Recommended approaches to the teaching and learning of Mental Computation
pedagogical approaches
"It is critical to find out how primary school children learn mental computation skills: Should teachers directly teach them those skills or should teachers encourage students to develop their own skills?" (Farron & Varol, 2007). The answer to these questions is within how well you know your student and their individual abilities.
The 20th century has seen many changes of pedagogical approaches regarding the teaching and learning of mathematics. Now rather than 'train students in mental disciplines' or drill them 'rote learning' it is accepted that when the child is developmentally ready they can successfully construct their own learning. This of course happens with teachers who really know their students and how they learn (Reys et al. 2012, pp. 6-8). One of the most important things you can communicate to your students is a positive attitude towards mathematics (Knaus 2013 p.6). If it isn't your strong point then you also need to become an active learner yourself. This will lead to "... a greater understanding and appreciation of ways to teach" (Reys et al. 2012, p.38). Children need to be able to articulate the strategies they come up with "...the emphasis should be on children developing their own strategies by exploring, discussing, and justifying their thinking and solutions." (Heirdsfield, 2011). "When we try to teach children to make relationships between numbers by teaching them algorithms, we redirect their attention from trying to make sense of numbers to remembering procedures... When children think in their own ways, they become more confident in their mathematical ability and go on to construct increasingly higher levels of thinking..." (Kammi & Dominick, 1997).
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Some difficulties children may have:
"...basic fact retrieval can be assisted through providing students with opportunities to visualise basic facts and to use thinking strategies to see patterns and connections between facts" (Dole & McIntosh, 2004)
"The overarching principle is to have children construct their understanding of mathematics themselves, rather than internalise what others present to them" (DEECD, 2009).
"Recent research into students’ learning suggests that the emphasis should be on helping students to acquire a flexible ‘toolkit’ of efficient strategies together with the ability to make suitable choices of these strategies for particular calculations.
Critical components of this approach are:
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work Example
Foundation Level: How to Share 5
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This student is performing basic number sentences with the focus on place value and procedure. Here we can see the child begin to really understand what makes a number.
Exposure to activities such as these provide a crucial step towards mental computation. Even if initially incorrect the overall concepts are filtering through. |
Foundation Level: How to Share 10
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Natural Manipulatives
" Materials enhance learning when they reflect what is natural and familiar and also introduce novelty to provoke interest and more complex and increasingly abstract thinking." (EYNF p.16 as cited in Knaus, 2013 p.7) |
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Pictures by Lara: [email protected]
Books to share: integrating mathematics
Constant mathematical reminders in other curriculum areas build strong mental pathways.
Movement and maths - physical numberline
![Picture](/uploads/2/0/8/1/20815378/4684720.jpg?1413766360)
- Create different moves and give them a numerical value - Jump = 5 Hop= 1 Spin=10 (depending on the skill level this could get quite complex)
- The children are going to move along their own numberline (this could be a physical line drawn with chalk on the basketball court or masking tape in a multipurpose room. You may just want to have a a starting point on one side of the school oval.
- Give them any number and they create it with the moves 33= 2x Jump + 2x Spin + 3xHop
This can be extended further by questioning and having the students explain what moves they made. They could draw pictures of their favourite moves and then make links with formal number sentences. Exploring different ways of representation builds a child's mental computation skills.