Teaching secondary mathematics
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# 2.1 Mathematics and the curriculum

The English national curriculum (DfE, 2014) states the following about mathematics:

> The national curriculum for mathematics aims to ensure that all students:

> 1. become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that students develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
> 2. reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
> 3. can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

The implication of this national curriculum is that being mathematical is about fluency in fundamental ideas, reasoning mathematically and solving problems.

## Activity 4 Connecting the curriculum

Allow about 90 minutes

Relate the ideas about connected knowledge and mathematical thinking discussed above to the aims of the English national curriculum (or to your own curriculum, if you are studying in another country).

Access your statutory or advised curriculum. Does the way that the curriculum is set out help you in your job of connecting mathematical ideas?

Does it encourage you to challenge your students to see how ideas in mathematics depend on one another and need to be seen as a whole interconnected system?

Can you teach the ‘content’ of the curriculum in your country using John Mason’s ‘essentials of thinking mathematically’? These include:

- specialising – trying special cases, looking at examples
- generalising – looking for patterns and relationships
- conjecturing – predicting relationships and results
- convincing – finding and communicating reasons why something is true.

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