A Rationale on the concepts and misconceptions of an area and how, as a teacher, I can progress children’s understanding
I chose to develop a Medium Term Plan (MTP) to study area with a year five class. The reason for choosing area was because I was surprised on placement how many children did not grasp immediately that the area did not change when the shape changed and I found this extremely challenging to overcome. By looking into the subject more deeply, I thought I would find ways to challenge these misconceptions.
Key Concepts and Misconceptions of Area
When defining area, Koshy et al (2000) discuss that it is a two dimensional concept and relies on comparison with a square due to measures of area being in centimetres squared (cm2) or metres squared (m2). Due to the nature of these measurements, it is easy to see why children misconstrue these concepts. The National Numeracy Strategy requires that teachers 'identify mistakes, using them as positive teaching points by talking about them and any misconceptions that led to them' (DCSF, 2006). When teaching children, it is not enough for them to simply be told that something is wrong. They must be given an opportunity to change these misconceptions by revising their ideas and concepts in a particular topic.
When looking at the conservation of area in particular shapes, Hansen (2011) discusses how children believe that children look at an amount of space a shape takes up, the more the surface area. This can be seen when looking at a parallelogram rather than a rectangle. When asked which shape has the greater area, most children will point out that the parallelogram has the greater area even though they are the same.
Another misconception is looking at the relationship between length and area. Hansen (2011) writes that if children are asked what would happen to the area of a rectangle if the length and width were doubled, some could assume that the area will be doubled. The children think this because the sides have been multiplied and this would apply to the area. This is not always true. The use of calculation is useful for rectangles when they are measured but children should be aware that they should only be multiplying the length and width as there have been may be the misconception that they are to multiply all the labeled sides. Progression Across the Age Range in Area
Children come across the concept of area in the foundation stage when they are painting surfaces in Nursery. This is developed throughout KS1 with children identifying objects that are ‘greater’ or ‘smaller’ using real life, practical examples in the classroom. Children are introduced formally to area in Year 4 and would have some knowledge of this when beginning this planned task for Year 5. They would have learned how to measure area using squared paper. In accordance to the Primary National Strategies (PNS) ‘Progression in Maths’, the Year 5 focus should now be on measuring the sides of shapes and use their measurements to calculate their area. They should also understand that area is measured in squared units such as cm2 or m2. They should be able to design rectangular areas using the length of the sides to calculate how much area they need. They can use these approaches in addition to other resources and use this formula to calculate the area of a rectangle. Once children have gained understanding of this should prepare them for Year 6. Here they will be expected to ‘estimate and compare areas of irregular shapes by counting squares and part squares and calculate the area and perimeter of compound shapes that can be split’ (DCFS, 2006).
Engaging the Learner and Addressing the Key Concepts of Area
The first lesson that I planned was an elicitation activity, giving me the opportunity to ascertain any misconceptions the children may have in regards to area, The use of visual shapes that have the same area but different perimeters. The NC...
Bibliography: DCFS. (2006). Year 5 Progression in Mathematics. Available: http://webarchive.nationalarchives.gov.uk/20110809091832/teachingandlearningresources.org.uk/collection/4863. Last accessed 9th April 2013.
DCFS. (2006). Year 6 Progression in Mathematics. Available: http://webarchive.nationalarchives.gov.uk/20110809091832/teachingandlearningresources.org.uk/collection/7990. Last accessed 9th April 2013.
DCFS (2006) Primary Framework for literacy and mathematics London: QCA
DfEE, (1999) Mathematics, the National Curriculum for England, London: DfEE
Hansen, A., (2008) Primary Mathematics: Extending knowledge in Practice, Exeter: Learning Matters.
Haylock, D. & F. Thanagata, (2007) Key Concepts in Teaching Primary Mathematics, London: SAGE.
Mooney, C. (2007) Primary Mathematics: Teaching theory and practice, Exeter: Learning Matters.
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