I know that this has been around for a while but I recently re-discovered the Gradual Release of Responsibility framework for classroom learning:
This model outlines a path of progression from teacher- to student-centred learning. It has four components.
1.The first involves the teacher in articulating and modelling the purpose of the lesson, using the type of thinking and language needed for it.
2.The second component is guided instruction: the teacher applies questions and prompts that gradually encourage students to assume responsibility for their own learning. The questioning may be addressed to the whole class but is more often used for smaller groups with similar learning needs.
3.The productive group work component involves students in collaboration around a task related to the central topic. The students are expected to use suitable academic language and are individually accountable for their efforts.
4.The final component is independent learning, in which each student applies what they have learnt within or outside the class.
I have been endeavouring to use more of the ‘questions and prompts for mathematical thinking’ at Stage 2 of the above framework this year in my instructional practice. Stage 3, group work, has been something that I have had doubts about. I use ‘Think, Pair, Share” quite frequently and divide the class up into groups to do follow-up material after assessments but I have not made full use of group work in my instruction as I believe that some students always dominate and some students always end up being more firmly bound to their lack of thinking as they just sit back and wait for others to do the thinking for them. Group work in mathematics can sometimes not add value to students’ thinking but become detrimental as the challenge and feeling of being ‘stuck’ is merely confirmed for some.
I am fortunate to be working with Ron Ritchhart of Project Zero at Harvard University again this year and he has introduced me to a protocol for use in group discussions called the Micro Lab protocol. I have now tried this out with a Year 10 class and a Year 12 class and I have been impressed with the way students have responded and how it has improved students’ approaches to problem solving in mathematics. It involves:
- Dividing the class into groups of 3
- Each member decides which problem to start on (a different one per member)
- Give 10 mins of individual time for students to work on their problem set
- 2 mins then for Problem 1 member to talk about how they went about their problem + 1 min quiet reflection time following this presentation
- 2 mins for Problem 2 person to do the above etc
- 10 mins for group to then come up with a consensus on all three problems
- Discuss these on the board with the class as w hole
I tried providing the same ‘stimulus’ material for all members of the group in one class (ie they all got the same problem to talk about) but this didn’t work as well as having three problems to discuss, each member having their own problem first of all. This protocol compels all students to talk about their thinking (not just the vocal ones) without interruption and allows for reflection time. I have found that students notice more things about the problems after they have had the opportunity to listen to someone else’s approach first. During the reflection time, I encourage students to note down any questions they might like to ask during the group discussion time, whether or not they agreed with the presenter’s approach to the problem and how this might compare with how they would go about that problem. When it comes to the group discussion time, students were more focused and had a way ‘in’ for each problem. No-one was completely stuck without a starting point. One of my Y12 students commented on how much she enjoyed the group work lesson as she felt more confident in her grasp of the mathematics, that it compelled her to engage more so than a ‘regular’ class.
What problems did I use? For one Y10 class they had a series of geometrical objects and had to determine whether they were geometrically possible or not, given what they knew (or what they thought they knew) about geometry.
In a Y12 class, students worked on problems to do with algebra of functions such as: