- One just needs to open a newspaper, listen to the radio or watch television to realise that numbers and quantitative procedures are important in the world we live in. Every day we are flooded with statistics and have to rely on sensible quantitative reasoning to make decisions based on information in the media and in the workplace. These decisions concern most aspects of our lives and determine issues such as our health, prosperity, safety and much more; we have to be statistically literate to cope in our world. Being able to reason statistically

- Statistics in most countries in the world, including South Africa, is not a separate subject in school curricula, but is included as a content area in the mathematics curriculum. Statistical thinking however differs from mathematical thinking. Cobb and Moore (1997) explain that this difference results from the focus in statistics on variability and the all-important role of context:

- Learners specifically need to develop the ability to reason about variability in samples and acquire a sense for expected variability to be able to predict results: ‘When random selection is used, differences between samples will be due to chance. Understanding this chance variation is what leads to the predictability of results’ (Franklin et al., 2005, p. 21). Exposure to appropriate activities to develop this understanding should therefore be frequent and well planned:

- Based on the System of Observed Learning Outcomes (SOLO) taxonomy (Biggs & Collis, 1982), a conceptual model for the categorisation of reasoning in repeated sampling tasks emerged in the research on variability in sampling situations (Canada, 2004; Kelly & Watson, 2002; Shaughnessy, 2007; Shaughnessy et al., 2004). The SOLO taxonomy is a neo-Piagetian framework for the analysis of the level of sophistication or complexity of a response on a specific task (Biggs & Collis, 1982, 1991). According to this model, learner responses in the Candy Bowl Task display four distinctive patterns of reasoning, following a progression from iconic, to additive, to proportional and finally to distributional reasoning (Shaughnessy, 2007). Iconic reasoning, such as relating personal stories and using physical circumstances, is usually evident in younger learners’ responses (Kelly & Watson, 2002). Examples of iconic reasoning do not refer to the actual contents of the candy bowl or the proportions of the candy mix in it. Such responses might refer to luck: ‘Maybe they are lucky and will get all the reds’ or the physical act of pulling out the candies: ‘They might get more reds because their hand could find them’ (Shaughnessy, 2007). Additive responses are characterised by reasoning where no acknowledgement is given to the role of proportions in the mixture; reasoning is just about absolute numbers or frequencies of reds in the candy mix. Implicit proportional reasoning focuses on ratio, percentage or probability of reds whilst referring back to the original composition of the mixture. Explicit proportional reasoning involves reasoning about sample proportions, population proportions, probabilities or percentages. Finally, distributional responses give evidence of reasoning about centres as well as the variation around the centres. Shaughnessy et al. (2004) categorise responses of secondary school learners in repeated sampling tasks in a chance setting into only three broad groups: additive reasoning, explicit and implicit proportional reasoning, and distributional reasoning. These authors regard proportional reasoning as the cornerstone of statistical inference and call for more opportunities for learners to improve their proportional reasoning skills. They furthermore emphasise that

- A problem-centred approach was used as point of departure for the series of workshops, focusing on statistical knowledge for teaching, which consists of content knowledge and pedagogical content knowledge in statistics. This model of statistical knowledge for teaching is based on the construct of mathematics knowledge for teaching developed by Ball, Thames and Phelps (2008), and includes:

- Seven of the workshop sessions lasted two hours each; a four-hour session on the use of the computer data exploration software Tinkerplots® (Konold & Miller, 2005) in a computer laboratory was also included. The first six workshops were presented twice a week, one on a weekday with a repeat on Saturdays for teachers who could not attend during the week because of full schedules. During the workshops teachers’ statistical knowledge as well as statistical thinking and reasoning skills were developed through rich learning experiences that included all components of the statistical investigation process: posing problems, collecting data, analysing them, drawing conclusions and making predictions. The following topics were addressed in the workshops (Wessels, 2009):