Mathematics is important in everyday life. It is integral to all aspects of life and with this in mind we endeavour to ensure that children develop a healthy and enthusiastic attitude towards mathematics that will stay with them. We promote a collaborative classroom ethos where peers take pride in, and view as important, the need to help one another with their learning. We believe in teaching and praising the perseverance of our pupils and having them view errors as an opportunity to learn.
St Joseph’s Mastery Approach to Maths
We push for a mastery approach where possible, by catering for different abilities within a classroom. We give concrete resources to help them grasp concepts and push the more able with more challenging questions and problems to work on. Those who are not sufficiently fluent with earlier material will consolidate their understanding, including additional practice, before moving on. We plan/adapt planning to meet the needs of the children in our class.
Using Maths No Problem: Our Rationale
Students can under-perform in mathematics because they find it boring or they can’t remember all the rules. This can lead to disengagement. We are developing an ethos of a growth mind-set. This means that mistakes are celebrated as new learning, and children feel encouraged and safe to take risks and persevere.
As professionals, we know that some children find learning by rote more challenging than others. This does not mean that some children should be better at maths than others. As a result, we have opted to take on a new approach in maths, ‘Maths No Problem’. The Singapore method of teaching mathematics develops pupils’ mathematical ability and confidence without having to resort to memorising procedures to pass tests – making mathematics more engaging and interesting. We aim for an ethos of engagement and enjoyment for success.
Features of Singapore Maths:
Emphasis on problem solving and comprehension, allowing students to relate what they learn and to connect knowledge.
Careful scaffolding of core competencies of:
- visualisation, as a platform for comprehension
- mental strategies, to develop decision making abilities
- pattern recognition, to support the ability to make connections and generalise
Emphasis on the foundations for learning and not on the content itself so students learn to think mathematically as opposed to merely reciting formulas or procedures.
Ofsted, the National Centre for Teaching Mathematics (NCETM), the Department for Education, and the National Curriculum Review Committee have all emphasised the pedagogy and heuristics used by Singapore. This method is now being used successfully in the UK by the Ark academies, the Harris Federation, Primary Advantage as well as numerous state, free, and independent schools. We are excited to be a part of this innovative style of teaching.
Dr Yeap talks about one of the fundamental ideas in mathematics: that items can only be counted, added, and subtracted if they have the same nouns. He uses a simple example with concrete objects, chocolates and glue sticks to illustrate the point and then shows how it relates to column addition and the addition of fractions.
Dr. Yeap explains how young children can use concrete materials and later use pictorial representations as number bonds. Number bonds represent how numbers can be split up into their component parts. Children can explore number bonds using a variety of concrete materials, such as counters with containers and ten frames or with symbols.
Dr. Yeap explains how standard column subtraction can be taught meaningfully by using children’s knowledge of number bonds. Once children can explain how numbers can be split into their component parts, they can adapt their understanding to the conventional column subtraction method.
Dr. Yeap discusses how children can develop an ability to calculate the four operations (addition, subtraction, multiplication and division) in their heads without the use of paper and pencil or calculators.
Dr. Yeap discusses how children can learn their times tables meaningfully by using visualisation and other strategies.
Dr Yeap discusses how children can learn to do long division meaningfully by first using concrete apparatus, such as base-10 materials, to perform the operations. They can then explore how this idea is represented in the long division algorithm.
Bar Model 1
Dr. Yeap discusses how diagrams can be used to represent a situation in a problem, such as rectangles representing (unknown) quantities. This method of visualising problems is known as the bar model.
Bar Model 2
Dr. Yeap gives another example of the bar model: how diagrams can be used to represent situations in a problem.
Dr Yeap Ban Har is the Director of Curriculum and Professional Development at Pathlight School, an autism-oriented K-10 school in Singapore. An experienced educator, Ban Har spent ten years at the National Institute of Education, Singapore, where he was involved in several funded research programmes in mathematics education, and where he taught a range of teacher education courses, including Problem-Solving Heuristics in Primary Mathematics and Curriculum Studies in Primary and Secondary Maths. He works regularly in collaboration with the Curriculum Planning and Development Division of the Ministry of Education in Singapore, and he was part of a team which reviewed the Singapore Maths curriculum for the revised 2013 syllabus.
He continues to teach courses at tertiary institutions such as the National Institute of Education (Singapore), Wheelock College (Boston) and Rajabhat Maha Sarakham University (Thailand). He also sits on the advisory board of the SEED Institute and several schools in Singapore and Asia.
Using Number Masters: Our Rationale
The programme of study for mathematics makes clear in its aims that pupils should “become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.”
Fundamental to this rapid and accurate recall of mathematical knowledge is the acquisition of computational fluency and automaticity. To address this, we are using a programme called Number Masters©.
Number Masters© is a unique two-year programme created by mathematics teachers in the Oval Cluster (a cluster of nine primary schools in Lambeth), led by Vauxhall Primary School, aimed at the development of number mastery and computational fluency in Key Stage 1.
Each lesson in the Number Masters© programme is designed to be taught to a small group of pupils, maximum of 8, by a class teacher or teaching assistant, for 15-20 minutes a day, five days a week. This is to ensure that children’s engagement with numbers is intensive and consistent, with the proven effectiveness of small-group work, using scripted materials. Assessment activities are planned for at the end of each week.
The Big Number Crunch
The Big Number Crunch was designed to improve calculation skills at St Joseph’s. It has broken down levels (or steps) of calculation in order to see and promote progression.
Each child will have an addition, subtraction, multiplication and division target. These targets are taken from the steps of calculation.
E.g. In year 6 one child has the following targets:
Addition – step 9 Subtraction –step 10
Multiplication – step 8 Division – step 7
These targets enable children to work at their own level and help them to see where to go next.
Big Number Crunch
Maths Clubs are designed to help children improve the speed of recalling key maths facts. Knowing the key maths facts will enable children to be more confident and progress further in the Big Number Crunch.
Children will work their way through the Maths clubs with regular tests in class. The tests are 3 minutes long. If the children pass the club on three separate occasions they will then move on to the next club.
Children work their way through the Time Clubs with regular tests in class. If they pass the club on three separate occasions they will then move on to the next club.
The story of numbers
The story of numbers is designed to help children recognise number bonds and the different ways numbers can be made up.