INGLIS, M. and MEIJA-RAMOS, J.P., 2008. How persuaded are you? A typology of responses. Research in Mathematics Education. 10 (2), pp. 119-133.
Several recent studies have suggested that there are two different ways in which a person
can proceed when assessing the persuasiveness of a mathematical argument: by
evaluating whether it is personally convincing, or by evaluating whether it is publicly
acceptable. In this paper, using Toulmin’s (1958) argumentation scheme, we produce a
more detailed theoretical classification of the ways in which participants can interpret a
request to assess the persuasiveness of an argument. We suggest that there are (at least)
five ways in which such a question can be interpreted. The classification is illustrated
with data from a study that asked undergraduate students and research-active
mathematicians to rate how persuasive they found a given argument. We conclude by
arguing that researchers interested in mathematical conviction and proof validation need
to be aware of the different ways in which participants can interpret questions about the
persuasiveness of arguments, and that they must carefully control for these variations
during their studies.