, 43:269 | Cite as

Is this a coincidence? The role of examples in fostering a need for proof

Original Article


It is widely known that students often treat examples that satisfy a certain universal statement as sufficient for showing that the statement is true without recognizing the conventional need for a general proof. Our study focuses on special cases in which examples satisfy certain universal statements, either true or false in a special type of mathematical task, which we term “Is this a coincidence?”. In each task of this type, a geometrical example was chosen carefully in a way that appears to illustrate a more general and potentially surprising phenomenon, which can be seen as a conjecture. In this paper, we articulate some design principles underlying the choice of examples for this type of task, and examine how such tasks may trigger a need for proof. Our findings point to two different kinds of ways of dealing with the task. One is characterized by a doubtful disposition regarding the generality of the observed phenomenon. The other kind of response was overconfidence in the conjecture even when it was false. In both cases, a need for “proof” was evoked; however, this need did not necessarily lead to a valid proof. We used this type of task with two different groups: capable high school students and experienced secondary mathematics teachers. The findings were similar in both groups.


Isosceles Triangle Dynamic Geometry Dynamic Geometry Environment Strong Confidence Mathematical Claim 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© FIZ Karlsruhe 2011

Authors and Affiliations

  1. 1.Technion-Israel Institute of TechnologyHaifaIsrael
  2. 2.New York UniversityNew YorkUSA

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