Every new generation of parents must scratch their heads when their children show them their maths homework, with methods of teaching and learning mathematics going through more changes than any other subject. Over the past fifty years there has been rote learning, then ‘new maths’, discovery learning, set theory and even computer-based individual learning programmes before everyone moved on to a 3-part lesson with chunking and grid methods. Now we have a mastery approach with an attempt to chase the success of Singapore and Shanghai.
However, have the methods and approaches used in the classroom altered that much over time? Effective teaching still involves good questioning, appropriate use of models, an understanding of progression in the curriculum and a knowledge of the connections and structures within mathematics. Perhaps there are small changes to techniques and procedures, but Skemp’s ideas (1977) are still valid – we teach maths with two kinds of learning in mind:
- Instrumental understanding: rote learning of rules, methods or algorithms
- Relational understanding: deep learning, with child able to understand the links, relationships and mathematical structures.
A mastery approach, with an emphasis on fluency of essential skills and the whole class having a deep understanding of a concept before moving on to the next small step, fits in to this nicely.
Parents need to know what is different now though, so these are the key features of a mastery approach to share with parents:
- class working together on the same topic
We have had a strong emphasis on every child making progress in every lesson and this was achieved through differentiation with different groups working at different levels. Now the emphasis is on keeping the class together until specific concepts or skills are mastered and then moving on together. Parents need to know that this does not mean that some children will be left behind or others not challenged. Differentiation is now achieved through intervention and deeper understanding, as explained below.
- speedy teacher intervention to prevent gaps
Those children that have not met the expected outcomes or have gaps in their understanding, will be helped by receiving short, immediate extra time on maths later in the day. Parents need to know that this is a positive opportunity to consolidate their understanding and short practice activities at home could certainly be part of this to follow intervention.
- challenge provided by going deeper not accelerating
For those children that have mastered the skill, concept or procedure they will be presented with higher order thinking activities, rather than accelerating through the curriculum. Some parents may find this difficult to understand so show them some problems and challenges that will highlight the mathematical thinking involved – better still give them some tasks to try.
- focused, rigorous and thorough teaching
Within mastery the idea is to focus on one small step at a time in a lesson, with an emphasis on the mathematical structures involved and the best way to represent these through models and images. Encourage parents to ask their child to explain and show methods or strategies rather than trying to help their child by demonstrating their own method that they learnt at school. Each small step is important as it builds towards deep understanding of a concept so parents providing alternative ‘tricks’ or techniques is likely to just confuse the learning.
- more time on teaching topics – depth and practice
The same topic is likely to have the same focus until the class has mastered the concept, skill or procedure being taught. This is particularly the case for number and calculations. Parents will need to know that, although the focus areas are being taught over a longer time, there are smaller steps of progress and the extra time is for practice and depth, making the learning effective.
The best way to give parents an understanding of a mastery approach is for them to see it in action or to be given a sample lesson or set of activities themselves. Show them the types of questions being asked, the language, models and images used and the way children approach problem-solving through reasoning and mathematical thinking. Hopefully this will give parents a good idea of the depth of understanding that is now expected of their children.
 Skemp, R.R (1977) Relational Understanding and Instrumental Understanding, Mathematics Teaching, 77: 20-6
Paul Broadbent MA B.Ed
Paul Broadbent is a full-time writer and maths consultant with 30 years experience in primary education. He is a best-selling author with over 450 maths books to his name, with recent texts published in the Middle East, Africa and the UK. Paul also has a worldwide reputation for inspiring teachers through his courses and workshops on primary teaching and the learning of mathematics. His MA in Education researched the nature of the deep subject knowledge that primary teachers need when teaching mathematics.
To find out more about mastery and to discover whole-class resources that will assist you in teaching with a mastery approach, visit our maths mastery website: www.collins.co.uk/MathsMastery
And why not read our blog post ‘What is Mastery?’ written by Laura Clarke: