Mason (2001) mentions a study that "found recently that most students (their study was with nearly 2500 children aged 14-15 in 90 schools) base their confidence in the truth for a finite number of cases (an empirical perspective of proof)". Mason mentions that checking on a finite number of cases has use in gaining confidence before taking on a proof by English standards. By French standards, this process is the proof, though it may not always be formal.
I think finding a proof involving all cases, by induction, is satisfying, knowing that there are no exceptions. However, to prove to myself, I find that a finite number of cases is enough to convince me. I often fall into, what Mason mentions in their article, the '"just because" or "it just is", or "X said so" thinking' when it comes to math. The way I was taught math in high school, I think, had an impact on how I think about mathematics. However, I am trying to be more curious and inquisitive about mathematics and dig deeper into proofs, as well as history and background.
Mason brings up a good point that I relate to, saying that when one tries to convince friends and associates, who in turn question and cast doubt on my explanations, I "respond 'in flight', by augmenting, elaborating or offering further examples to help them ‘see what you are trying to say’". I often give up because I don't think I have sufficient knowledge in math. However, if it is something I am confident in, Mason says that "you try to express your reasoning, your way of seeing, so that it stands alone without the need for you to be present.". I aspire to be able to explain in a way where there is no need for interpreting, elaborating, or augmenting and my reasoning leaves the person who receives the information thinking about what I said.
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