Key Ideas - Chapter 6: Reasoning about data
A list of resources to support the book and website "Key Ideas in the Teaching of Mathematics"
How Faithful Is Old Faithful?
This article by J. Michael Shaughmessy and Maxine Pfannkuch is subtitled "Statistical Thinking: A Story of Variation and Prediction" considers work carried out by students using real data.
Crime Scene Evidence
This task, produced by the Royal Statistical Society with Plymouth University, uses a problem-solving approach.
The resource enables teachers to lead pupils through a crime investigation to help solve the problem of whodunit? A theft has occurred and the only clue to identify the culprit is a footprint.
Pupils investigate how helpful the footprint may be in identifying the thief. They use averages, histograms and scatter diagrams to explore the likelihood of various suspects being the culprit.
Chapter 3: Using Random Samples of Real Data
This chapter in the booklet Relevant and Engaging Statistics and Data Handling from the Royal Statistical Society Centre for Statistical Education (RSSCSE) describes the steps needed to both take and use random samples of real data from the CensusAtSchool website. In addition it offers some ideas to allow students to use samples of real data in their data handling and statistics lessons.
Chapter 6: Data Visualisation
This chapter in the booklet Relevant and Engaging Statistics and Data Handling from the Royal Statistical Society Centre for Statistical Education (RSSCSE) looks at ways to visualise data. In particular how data can be displayed in tables and charts having been retrieved from an online database, particularly the AtSchool database, using a Database Interrogation Tool.
Examples of common visualisations include: tables, matrices, charts, graphs, maps, Venn diagrams, and Chernoff faces.
Data With No Name
In this resource from CensusAtSchool, a set of data is presented with little background information. Students are invited, via a series of questions, to turn the data into usable, useful information applying both mathematical reasoning and use of statistical methods.
It encourages the use of spreadsheets as a means to further enhance the quality of the work and provides scope for further investigation. Students will be engaged in using frequency tables, grouped data, mean, median, mode and range, and in comparing distributions.
Towards The Construction of Meaning for Trend in Active Graphing
This link is to a PDF of a paper by Ainley, Nardi and Pratt on the Institute of Education website.
Page 12 describes two tasks that were used in the research, ostensibly to engage students in the use of scatterplots. However, the students also need to consider the signal and noise in the data that emerge during the active graphing process, particularly in the helicopters task.
As students carry out the tasks, the bivariate data are plotted using a spreadsheet. For example, in the case of the helicopter task, the students might be aiming to find the ‘best’ helicopter – the one with the longest time of flight. They might consider the time of flight when helicopters of differing wing lengths are dropped.
The data are likely to be quite noisy given the need to measure lengths and durations of time. Nevertheless, the plot of wing length against time should gradually reveal a wing length that seems to offer the maximum time of flight. The signal that emerges through the noise is likely to be a humped shape with large or small wing lengths resulting in helicopters that drop very quickly.
Visualisation Inference Tools
This is a link to Chris Wild’s personal website in which he reports on the latest developments of his visual inference tools.
This is not a tool to use directly with younger students, but it provides the reader with an interesting insight into how modern tools are beginning to make sophisticated ideas about statistical inference easier to visualise. This is work in progress but well worth monitoring.
The website links to seminars, webinars and movies describing the tools. It is also possible to download and install the software for the tools themselves. The emphasis is very much on visualisation. By sampling and re-sampling many times, and keeping a graphical trace of the parameters of interest, it becomes possible to imagine sampling distributions as animations.