What We Know
Data analysis includes the processes of gathering data, organizing it, displaying it in a useful way and drawing appropriate conclusions for decision making. The ability to analyze data is important for today's students who enter a society in which data is constantly available and sometimes misused for persuasion (Principles and Standards for School Mathematics, 2000). Despite its importance, data analysis is not given sufficient emphasis; "very few secondary schools offer a separate course in probability and statistics" (Shaughnessy & Bergman in Wilson, 1993, p. 178).
Students often lack an understanding of concepts basic to work in data analysis, including the concept of mean. Part of the problem may simply be with terminology; students are more familiar with the word average (Bright & Hoeffner in Owens, 1993). The problem may also lie in how students are first taught the measures of center. A procedural manner of instruction may not be effective. Mean, mode and median must be taught using children's informal descriptions of the shape of their data as a starting point (Russell & Friel, 1989). Research suggests an emphasis on applications - which includes asking students to characterize the overall shape of the data, summarize the data and interpret the data - will help students develop critical conceptual understandings of statistics (Russell & Friel, 1989). An emphasis on real-world problem-solving (Russell & Friel, 1989) and questioning (Mokros & Russell, 1989) also help develop statistical reasoning.
The American Association of the Advancement of Science (1993) outlines the reasoning skills students should develop in the use of data:
- Reasoning about data: identifying the data type (such as quantitative, qualitative, discrete or continuous) and knowing how a type of data leads to a particular data representation or statistical measure.
- Reasoning about representations of data: understanding how different representations represent data differently and knowing how to modify a graph to better represent data.
- Reasoning about statistical measures: understanding how the measures of center, spread and position portray data sets.
- Reasoning about uncertainty: understanding and using randomness, chance and uncertainty to make decisions about uncertain events; knowing that not all outcomes are equally likely; knowing how to determine the likelihood of an event using an appropriate method.
- Reasoning about samples: knowing how samples are related to populations and what may be inferred (for example, a larger sample better represents the population while a smaller set may be biased).
- Reasoning about association: knowing how to judge a relationship between two variables.
"Work in data analysis and probability offers a natural way for students to connect mathematics with other school subjects and with experiences in their daily lives."
--Principles and Standards for School Mathematics, 2000, p. 48
"All of our students...eventually become consumers and citizens...they will enter a society in which the use of data and graphs to communicate information and to influence decisions is ever increasing."
--Shaughnessy & Bergman in Wilson, 1993, p. 178