The complex interplay between examples and proving: Where are we and where should we head?

Our work suggests re-conceptualization of research concerning students’ over reliance on example-based reasoning, moving from a view of such reasoning as a stumbling block to quickly overcome toward a view of such reasoning as a necessary and critical foundation in learning to prove. We have extended prior research and have developed a comprehensive analytic framework (CAPS: Criteria-Affordances-Purposes-Strategies) for characterizing and making sense of the roles and uses of examples in proving-related activities of secondary school students, undergraduate students, and mathematicians. This framework constitutes a substantial contribution to the field, as it helps in illustrating the complexity of example use in proving-related activities, contrasting various aspects of example use among learners, and highlighting categories and patterns of example use that are identified with productive proving-related activities. We have documented the example use and thinking of secondary school and undergraduate students as well as mathematicians, and have identified patterns of productive (and unproductive) example use and strategies.
 
Lead Organization(s): 
Year: 
2018
Short Description: 
Our work suggests re-conceptualization of research concerning students’ over reliance on example-based reasoning, moving from a view of such reasoning as a stumbling block to quickly overcome toward a view of such reasoning as a necessary and critical foundation in learning to prove.