James Calleja
©2015
OBJECTIVES OF PROFESSIONAL DEVELOPMENT Ø To explore opportunities in which collaborative work may benefit student learning
Ø To reflect upon concerns in introducing and managing small-‐group collaboration and discussion Ø To understand the roles of students and the teacher within a collaborative environment
Ø To promote effective small-‐group discussion
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Teaching and Learning Mathematics through Inquiry
LOOKING AT STUDENT TALK IN SMALL-‐GROUP DISCUSSIONS Neil Mercer (1995) identified three typical ways of talking among students as they work in small-‐groups – disputational talk, cumulative talk and exploratory talk.
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Disputational talk Involves disagreements and individual rather than collective decision-‐ making. Exchanges are usually brief and consist of assertions or counter-‐assertions. Cumulative talk Represents a building of ideas based on each other’s suggestions aimed at providing a common consensus. Exchanges in this type of talk are usually repetitions, confirmations and elaborations Exploratory talk Characterised by critical but constructive engagement with each other’s ideas. Challenges are justified and alternatives suggested. Joint agreement in decision-‐making is the end result.
Disputational talk, in which students simply disagree and go on to make individual decisions, is not beneficial. Cumulative talk, in which students build uncritically on what each other has said, is also undesirable. For true collaborative work, students need to develop exploratory talk consisting of critical and constructive exchanges, where challenges are justified and alternative ideas are offered. The most helpful talk appears to be that where the participants work on and elaborate each other’s reasoning in a collaborative, rather than competitive atmosphere (PRIMAS, 2011). Mercer (1995) argues that in planning collaborative activities in the mathematics classroom, we should be aiming to promote exploratory talk: By incorporating both conflict and the open sharing of ideas, represents the more 'visible' pursuit of rational consensus through conversation. More than the other two types, it is like the kind of talk which has been found to be most effective for solving problems through collaborative activity. (p.105)
Reference: Mercer, N. (1995). The guided construction of knowledge: Talk amongst teachers and learners. Clevedon: Multilingual Matters. PRIMAS (2011). Students Working Collaboratively: How can we foster scientific discussion? PD Module 5: Students working collaboratively. Available online on: www.primas-‐project.eu/artikel/en/1221/Professional+development+modules/view.do
Teaching and Learning Mathematics through Inquiry
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COLLABORATIVE WORK – WORKING AS A GROUP
Collaborative work in small groups has a positive effect on both social skills and mathematics learning. However, this depends on the existence of shared goals for the group and individual accountability for attaining those goals. Dylan Williams explains that collaborative learning is effective when teachers create ‘group goals’ – getting students working as a group rather than working in a group. To achieve this, teachers need to create two conditions for students in their classrooms: collective responsibility and individual accountability. Visit the ‘Videos’ section on our Google Community and watch ‘Collaborative learning Dylan Williams’
Collaborative work is ideal for developing students’ conceptual understanding or strategies for solving more challenging and complex problems. Small group-‐work involves students working in collaborative rather than a competitive atmosphere by sharing and exchanging ideas, and challenging each other through critical and constructive talk. Group-‐work may be difficult when students do not have adequate sharing skills, participation skills, listening and communication skills. In this case, the teacher needs to provide opportunities for students to develop these skills. Visit the ‘Videos’ section on our Google Community and watch ‘How to Teach Math as a Social Activity’
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Teaching and Learning Mathematics through Inquiry
GROUND RULES FOR COLLABORATIVE WORK
The list below is taken from the PRIMAS PD materials available online: www.primas-‐project.eu Here are some suggested 'ground rules' for students to use as they work in groups. These ‘ground rules’ may be displayed and ideally reinforced over time. Maybe you could also try to involve you class in drawing up a similar list. 1.
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Give everyone in your group a chance to speak Listen to what people say
"Lets take it in turns to say what we think". "Claire, you haven't said anything yet." "Don't interrupt – let Sam finish". "I think Sam means that..." "What did Sue just say?"
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Check that everyone else listens
"I just made a deliberate mistake – did you spot it?
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Try to understand what is said
"I don't understand. Can you repeat that?"
Build on what others have said
"I agree with that because..."
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Demand good explanations
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Challenge what is said
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Treat opinions with respect
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Share responsibility
"Yes and I also think that..." "Why do you say that?" "Go on... convince me." "That cannot be right, because..." "This explanation isn't good enough yet." "That is an interesting point." "We all make mistakes!" "Let's make sure that we are all able to report this back to the whole class." "We've got the general idea, but we need to
10. Reach agreement
"Can you show me what you mean?"
agree on how we will present it."
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THE TEACHER’S ROLE DURING SMALL-‐GROUP DISCUSSION
The list provide below is taken from the PRIMAS PD materials available online: www.primas-‐project.eu
Make the purpose of the task clear
Explain what the task is and how they should work on it. Also, explain why they should work in this way. ‘Don’t rush, take your time. The answers are not the focus here. It’s the reasons for those answers that are important. You don’t have to finish, but you do have to be able to explain something to the rest of the class.’
Keep reinforcing the ‘ground rules’
Try to ensure that students remember the ground rules that were discussed at the beginning. Encourage students to develop a responsibility for each other’s understanding. ‘I will pick one of you to explain this to the whole class later – so make sure all of you understand it’.
Listen before intervening
When approaching a group, stand back and listen to the discussion before intervening. It is all too easy to interrupt a group with a predetermined agenda, diverting their attention from the ideas they are discussing. This is not only annoying and disruptive (for the group), it also prevents students from concentrating.
Join in, don’t judge
Try to join in as an equal member of the group rather than as an authority figure. When teachers adopt judgmental roles, students tend to try to ‘guess what’s in the teacher’s head’ rather than try to think for themselves: ‘Do you want us to say what we think, or what we think you want us to say?’
Ask students to describe, explain and interpret
The purpose of an intervention is to increase the depth of reflective thought. Challenge students to describe what they are doing (quite easy), to interpret something (‘can you say what that means?’) or to explain something (‘can you show us why you say that?).
Make students do the thinking
Many students are experts at making their teachers do the work! They know that if they ‘play dumb’ long enough, then the teacher will eventually take over. Try not to fall for this. If a student says that he or she cannot explain something, ask another student in the group to explain, or ask the student to choose some part of the problem that she can explain. Don’t let them off the hook! When a student asks the teacher a question, don’t answer it (at least straight away). Ask someone else in the group to do so.
Don’t be afraid of leaving discussions unresolved.
Some teachers like to resolve discussions before they leave the group. When the teacher leads the group to the answer, then leaves, the discussion has ended. Students are left with nothing to think about, or they go on to a different problem. It is often better to reawaken interest with a further interesting question that builds on the discussion and then leave the group to discuss it alone. Return some minutes later to find out what has been decided.
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Teaching and Learning Mathematics through Inquiry
ORGANISING GROUPS – SOME GUIDELINES
ü Working in pairs and in threes is usually the most effective. However, the teacher can profit from occasionally having students working in groups of four as it allows more time to assess students’ work and learning process. ü Initially start with pairs and later move on to slightly larger groups (even within the same lesson). ü Group dynamics appear to be more dependent on students’ personalities and relationships than on their mathematical competence. ü Allowing students to choose their group offers students a greater responsibility in making their group work more effectively. The teacher then has ‘more power’ in determining who should work with whom when s/he feels that changes need to be done.
ü It is also recommendable to alternate between student-‐selected groupings, heterogeneous (mixed-‐ability) and homogeneous groupings.
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