A curriculum for a data rich world
At the level of school education, the need for statistical literacy is recognised by Australian education systems and teachers of school mathematics, and 'Statistics and probability' has been proposed as one of three content strands in the forthcoming Australian curriculum (ACARA 2009, p 5). The Australian Bureau of Statistics (ABS) itself also offers assistance in this regard, through a Statistical Literacy unit and its Education Services section.
The need for further attention to this issue is underlined, however, by recent research into current levels of students' statistical literacy. A study of students' understanding of statistical language by Watson and Kelly (2003) found more than 60% tested in Grades 3, 5, 7 and 9 could not adequately explain the terms 'sample', 'random' or 'variation', and large proportions of students showed no understanding of the terms at all. Research by Mathews and Clark (2007) indicated that tertiary students who achieved above-average marks in an introductory statistics course had only a rudimentary understanding of the statistical concepts, and relied heavily on memorised algorithms.
A related concern is that statistics faculties at universities attract fewer and fewer students, and as a consequence, organisations such as the ABS are finding it difficult to recruit statisticians.
Over recent years research has looked at the acquisition of statistical understanding at younger ages, in the primary and secondary years of schooling. Much research is looking at what statistical ideas should be introduced at what stage of schooling, how best to teach statistical concepts and what the developmental stages of statistical understanding may be. The evidence gathered from these studies offers ways to build on the work schools are currently undertaking to help students improve their statistical literacy.
There is a general consensus that statistical literacy is about understanding rather than computation, that it requires knowing how and why data are produced, and that it requires a familiarity with basic ideas and terms. Statistical literacy also requires an understanding of the basic concepts of probability, as well as knowledge of how statistical conclusions and inferences are made.
The Australian Bureau of Statistics Education Services section considers four competencies to be essential to statistical literacy: data awareness; the ability to understand statistical concepts; the ability to analyse, interpret and evaluate statistical information; and the ability to communicate statistical information and understandings.
What students need to improve statistical literacy
To develop these elements of statistical literacy students must gain an understanding of key concepts, including variability, uncertainty, ambiguity, and the role of probability. Students must also learn how to question data and its assumptions, and develop an understanding of the differences between and different uses of empirical and observational data.
The enrichment of current learning opportunities can occur through further enhancements in the areas of curriculum, pedagogy, technology, assessment, training and research, and also by providing students with additional exposure to statistics in practical contexts.
While statistics is most formally encountered within the mathematics subject area, it can be found in all areas of the curriculum. Students may employ statistics across areas such as population density in geography, environmental statistics in SOSE/HSIE and science, economic indicators in economics, voting patterns in civics, persuasive argument in English, and experimental design in science.
Many educators recognise the need for statistical understanding across different subject areas. However, effective cross-curricular implementation requires that someone take responsibility for its coordination. Without this investment of resources, statistical literacy may, like the critical thinking movement in the USA, become everybody's, and therefore nobody's, responsibility, and despite general agreement about its value, may simply disappear.
Genuine statistical literacy, rather than rote learning of algorithms, requires that students encounter real, and not just realistic, data. Teachers need to ensure that students have opportunities to construct their understandings of statistical ideas by engaging meaningfully with data and grappling with real problems. Time needs to be available for students to build understanding rather than just familiarity with formulae, and to identify and address their misconceptions.
A further issue that has implications for pedagogy is research evidence that suggests that students do not readily transfer knowledge from one area to another. While schools need to ensure that statistics is introduced in a coordinated manner across subject areas, teachers of all subject areas must also introduce relevant statistical concepts in ways that improve students' understanding; this instruction needs to occur overtly across all relevant contexts. This scaffolding to learning needs to be removed slowly and carefully.
With the availability of computer technology in the classroom, teachers not only have access to real and relevant data, but to tools that can be used to enhance understanding. Recent research by Ridgway and his colleagues (2008) has shown how technology can be used by students to manipulate multivariate data to improve both their statistical and content understanding. The use of technology in classrooms also allows students to engage meaningfully with real data in which they are interested.
In order to gain adequate experience in examining and asking questions of data, students also need to be exposed to 'dirty data'. This too can be facilitated by technology. The CensusAtSchool datasets from ABS Education Services, for example, contain the responses of over 112,000 students from across Australia. As these datasets contain raw data, students need to ask particular questions, such as those which take into consideration whether certain responses represent outliers, extreme values or errors, in order to examine it.
Taking advantage of currently available technology and of a coordinated curriculum offers opportunities for the use of new and potentially more effective pedagogies.
Assessment and training
The assessment of students' statistical knowledge is an area that needs further attention. There is a need for assessment practices and tools that assess students' deeper understanding rather than simply measuring their ability to plug numbers into formulae. While current technologies offer a useful means to address this issue there is still much work to be done to both develop such assessments, and to understand the knowledge and understandings being assessed.
Professional development programs that address both the teaching of statistics, and the technology that can facilitate that teaching, is also necessary.
With statistical literacy considered essential for the 21st century, educators and policymakers must address the requirements that need to be met in order for students to gain this skill.
It is important that statistical concepts be explicitly taught, from an early stage, across the curriculum, and that schools develop a coordinated approach to teaching statistical ideas across different subject areas. In addition, to promote engagement and deeper understanding, students need to have access to real data, and to technology that can be exploited to assist teaching and learning of statistical concepts. Moreover, it needs to be recognised that statistical literacy is about understanding, and not simply calculation.
Australian Curriculum, Assessment and Reporting Authority (2009) Shape of the Australian Curriculum: Mathematics.
Mathews, David & Julie M. Clark (2007) Successful Students' Conceptions of Mean, Standard Deviation, and The Central Limit Theorem Paper presented as part of the Research in Undergraduate Mathematics Education Community.
Ridgway, Jim, Sean McCusker & James Nicholson (2008) Alcohol and a Mash-up: Assessing Student Understanding EARLI SIG Berlin.
Watson, Jane M and Ben A Kelly (2003) The Vocabulary of Statistical Literacy Proceedings of the AARE conference.
Information and Communications Technology (ICT)
Teaching and learning