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Maths assignment - Helping children to develop their understanding of…
Maths assignment - Helping children to develop their understanding of calculation
Lesson coherence
Conceptual understanding
Children do not have the mental maturity to grasp abstract mathematical concepts presented in words or symbols alone and need many experiences with concrete materials and drawings for learning to occur. (Piaget, 1952 cited in Moyer, 2001?)
Zoltan Dienes's (1969) work convinved researchers that the use of various representations of a concept, or 'multiple embodiments', were needed to support students' understanding. (cited in Moyer, 2001?)
Links to the manipulative - dienes
Representations can make abstract mathematical concepts more accessible (Flores, 2002, cited in Mitchell, DATE?)
WHAT I THINK: Children need to have a good understanding of mathematical concepts in order to develop their understanding of calculation. For example, a child is going to be unable to do an addition calculation without understanding the mathematical concept of addition and having knowledge of different strategies for undergoing this calculation e.g. partitioning.
Commutative law - when you add or multiply numbers, you get the same answer if you swap the numbers round.
Associative law - does not matter how we group the number e.g. which number we calculate first.
National curriculum statement - Add two two-digit numbers using concrete objects.
Key vocabulary / language
Prior learning experience
Choice of resources / manipulatives - Dienes
Procedural understanding
Rationale - strengths and limitations of using representations/manipulatives e.g. dienes.
One challenge relates to using representations without building mathematical meaning. This might happen when students are forced to imitate procedures without the opportunity to reflect on their actions or the guidance to make connection between representations and underlying mathematical ideas. (Clements and McMillen, 1996; Stein and Bovalino, 2001 cited in Mitchell, DATE?)
What have I learned from planning this lesson introduction? How will it influence my future practice?
