The Role of abstraction in learning about rates of change

ion Abstraction has many facets and there is no consensus among researchers with regard to a unique meaning (Hazzan, 1999). But all agree on two aspects: (1) A new mental object is created as a result of an abstraction process. For example, Mason claims that abstraction in mathematics is a common experience, “an extremely brief moment which happens in the twinkling of an eye; a delicate shift of attention from seeing an expression as an expression of generality, to seeing the expression as an object or property” (1989, p. 2). (2) This new object separates out some relevant features from others considered irrelevant. Thus Davidov (1990, p. 13) defines abstraction as the process of “separating a quality common to a number of objects/situations from other qualities”. Where researchers differ is on the abstraction process itself. The empirical abstraction model. Skemp’s (1986) defines abstraction as “an activity by which we become aware of similarities among our experiences” (p. 21). Mitchelmore & White (2004), following Skemp, claim that the first phase of the abstraction process is the recognition of common features in a variety of different situations. In everyday experience these features may be superficial (e.g., colour), but in mathematics they are always structural (e.g., number). In the second phase, the similarity that has been recognised becomes abstracted and forms a concept which in a sense embodies that similarity. Theion has many facets and there is no consensus among researchers with regard to a unique meaning (Hazzan, 1999). But all agree on two aspects: (1) A new mental object is created as a result of an abstraction process. For example, Mason claims that abstraction in mathematics is a common experience, “an extremely brief moment which happens in the twinkling of an eye; a delicate shift of attention from seeing an expression as an expression of generality, to seeing the expression as an object or property” (1989, p. 2). (2) This new object separates out some relevant features from others considered irrelevant. Thus Davidov (1990, p. 13) defines abstraction as the process of “separating a quality common to a number of objects/situations from other qualities”. Where researchers differ is on the abstraction process itself. The empirical abstraction model. Skemp’s (1986) defines abstraction as “an activity by which we become aware of similarities among our experiences” (p. 21). Mitchelmore & White (2004), following Skemp, claim that the first phase of the abstraction process is the recognition of common features in a variety of different situations. In everyday experience these features may be superficial (e.g., colour), but in mathematics they are always structural (e.g., number). In the second phase, the similarity that has been recognised becomes abstracted and forms a concept which in a sense embodies that similarity. The