by Mel Muldowney, a secondary school maths teacher working in Warwickshire
We know there are topics that students often mix up - so should these be taught close together with the aim of drawing our pupils' attention to their similarities and differences, or should they be taught separated as far as possible by a period of time and by other areas of the curriculum? Concepts such as area and perimeter or mean, median, mode and range are topics that are usually used in this discussion (what do you do? Let us know) but I’ve recently found evidence that frequency trees and probability tree diagrams should also be included.
Our department made the decision that there was a logical link between these two concepts, and so when I taught frequency trees, which is a new GCSE topic, to my year 10 group I made the link to probability trees. Finding the first incorrect answer in a recent assessment didn’t trigger any alarm bells, but after three or four answers with the same (incorrect) solution I began to wonder what these students were thinking.
During our usual “post-mortem” of the assessment all of the students that dealt with the probability trees as you would a frequency tree claim not to have even considered that the sum of the probability in each “branch” must equal 1. However, when asked about why the probability of Wendy not winning at Hoopla was 0.6 one of them instantly stated “well, that’s obvious, the probability of the events must equal 1”. When asked what could have been done to check her thinking this student said “I suppose I could have checked it by working out the probability of ALL the combinations of outcomes which must also add up to 1”.
Was it that these two topics were taught so close together that meant the students hadn’t been able to form separate schema in their own minds? I’m not sure but it is something we will consider as we refine and revise our scheme of work.
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