Thornhill’s key principles for the teaching and learning of mathematics:

"Everything around you is mathematics. Everything around you is numbers." - Shakuntala Devi

Connections, context and creativity

At Thornhill, our vision is for each child to have a solid foundation in the concepts and vocabulary of maths so that they can apply it in solving a diverse range of problems connected to the world around them.

Throughout the school, daily lessons follow the concrete-pictorial-abstract approach to maths learning. Using ‘concrete’ objects and resources helps children to understand the abstract concept of number. In creating their own pictorial representation at the next stage, children distil and assimilate this knowledge to create their own unique understanding. Going through these stages creates the solid foundation that learners need to become fluent in using more abstract methods to solve problems.

Creating opportunities for children to learn in this way is the goal of our teaching staff, who use a combination of their professional knowledge and varied resources to tailor daily activities. In this way, our staff provides quality first teaching. Teachers are supported in achieving this goal by leadership, benefitting from provision of up-to-date, varied resources, targeted professional development and supportive feedback from monitoring.

As well as a solid foundation in number, we guide and support children’s learning in key areas of mathematics:

• Vocabulary – Understanding subject-specific language is vital to improving fluency in thinking and discussion. New words are explicitly introduced and explained with further activities planned to practise their use. Frequently updated displays (working walls) provide reminders of usage.

• Reasoning – Further opportunities to grasp the true meaning of mathematical language are provided through reasoning. Exploration of definitions in class activities, as well as of patterns and qualities of numbers, deepen understanding of the concepts words represent. Guided support is provided at age-appropriate levels to test out statements and give proofs.

• Problem-solving – Wherever possible, we promote creativity, provide meaningful contexts and encourage the children to apply their learning to everyday situations. Learning on each topic is encompassed by a ‘Big Question’ to which children can relate their activities from each lesson. This encourages cognitive activation, which in turn helps children to make links within their maths learning. Teachers promote reflection on approaches to problems and use open questioning to guide children’s thinking.

To support all children in their maths learning, Thornhill provides opportunities for further study outside of the classroom. Weekly homework on recent class topics gives children the chance to repeat and rehearse their new knowledge with the intention of improving recall. Children and families can choose from a range of websites to which we provide free access – Mathletics, Maths With Parents, Times Table Rockstars – in order to practise their skills.

Assessment and monitoring of learning by all teaching staff contribute to identifying children for whom extra support is needed. Interventions are tailored to the needs of groups or individuals to give them the support that they need in order to gain greater understanding of the subject. We believe that all children have the ability to develop their understanding of mathematics, to solve problems using this ability and to recognise the presence of this incredible subject in the world around them.

The effective teaching of mathematics at Thornhill

• Design: Strong subject knowledge of the National Curriculum’s mathematics schedule means that our teaching staff is perfectly equipped to design sequences of learning for their year group. Our calculation policy gives guidance and examples so that expectations are clear and progression assured. Prepared and differentiated resources for each lesson give all learners access to achieve curriculum goals.

• Instruct and model: Delivery of each lesson includes clear use of language to demonstrate how new concepts, mathematical vocabulary and arithmetic methods can be used correctly. Presentation slides, vocabulary cards and sentence stems encourage children to incorporate key terms into their talk and practice of maths immediately.

• Explore: Opportunities to explore new concepts are given through use of concrete resources in class. Children are also encouraged to make links with other subjects and the world around them, looking for patterns and number in maths walks around our school or in specific teaching points across the curriculum.

• Discuss: Paired and group tasks are utilised in class to encourage children to apply vocabulary and test out ideas. Different outcomes and approaches are evaluated as part of whole-class teaching.

• Practise and apply: “The only way to learn mathematics is to do mathematics.” As Paul Halmos stated, practising skills, whether newly acquired or part of students’ existing skill-sets, is the most fundamental part of mathematics learning. In each sequence of learning, each day is planned to give students the opportunity to practise and apply their skills at a variety of differentiated levels with numerous questions and further challenges.

• Reason: From simple true/false evaluations in KS1 to evidenced proofs in KS2, students are guided in how to reason logically. Statements that require children to examine the concepts behind key vocabulary are carefully planned so that children can test and evaluate them and deepen their understanding.

• Problem-solve: Our ‘Big Question’ for each sequence of learning promotes engagement from students and an open approach to problem solving. Daily questions or challenges require students to show important characteristics such as curiosity and resilience as well as application of taught skills.

• Assess: Assessment in mathematics at Thornhill is an ongoing process, from initial assessments of learning to inform planning, through daily review and feedback, including self- and peer- assessment by the students, to summative tests administered once a term. Teachers log progress towards curriculum goals on Target Tracker, adjusting planning and delivery of learning accordingly, all the while encouraging students to be aware of their own achievements and areas for development.