# Mathematics

## We reject the idea that a large proportion of people ‘just can’t do mathematics’. 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.
Mastery is achieved through developing procedural fluency and conceptual understanding in tandem, since each supports the other. |

We will adopt a 5-Year pedagogic scheme of learning which allows students to make progress through manageable steps through the curriculum. Differentiation will be 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 will be challenged by deeper analysis of the lesson content and by applying the content in new and unfamiliar problem-solving situations. Lesson design will define the new mathematics that is to be taught, the key points, the difficult points, misconceptions and a carefully sequenced learning journey through each 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 will aim for practice to be ‘intelligent’ - that develops students’ conceptual understanding and encourage reasoning and mathematical thinking, as well as reinforcing their procedural fluency. We will use well-crafted examples and exercises which, through careful use of variation focuses students’ attention on the key learning point. Significant focus will be placed on developing a deep understanding of the key ideas and concepts that are needed to underpin future learning. The structures and connections within the mathematics will be emphasised, and this will help 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, will be practiced regularly in order to avoid cognitive overload in the working memory. This will help students to focus on the new ideas and concepts being taught. We have elected to focus our assessment strategy on identifying the level of mastery each individual has achieved within each topic area studied. This regular on-going assessment provides both teacher and student with information regarding current levels of understanding and the ‘learning gaps’ that may exist. We will record this information for each individual thus providing each individual with a ‘progression passport’ in mathematics. This passport will travel with the individual student from year-to-year so that their current level of understanding is available to all staff thus allowing future teachers to plan appropriately based on previous learning. To enable students to become independent learners homework tasks will be regularly set to allow students to practice the mathematics learned. These well focused homework tasks will form an essential part of the learning process. |

**Maths Curriculum Impact Statement:**

**Students will be Mathematically Coherent**By focusing on learning for mastery, deep and sustainable learning will follow. Students will be able to make mathematical connections when something has been deeply understood and mastered. This will be used in the next steps of learning.

**Students will use Representations to understand the Mathematical Structure**Representation exposes the structure of the mathematics being taught. They will be used to guide the student through their learning. Students will be encouraged to move from the ‘structural’ to the ‘verbal’ to ‘abstract’ through their leaning journey.

**Students will appreciate the importance of Variation**Students will be encouraged to avoid mechanical practice, instead to practice the thinking process (intelligent practice). The central idea of teaching with variation will highlight the essential features of a concept or idea through varying the non-essential features.

**Students will develop Mathematical Fluency**Fluency will demand more of students than memorising a single procedure or collection of facts. It will encompass a mixture of efficiency, accuracy and flexibility. Quick and efficient recall of facts and procedures will be important in order for students to keep track of sub-problems, think strategically and solve problems. Fluency will also demand the flexibility to move between different contexts and representations of mathematics, to recognise relationships, to make connections and to make appropriate choices from a whole toolkit of methods, strategies and approaches.

**Students will be Mathematicians**Mathematical thinking is central to deep and sustainable learning of mathematics. Taught ideas will be understood deeply and worked on by the student and not ‘received’ passively. Taught ideas will be thought about, reasoned with and discussed. Mathematical thinking will involve looking for patterns in order to discern structure; looking for relationships and connecting ideas; reasoning logically, explaining, conjecturing and proving.