This prompt was inspired by Mary O'Connor's article published in the research journal Educational Studies in Mathematics in 2001. In the article, O'Connor analyses the discourse between a teacher and her grade 5 class that is initiated by the framing question: ‘Can all fractions be turned into decimals?’ What results is a 'position-driven discussion' in which the teacher skilfully manages the pupils' examples, counter-examples, conjectures and conceptions.
In line with the aim of the inquiry maths model to promote students' questioning, the question in O'Connor's article is written as a statement. This allows the teacher to draw on and simultaneously develop students' curiosity around of the issue of whether all, part or none of the statement is true. It also allows the teacher to assess the students' existing knowledge through the types of questions they pose or comments they make about the prompt.
The first part of the prompt can be presented on its own. In one case when a teacher took this approach with a year 7 class, a student suggested in the orientation phase of the lesson that the class inquire into the reverse statement. The teacher decided to restrict the first part of the inquiry to conversion from fractions to decimals, but opened a new inquiry pathway at a later date when the class went on to consider converting decimals (including recurring decimals) to fractions.
Areas of the curriculum that have been covered in this inquiry are:
- Simplifying fractions
- Short division
- Converting fractions to decimals
- Categorising fractions that give terminating and recurring decimals
- Factors and multiples
- Explaining why fractions give terminating and recurring decimals (referring to the prime factors of the denominators)
- Converting decimals, including recurring decimals, to fractions
- Irrational numbers