Comparative study with statistics education in New Zealand

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Mathematics Curriculum. It is a leader in the world” (ibid., p. 12).

The current curriculum was then released in 2007, and statistics education held an even more important position. The main change was to rename the mathematics curriculum from ‘Mathematics’ to

‘Mathematics and Statistics’—that is, the statistical domain is treated not as one of domains in mathematics but rather as an independent subject like mathematics. This mathematics and statistics curriculum explicitly emphasising the formation of statistical literacy across all school types and grades is extremely rare worldwide (Watson, Fitzallen, Fielding-Wells, & Madden, 2018). As shown in Figure 3-1, the level corresponding to each grade is clearly indicated and divided into eight levels, so the mathematics curriculum also comprises eight levels.

Figure 3-1. Years and curriculum levels (Ministry of Education, 2007a, p. 1)

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Levels 1 to 6 consist of three areas: Number & algebra, geometry & measurement, and statistics.

Levels 7 and 8 consist of two areas: Mathematics and statistics. While the teaching weight of number &

algebra is high at Level 1, those of geometry & measurement and statistics increase as the level progresses, and the teaching weight of these three areas is set to be the same at Level 6 (Ministry of Education, 2007b, pp. 19-21). At Levels 7 and 8, with the two areas of mathematics and statistics, there is no description of teaching weight. Figure 3-2 shows the changes in the teaching weights of the three areas from Level 1 to Level 6.

Figure 3-2. The change in the teaching weight of areas in ‘Mathematics and Statistics’

(Ministry of Education, 2007b; extracted and edited by the author from pp. 19-21;

Aoyama, 2013, p. 33)

The curriculum includes the teaching contents of statistics at each level, and it details are in Appendix A. The major changes in the statistics curriculum from 1992 to 2007 have occurred as follows:

“from skills to immersing learning within the PPDAC (problem, plan, data, analysis, conclusion) statistical investigation cycle; from how to construct plots to how to reason from and interpret plots; from hand-drawn plots to automated plots; from reasoning from descriptive statistics to reasoning about populations from samples and underpinning inferential concepts including an appreciation and awareness

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of sampling variation; and from a non-assessed and hence non-taught interpretation and evaluation of media reports to an assessed statistical literacy component” (Pfannkuch & Wild, 2013, p. 609). Thus, it is necessary to form method knowledge for making decisions under uncertain situations using the PPDAC cycle. This is consistent with the international direction and also for future statistics education in Japan.

As mentioned above, the name of the subject in New Zealand has become ‘Mathematics and Statistics’. There seems to be awareness of the difference between statistics and mathematics. As the previous studies stated, data with context is the object of statistics, while number without context is the object of mathematics. This is why statistics education in New Zealand may value context. Thus, the analysis of New Zealand may provide implications to consider the context-related characteristics and issues of current statistics education in Japan. Therefore, this research takes the case of New Zealand.

Furthermore, it would be important to focus on New Zealand from the perspective of the future of Japanese society, even though it is not directly related to this research. Since mathematics education is established as a social-historical practice (Abe, 2010; Iwasaki, 2007), it is to be expected that students’

range of values to be dealt in mathematics education will expand not only to mathematical values but also to social ones¹ (Baba, 2007, 2009; Shimada, 2017; Shimada & Baba, 2012, 2014, 2015, 2016). Indeed, this should also apply to statistics education. Under this situation, education in New Zealand is informative for that in Japan. New Zealand is originally inhabited by Maori people, but has received many immigrants through English colonisation. It has a longer history as a multi-ethnic/multicultural nation than any other country, despite having a history of just over 70 years as a modern nation (Aoki & Sato, 2014). New Zealand has “the appearance of a high-quality welfare state supported by the spirit of mutual assistance in which everyone has equal rights and responsibilities” (Fukumoto, 2014, p. 93; translated by the author), and has led the world in implementing numerous pioneering social policies (i.e., the world’s first women’s suffrage law, the world’s second elderly pension law, the world’s second social security law, a community welfare law for disabled persons, anti-nuclear policy, and so on). This is because New

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Zealand has a wealth of experience as a multi-ethnic/multicultural nation, utilises its direct experience with various conflicts between ethnic groups and cultures (i.e., tensions between the indigenous Maori and British immigrants), and has a method to implement policies before tension erupts. “The spirit of mutual assistance in which everyone has equal rights and responsibilities” (ibid., p. 93; translated by the author) also impacts the educational community, and this spirit is apparent throughout the curriculum (see Appendix A). It would be beneficial for Japan, which is expected to face the impending pressures of globalisation and internationalisation, to pay attention to education in New Zealand in such a sense that it has faced unification as a nation and diversification as multi-ethnic/multicultural one.

As mentioned in Chapter 1, it is not enough to mention the context in the course of study in Japan. Moreover, the New Zealand Curriculum (see Appendix A) also shows educational contents. The contents are not the specific contents to be taught but the abilities and skills to be required and acquired.

Therefore, it would seem impossible to compare the Japanese course of study with the New Zealand curriculum.

Alternatively, this research focuses on textbooks and compares statistics education in Japan with that in New Zealand. The purpose as externalised values (Ernest, 2015) and the knowledge as the product of activities (Leontyev, 2009) are externalised things which are difficult to visualise, and “almost all issues in mathematics education are reduced to those in notation” (Hirabayashi, 1987/2013, p. 390;

translated by the author). In this sense, it is textbooks as the central repository of mathematical notation that directly affects this purpose and knowledge. Furthermore, it is not an exaggeration to say that the purpose and knowledge mentioned above dominate all matters described in the textbooks since, under Article II of Act on Temporary Measures concerning Publication of Textbooks, it is obligatory for all schools from elementary to upper secondary to use textbooks in Japan. Therefore, this research focuses on textbooks for its comparison of Japan and New Zealand. This textbook comparison is conducted by quantitative analysis and case analysis.

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In addition, the specific contents and methods for acquiring the abilities and skills shown in the New Zealand mathematics curriculum are entrusted to each teacher, and all matters, such as the contents of educational practices, their construction, and teaching materials, are up to the teacher because there is no compulsory system for textbooks (Ministry of Education, 2007c, pp. 37-44). Therefore, these may be unique characteristics related to context even in educational practices regarding statistics in New Zealand.

For this reason, this research also analyses educational practices by a teacher qualitatively because the treatment is left up to each teacher in New Zealand unlike Japan. For this analysis of educational practices, a comparison with educational practices of statistics in Japan is not conducted because the educational practices for statistics in Japan are basically based on textbooks and reflect the same contextual characteristics as those of textbooks.