Williams, 2007) and may present difficulties to pupils who have a right brain hemispheric dominance (and so possibly have a predilection to more logical algebra and number topics) who struggle to think in a more creative, left-brained manner (Sperry, 1945 as cited in Cherry, 2011). Although there are a range of factors, I would venture that teaching style, confidence, level of skill and the perception of errors and misconceptions are the most influential because of their impacts both in the classroom and in life. Using AfL as a solution to stop these factors becoming barriers is particularly important in Geometry as it is needed in every branch of mathematics (Cuoco, Goldenberg and Mark 1986) and a comprehension of it is vital to pupils if they want to participate fully in society (Johnston- Wilder and Mason, 2005).
All of these factors are bipolar- they can both aid and inhibit progression. They vary by individual, gender, age, year group, school, region and in particular by what strand of mathematics the topic is in. Assessment for Learning (AfL) acts as a buffer' to stop these factors becoming barriers and making progression non- linear as it provides pupils with an accurate indicator of where they are, what they need to learn and how they get there (DCSF, 2008). In other words, it helps pupils to identify what point they are at on their learning journey and to try and identify a linear progression forward. It is fundamental to every single maths lesson as children need to know what level they are at in order to progress. In addition, AfL benefits teachers: they can modify their teaching style and the learning activities children are engaged in to enable progress and more enhanced, sophisticated understanding of a topic (Lee, 2004 pp. 101 and Lee, 2013).
[...] Perhaps this was down to the teacher facing external pressures such as achieving high exam results and so subconsciously resorted to the aptly named teaching' where pupils only gain a superficial, surface understanding of a topic rather than a deeper appreciation of its complexities (Entwhistle and Marton, 1994). There are lots of factors that influence progress in Maths: All of these factors are bipolar- they can both aid and inhibit progression. They vary by individual, gender, age, year group, school, region and in particular by what strand of mathematics the topic is in. [...]
[...] Maths is a subject that many children and adults struggle with: the recent Skills for Life survey found that almost half of the working population has the mathematical ability of an 11 year old (BIS, 2011). Further manipulation of the results show that 78% of the population are working at the equivalent of Grade D or below at GCSE Level (TES, 2012). This seems to emphasise just how difficult the majority of the population find maths which is critical considering how essential it is daily life- ask yourself how many times you used maths today and you will be surprised. [...]
[...] Supplementary angles (angles on a straight line) add up to 180 degrees. Angles in a quadrilateral = 360 degrees either known as an arbitrary convention or that sum of interior angles in a polygon= (number of sides x 180 degrees. A student who perhaps is overconfident about this question will perhaps make the reasonable assumption that because angle a looks the same size as 115 degrees so it must equal that. They may even justify that by saying that a equals 115 degrees because alternate angles are equal (again another logical solution as the lies do seem to make the characteristic ‘Z' shape of alternate angles). [...]
[...] Teachers could have more of a literacy focus in their lessons by making sure students know the definition of key terms, all working out is laid out properly and verbal/oral tasks are incorporated into the lesson. Not only would this get pupils to make authentic cross- curricular links (Savage, 2011) with English, the effect of this would be even greater if departments worked together on this approach (Elliott, 2007,pp.67). All of this would seem to emphasise that AfL plays some role in preventing confidence being a barrier to progression in Maths and that if teachers take meaningful actions to provide compelling learning experiences then both their confidence and attainment will increase (QCA, 2005). [...]
[...] Also, the competitive element of tasks such as these should not be exaggerated as less confident pupils may withdraw and not contribute as much (Comer, Darling- Hammond and Kirsch et al. 1998). Activities like these may allow for students develop a more connectionist orientation (Askew, Brown, Johnson et al., 1997) where they notice the relative change between shapes and angles (e.g. the angles in a square add up to 360 which is double the sum of the angles in a triangle) instead of the absolute change (e.g. a square has one more angle than a triangle) (Bennett and Briggs, 2005). [...]
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