Educational practices in New Zealand

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of context within the problem itself. In addition, the synthesis of contextual knowledge and statistical knowledge is also an issue, as pointed out by Makar, Bakker, and Ben-Zvi (2011).

4.2 Educational practices in New Zealand

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and the teacher observed how the students were engaged with the activity and responded to students who requested the teacher’s attention by raising their hands. The second is ‘transmission of knowledge to the students’. Some of the questions that the students asked were not solvable without new statistical knowledge. In that case, the teacher not only responded to the student who raised the question, but also explained the new statistical knowledge to the whole class. For example, when making a future prediction by analysing time series data, a student was not sure of the method needed to express in numerical form the value that she could plot on the graph. In this instance, the teacher shared knowledge of regression lines with the whole class. In New Zealand, statistical exploration of data is performed using statistical knowledge. In other words, statistical knowledge is a tool for further statistical exploration. Consequently, the role of the teacher in New Zealand, ‘to transmit knowledge to the students’, is more accurately described as ‘to transmit knowledge to the students unilaterally according to the students’ needs’. Whether or not this is a general role of the teacher in educational practices in New Zealand is not clear, but at least this was evident by the observation. In addition, in the educational practices in New Zealand, the students were given a single task: ‘To explore data and to write up a report’. The basic datasets were provided to the students, but if different information was required during the exploration, the students would look up it in the Internet by themselves. Since the students took an initiative in deciding which data to focus on from the given datasets, as well as what to explore, they engaged themselves with the exploration on their own volition. With reference to the other role of the teacher, ‘to facilitate students’ exploration activity’, the teacher is required to have a depth of knowledge to respond to the students’ needs at different levels of exploration.

4.2.2 Lesson analysis through episodes

Some episodes from a student’s exploration (hereafter, Student A) in the educational practice that the author observed are discussed here. Student A focused on the time series data of wine consumption

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in New Zealand from the given datasets, and based on the time series graph (Figure 4-1), posed the question, ‘Why did wine consumption, which was on the rise for several years, decrease in 2007 and 2008?’

Figure 4-1. A screen shot of time series graph Student A made (The letters on the left are rewritten by the author)

To solve this question, she investigated New Zealand’s social situation around 2007 and 2008. After this investigation, she expected that the reason for the decrease of wine consumption in 2007 and 2008 was related to the financial crisis. Then, Student A focused on the next question, ‘Why did wine consumption, which was on the rise for several years, decrease in 2011?’ She then started the exploration. A hypothesis that the earthquake in Christchurch in 2011 could be a factor was formed. As shown in Figure 4-2, she performed an online search with ‘wine’, ‘decreased’, ‘trend’, ‘2011’, and ‘christchurch earthquake’ to determine if the hypothesis would hold.

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Figure 4-2. A screen shot of Student A’s search 1

Next, Student A hypothesised that the climate might be a factor and performed another search on the Internet. Student A also noted that wine consumption in New Zealand was highest in 2010, and explored the question, ‘Why was consumption highest in 2010?’ In this exploration, the Internet was again used, and, as shown in Figure 4-3, a search for the question ‘why are there highher wine consumption in 2010’ was performed in Google Scholar, a search engine for academic articles. In other words, Student A searched for academic articles on wine consumption in New Zealand, continuing her exploration using a variety of academic articles.

Figure 4-3. A screen shot of Student A’s search 2

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Student A’s exploration has been described above. It may be said that activities for looking into the historical and geopolitical background of New Zealand using the Internet and Google Scholar are not very meaningful for statistics education. However, the author saw Student A’s exploration in investigating the historical and geopolitical background of New Zealand’s society as a process of analysing the time series data on wine consumption in New Zealand. It is important to combine contextual thinking and statistical knowledge for the statistical literacy within today’s world. Therefore, it is very likely that such an approach to history and geopolitics will become a factor in the statistical inquiry cycle involving the use of the Internet. This is because the Internet is now the main method for acquiring information and knowledge in contemporary society. Research into ‘questioning the world paradigm’ (Chevallard, 2015), which investigates a problem in mathematics education by means of the Internet has begun to be pursued.

Ben-Zvi (2007) has looked into exploration using Wikipedia, the Internet-based encyclopaedia, in statistics education.

Through the observation of educational practices in a New Zealand school and the author’s analysis of the New Zealand curriculum, it can be suggested that statistics education should not only handle data but also involve contextual thinking. Contextual thinking means that students think about what kinds of data should be used, how to interpret the data processing, and so on. In other words, contextual thinking refers to the emergence of another context when thinking about a specific context. To capture the background of data, students must acquire knowledge on various disciplines and use an interdisciplinary approach. This is one of the current issues in statistics education worldwide.