Content 

The mathematical curriculum content is divided into declarative, procedural and conditional knowledge. Declarative knowledge is static in nature (I know that) and consists of facts, formulae, concepts, principles and rules. Providing knowledge of the early mathematical code: facts, concepts, vocabulary and symbols is vital for students’ success. Students must be taught core facts, formulae and concepts that are useful now and in the next stage of education. It is also imperative that students develop their automatic recall of core declarative knowledge, rather than rely on derivation, guesswork or casting around for clues.

Procedural knowledge is recalled as a sequence of steps (I know how). The category includes methods, algorithms and procedures: everything from long division, ways of setting out calculations in workbooks, to the familiar step-by-step approaches when solving quadratic equations. Students need to learn non-distracting and accurate mathematical methods that encourage them to use recall over derivation. Over time students learn use more efficient, systematic and accurate mathematical methods that they can use for more complex calculations and in their next stage of learning. This supports students to see new connections of number, geometry and time.

Conditional knowledge gives students the ability to reason and solve problems (I know when). Useful combinations of declarative and procedural knowledge are transformed into strategies when pupils learn to match the problem types that they can be used for. Students learn useful, topic-specific strategies, as well as how to match them to types of problems. They develop confidence in using linked facts and methods that are the building blocks of these strategies and use core, systematic strategies rather than resorting to guesswork or unstructured trial and error.

From Reception to Year 6, pupils will be encouraged to use a range of strategies to support their learning. These include the use of counting materials (fingers, rulers, counters) pictures, jottings or a formal written method. Children are encouraged to look at a calculation with ‘number sense’ and use their ‘number knowledge‘. The child will decide on the best approach to solve the problem, for example whether to solve it mentally, to draw the problem out or use a written method.

As we teach each granule of mathematics, we ensure the children move through three specific stages which support their development of understanding. These stages are called Concrete, Pictorial and Abstract.