Mathematical proof is defined as a thorough and believable argument to support the truth of a prediction in maths, which turns the assumptions into valid conclusions (Haylock and Manning, 2014). Children may be encouraged to move towards the understanding of proof by asking questions, such as ‘Are you positive that it will happen every time?’ (Mooney et al., 2012; Pepperell et al., 2009). There are many different types of proof in

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The importance of this is that if children are able to complete a valid proof, it shows they have an understanding of problem and if they have been able to prove a conjecture, it does in turn show a deeper understanding in mathematics (Goldberger, 2002). The quality and variety of language that pupils hear and speak are important factors in presenting a mathematical proof (Department for Education, 2013), children gain knowledge from one another therefore discussion is used to build secure foundations and help with deriving at a proof. A way to improve the use of proof in Mathematics is by increasing activities within the lesson, by including discrete manipulatives that students’ can physically use to help with their understanding and improve their confidence due to hands on experience (Waring, 2000). Students at all levels should learn to explore their own conjectures by using concrete manipulatives increasingly through primary school (lee,

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Additionally, those processes support students when solving problems and guides them to understand the Maths they are learning and using (Carpenter et al., 2003; Lannin, Ellis, and Elliott, 2011). These specific methods used in mathematics are evident in the 2014 national curriculum for Mathematics. The national curriculum states how all pupils should reason mathematically following a line of enquiry, conjecture relationships and generalisations, and develop a proof using mathematical language (Department for Education, 2013). The current national curriculum has shown a massive change in the use of proof in the classroom from when it was first heavily introduced in both primary and secondary schools (Waring, 2000). Proof has become more emphasised in the national curriculum over the past years because children are now required to be fluent in Maths with a deeper understanding and have the ability to reason mathematically to reach conclusions, especially since the introduction of the mastery