strategies look like in practice at the elementary and middle school level for math, presented as 6 tips for using within your classroom.

This article draws from reports by the George Lucas Educational Foundation and the Education Endowment Fund (EEF), a UK-based education charity that researches strategies to raise achievement. We refer to the research from these two foundations throughout this article, as we believe it offers useful insights for classrooms globally. 

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The power of metacognition is something we have hard wired into the Third Space Learning methodology for our 1-to-1 math interventions. Metacognitive strategies used by tutors help us to ensure students make excellent progress in math.

Here we explain exactly what we do, to help you better understand the steps you can take with learners in your elementary and middle school classrooms to improve their metacognitive abilities and reach their learning goals.

To get the first question out of the way: Why should you care?

As the George Lucas Educational Foundation says:

‘With greater awareness of how they acquire knowledge, students learn to regulate their behavior to optimize learning. They begin to see how their strengths and weaknesses affect how they perform.

The ability to think about one’s thinking is what neuroscientists call metacognition. As students’ metacognitive abilities increase, research suggests they also achieve at higher levels.’

Broadly speaking – it works. The benefits of metacognition are multifold. Together with cognition and motivation, metacognitive practices are key to being a self-regulated learner who is actively engaged in improving their own learning.

So, here are 6 tips with guidance to show you how to implement these metacognitive strategies in your elementary or middle school  and classroom. 

This is what we’ve learned about using metacognition to give the 5,000+ students we teach 1-to-1 math every week the best chance to move their learning forward.

1. SKILLS: Teachers should acquire the professional understanding and skills to help students learn how their brains are wired for growth

Over a period of initial and continuous professional development, our 1-to-1 math specialist tutors receive explicit training on the best math strategies for elementary and middle school students. 

What some reports on metacognition refer to as ‘motivation’, we refer to as ‘emotions’ as we believe enjoyment and fluent dialogue is also key.

How to develop your metacognitive skills in primary
Third Space Learning framework for student success, with a focus on metacognition and cognition

For more on the emotional aspect of student success, read our blog on how to make math lessons engaging.

5 ways that a teacher can help a student be more metacognitive

The George Lucas Educational Foundation suggests that teachers can begin teaching about metacognition by introducing the role that the brain plays. They go on to list 5 ways that teachers can help their students become more metacognitive. 

  1. Explicitly teach students about this essential learning skill by defining the term metacognition.
  2. Ask students to describe the benefits and supply examples of ‘driving their brains’ well.
  3. Whenever possible, let students choose what they want to read and topics they want to learn more about.
  4. Look for opportunities to discuss and apply metacognition across core subjects and in a variety of lessons so that students can transfer it for the most benefit.
  5. Model metacognition by talking through problems.

Understand the metacognitive stages for a learner on any task

The first stage for your development is knowing about the processes that a learner goes through.

This diagram represents the metacognitive regulation cycle as applied to a math problem:

the metacognitive stages for a learner
Cognition and Metacognition as applied to an elementary school math problem. Please note, as this is a UK-based charity, the currency is in GBP but the problem is applicable to US elementary classrooms [Source: EEF Report]

Once you understand that ‘self-regulated learners are aware of their strengths and weaknesses and can […] improve their learning’ (EEF) you will be closer to supporting them to develop their learning process.

2. MONITOR: Explicitly teach students metacognitive strategies to increase students’ monitoring skills

During the opening of a 1-to-1 lesson, tutors are directed to focus on metacognitive knowledge.

They’re taught to ask questions around the students’ attitudes and their ability in the topic at hand before they’ve even started on the math.

From our practice, we’ve found questions like:  ‘How do you feel about this topic?’ or ‘How confident are you in solving these types of questions?’ are a simple but effective starting point.

Questions you can use to start the metacognitive process in the elementary classroom

Tutors also investigate what the student already knows about the topic and what strategies they are aware of for solving this type of activity, using questioning in the classroom techniques like:

‘What strategies do you use when problem solving?’

‘What do you notice?’

‘What things should you pay careful attention to when solving questions like these?

‘Where have you seen these types of questions in real life before?’

Keep prompting your students to be aware of their thought processes in your math lessons

Tutors are not telling students what to do but rather combining explicit input with interactive questioning, student choice and feedback.

The tutors use this information to help the student with metacognitive regulation (planning, monitoring and evaluating) throughout the lesson.

As an example they remind the student about strategies they themselves have highlighted as important in the beginning of the lesson, when they get stuck on a question later on.

Questions to use as prompts to elicit metacognition during practice math tasks

Tutors get tutor notes for each slide (only seen by the tutor) which guide them through this metacognitive process, too. See this information to the left in the image below.

There are three parts which help a student articulate their knowledge of themselves, the task; and strategies. Namely:

‘What do you notice?’,

‘What do you know?’,

‘Can you show me your work?’

Reflection questions are also an important part of the process e.g.

‘Does your answer seem reasonable? Why?’.

This maps onto the monitoring and evaluating aspect of regulation strategies.

Questions to use as prompts to elicit metacognition
Example of tutor notes provided to support tutors in the development of monitoring and evaluation strategies in students

Metacognitive questions to end a math lesson

In closing, each lesson ends with a reflection which once again mimics this continuous cycle of metacognition. The student will evaluate specific and general progress, skills and strategies which will inform their monitoring and planning for the next time they are working on this topic.

How should teachers teach metacognitive strategies at elementary and middle school

Here is the seven-step model for explicitly teaching metacognitive strategies. These strategies come from a report by the EEF, however, these same strategies are used within US classrooms across the nation:

  1. Activating prior knowledge;
  2. Explicit strategy instruction;
  3. Modeling of learned strategy;
  4. Memorization of strategy;
  5. Guided practice;
  6. Independent practice;
  7. Structured reflection.

To see how this works in practice, let’s look at the progression of a Third Space Learning math lesson. We recommend you use this as a model for adapting and adjusting your own plan for a lesson built around metacognition. 

1) Activating prior knowledge

The first slides of our math lessons deal explicitly with activating prior knowledge. Here the tutor works with the student to test recall from the previous week, determine what the student understands about the topic already, elicit the topic’s application to the real world, and to help make connections and plan goals for the lesson.

tsl lesson slide on linear sequences
Lesson warm up for a lesson on linear sequences
Lesson slide on linear sequences
Lesson slide on linear sequences

Tutors then work through the next four steps using a range of slides (from highly scaffolded to more independent practice) which helps a tutor work through each of these.

2) Explicit strategy instruction

Read more: Direct instruction and Learning From the Principles of Rosenshine

3) Modeling of learned strategy

tsl lesson slide on modeling of learned strategy

4) Memorization of strategy

5) Guided practice

6) Independent practice

tsl independent practice questions
Lesson slide showing practice time

After the instruction period, lessons have ‘practice time’ where students can independently complete calculations with the tutor there to ask deeper questions and prompt thinking and reasoning.

At the end of the lesson, a child is required to undertake multiple choice questions alone to practice what they have just learned and embed their learning. 

7) Structured reflection

All lessons end with a three part reflection slide as above asking questions around attitude and motivation, metacognition and a chance to evidence progress.

Each of these steps is directly replicable in your elementary classroom when teaching math. 

3. MODEL: Model your own thinking to help students develop their metacognitive skills to understand what they do and don’t understand

Teachers should model the process as they proceed through a lesson, deliberately moving from a more teacher-led activity to one directed by the student. 

Third Space Learning’s 1-to-1 Elementary math lessons are structured to start with a worked example or highly scaffolded slide where a tutor can model best practice.

This level of differentiated instruction and scaffolding is gradually reduced to partly completed examples right through to ‘Practice time’ where a student should be able to practice more independently.

Look at the transition of these slides, as they move from a more scaffolded approach, where more modeling occurs, towards a less and less scaffolded approach as the student starts working more independently.

Could you do this in your classroom?  

tsl lesson slide on ordering and comparing numbers
Lesson slide on ordering and comparing numbers
tsl lesson slide on ordering and comparing numbers 2
Lesson slide on ordering and comparing numbers
tsl lesson slide on ordering and comparing numbers 3
Lesson slide on ordering and comparing numbers
tsl lesson slide on ordering and comparing numbers 4
Lesson slide on ordering and comparing numbers

4. CHALLENGE: Provide students with opportunities to reflect on their thinking

It is important to challenge students to develop self-regulation and metacognition. Without challenge, students will not engage in self-reflection on their existing learning strategies or develop new and useful ones.

For example, if you received a good grade in a test, it wouldn’t prompt you to reflect on your study strategies (even if they were poor, and the exam was just easy or you got lucky!).

However, if you are faced with challenges in the test or receive a low grade, you may more thoroughly reflect on your study habits and try new ones to help you succeed in the next test.

Examples of how to keep challenge level up

Our tutors are evaluated each week on one of their math lessons. ‘Challenge’ and ‘Questioning’ are key components of this evaluation.

Tutors are guided to make sure the student is appropriately stretched and challenged according to his/her ability and/or encouraged to develop critical thinking skills.

In our lessons, we have built opportunities for this into our ‘Go further’ slides.

tsl challenge slide opportunities for metacognition
Challenge slide opportunities for metacognition

What is an appropriate level of challenge? Looking at John Sweller’s cognitive load theory or Vygotsky’s ‘Zone of proximal development’, we see it is important to make it not too hard, not too easy, but just right.

As we teach 1-to-1, our tutors are able to adapt in real time with the correct amount of scaffolding to provide personalized instruction to each student.

However, even with a full elementary or middle school math class, you will be an expert at building differentiation in the classroom and adapting the task to each child, whether they are high or low ability students.

5. TALK: Facilitate reflexive thinking

When teachers ask challenging questions, guide students with oral feedback, prompt dialogue, and scaffold talk through sentence stems, they are helping students to share and develop their learning further. 

Tutors leading our math lessons are encouraged to ask open-ended questions with a focus on reasoning, discussing, arguing and explaining.

Verbal reasoning is one of the first areas teachers notice improvement in with their students on Third Space Learning.

‘It’s a fantastic way to get the children TALKING about their math and explaining their thinking. Children are willing to participate in the sessions and enjoy them.’

Sara Ellis, Deputy Headteacher, Wyke Regis Junior School (UK)

Tutors are trained to think about the different purposes of questions posed and we use Bloom’s Taxonomy to help tutors distinguish between them. The ultimate aim is to get to the top layer of cognition (see image below) where a student is able to create, evaluate and analyze ideas in a specific topic.

Obviously, it is also important and useful to use aspects of remembering, understanding and applying style questions, in order to build the metacognitive knowledge in this domain. This allows access to these higher order skills and reduces students cognitive load.

Bloom’s Taxonomy
Bloom’s Taxonomy: the ultimate aim is to get to the top layer of cognition

Giving students a voice is essential to them being able to construct their own meaning and understanding. Tutor talk time should not dominate the lesson as this restricts student voice.

At Third Space Learning, we strongly believe this and we are currently working on assessing word count of audio in real time to warn a tutor if they are speaking too much, so they can adjust accordingly.

Are you vigilant to your balance of student and teacher talk in your practice?

6. ORGANIZE: Explicitly teach students how to organize and effectively manage their own learning 

In order to help students achieve self-regulated learning, it is important to support students in metacognitive activities, such as planning and evaluating their progress monitoring.

These things can be done in many different ways. One way we suggest for your classroom is to have your students keep a learning journal. 

Our tutors encourage students to assess and judge their own thinking processes and understanding during the lesson, in the reflection and formally by completing a student feedback form at the end of each lesson. 

This makes metacognitive learning explicit and allows students multiple opportunities to improve accuracy in judgment, especially younger ones, as they tend to struggle with reflective thinking and having a realistic view of how well they learned something.

By introducing these important metacognitive skills at this stage, it prepares students for more self-directed learning as they progress through middle school, high school and beyond.

Similarly, by explicitly teaching these skills you can show how planning, monitoring and reflection are applicable to a range of learning activities, far beyond the math curriculum.

In addition, the learning program has been created to help a tutor best enhance student learning with the most effective learning techniques, such as retrieval practice, practice testing, distributed (‘spaced’) practice and interleaved practice, built in as standard.

Schools should support teachers to develop their knowledge of these approaches and expect them to be applied appropriately 

As with any changes to classroom practice and pedagogy, teachers need a lot of support, training, and time to practice in order to implement them effectively.

Every week with Third Space, every tutor has one of their lessons evaluated by an expert and they are then given support in integrating metacognitive and other teaching strategies into their teaching.

Continuous professional development is also delivered and used to help tutors understand how to encourage and support students’ metacognition in the specific domain of math.

Make sure that metacognition is on your timetable for discussion each year at your in-school professional development sessions. You’ll be surprised how many teachers will already be using these metacognitive strategies without realizing it. It’s part of good, quality first teaching.

How do we know if our metacognitive strategies in math are working?

In order to help guide our understanding of self-regulation and metacognition at TSL, we assess our impact by using a form of self-assessment, student self reporting questionnaires.

Each program begins and ends with a ‘Mission Zero’ where we ask cognitive (domain specific), affective (emotional) and meta-cognitive questions. We use machine learning to cluster students into groups and then track which areas they have improved in.

This gives Third Space Learning an idea of which areas we are having the most (or least) impact in and this informs and supports our continuous professional development of tutors and curriculum design.

tsl mission zero
Mission Zero
metacognition example questions
Example of metacognition questions

Never too early to start teaching metacognition in elementary school

Our tutors work with many elementary school students, plugging gaps and fixing common math misconceptions that have developed over the years in elementary school.

But you can start your own work in your school or classroom today, no matter what grade you teach or are responsible for, in much the same way you might have incorporated a growth mindset in the classroom.

Despite older students, such as middle school and high school age, typically exhibiting a broader range of metacognitive strategies, children as young as three are able to engage in metacognitive and self regulatory behaviors.

Now you’ve got the evidence and some practical strategies that we know work to develop metacognition in the classroom, what are you going to do about it? 

Read more

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Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way.

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The content in this article was originally written by primary school teacher Candida Crawford and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.

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