Academic journal article Australian Mathematics Teacher

Helping Students Interpret Large-Scale Data Tables

Academic journal article Australian Mathematics Teacher

Helping Students Interpret Large-Scale Data Tables

Article excerpt

Introduction

New technologies have completely altered the ways that citizens can access data. Indeed, emerging online data sources give citizens access to an enormous amount of numerical information that provides new sorts of evidence used to influence public opinion. In this new environment, two trends have had a significant impact on our increasingly data-driven society:

1) the increasing use of large-scale databases within the open data movement, and 2) the growing use of big data.

The open data movement supports the availability of high quality data sets collected by national statistics offices and non-government organisations for a specific purpose. These data are characterised by several features: the data are multivariate, consist of clearly defined measures, the population is known, and the data generation and presentation have been subjected to extensive scrutiny. These data are made available to all citizens. The open data movement has had significant success in recent years in persuading major data providers, and national statistics offices, (for example, the Australian Bureau of Statistics [ABS]) to give citizens access to huge databases in order to create new variables, and explore new relationships.

Big data, in contrast to open data, is not generated by national statistics offices, and therefore is not publicly available. It is only available through proprietary sources, and is owned by companies that gain financial advantage from using it.

These two trends offer considerable promise in enhancing people's understanding of complex scientific and societal issues, such as political and organisational change, population growth, and immigration.

This new access to data is having a profound impact on teaching statistics and modernising curricula to prepare students for a world filled with open and big data, or the so-called "data deluge". The comprehension and interpretation of large data tables are important skills to possess.

This article focuses on a specific technique for teaching students to read data tables. Using a general framework suggested by Australian researchers, the article looks at a specific implementation of the framework in teaching specific tables.

Theoretical framework

The expanding use of large-scale data for prediction and decision-making in almost all domains of life makes it a priority for mathematics school curricula worldwide to help students develop their understanding of key statistical ideas prior to entering college. This includes understanding of data presented in tabular form, which is a core aspect of statistics, essential to conducting meaningful data analysis.

Data-tables are used broadly in the media to present, disseminate, and explain information, thus students need to be able to read and interpret them in meaningful ways. Koschat (2005) identifies three main advantages when using tables for providing information. Firstly, a table represents data, or a summary of data, in numerical form. Secondly, people can easily use the data and convert it to other forms such as a graph or a model if they wish to do so, but it is not easy in reverse. Thirdly, it can quite often be the case that the reader wants to interpret the actual numbers. For the reasons described by Koschat (2005), tables are important, and therefore it is important for teachers to help their students develop the ability to read tables effectively. It is expected that teachers would provide learning experiences and discussion regarding ways in which data may be collected and summarised in the table, therefore helping students with developing awareness of the potential pitfalls and distortions of data collection. Teachers can bring an awareness of the process of data collection to their interpretations of data.

A number of research studies about the difficulties that learners experience showed that students have particular difficulty in drawing inferences from tables and graphs, in interpreting the data, and making predictions from tables and graphs (For example, Estrepa, Batanero, and Sanchez, 1999; Friel, Curcio, and Bright, 2001; Pereira-Mendoza and Mellor, 1991; Sharma, 1997; 2013), but beyond these studies, there appears to be little research on learners' comprehension of tables, despite the pervasive use of data-tables in statistical data analysis and textbooks of statistics. …

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