Mathematicians teaching English
“I became a maths teacher so I wouldn’t have to mark essays”
“I’m having trouble getting the students to write down their own ideas”
“When I give them templates I feel as if it’s spoon-feeding them”
These are comments I hear as I visit mathematics teachers who are teaching the new statistics curriculum in New Zealand. They have a point. It is difficult for a mathematics teacher to teach in a different style. But – it can also be rewarding and interesting, and you never get asked, “Where is this useful?”
The statistical enquiry cycle shown in this video provides a structure for all statistical investigations and learning.
We start with a problem or question, and undergo an investigation, either using extant data, an experiment or observational study to answer the question. Writing skills are key in several stages of the cycle. We need to be able to write an investigative question (or hypotheses). We need to write down a plan, and sometimes an entire questionnaire. We need to write down what we find in the analysis and we need to write a conclusion to answer the original question. That’s a whole heap of writing!
And for teachers who may not be all that happy about writing themselves, and students who chose mathematical subjects to avoid writing, it can be a bridge too far.
In previous posts on teaching report writing I promote the use of templates, and give some teaching suggestions.
In this post I am concentrating on analysing graphs, using a handy acronym, OSEM. OSEM was developed by Jeremy Brocklehurst from Lincoln High School near Christchurch NZ. There are other acronyms that would work just as well, but we like this one, not the least for its link with kiwi culture. We think it is awesome (OSEM). You could Google “o for awesome”, to get the background. OSEM stands for Obvious, Specific, Evidence and Meaning. It is a process to follow, rather than a checklist.
The following video takes you a step at a time through analysing a dotplot/boxplot output from iNZight (or R). Through the example, students see how to apply OSEM when examining position, spread, shape and special features of a graph. This helps them to be thorough in their analysis. For the example we use real data. Often the examples in textbooks are too neat, and when students are confronted with the messiness of reality, they don’t know what to say.
I like the use of O for obvious. I think students can be scared to say what they think might be too obvious, and look for tricky things. By including “obvious” in the process, it allows them to write about the important, and usually obvious features of a graph. I also like the emphasis on meaning, Unless the analysis of the data links back to the context and purpose of the investigation, it is merely a mathematical exercise.
Is this spoon-feeding? Far from it. We are giving students a structure that will help them to analyse any graph, including timeseries, scatter plots, and histograms, as well as boxplots and dotplots. It emphasises the use of quantitative information, linked with context. There is nothing revolutionary about it, but I think many statistics teachers may find it helpful as a way to breakdown and demystify the commenting process.
Class use of OSEM
In a class setting, OSEM is a helpful framework for students to work in groups. Students individually (perhaps on personal whiteboards) write down something obvious about the graph. Then they share answers in pairs, and decide which one to carry on with. In the pair they specify and give evidence for their “obvious” statement. Then the pairs form groups of four, and they come up with statements of meaning, that are then shared with the class as a whole.
Spoon feeding has its place
On a side-note – spoon-feeding is a really good way to make sure children get necessary nutrition until they learn to feed themselves. It is preferable to letting them starve before they get the chance to develop sufficient skills and co-ordination to get the food to their mouths independently.