The intent of our mathematics curriculum is to design a curriculum, which is accessible to all and will maximise the development of every child’s ability and academic achievement. We deliver lessons that are creative and engaging. We want children to make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. We intend for our pupils to be able to apply their mathematical knowledge to science and other subjects. We want children to realise that mathematics has been developed over centuries, providing the solution to some of history’s most intriguing problems. We want them to know that it is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. As our pupils progress, we intend for our pupils to be able to understand the world, have the ability to reason mathematically, have an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.
Singapore has become a “laboratory of maths teaching” by incorporating established international research into a highly effective teaching approach. With its emphasis on teaching pupils to solve problems, Singapore Maths teaching is the envy of the world. As a result, we have implemented a mastery curriculum based on the principles of Singapore Maths
Programme Based On Established Theories
Singapore Maths is an amalgamation of global ideas delivered as a highly effective programme of teaching methods and resources. The approach is based on recommendations from notable experts such as Jerome Bruner, Richard Skemp, Jean Piaget, Lev Vygotsky and Zoltan Dienes.
Bruner studied how children learned and put forward the Concrete Pictorial Abstract (CPA) approach to learning. He also coined the term “scaffolding” to describe how children build on the information they have already mastered. In his research on the development of children (1966), Bruner proposed three modes of representation: concrete or action-based (enactive representation), pictorial or image-based (iconic representation) and abstract or language-based (symbolic).
Based on his findings, Bruner proposed the spiral curriculum: a teaching approach in which each subject or skill area is revisited in intervals at a more sophisticated level each time. Using this technique of a spiral curriculum, material is presented in a logical sequence. Initially a concept is enacted with “concrete” materials, later it is represented by models (pictures) and then by abstract notation (such a plus or equals sign). These learning theories are the basis of the Concrete Pictorial Abstract approach which runs throughout the Maths — No Problem! Programme.
Skemp wrote about instrumental and relational learning in his paper “Relational Understanding and Instrumental Understanding” (Richard R. Skemp Department of Education, University of Warwick. First published in Mathematics Teaching 7 in 1976).
Skemp distinguishes between the ability to perform a procedure (instrumental) and the ability to explain the procedure (relational) and argues that these are two different methods of learning - relational and instrumental. Singapore Maths aims for pupils to progress beyond seeing mathematics as a set of arbitrary rules or procedures so that they have a relational understanding.
Based on Dienes’ ideas (1960), systematic variation is used throughout the series. The idea is that you vary the lesson through a series of examples that deal with the same problem or topic. Variation can take the form of mathematical variability, where the learning of one particular mathematical concept is varied, and perceptual variability, where the concept is the same but the pupils are presented with different ways to perceive a problem and use different ways to to represent the same concept. The Singapore Maths approach presents this in a systematic way to ensure pupils comprehend what they are learning.
We use Maths No-Problem! as our core resource. Click for more information
This approach starts from the moment our children enter the school in EYFS. During this time we ensure all children develop firm mathematical foundations in a way that is engaging, and appropriate for their age.
In our EYFS the children explore six key areas of early mathematics, which collectively provide a platform for everything children will encounter as they progress through their maths learning at primary school, and beyond:
Cardinality and Counting: understanding that the cardinal value of a number refers to the quantity, or ‘howmanyness’ of things it represents
Comparison: understanding that comparing numbers involves knowing which numbers are worth more or less than each other
Composition: understanding that one number can be made up from (composed from) two or more smaller numbers
Pattern: looking for and finding patterns helps children notice and understand mathematical relationships
Shape and Space: understanding what happens when shapes move, or combine with other shapes, helps develop wider mathematical thinking
Measures: comparing different aspects such as length, weight and volume, as a preliminary to using units to compare later.
Teaching begins with a heavy focus on language development and teaching children to use the language of maths that they will be hearing and using throughout school. Children are encouraged to explain and reason their maths knowledge in order to show a deeper understanding of the mathematical concepts that they are taught. The children are also introduced to many manipulative resources that will support their learning throughout school, such as numicon and ‘count up’.
Children are encouraged to complete weekly independent maths challenges to further demonstrate the concepts that they have been taught. Mathematics is also highly encouraged in areas of our curriculum which tie into our STEM agenda, such as construction.
Children Ks1 and KS2 are taught mathematics through a mastery approach, utilising the Maths - No Problem!, scheme of work. It complies with the UK’s High Quality Textbook guidance published by the NCETM and was selected by the DfE for use in the Maths Hub programme. The Singapore approach to mathematics teaches pupils to understand maths in stages, beginning with concrete (using counters, Base 10, number disks and so on), then moving to pictorial (solving problems where pictures are involved), and finally working in the abstract (where numbers represent symbolic values). Through this process, children learn numerous strategies to work with numbers and build understanding.
The whole class works through the programme of study at the same pace with ample time and practice in each topic before moving on. The concept of teaching to mastery is to ensure that topics are well developed. An idea is well-formed then reinforced by practice. New knowledge is then used in subsequent lessons so that all ideas build on top of each other and pupils have plenty of opportunities to develop relationships between topics. Ideas are revisited in a spiral as pupils progress through the years, each time at a higher level.
Each lesson is divided into distinct parts: an anchor (or ‘In Focus’) task, guided practice and independent practice. During the anchor task, children work in groups on a single problem from the textbook allowing the teacher to assess what they currently know and extend their understanding. In the guided practice section, children work through further questions from the textbook with a partner but under the guidance of the teacher, to practise an idea that has been developed in the anchor task. The final section of the lesson is independent practice where the children work in the workbook to apply the ideas and taught that lesson.
Additional mastery resources are chosen carefully by teachers to support our core scheme, including White Rose and further problem solving and reasoning publications. Journaling should take place at the end of the ‘In Focus’ section. It is the point of the Maths lesson where children record one or more methods/ideas from their ‘In Focus’ investigation. For more information see the Journaling Guidance. Feedback to learners is provided through daily verbal feedback sessions at the start of each maths lesson. Misconceptions are addressed and challenges set for ‘rapid graspers’. We believe this is far more effective than written feedback, as understanding a child’s misconception is not always possible through distant marking.
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