# Proof In The Primary Classroom

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The complexity of proof in primary school changes as children progress through different key stages, there is seen to be a huge change of proof in secondary schools compared to primary school. Proof has received a prominent role in Maths for secondary school, a key part of all student’s Maths experience (Knuth, 2002). However, it is still included in the primary curriculum just with more depth in secondary schools. Primary school children may not be able to explain their Maths conclusions in depth by a means of formal proof but they can begin to demonstrate and clarify why something is true to then reach a valid proof (Haylock and Manning,

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A technique like this is useful as children can make a hypothesis to test out, for example giving children ‘Two positives make a positive’ and asking them to say whether it is always sometimes or never true, therefore creating an axiom. Extending the children’s knowledge further is a good technique to develop their thinking, if the answer is sometimes, the teacher can then ask the students to come up with a counter example for that conjecture. Examples of ASN questions gradually become harder throughout the school, an example of an ASN question for proof that could be used in year 1 is ‘all 3D shapes have at least four faces’ moving onto year 6 ‘when you cut off a piece of a shape you reduce its area and perimeter’ (Issue 34, 2011). The complexity of these particular type of proofs can be adjusted to fit in with the national curriculum at the appropriate ages. Another technique is the use of a conjecture, this is reasoning in order to develop statements in mathematics which are considered true but in fact have not actually be proven true (Herringer, 2013). Children can create a conjecture which has not yet been checked, this is identified as blooms taxonomy which allows deeper learning and requires more complex thinking skills (Piggott, 2011), children are then able