PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
The Emergence of a Prototype of a Contextualized Algorithm in a Graph Theory Task
Page: 1006
Research has described the necessity and dangers of prototypes in mathematical learning, without offering explanations for what makes prototypes appropriate or inappropriate, or indeed how prototypes emerge in the first place. We explore one part of the emergence of a prototype: how a feature of a concept’s example becomes predominant in subsequent generated examples. We describe how three students developed what they regarded as four examples and one non-example of an algorithm suitable for a client with a contextualized graph theory problem. The students engaged in a ‘patching process’ that preserved an inappropriate feature of the initial example in the other examples that were generated. We argue that the development of appropriate prototypes may depend on the types of processes (like the ‘patching process’) that students use to abstract and preserve features of the concept examples.