I am going to go out on a limb and say something controversial here: I think that maths teachers are the worst people to teach statistics.
In recent years, there has been a growing international consensus that statistics should not be taught as a collection of techniques, but as a method for solving problems and gaining insight. Yet due to its existence as a component of the maths curriculum, many students’ experience of statistics is repeatedly calculating using a single technique on small data sets shorn of context.
Many textbook exercises are dominated by “calculate the mean from sets of five numbers”-style questions, with interpretive work left until last. Lower-attaining students, in particular, may rarely get to experience the act of making decisions about which technique to use, or have the opportunity to observe how different techniques bring different observations to the surface. These skills should not be seen as add-ons for the most able, but as a fundamental part of statistical literacy.
However, where statistics are used in other subjects, students tend to have a far richer experience. They use data alongside images and text to discuss the meaning of the information provided in a clear context.
Of course, in subjects such as geography, teachers do not necessarily have the time or the curriculum responsibility to focus on developing proficiency in the underlying techniques, so as a profession we need to think more carefully about how we can coordinate and share the load, adding more technical practice to subjects that use statistics, and more interpretive and contextual practice to statistics in maths lessons.
So how can a maths teacher teach statistics through other topics and in context, more like a geography teacher would?
Here is a simple example around practising measuring angles. Begin by giving all students the same angle to measure, using a protractor. Ask them to call out the angle values they measure and record them in a spreadsheet. Then show them a bar graph of the very messy set of results. What should be apparent is that there are some noticeable features to the data. It’s likely for example that there will be two peaks on the graph.
Spend some time discussing with the students what they think the correct measurement is. If there are two peaks, explore why this might have happened. During the course of these discussions, students who have prior knowledge can describe the technique of how to measure angles. You can also identify the common mistake of reading the wrong scale and strategies for addressing this can be established.
Developing statistical literacy
Now, give the students whatever practice task they would normally get, perhaps assigning higher-attaining students the task of supporting their classmates. At the end of the lesson, provide a new angle for all students to measure and again collect their results before displaying the new graph alongside the original. It should now be significantly less messy; perhaps there are still two peaks, but one is much larger than the other; perhaps the variability has reduced.
Again, time can be spent discussing which features of the graph demonstrate that the class has improved as a whole. Perhaps you could even focus on the degree of accuracy of the measurements.
By the end of the lesson, students should be able to measure angles better than they could at the beginning of the lesson, but, as a secondary benefit, they will also have improved their abilities in interpreting variability in graphical representations.
There are loads of opportunities to use student activity to generate data and, as maths teachers, we should be proactive in seeking them out in order to help develop our students’ statistical literacy and not just their ability to reproduce statistical techniques. Only by exploring data in context can maths teachers once more lay claim to being the best people to teach statistics.
Darren Macey is framework developer for Cambridge Mathematics and a former secondary maths teacher