Improving children's perseverance in mathematical reasoning : creating conditions for productive interplay between cognition and affect

Mathematical reasoning can be considered to be the pursuit of a line of enquiry to produce assertions and develop an argument to reach and justify conclusions. This involves processes such as conjecturing, generalising and forming arguments. The pursuit of a line of mathematical reasoning is not a routine process and perseverance is required to overcome difficulties. There is a lack of research on pedagogy to foster children’s perseverance in mathematical reasoning, hence this study sought to answer the research question: how can primary teachers improve children’s perseverance in mathematical reasoning? The study took place in two year 6 classes in different English schools. The study group comprised eight children, purposively selected for their limited capacity to persevere in mathematical reasoning. An action research approach was used to develop and evaluate two interventions. Data relating to the children’s cognitive and affective responses and the focus of their attention, a conative component, were collected by observation and interview. Data analysis synthesised the children’s reasoning processes with their affective responses and their conative focus. The use of this tripartite psychological classification to analyse children’s mathematical reasoning offered a new approach to analysing the interplay between cognition and affect in mathematics learning and revealed the role that engagement and focus play in both restricting and enabling children’s perseverance in mathematical reasoning. The interventions comprised providing children with representations that could be used in a provisional way and embedding a focus on generalising and convincing in mathematics lessons. These enabled children to improve their perseverance in mathematical reasoning; they were able to strive to pursue a line of enquiry and progress from making trials and spotting patterns to generalising and forming convincing arguments. This study found that children were not necessarily aware of when they encountered a difficulty. This lack of cognisance impacted on their capacity to apply the self-regulatory actions needed to monitor and adapt their use of reasoning processes. One outcome of this was that they tended towards repetitious actions, in particular, creating multiple trials even when they had spotted and formed conjectures about patterns. Their perseverance in mathematical reasoning was further compromised by their enjoyment of repetitious actions. When the children engaged in activities involving reasoning, their common affective response was pleasure, even in instances when they demonstrated limited perseverance. However, when they were able to persevere in reasoning so that they generalised and formed convincing arguments, they expressed pride and satisfaction. They attributed these emotions to their improved mathematical understanding. The bi-directional interplay between children’s cognition and affect in mathematics is discussed in literature; however, the impact of children’s focus on their cognitive understanding and affective experience augments existing literature.