Making use of social prototypes: From fuzzy concepts to firm decisions

Evidence suggestive of the ‘fuzzy’ structure of many natural language (as opposed to scientific) categories is reviewed. Examples are drawn from categorization schemes for objects, such as cars, fruit or tables, as well as for people, such as extroverts, hippies and ‘fraternity types’. It is argued that despite the fuzziness of natural categories, there is orderliness and utility to these concepts, as well. Specifically, natural categories are organized around prototypes, representative category members, which serve as reference points for the category. The identification of category members involves a prototype-matching process. Prototypes about ‘kinds of people’ can be very useful in decisions about people with whom to affiliate and places in which to live. This process was illustrated by reference to a case analysis of students' preferences for university housing. It was concluded that natural categories may well be fuzzy, but they are far from being dispensible.     

Graphing formulas: Unraveling experts’ recognition processes

An instantly graphable formula (IGF) is a formula that a person can instantly visualize using a graph. These IGFs are personal and serve as building blocks for graphing formulas by hand. The questions addressed in this paper are what experts’ repertoires of IGFs are and what experts attend to while recognizing these formulas. Three tasks were designed and administered to five experts. The data analysis, which was based on Barsalou and Schwarz and Hershkowitz, showed that experts’ repertoires of IGFs could be described using function families that reflect the basic functions in secondary school curricula and revealed that experts’ recognition could be described in terms of prototype, attribute, and part-whole reasoning. We give suggestions for teaching graphing formulas to students.     

A geometry teacher's use of a metaphor in relation to a prototypical image to help students remember a set of theorems

This article asks the following: How does a teacher use a metaphor in relation to a prototypical image to help students remember a set of theorems? This question is analyzed through the case of a geometry teacher. The analysis uses Duval's work on the apprehension of diagrams to investigate how the teacher used a metaphor to remind students about the heuristics involved when applying a set of theorems during a problem-based lesson. The findings show that the teacher used the metaphor to help students recall the apprehensions of diagrams when applying several theorems. The metaphor was instrumental for mediating students’ work on a problem and the proof of a new theorem. The findings suggest that teachers’ use of metaphors in relation to prototypical images may facilitate how they organize students’ knowledge for later retrieval.