Intimations of Infinity
نویسندگان
چکیده
The comments above (see below for who made them and when) represent one type of thinking about infinity. There are other types, as we will see, and they all create difficulties for students, philosophers and even mathematicians. The purpose of this article is to show how a particular theory about how people come to understand mathematics, APOS Theory, can be helpful in understanding the thinking of both novices and practitioners as they grapple with the notion of infinity. In APOS theory, which will be more fully explained later, an individual develops an understanding of a concept by employing certain mechanisms called interiorization, encapsulation and thematization. These mechanisms are used to build and connect mental structures called actions, processes, objects and schemas. To get a feeling for the complexity of how people grapple with infinity, see how you and perhaps some of your colleagues would answer the following questions. How do you think your answers compare with what has been said by western mathematicians and philosophers over the last 3000 years, or by students today?
منابع مشابه
Intimations of Infinity, vol. 51, number 7
Overture The comments above (see the next page for who made them and when) represent one type of thinking about infinity. There are other types, as we will see, and they all create difficulties for students, philosophers, and even mathematicians. The purpose of this article is to show how a particular theory about how people come to understand mathematics, APOS Theory, can be helpful in underst...
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