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Angles in 2-D Shapes: A progressive overview

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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. [...]

[...] In this case it would be a negative correlation with both emotional state and performance depreciating. AfL strategies that could combat this could be a teacher observing a pupil more closely whilst circulating around the room and differentiating by output (Elliott pp and Bills and Brooks pp.75) by offering the pupil intensive assistance (scaffolding) and one-one tuition possibly after class. This could involve the teacher going through the fundamental concepts of angle and trying to get the pupil to understand the arbitrary conceptions of the topic. [...]

[...] In this case, AfL might make them perform more successfully if they are secure in their knowledge and excited about what they are learning (Boekaerts and Oatley and Nundy pp.257). Conversely, a high level of confidence may be beneficial in that students are not afraid to confront new subject matter. On the flip side, overconfidence may lead students to make careless mistakes by rushing through questions where a more patient, logical approach is needed (Comer, Darling- Hammond and Kirsch et al. 1998). [...]

[...] On the other hand, this could possibly alienate the pupil from the rest of the class if it is perceived as favouritism from the teacher to that particular pupil. Constructive, specific feedback when marking the student's work of what they have done incorrectly and how to correct their work could really promote progression if the child is responsive to that feedback and actively addresses it (DfES, 2004). An alternative technique to address errors in student's work is to teach them formal proofs such as the angles in a triangle add up to 180 degrees: D A DE is parallel to BC. [...]

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