Context influence on mathematical reasoning

The problem studied in this paper is how and under which conditions students accept or refuse the rules of formal deduction. In particular, the focus is on the role of the context in the activity of proving, where by ‘context’ we mean the ‘semantic context’ of the statement to be proved and not the global context in which the classroom is set. Our study is based on the analysis of the answers of 40 students aged 16 years to a questionnaire on the introduction and elimination of ‘and’, and on the introduction of ‘or’. The results of our analysis reveal, in our opinion, a remarkable interference of the context, which includes both the semantic meaning of the propositions involved in a deduction step and certain implicit assumptions induced by the common usage of certain words in the natural language; this is particularly evident in the case of the introduction of or.