One of the factors for developing mathematical resilience is about having an awareness of the support that is available from peers and other resources (Johnston-Wilder et al., 2013). Thus working with peers as pairs or in groups was going to be an important feature within this action research project. For this reason, it was useful to consider the literature focussed on group work in mathematics.
Wright and Taverner (2008) have found that in many subjects in UK, group work is commonly used as part of a lesson. However, in mathematics, group work is rarely used by many teachers. Ofsted (1999) said that in order to improve
48
mathematics further, schools should give learners adequate opportunities to discuss mathematics. More recently, Ofsted (2012) reported that in the very best lessons, learners were extensively working collaboratively with each other, using this learning opportunity to enhance their understanding of mathematics.
The theory of learning known as Constructivism emphasises that learners must take an active role in their own learning. The later literature on this theory grew from the work of Piaget and Vygotsky. Piaget (2001) conjectured that one of the main influences on child development was maturation, a term used to describe the changes that take place as a child grows older. He suggested that learning occurs in four stages: the sensori-motor stage (approximately birth to two years old), the pre-operational stage (approximately two years old to seven years old), the concrete operational stage (seven to twelve years old) and the formal operation stage (twelve years old and upwards). The last of these stages is most relevant to this research because in the school in which the research took place all the learners were fourteen years old or above. At this stage, Piaget (2001) states learners are able to see that their personal experience is only one possibility and they are able to generate systematically different scenarios for any situation. Essentially, Piaget (2001) is saying that a child grows older, the tools they use to think extend, allowing them to have a different view of the world.
Muijs (2004) amongst others argues that although Piaget’s theory has been highly influential, the stages given are far too rigid. He criticises Piaget for seeing learning as being largely dependent on their stage of development and does not take into account social interactions with other learners. Vygotsky (1978) also did
49
not think that maturation on its own was enough and his research led him to believe that children’s development came through interaction with others of both similar intellectual levels and those of higher intellectual levels. One of his main ideas is that the learner has a ‘Zone of Proximal Development’ which was discussed in section 2.3.
Muijs (2004) felt that while Vygotsky’s work filled in some of the gaps in Piaget’s research, it lacked reference to the links between a child’s natural development and the effects it had on their learning. He states that Piaget’s research needs to be complemented by more recent research that has developed in the field of brain functions. However, Vygotsky’s ideas have influenced classroom practice and the development of many of the ideas behind collaborative learning (Muij, 2004).
Based on personal experience, mathematics teachers have mentioned that they have found collaborative learning or group work to be an ineffective use of lesson time, stating that their learners have spent a large proportion of the lesson off task with only a few learners undertaking the work. Personal research has found that this is not usually the case in other subjects where learner routinely work effectively as groups, which results in the conjecture that this could be caused by a lack of certain skills in many mathematics teachers, potentially caused by their own school experience of mathematical teaching.
Wright and Taverner (2008) and Swan (2005) have both identified that many mathematics teachers consider collaborative learning as a possible problem and both give teachers similar advice about their role during group work. They both
50
emphasize the importance of having a clear purpose for the task. Learners must know what they are trying to achieve and must realise that it is often not the final answer that is important but the method used to reach the final answer. It is also important for teachers to listen to learners before any intervention takes place. Poor interventions could divert learners’ attention away from what they are discussing and attempting to learn. This is true not only for group work but for mathematical learning in general. Any intervention by the teacher should be about asking learners to describe, explain and interpret what they are discussing and encouraging them and the group as a whole to think about their ideas in more depth. Kilpatrick (1987) showed that teaching needs to become more about using procedures to generate understanding. In this case, the carefully planned interventions are used to generate the learners’ understanding and assist the learning process. Wright and Taverner (2008) report that poor intervention into the discussion from the teacher can often lead to learners stopping talking when they realise that the teacher is listening so it is vital when using group work to try and only ‘eaves drop’ on conversations at least some of the time.
It is also important to remember that a learner’s ability to work in groups takes time to develop. Teachers need to devote time within their lessons to discussing effective group work and allow time to develop team working skills. A problem they may need to overcome is convincing learners that mathematics is not a subject where you always work independently, something that they may have believed for the majority of their time at school. Once learners are confident in working collaboratively when necessary it seems that they are more likely to stay
51
in the Growth Zone (Johnston-Wilder et al., 2013) by making use of available support to keep them away from the Anxiety Zone.