Dr David Braithwaite - The role of examples in logical reasoning with mathematical content

IAS Residential Fellow Dr David Braithwaite delivers a seminar on their research - Mathematical reasoning often involves general statements, such as “The sum of any two even numbers is even.” Psychological theory implies that such reasoning should depend critically on knowledge of examples. This hypothesis was tested in a series of studies with university students (not specialized in maths). Students spontaneously referred to examples when engaged in logical reasoning about maths (Study 1), knowledge of relevant examples predicted accuracy in logical reasoning (Study 2), and a manipulation designed to increase knowledge of examples led to more accurate logical reasoning (Study 3). Ongoing work explores how examples affect individuals’ evaluations of general mathematical statements. Initial findings (Study 4) indicate that apparently confirming examples increase belief in true statements without affecting belief in false statements. I will discuss implications of this work for psychological theories and educational practice in maths. For more information about the IAS, please visit - https://www.lboro.ac.uk/research/ias