Educators Viewpoints

Student's Individual and Collective Statistical Thinking

In an effort to identify statistical thinking framework, educators from Illinois State University have identified four key statistical processes: describing, organizing, representing, and analyzing and interpreting data. They based their framework on the assumption that primary school students would exhibit four levels of statistical thinking that were described as idiosyncratic, transitional, quantitative and analytic.

Key processes

The first process is to describe data or 'reading the data', which involves extracting information explicitly stated in the data displayed, recognizing graphical conventions, and making connections between context and data. For example, questions such as 'what does the graph tell you?' requires this thinking process.

The second process which is to organize and reduce data requires mental actions such as ordering, grouping, and summarizing data. One example of questions that require this thinking is 'what is the average number of students in the school?'

Representing data incorporates constructing visual displays that require different organizations of data. For instance, students would use this thinking process when asked to compare the number of sold ice cream to the number of sold salad bowl in a school canteen. Students need to figure out which type of graph will best show this comparison.

Students who are able to recognize patterns and trends in the data presented and make inferences and predictions from the data practice the final statistical thinking process, that is analyzing and interpreting data.

Thinking Levels

Based on the respondents answers, the below conclusions are made about how students act at different levels of statistical thinking.

Level 1: Idiosyncratic. At this level, students are limited to idiosyncratic reasoning that was often unrelated to the data presented. They often focus on their own personal data banks that may not be relevant to the given data.

Level 2: Transitional. Level 2 thinkers begin to realize the importance  of quantitative thinking and use numbers to invent measures for center (median/ mean of data) and spread (range of data). Their perspective on data is generally single-minded and there are seldom connections between representations or analyses of the data to its context.

Level 3: Quantitative. Students who are able to think at this level use quantitative reasoning consistently as the basis for statistical judgments and begin to form valid conceptions of center and spread. Students at this level are aware of both the context and the data but connections between the both are seldom made.

Level 4: Analytical. Students who exhibit this thinking use more analytical approaches in exploring data and can make connections between context and the data. They are also able to adopt both a macro and micro view of the data.

These are some examples collected from responses from interviewees that show the different responses at different level of statistical thinking.

Other Educators Viewpoints

Beth Chance& Allan Rossman (Professor of Statistics at Cal Poly and San Luis Obispo) suggested that statistical thinking involves careful design of a study to collect meaningful data to answer a focused research question, detailed analysis of patterns in the data, and drawing conclusions that go beyond the observed data.

Joel B. Greenhouse suggested that good statistical thinking requires a nontrivial understanding of the real-world problem and the population for whom the research question is relevant. It involves judgments such as those about the relevance and representativeness of the data, about whether the underlying model assumptions are valid for the data at hand and about causality and the role of confounding variables as possible alternative explanations for observed results. Finally, an essential component of good statistical thinking is the ability to interpret and communicate the results of a statistical analysis so non-statisticians can understand the findings.

Beth Chance (2002) also suggested statistical thinking is the ability to see the process as a whole (with iteration), including “why,” to understand the relationship and meaning of variation in this process, to have the ability to explore data in ways beyond what has been prescribed in texts, and to generate new questions beyond those asked by the principal investigator.