We reject the idea that a large proportion of people ‘just can’t do maths’. All students are encouraged by the belief that by working hard at mathematics they can succeed and that making mistakes is to be seen not as a failure but as a valuable opportunity for new learning. Our Head of Department is an NCETM secondary Mastery lead teacher, who has completed a three year Mastery programme, which included an exchange visit to Shanghai. The principles of TfM (Teaching for Mastery) are now a key feature of the department.
Mastery is achieved through developing procedural fluency and conceptual understanding in tandem, since each supports the other. Lessons are designed to have a high-level of teacher-student and student-student interaction where all students in the class are thinking about, working on and discussing the same mathematical content. Challenge and the opportunity to deepen understanding of the key mathematical ideas is provided for all.
Every attempt is made to keep the whole class learning together. Differentiation is achieved, not through offering different content, but through paying attention to the levels of questioning, support and challenge needed to allow every student to fully grasp the concepts and ideas being studied. This ensures that all students gain sufficiently deep and secure understanding of the mathematics to form the foundation of future learning before moving to the next part of the curriculum sequence.
For those students who grasp ideas quickly, acceleration into new content is avoided. Instead, these students are challenged by deeper analysis of the lesson content and by applying the content in new and unfamiliar problem-solving situations. If some students fail to grasp an important aspect of the lesson, this is identified quickly and early intervention ensures that they are ready to move forward with the whole class in the next lesson.
Lesson design identifies the new mathematics that is to be taught, the key points, the difficult points and a carefully sequenced learning journey through the lesson. In a typical lesson, the teacher facilitates whole-class interactive discussion, including active debate and argument based around the tasks offered. Through teacher-student and student-student interaction the teacher encourages demonstration, explanation, exploration, analysis and generalisation (leading to proof where appropriate).
We recognise that practice is a vital part of learning, we aim for the practice to be intelligentpractice that develop students’ conceptual understanding and encourage reasoning and mathematical thinking, as well as reinforcing their procedural fluency. Our teachers use well-crafted examples and exercises which, through careful use of variation (including what to keep the same) focuses students’ attention on the key learning point. Significant time is spent developing a deep understanding of the key ideas and concepts that are needed to underpin future learning. The structures and connections within the mathematics are emphasised, which helps to ensure that students’ learning is sustainable over our 5 year curriculum. Key facts such as number facts (including multiplication tables), formulae and relevant theorems, as well as key algebraic techniques, are learnt and practiced regularly in order to avoid cognitive overload in the working memory. This helps students to focus on new ideas and concepts.
We have elected to assess students using GCSE grades, in all year groups. Students are expected to sit an Edexcel GCSE paper, modified as appropriate, on a regular basis, in a formal setting. This regular on-going assessment provides both teacher and student with information regarding current attainment and the ‘learning gaps’ that may exist. When students complete an assessment they use Pinpoint Learning to analyse their individual learning gaps. In Year 11 students are entered for either the ‘Higher’ or the ‘Foundation’ Edexcel GCSE examination. We aim to enable students to achieve their full potential in external examinations so that they can continue to study mathematics further.
To enable students to become independent learners and to assist parents who may wish to offer guidance with homework, we have registered all students with MathsWatch and MyMaths websites. There is also a regular homework club two lunch times a week for those students who need extra support and guidance.
Extra-curricular activities are embedded within our departmental culture, we seek to engage the students in exploring topics across the curriculum and to take them to new levels of thinking. The UKMT (United Kingdom Mathematics Trust) club meets weekly for students of all ages where time is spent problem solving, through this, team work is developed and new strategies are explored. Individual competitions allow our students to compete against other students throughout the country.
Our STEAM club is an established feature of the school, where students and teachers (from different departments) meet weekly to delve into mathematical modelling; or to compare reaction times; or even to work out the cheapest way to package ping pong balls!
1: Students are Mathematically Coherent
By focusing on one key point each lesson deep and sustainable learning is achieved.Students are able to make mathematical connections when something has been deeply understood and mastered, it is then used in the next steps of learning.
2: Students use Representations to understand the Mathematical Structure
Representation expose the structure of the mathematics being taught. They are used to guide the student through the learning. Students are encouraged to move from the ‘structural’ to the ‘verbal’ to ‘abstract’ through their leaning journey.
3: Students appreciation the importance of Variation
Students are encouraged to avoid mechanical practice and, instead, to practice the thinking process (intelligent practice). The central idea of teaching with variation is to highlight the essential features of a concept or idea through varying the non-essential features.
4: Students are mathematically Fluent
Fluency demands more of students than memorising a single procedure or collection of facts. It encompasses a mixture of efficiency, accuracy and flexibility. Quick and efficient recall of facts and procedures is important in order for students to keep track of sub-problems, think strategically and solve problems. Fluency also demands the flexibility to move between different contexts and representations of mathematics, to recognise relationships and make connections and to make appropriate choices from a whole toolkit of methods, strategies and approaches.
5: Students Think Mathematical
Mathematical thinking is central to deep and sustainable learning of mathematics.
Taught ideas that are understood deeply are not just ‘received’ passively but worked on by the student. They need to be thought about, reasoned with and discussed.Mathematical thinking involves: looking for pattern in order to discern structure; looking for relationships and connecting ideas; reasoning logically, explaining, conjecturing and proving.
Mr G. Kane
Mrs A. Mckay
Mrs R. Miszkurka
Dr P. Spence
Mrs S. Stanton
Mrs C Taiwo
Mrs E. Thomas