Irrational Numbers: Dimensions of Knowledge.

Irrational Numbers: Dimensions of Knowledge Student: Is pi the only irrational number? Teacher: No, because there is also root-two. Mathematically, of course, it is a correct answer. Pi cannot be the only irrational number if there exists another one. However, we note in this reply a missed opportunity, perhaps due to the teacher’s limited understanding of the concept, to extend the discussion of irrational numbers. This exchange, observed by one of the authors of this proposal, inspired a study on prospective secondary teachers’ (PST’s) understanding of irrationality, part of which is reported here. The purpose of the study was to provide an account of PST’s understandings and misunderstandings of irrational numbers, to interpret how the understanding of irrationality is acquired, and to explain how and why difficulties occur. [ABSTRACT FROM AUTHOR]