for the learning of mathematics

an international journal of mathematics education

Nicholas Wasserman - Vol. 39 Num. 3 (2019)
 Duality in combinatorial notation


In combinatorics, combinatorial notation, e.g., C( n, r), is explicitly defined as a numerical value, a cardinality. Yet, we do not use another symbol to signify the set of outcomes–the collection of objects being referenced, whose cardinality is, for example, C( n, r). For an expert, this duality in notation, of signifying both cardinality and set, is not especially problematic; for a learner, however, it can be. This paper explores how combinatorial notation may, unintentionally, signify to learners something that does not lead to developing the conceptual, set-oriented ideas about combinatorics that experts have. Potential resolutions are discussed for combinatorics education.