Statistics as Measurement: where is the origin?

Presented by Dr. Erna Lampen, Stellenbosch University, South Africa

Statistics as enquiry and modelling requires reasoning at the intersection of everyday and mathematical reasoning. Teaching statistics meaningfully at school level requires that mathematics teachers conduct classroom discussions in ways that give statistical meaning to everyday concepts and mathematical concepts, and that enable learners to develop integrated statistical thinking. Key to statistical discourse are narratives about variation within and between distributions of measurements and comparison of varying measurements to a central anchoring value. Teachers who understand the concepts and tools of statistics in an isolated and processual way cannot teach in such a connected way.

Using Sfard’s (2008) definition of cognition as communication, I will present a discursive analysis of the discussion of a group of high school teachers’ attempt at providing an existential or object definition of the statistical mean. I argue that even statistical dictionaries fail to provide a meaningful object definition for the mean, and therefore both statisticians’ and teachers’ discourses about the mean tend to be particularly processual.

The findings suggest that discourses for instruction in statistics should explicitly differentiate between the everyday ‘average’ and the statistical mean, and explain the meaning of the arithmetic algorithm for the mean. I propose a narrative that logically explains the ontology of the mean algorithm in order to establish the mean as an origin in a measurement of variation discourse.