It is a poignant time to be writing an article on learning styles. After the riots of August 2011, what can be said to colleagues around the country about the inclusive appeal of learning styles? How can we engage these angry men and women to believe in the transformative opportunities of learning and of mathematics? It is worth stopping for a moment to reflect on what we know; what our learners have already told us. ‘Good’ teachers know their learners; they stimulate a learning environment where it is safe to speak out, yet challenging enough to encourage new ways to look at, think about, and use maths.
So how can we achieve this ‘good’ practice without falling the trap of expecting, or being prescribed, a ‘perfect’ recipe for teaching, or for learning, mathematics?
Many teachers, particularly those coming from a sociological perspective, hold some reservations of a direct correlation between learning styles and success rates and research confirms a continuing need for such scepticism. People are complex, as are their reasons for returning to learning, but whilst empirical evidence suggests that the use of learning styles, in isolation, is unlikely to significantly impact on success rates, we also know that inclusive learning doesn’t just ‘happen’.
Whilst few would dispute the usefulness of a platform, to share our understandings of how we learn; the sheer number of models all but prevents a unified position to discuss the inclusive nature of learning styles. The aim of this article is neither to justify what constitutes a learning style, nor to isolate each model; but instead to link theory to practice, through existing discussions on the nature of inclusive learning and through concrete examples of learning materials that are freely available on the web.
The Visual, Auditory, and Kinaesthetic/Tactile (VAKT) model places emphasis not on mathematical content, but on the sensory receivers (see, hear, feel) that an individual uses to process new information. The VAKT model almost attempts to create a personalised scale of preference; where learners are encouraged to try different materials that are visually, discursive and/or action based, before placing each of the VAK senses, as moveable points, on an “I like to learn by (visualising/discussing/doing) … maths”. Kolb’s learning style inventory also lies within the same affective domain, but by encouraging learners to situate themselves as learners (not restricted to sensory receivers) provides an powerful language for learners to reflect on their past, and present, experiences of learning.
Honey and Mumford (often used in the UK) have simplified Kolb’s model into four broad categories. Those that prefer to feel how maths works, tend to prefer concrete examples in the real world. Those that prefer to do maths like active experiences, whilst those that like to watch tend to prefer time for reflection. Finally those that like to think about how mathematics might work, given new variables, tend to prefer abstract concepts and it is this detail, in addition to the VAKT preferences, that provides a platform for co-planning with consideration, but not restricted to, individual preference. Of course the categories are not mutually exclusive; learners who like to think might also like to test their ideas by doing maths.
Skillswise and Bitesize ensure a great deal of choice for learners, but if you do not have access to computers the Standards Unit & MathsforLife (Thinking Through Mathematics and booklets) available from the NCETM website suggest activities that encourage learners to visually explore, discuss, and make models to test their mathematical ideas.
Moving from the affective to the cognitive domain, the inchworm (sequential) and grasshopper (holistic) metaphor describes learning in terms of a processes rather thant style. The left hemphisphere of the brain is associated with verbal, sequential and analytical thinking whilst the right, with visual spatial, holistic and emotive thinking.
The Excellence Gateway website has a video that shows how a learner using the left hemisphere may differ from a learner using the right, and although interesting as a tool to compare top down (using the value, the whole picture, to make sense of the question) against a bottom up (step by step) approach, it also illustrates the need for caution. If taken too literally, this kind of matching of learner to thinking style exemplifies the risks that can entrap a learner into thinking they ‘should’ solve a problem in a particular way.
Also categorised within the cognitive domain, Entwistle’s deep/surface learning is concerned with how learners acquire, analyse, and make sense of new information. Deep learning tends to require learners to make their own connections, to make sense of the relationship between new and existing knowledge, values, and beliefs.
Perhaps counter-intuitively, learners who tend to use deep learning strategies are often not the most ‘successful’, at gaining a qualification, as they tend to follow their own interests with little regard for assessment criteria. In contrast, surface approaches to learning tend to be motivated by a desire to ‘suss out’ what is required and often characterised by rote learning of isolated facts.
There is an argument that ‘success’ in formal education requires a strategic approach; learners to create personalised, connected networks of knowledge that are prioritised by key assessment criteria. Swan, very effectively, uses the cognitive domain to structure Higher Order Thinking questions and/or activities (sometimes known as HOTS) that stimulate learners to compare, create, evaluate and modify mathematical information.
Examples of higher order thinking activities and questions can be found on Nrich and NCETM and advice to structure activities can be found in the CPD sections of SU and M4L modules and M4L booklets.
In conclusion, an understanding of learning styles can not ‘solve’ the frustration and anger of an individual trapped by past and present experiences. Nor can it resolve the tension and guilt of a learner distracted by substantial caring commitments but in recognising the limitations; few would disagree that mathematics has traditionally been taught aurally, sequentially and many of our learners were not given inclusive opportunities to learn.
An enhanced awareness of the pschology of learning can create space and structure to personalise innovative teaching strategies; expertise that can help to progress the learner disadvantaged by sensory, particularly auditory, processing skills, and/or needing a reason for why maths is relevant. Most importantly, it provides a shared language to empower and motivate a learner who may have become distracted, for many reasons, by a surface approach to learning maths.
Coffield learning styles report
Learner centred VAKT survey
The sequential inchworm learner
The National Centre for Excellence in the Teaching of Mathematics
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