TL9: Is this really all worthwhile? – The Pivotal Lesson
TL9: Is this really all worthwhile? – The Pivotal Lesson
These vignettes are written by two members of the writing team, both of whom taught the lessons. The message here is for teachers to persevere - and to reflect on the overall sequence lessons at the end of the case. Teaching the case, twice or thrice, improving on the teaching method each time, would obviously be ideal.Teacher 1
During my two experiences teaching this case and then watching a colleague teach this case, there was a pivotal moment during lessons three and four where the case “came alive”. When pupils had completed the preliminary background work and took possession of their own joey to save, the case appeared to become more meaningful and personalised for the pupils. The pupils appeared to enjoy some independent work at this stage and were able to work with more freedom for an extended period. From a teacher’s point of view, it was good to be able to watch the action take place and listen to the rich discussions between pupils as they applied their skills and overcame mathematical problems in a genuine real life context.
Teacher 2
I taught the case to a mixed ability group. I spent a lot of time preparing the first two lessons, ensuring that I had kangaroo photos, worksheets, overheads, and large sheets of brainstorming paper. I had taught this particular class of pupils for the whole year, and so I felt confident that this would be an activity that firstly, they would enjoy doing, and secondly, that they would really see how maths could be used as a tool to solve a real-life problem. Lesson 1 and 2 were hard work, and at the end of Lesson 2, I felt quite disappointed with the pupils’ lack of understanding of the maths which was being used to solve the problem and lack of enthusiasm. They had seemed to participate in the activity more because they were the type of class who just ‘did what I asked, mostly without question’ – rather than because they were really enjoying what they were doing.
It was with great effort that I planned the next 3 lessons, trying to think about how I could get the pupils to become more actively and passionately involved. Lesson 3 changed all of that. Once I had set the Task, the pupils came ‘alive’ – they suddenly seemed to understand what I was trying to do with them, they took a personal interest in the fate of their joey - and their graphs and measurements immediately became meaningful. Rich and varied discussion followed. This enthusiasm carried throughout the remainder of the case.
Other teachers have also commented on the same pattern emerging in their classes: starting with important background, but hard work for the teacher and the pupil, and then, as if by magic, the “pivotal lesson”, the lesson in which the pupils meet their joey and ‘come alive’.
The “Pivotal lesson” – as described by a third teacher (L) to one of the writing team (P)
P – tell me about your pivotal lesson
L – when the pupils did the first graph representing the growth of their joey – they were really into it
P - what were the differences between this lesson and the previous lessons?
L-They worked the whole lesson – they did their graphs.
P - how were the kids responding differently?
L – they were really engaged – I don’t know why. Maybe it was because I understood the project a bit better by then – so my better understanding therefore was passed onto the pupils– the first lesson was quite rushed in terms of preparation– I did not really understand what I was doing with the first lesson P - so in the WOW lesson you felt as if you knew what you wanted to get through, knew what you wanted your end point to be L– yes