While the world is changing rapidly with respect to the prevalence and use of statistics, the curriculum in schools tends to be slow to respond to these changes. Although statistics as a content domain is widely accepted, typically statistics is not an independent topic in the school curriculum but is taught as part of mathematics. Consequently there is a need for a better preparation of primary and secondary school mathematics teachers, who are responsible for teaching statistics at these levels. Teachers’ statistical conceptions and beliefs deserve attention, since mathematics teachers’ thinking is the key factor in any movement towards changing mathematics teaching and determines both the students’ knowledge and the students’ beliefs concerning mathematics and hence statistics (Batanero & Díaz, 2010).
Reports from different Studies agreed that many of the current teacher training programmes do not yet adequately educate those who are teaching statistics for their task to prepare statistically literate citizens. Even when many prospective secondary teachers have a major in mathematics, few of them have received specific preparation in designing sample collections or experiments, analysing data from real applications or using statistical software (Batanero & Díaz, 2010). These teachers also need education in the pedagogical knowledge related to teaching statistics as described above, given that teaching mathematics is different from
teaching statistics (see Franklin et al., 2005, or Burrill & Biehler, ). The situation is even more challenging for primary teachers, since in many countries statistics is included in the school curriculum for children beginning in grade 1 (6 year-olds). Clearly, teaching statistics to these children needs different approaches, tasks and methods than teaching statistics in secondary or high school, so primary school teachers, in addition to their knowledge of other basic disciplines, require a profound knowledge of children’s cognitive development in statistics and probability. In spite of this need, few primary school teachers have had suitable training in either
theoretical or applied statistics, and traditional introductory statistics courses will not provide them with the didactical knowledge they need (Batanero, Godino & Roa, 2004; Stohl, 2005: Franklin & Mewborn, 2006).
Some suggested approaches in the training of teachers include: promoting teachers’ statistical literacy and statistical reasoning; engaging teachers with real data and training teachers with project work and statistical investigations; working with technology; and connecting teacher education to their own practice. Below are comments on these approaches.
Promoting teachers’ statistical literacy (Ridgway, Nicholson, & McCusker, ) and statistical reasoning (Pfannkunch & Ben-Zvi, this book). In many countries, statistical offices and agencies are providing resources that can be used to support the introduction of statistical literacy in schools. However, without wide-reaching education and professional development of teachers, such resources are unlikely to have an impact on students. Moreover, in order for teachers to develop a deep and meaningful understanding of statistics that later they can use to help students develop the ability to think and reason statistically, it is important to create a statistical reasoning learning environment in courses they take that later they can use in their own teaching (Garfield & Ben-Zvi, 2009).
Engaging teachers with real data (Hall, this book) and statistical investigations (Makar & Fielding-Wells, this book). A conclusion of the Conference discussion was that teachers should experience the full cycle of research with statistical projects, if the goal is to change how statistics is experienced in the classroom Moreover, when time available for working with teachers is scarce, some papers (e.g., Godino et al., 2008;
Batanero & Díaz, 2010) suggested that a formative cycle where teachers are first given a statistical project and then carry out a didactical analysis of the project can help to simultaneously increase the teachers’ statistical and pedagogical knowledge. Working with technology can be used both as amplifier and reorganiser to engage teachers in tasks that simultaneously develop their understanding of statistical ideas and
allow them to experience how technology tools can be useful in fostering statistical thinking (Lee & Hollebrands, 2008). However, teachers also need adequate pedagogical knowledge about how to use technology in the statistics classroom.
Connecting teacher education to their own practice and promoting collaborative work among teachers (Ponte, ) is essential to improving professional practice. It is through the exchange of ideas and materials among teachers who have common problems and needs that new ideas emerge for the introduction of new activities, new practices or new competencies (Arnold, 2008). In particular, analysing collective case
studies and discussing teaching experiences and students’ responses to given tasks can reveal the teachers’ lack of specific knowledge of some statistical concepts and promote their statistical and pedagogical content knowledge (Groth & Shihong, this book). The affordances offered by modern Internet technologies provide new distance-learning opportunities for the pre-service and in-service training of teachers, making it possible
to overcome the restrictions of shrinking resources and geographical locations and to offer high quality learning experiences to geographically dispersed teachers (Meletiou & Serrado, ).
The issues effecting teaching of statistics to be dealt immediately are described below:
1.Fundamental ideas in the school statistics curriculum. Some common agreement about which basic ideas should be included at school level in number sense, measurement or geometry seems to exist with respect to international curricula, but there is no such agreement with respect to statistics, as curricula around the world show a notable variation. An important area of work was the identification of those statistical ideas that seem to be fundamental for understanding and being able to use statistics in the workplace, in personal lives and as citizens. Burrill and Biehler use different educational perspectives in statistics to propose a list of fundamental statistical ideas that should be taught to every student.
2.The role of probability in teaching and learning statistics. Although the focus of the study is statistics, since statistics and probability are linked in school mathematics in many countries and within mathematics theory and practice, a reference to probability in the book was needed, as didactic problems still need to be solved in the teaching of probability (Girard & Henry, 2005). Probability is a field that can connect to the study of mathematical modelling; but while probability theory often when taught in a finite context can be very simple, its abstract model part is not direct and could require a long period of learning (Chaput, Girard & Henry, 2008). Finally the school curriculum seems to ignore the subjective point of view of probability, which is widely used today in the applications of statistics (Carranza & Kuzniak, 2008).
3.Technology. Technology has changed many aspects of modern life, and this change has been reflected in statistics education. With software such as Fathom™ and Tinkerplots™ designed to support learning statistics, data analysis is no longer the exclusive domain of statisticians; students and teachers today can work on their own statistical projects and be engaged in the game of statistics, experimenting with the complete cycle of statistical reasoning (Wild & Pfannkuch, 1999). In addition to exploring data, technology now is used to explore complex statistical ideas or processes via simulation. Computer software offers the opportunity for students to learn about modelling, enabling students to build their own models to describe data and to generate simulations that can be explored. According to Pratt, Davies and Connor , by taking advantage of this kind of software students can see real world phenomenon through a mathematical model (rather than seeing the model through the data).
4.Teaching through project work. Projects and investigations are ideal vehicles for student engagement, for learning to solve problems in context, and for synthesizing components of learning (Makar, 2010; McGilliwray & Pereira-Mendoza). The emphasis should be on students posing their own questions about the data, interrogating the data, and learning new information about the real world from the data (Pfannkuch & Ben-Zvi). The amount of data that can today be accessed on the Internet suggests that students can choose nearly any topic of interest to them for their work in the statistics classroom, which can increase student motivation. Working with real data also helps students investigate issues that do not often appear in textbook problems: for example, recognising different types of data, managing missing or incomplete data, defining variables and categories of classification, dealing with reliability and validity issues in measurement, designing questionnaires or experiments, screening data, and dealing with outliers (Hall).
5.Mathematical and statistical thinking. An ongoing discussion in the statistics education community is how to make teachers aware of statistical thinking as something different from mathematical thinking, both of them being essential to modern society and complementing each other in ways that strengthen the overall mathematics curriculum for students (Gattuso, 2006; Scheaffer, 2006). The differences between statistics and mathematics are reflected in the philosophical, ethical, procedural and even political questions that are still being debated within statistics and its applications, a debate that does not happen often in most areas of mathematics. Statistics is much more closely related than mathematics to other sciences (from linguistics or geography to physics, engineering, agriculture or economy) where it is used as the language and method of scientific enquiry and from which many statistical methods were developed (e.g., agriculture). In this sense it is also easier in statistics than in mathematics to establish connections with other school curricular areas. In spite of these differences, teachers often teach statistics in a similar manner to the way they teach mathematics, which is not well-suited to the unique nature of statistics (Makar & Confrey, 2003).
6.Assessment. Assessment of student learning is an important part in every educational process as it provides information about student achievement in relation to the intended learning outcomes. Consequently, assessment has received much attention in statistics education in recent years (see, for example, Gal & Garfield, 1997). Garfield and Franklin (this book) analyse three basic components, cognition, observation, and interpretation, that underlie all assessment and that must be explicitly connected in designing a coordinated whole relative to the purpose of assessment. In addition to the classical distinction between assessment of learning (summative), and assessment for learning (formative), the authors suggest that assessment as learning could combine both summative and formative methods and situate the student at the center of the process, engaging students in new learning by monitoring and adapting their own understanding via the assessment process.
The time was ripe for collaboration between mathematicians and statisticians to address challenges related to
the advancement of both teaching and research in statistics education and in the preparation of teachers to teach statistics. However, continuous changes and the rapid development of statistics education as part of the mathematics curriculum at the school level and the subsequent need for a better preparation of teachers imply that this collaboration is not finished with the publication of this article but should continue in the coming years.
While the article try to provide directions to improve the education of teachers, it is important to expand the empirical base of studies to larger samples and different contexts to assure their validity. Thus, the hope is that the analyses, research and case studies presented and discussed in the article will provide a rich starting point for new research related to improving the teaching of statistics at the school level and the preparation of teachers to deliver that teaching. The recommendations for further research constitute a rich research agenda and show the existence of statistics education as a research field where international collaboration is not only possible but fruitful.
Many people, across many countries, have contributed to the Study, each has shown a keen interest in improving the teaching of statistics in school mathematics in one way or another but like all large scale implementation of change there is always more that can be done. Now that you have read the article do not just put it down and forget. Focus on your area of interest, decide how you can contribute through teaching, research or teacher training, and become an active component of the changing profile of the teaching of statistics in school mathematics and/or the training of teachers to teach statistics.
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