Embedded Files
The starting point of this lesson was the Outbreak lesson sequence from the Bowland website www.bowlandmaths.org.uk/projects/outbreak.html. The task concerns an infectious disease spreading within a city under quarantine. Two vaccinations exist, and students are given their costs and percentage effectiveness, and told that a budget of £5m is available. The population of 946,000 is broken down into occupations such as “medical workers”, “farmers and food producers”, and so on, and the numbers of people in each are stated. Students are asked to recommend how many of each vaccine should be made and who should get them. The task does not specify precisely what the students’ objective should be – this is left open.
With this task as a starting point, planning began about three weeks before the research lesson. The lead teacher, who taught the lesson, initially suggested the research question "How well are my students able to adapt their problem solving skills when the conditions are changed?" In the lesson plan the planning team explained their rationale: “During part of this lesson the constraints regarding the vaccinations will change, which means that the students are now likely to have to change their current approach to solving the problem.” The initial and subsequent values chosen were as shown in this Table.
In this video the Head of Maths, who will be the research lesson teacher, and the knowledgeable other or outside expert, Malcolm Swan from the University of Nottingham Centre for Research in Mathematics Education, and two teachers form the planning team. They consider carefully all details of the lesson and the research question.
Here is the plan for the research lesson - the research proposal.
outbreak lesson plan.docxThe team chose to give the task to students to work on individually for 15 minutes in a previous lesson and then collect in their responses and assess them. Using their experience of seeing the task used with other classes, the planning team developed a detailed list of key issues that they expected to arise, along with suggestions of how the teacher might respond to each. They also produced a progression grid, indicating different levels of achievement with the task, with suggested prompts to support students’ progress to the next level. Developing and refining these tools took a great deal of time and discussion.
On the day of the research lesson, before teaching the lesson the planning team briefed the observers about what their intentions were for the lesson and therefore what they might pay attention to when observing students working on the task.
Two things to note:
(i) the teacher used the students' prior individual work to find out the approach they had taken and then sat students with different approaches to sit and work together during the research lesson
(ii) the teacher provided a brief overview of all the decisions that had been taken during the planning meeting.
The lesson observers were also reminded to :
observe student learning, not to judge the teaching.
focus on observations that may help address the research question.
avoid distracting students by talking to them.
make detailed notes about specific examples to contribute to the post-lesson discussion.
The lesson
The lesson
Sequences from Outbreak lesson (at a first time of watching it might be best to watch through in the order presented here)
1
2
3
4
5
6
Post lesson discussion
Post lesson discussion
In these two video sequences the observering teachers make comments on what they observed to discuss the research lesson and its research questions. (Note these teachers worked across a number of schools participating in the Lessons for Mathematical Problem Solving project (LeMaPS).
Final commentary
Final commentary
At the end of the post-lesson discussion one of the lead researchers, Malcolm Swan from the University of Nottingham, who had worked across the schools participating in the project exploring teaching for problem solving gave a final commentary.
In the style of Japanese Lesson Study, Malcolm, had prepared in a substantial way so that not only does he draw on his own evidence of what he observed together with the observations and comments of the other observers, but he also draws on his reading of appropriate research. His comments are specifically designed to take forward the thinking and work of the group.
Teachers' reflections
Teachers' reflections
Here some of the participating teachers refelct on their experiences of lesson study.
Finding out more
Professional learning through the collaborative design of problem-solving lessons
Geoff Wake, Malcolm Swan, and Colin Foster
The Outbreak lesson is central to this paper that draws on theory to understand teacher learning of the CLR group.
© CLR-UK 2023
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