How We Teach Mathematics
All classes at St Michael’s C of E Primary School use the Power Maths scheme, which aims for the children to achieve mastery in their maths learning. Mastery maths aims for children to acquire a long-term, deep, confident and adaptable understanding of maths concepts. The maths curriculum for each year is detailed below.
Key principles underpinning Maths Mastery learning:
Fundamental to this approach is the belief that every child can understand and succeed in mathematics – to dispel the perception that some people just can’t do maths – no one would say that they just can’t do reading.
Children are taught through whole-class interactive teaching, where the focus is on all pupils working together on the same lesson content at the same time. This ensures that all can master concepts before moving to the next part of the curriculum sequence, allowing no-one to be left behind. Where appropriate, there are also opportunities for the children to deepen their understanding still further.
Children master concepts one at a time, building on prior learning to help them see patterns and connections. For each year group the curriculum is broken down into core concepts, taught in units (link to year group units). Each unit divides into smaller learning steps, which make up the different lessons. Each unit begins with a unit starter, which introduces the learning context and the key mathematical vocabulary, structures and representations.
Children are praised for the hard work they put into their learning because, by praising effort rather than success, they will be more willing take risks and persevere.
It’s OK to get things wrong, mistakes are valuable opportunities to re-think and deepen understanding.
The language used in class encourages all: Everyone can! Mistakes can help you learn. Just try for a little longer. We can’t solve it YET!
Every child is expected to contribute in every lesson, answering questions and explaining or demonstrating their understanding.
Same day intervention ensures the class keeps progressing together. Teachers identify which children need extra support, which is given either during the lesson or at another time in the school day.
The learning of precise mathematical language is carefully planned. Key vocabulary is highlighted at the start of every lesson and new terms are clearly explained. The connection between symbols and language is stressed early on so that children quickly become familiar with them. Teachers model using mathematical language to explain reasoning and every child is expected to use the correct mathematical terms in full, responding in complete sentences, when reasoning, explaining or discussing maths. Children are given sentence models to work with, eg. “4 is a part, 5 is a part, 9 is the whole.” “There are 8 groups, there are 5 in each group.” This can initially be difficult for children who find maths easy and have been used to saying, “I just know!”
Mental maths facts such as multiplication tables and addition and subtraction facts within 10 are learnt automaticity to avoid cognitive overload in the working memory and enable pupils to focus on new concepts.
Individual practice is a vital part of learning, but the practice used is intelligent practice that both reinforces fluency and understanding. Rather than solving exactly the same type of problem during practice time, children solve problems that differ incrementally in the way they are presented and the approach required, which allows for deeper learning. The children have to think!
The concrete – pictoral – abstract approach (see calculation policies below) requires the use of clear mathematical models. Traditionally children have been expected to use purely abstract representations of mathematical problem solving too soon, with a negative impact on learning. In Maths Mastery they learn to use practical mathematical equipment – counters, etc., and pictoral representations to solve mathematical problems, all the way up to year 6. This helps the children make connections, grasp concepts and clarify and demonstrate their understanding.
The concrete-abstract-pictoral approach
Concrete – uses real objects that children can use to help bring maths to life. It is important that children understand links between models and the objects they represent eg. 3 cakes represented by 3 pretend cakes/ 3 counters/3 straws. Good concrete models are an essential first step in understanding.
Pictoral – uses pictoral representations of objects to let children see what particular maths problems look like. This helps them make connections between the concrete and pictoral representations and the abstract concept. It also helps if the children can see a concept presented in a number of ways – eg, the number 6 can be represented by 6 pens, 6 counters, 6 dots, 6 cubes …
Abstract – the ultimate goal is for children to understand abstract mathematical concepts, symbols and notation: some children reach this stage more quickly than others. To work with abstract concepts, a child must first be comfortable with the meaning of the relationships between concrete, pictoral and abstract.
Concrete Pictoral Abstract
Typical Power Maths Lesson Format
The lesson starts with a short power up activity which supports fluency in key number facts.
Discover and share – practical real-life problem-solving, usually as paired work, using concrete objects to solve the problem. Sharing highlights the variety of methods that can be used to solve a single problem and gives every child the opportunity to offer answers.
Think together – children work in groups and pairs, discussing methods and solutions to problems. This encourages all children to think about how they solved the problem and explain it to their partner. Concrete materials are on tables to support and reinforce learning.
Practice – children work independently from practice books, while staff circulate to check progress. Sometimes staff will work with specific groups or individual children. Practice questions are presented in logical sequence, problems are represented in different ways, requiring different approaches. This encourages the children to think more creatively about how to reach a solution.
Reflect – the class comes together, giving the children the opportunity to review, reason and reflect on their learning. Open-ended questions, eg spot the mistake, allow teachers to check how deeply children have understood the day’s concept and plan for additional intervention accordingly.
Though we are following the Power Maths scheme, using text books, interactive teaching tools, practice books and lesson plans, the teachers will adapt and supplement these materials from other sources when they judge this necessary.