Academic journal article Australian Mathematics Teacher

# Supporting Students to Make Judgements Using Real-Life Data

Academic journal article Australian Mathematics Teacher

# Supporting Students to Make Judgements Using Real-Life Data

## Article excerpt

Introduction

Numeracy in schools is becoming an increasingly important part of mathematics learning and teaching. This is because we want students to engage with mathematical concepts more deeply, use mathematics to make sense of their environment and make decisions that are based on the analysis of mathematical information. In order to be numerate, students must be able to acquire mathematical concepts and procedures, and apply these flexibly in a range of real life contexts. The school mathematics curriculum provides a number of strands of mathematics from which students can draw from, such as geometry and algebra in order to exhibit their numeracy skills. In the present study, numeracy is investigated from the perspective of students' abilities to gather, display and interpret data--an area of numeracy that has been broadly referred to as statistical literacy (Watson, 2011). A statistically literate student can be expected to demonstrate an ability to use statistical concepts to make sense of his or her immediate environment. This area of students' numeracy continues to be challenging for many students (Shaughnessy, 2007).

In this paper we draw on our recent research that focuses on the interpretative aspects of real-life data and generating ideas for activities that would better engage children in the complex and somewhat more demanding area of statistical literacy. We do this firstly by advancing a model of phases that we suggest students go through from being able to draw a graph to being able to interpret a graph and make decisions. Secondly, we present findings from an authentic real-life context that we investigated in order to examine the usefulness of the phases outlined in our model. Finally we examine possible strategies for classroom practice.

Phases in data handling

When students learn about data they can be expected to go through a number of phases. We regard the following four phases as being the key components of the process underlining data representation and interpretation.

* Phase 1: Construction of graphs using a given set of decontextualised data. In this phase students generally translate numbers given in a table to graphs. This process is indicative of their understanding of how to draw different types of graphs. Including the construction and labelling of titles, scales, legends and axes, etc. These are necessary building blocks for the construction of graphs in early phases of learning to represent data.

* Phase 2: Extraction and Tabulation/organisation of data from a real-life context (contextualised data).

This second phase involves students having to extract data from the context and then organising or tabulating the data before constructing an appropriate graph. A critical element in this phase is to be able to make sense of the data and understand how it could be organised.

* Phase 3: Construction of different types of graphs using organised data from Phase 2.

In this phase students explore the construction of different types of graphs using the same data. As their experience in drawing graphs matures the emphasis on graphs shifts from being able to draw a graph to making judgement about the type of graph being drawn and whether it is appropriate for the information they have.

* Phase 4: Interpreting information from the graph.

Using graphs to draw conclusions and make sense of their data is the fourth phase. Drawing reasonable conclusions is predicated on students' ability to observe the numerical data in its graphical form. Beyond that the students should be able to look at their graph and unearth visible patterns that convey something about the context. They need to give an overall interpretation and comment with understanding about the background of the information looking between variables and making comparisons. The demands at this point get more complicated when students have to extract information from real-life contexts that is multi-dimensional. …

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