Essay on Evaluate the Factors That Affect Successful Mathematics Teaching and Learning
Number of words: 1388
Fisher (1990) states that there are 3 sets of interacting factors which affect the success of problem solving in mathematics: Attitude, Cognitive Ability and Experience with a mathematics learner ideally possessing all 3 of these attributes in being able to think meta-cognitively by realising how they know things and why things work. Hiebert (1986) applies this to the secondary school, defining this as proceptual knowledge where a child has a thorough knowledge of the concepts and processes behind a topic and is able to apply different methods selectively to a problem.
Cognitive Ability
The success of pupils in investigations and problem solving in Mathematics seems to depend on Fisher’s 3 factors. Some pupils may be pure mathematicians and may be naturally adept in the subject, but those who are good at Literacy may enjoy the problem-solving aspects of Mathematics more as there is often a literary element in the investigations, in terms of writing and reflecting on findings. Sperry (1961) notes that this depends on the hemispheric dominance in the brain: left-brained students prefer logical subjects like maths, whereas right-brained students like more creative subjects like English.
Gregorc (1986) suggests that teachers will often try to teach pupils in the way they prefer to learn and inspire similar qualities in the learners to what the teacher possesses. However, this could lead a teacher to neglect pupils who do not have the same preferred learning style as them. Herrmann (199) argues that if a teacher has a good lateralisation in the brain and is able to use both hemispheres competently then this will help increase the academic attainment of their pupils. However, Geschwind and Galaburda (1987) hypothesise that males and females have different cognitive abilities and that boys are more pre-disposed towards left-brained logical subjects like Mathematics and Science. These preferences may make it harder for a teacher to appeal to all pupils as there is such a wide array of learning styles within the class.
Mathematics can often contain topics which require a student to be both creative and logical simultaneously. For example, proof by induction involves a formal, logical element but also covers creative topics like graphing functions and inequalities. Johnston-Wilder (2011) argues that a mathematics teacher should be able to display topics using multi-sensory approaches so that pupils can have an array of methods from which to select their preferred one. Gardner (1993) advocates teachers recognising all modalities of intelligence and refining their teaching strategies accordingly to suit the learners in their class. However, this may be impractical considering larger class sizes and the likely diaspora of learning styles within a class, especially if it is a mixed ability group.
Experience
A teacher may also be inhibited by the subject matter in order to promote successful learning in pupils. Some topics have real life applications whereas more formal topics like Algebra are harder to link to the real world and may be less interesting to pupils, though it links to other areas of mathematics. Ultimately, Norton (2000) argues that a teacher’s identity may be the most important factor in the success of teaching, particularly if it is connectionist (Askew et al., 1997). Van Hiele (1985) notes that a connectionist orientation works well when teaching Geometry.
This seems to imply that if a teacher has a connectionist orientation and strong literacy skills then they can stimulate successful learning in pupils. Investigations could be a useful method of promoting literacy across the curriculum, with pupils having to represent their work in a logical and coherent manner whilst also using the right mathematical notation (DfE, 2013). This could also be a useful method of employing cross-curricular links within a lesson, with pupils able to see the significant, but subtle links between English and Mathematics. Waring (2000) promotes the value of proof in investigations as it gives students a conceptual, rather than procedural understanding of topics. However, Piaget (1953) notes that children are unable to think in such an abstract manner until they are 12, which makes the introduction of proof in mathematics teacher before that age redundant. Lawton (2011) extends this by anecdotally stating that children do not reach this level of cognition before they are 14.
Watson (2006) suggests that a strong literacy base may be crucial to progress in mathematics learning. DfE (2010) note that this is particularly pertinent, given the increasing prevalence of worded questions in GCSE Mathematics exams, where pupils have to ‘decode’ questions and work out the mathematics they need to do to answer the question.
Attitude
Watson and Mason (2006) advocate mathematics teachers using investigations as a medium of inspiring and engaging pupils’ interest in the subject. They can potentially become interested in mathematics by doing an investigation into a topic outside the curriculum and seeing its relevance to the real world. However, Wigfield et al. (2004) argue that students need to be intrinsically motivated to be captivated by Mathematics and have an innate passion for it. Dweck (2006) argues that mindset determines performance: if a learner has a ‘growth’ mindset then they will respond well to challenges and seem them as necessary to progress in their learning. However, if a student has a ‘fixed’ mindset then they may struggle to cope with challenge and disengage. They may be less likely to persist and fulfil their potential in mathematics if they see every obstacle as a negative. Goleman (1995) reaffirms this by arguing that emotional intelligence is more successful in determining success in life than academic attainment. Ultimately, the nature and significance of the task itself may be the most important factor in a student’s performance. If pupils do not enjoy a topic, then their motivation may decrease, though a combination of good pedagogy, persistence and a good teacher-student rapport could counteract this.
In conclusion, there seem to be numerous factors which effect successful mathematics teaching and learning, including learning style, hemispheric dominance and teaching philosophy. Ultimately, the learner’s mindset and attitude towards their learning may be the most important factor in determining whether they are successful at learning Mathematics.
Reference List
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