Mastery in Maths: A teacher's guide

Paul Main

What exactly is Mastery in Maths and how can classrooms embrace this educational concept to advance learning outcomes?

What is Mastery in Maths?

Mastery in Maths is an approach to teaching and learning that aims for children to develop a deep understanding of Maths rather than memorising key concepts or resorting to rote learning.

The main objective and expectation are for all children (with rare exceptions) to have acquired the fundamental concepts and facts of maths for their key stage such that by the end of the unit they have attained mastery in the maths they have been studying. At this point, they must be ready to move confidently on to their more advanced level of Maths.

Maths Mastery is a concept that means pupils can use their conceptual understanding to solve unfamiliar maths problems and show complex reasoning, using the relevant mathematical vocabulary.

Mastery in Maths is not a quick fix to mathematical knowledge, but a journey of learning that the pupils and teacher go on with one another, with frequent diagnostic assessments to check the children's understanding of Maths and direct instruction that teaches to any learning gaps.

What is teaching for mastery?

Teaching for mastery means the teachers (mostly with the support of school) must organise the classroom resources and classroom time in such a way that their students can experience mathematics mastery with them. Another concept that has been proven very popular for teachers in mathematics is the concrete, pictorial, abstract model. These teacher strategies enable primary pupils and secondary school pupils to experience mathematical concepts with their hands. The idea behind the concept is to make abstract ideas more concrete using simple physical and visual tools. One such tool is the bar method that originates from Singapore. Another framework that can be used within teacher planning for mastery is the Universal Thinking Framework. This taxonomy helps educators cover the curriculum for mathematics at deeper levels. These types of mastery learning approaches enable pupils to really think through concepts before moving on to more complex ideas.

Embracing physical resources for Maths Mastery
Embracing physical resources for Maths Mastery

What are the core elements of the Teaching for Mastery model?

Mark McCourt has identified 6 core elements of teaching for mastery.

  1. Diagnostic pre - assessment with pre-teaching: Firstly, careful pre-planned assessments are performed to remove any misconceptions that a pupil may have before starting a new topic. This element of the model is used to see if the pupils have the foundational knowledge required to grasp the new knowledge that is coming up. Depending upon the student outcomes, pre-teaching would be performed to make sure that the pupils are ready to learn the new mathematical concept. Primary teachers can make use of this element by finding questions about the same topic but from the past years and asking those questions from the students before a new topic commence. Use the information from that assessment to ensure appropriate pre-teaching for those who will need it.
  2. High-quality group-based initial instruction: The second element of the mastery model highlights the need for engaging all pupils through developmentally appropriate, high-quality, research-based teaching in a classroom ensuring the maximum chance of academic success for pupils.
  3. 3. Regular Formative Assessment to Monitor Progress: Regular formative assessments are carried out to ensure pupils understanding of Mathematical ideas that have already been taught. At this stage, students are expected to answer questions asked by the teacher. A teacher would provide immediate feedback to the pupils as necessary.
  4. 4. High-Quality Corrective Instruction : The fourth element relates to the teachers’ response after realizing that the student did not understand any of the Maths concepts. At this stage, the teacher does not reteach the same concept in the same old way. An effective and expert Maths teacher would use his vast didactic and pedagogical knowledge to instruct the concept in any other way that the pupil could understand. For a unit of one or two weeks duration, high-quality corrective instruction may last one to two days. The primary schools' Maths teachers may use a wide range of real-life situations, evidence-based approaches, unfamiliar situation, challenging enrichment activities, and a variety of Mathematical procedures and explicit instruction strategies to make sure that the student has the best chance of grasping the Maths lesson.
  5. Second, Parallel Formative Assessment: The 5th element involves the continuation of the Maths teaching and checking for the students understanding as a result of introducing a new teaching strategy at the 4th element. An important aspect of the mastery approach is that is not the final assessment of subject knowledge. The cycle of practice and learning continues until a student achieves the level of mastery of the concept.
  6. Enrichment Activities / Extension Activities: The last element is to offer challenging enrichment activities providing a valuable classroom learning experience but, crucially, does not move students on to new concepts of Maths. The last element may look at previously developed Maths skills. Those, who have passed the assessment at the 5th element will move to the 6th element, but those that fail will go on to obtain corrective instruction until achieving Mathematics mastery.

It is important that the Maths Teaching provided here involves additional material that must not be provided to everyone. Primary school Mastery Curriculum must make clear which of the content is supposed to be understood by the majority of pupils and which involves depth of understanding and can be taught to those who master mathematical concepts quicker than others.

Utilising the Universal Thinking Framework for Mastery Learning
Utilising the Universal Thinking Framework for Mastery Learning

What is the role of a teacher in Maths Mastery?

From the description of the elements of the mastery model, one may easily see how the Maths to primary school teachers play a crucial role in each section. The primary and secondary schools Maths teachers play a key role in locating and designing the most effective pre-assessment activities and they can eliminate and correct misconceptions in real-time. Also, they deliver high-quality instruction and know many ways of defining different ideas so that each pupil gets the tremendous opportunity to gain Mathematics Education.

All teachers experience the continuum of beginner to expert in Maths teaching. Through spending time on teaching and professional development training teachers progress from the novice-expert continuum where the emphasis is on strategic knowledge – lessons learnt from teaching to apply mastery teaching approach. This process may take around ten years of providing Maths education. Throughout a Maths lesson, children must be encouraged to discuss their thinking and justify their responses. These frequent opportunities to talk about their Maths lesson In a one to one environment with their Maths teacher helps to build childrens’ confident reasoning, and improve their verbal fluency, and problem-solving skills.

Application of Maths mastery approach can improve and help both secondary and primary schools teachers become more effective. Senior Leadership Team must provide professional development training to their teaching staff with a specific focus on the didactic and pedagogical knowledge of maths teaching, for instance, key procedures of teaching Maths using maths manipulatives.

Using manipulatives for maths mastery
Using manipulatives for maths mastery


Final thoughts on mastery learning approaches

Through carefully selecting pedagogy and knowledge of multiple didactic options, Maths teachers can help students to see the interconnectedness of mathematical concepts. It is important not to see Maths as a mixture of procedures to memorize and Maths Curriculum to get through. Maths must be seen as a journey to understand the world around us. Therefore, it is important to teach Mathematical concepts correctly the first time so that everyone can understand Maths and take part in the conversation. Maths mastery learning and teaching can take a long time, but it is something that is definitely worth the effort one may put in to reach the top.

Concrete - pictorial - abstract approaches
Concrete - pictorial - abstract approaches