Editorial Abstraction in Mathematics Learning

Abstraction has been a frequent discussion topic since the days of Aristotle and Plato. Constructivist theories often espouse the notion of levels of abstraction. Hiebert and Lefevre (1986, pp. 4-5) put it this way: It is useful to distinguish between two levels at which relationships between pieces of mathematical knowledge can be established. One level we will call primary. At this level the relationship connecting the information is constructed at the same level of abstractness (or at a less abstract level) than that at which than the information it is connecting. Some relationships are constructed at a higher, more abstract level than the pieces of information they connect. We call this the reflective level. Relationships at this level are less tied to specific contexts. They often are created by recognising similar core features in pieces of information that are superficially different. The relationships transcend the level at which the knowledge currently is represented, pull out the common features of different