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The Video:
Learning Mathematics through Discussion and Refection Algebra at GCSE. Malcolm Swan and Muriel Green
A video produced by the Learning and Skills Development Agency (LSDA): (a free copy has been sent to every FE College)
The facilitator introduces the video saying:
You are about to see a video on mathematics teaching
The students are GNVQ Foundation Students
Its doesnt matter if you are not a mathematics teacher, you can still apply similar strategies in the teaching of any subject
Mathematics teachers and others interested might like to see the interactive CD-ROM which goes with the video. It contains over 100 pages of student worksheets and other materials.
Task 1 Evaluating the teaching strategies on the video
a. Bearing in mind the questions in task 2, watch the video taking notes if this will help task 2. About 15 minutes
b. Get into groups of 2 to 5, preferably in teaching teams, and decide on answers to the following questions:
Which teaching and learning strategies impressed you most?
Why do these strategies impress you?
Agree some statements you think worth making either raised by the video, or by other issues you have considered in discussing it. Focus on what teachers can do in their teaching.
Conclude your discussion by agreeing some experiments you would like to try based on what your group learned from watching the video
About 15 minutes
Task 2 Using reflection and discussion in my subject
How could similar strategies be used in your subject?
What other ways are there for engaging students in discussion and reflection in your subject? For example tell your partner or your team the strategies you use already.
Explain and justify your answers to task 2 to the facilitator and the other groups
Task 3: Action Planning
If you completed this activity in a teaching team you could agree some activities for your Differentiation Action Plan. Consider agreeing experiments to try and then sharing these out so that everyone has an experiment to try for the team.
Notes to the facilitator on the video activity.
Stress that discussion and reflection and decision-making are hardly the exclusive preserve of mathematics. They can be encouraged in the teaching of every subject.
It is of course not possible to know in advance what issues the video will raise, but here are some worth raising if participants do not.
The activities require students to make decisions which in turn require understanding rather than simply remembering mathematical procedures.
Students have verbal interaction. Expressing your understanding is an excellent way of forming it and consolidating it.
There was plenty of student engagement: students really seemed to enjoy the activities
Activities such as explaining, translating one mathematical expression into another form, decision making, evaluating other students ideas, writing questions for other students to do, etc are all high order tasks that create deep learning.
Students help and support each other
Alternative methods such as students doing exercises, while helpful, may encourage students to remember rote procedures that get the right answers, rather than try to understand algebraic expressions.
Students create something tangible to show the teacher and others and so get a sense of achievement.
In talking mathematics students become familiar with the vocabulary and the concepts.
Representing abstract concepts like n(n + 3) in a visual way (e.g. as an oblong with sides of n and n + 3) helps students understand the concepts
Students were motivated by the sense of achievement they got from completing these activities.
Misconceptions are discovered and corrected
Big and difficult issues.
Time: Some staff will say that it would be great to teach like this but there isnt enough time. This is a good point, teaching time has been reduced for most courses in the last few years without an equivalent reduction in the syllabus content. This should be acknowledged openly. However stress that it is usually due to changes in funding not management whim.
However lack of time is an argument for using discussion and reflection in a well focussed and time constrained manner. It is not an argument for never using discussion and reflection.
The teachers in the video all tried these methods and like them. They continue to use them and are working within the same constraints as other teachers in the sector.
Lack of time is not an excuse to teach badly but a spur to teach very effectively with methods that encourage real understanding.
If time constraints are an issue, the strategies used should be those that create the deepest learning, with the best recall, in the shortest time. These include student centred activities. However teacher centred methods are also important. For example the teacher would need to explain and demonstrate the use of greater than and less than signs (> and <) before students did an activity requiring them to discuss, reflect and decide on expressions using these signs. There needs to be a balance between time used to explain new concepts and time used on the student activity required for deep learning .
Noise: Some staff will say that the problem with this sort of teaching is that the class will become noisy, and may get progressively out of control.
Point out that some noise is productive, but acknowledge that some classes will need careful classroom management on short activities before they are able to engage productively in such activities for a long time.
Point out that the video is a Foundation class and that Level 1 students are not noted for their quiet application to algebra.
If necessary ask staff to brainstorm mutual advice on class room mangement. This will raise issues such as:
Make the task very clear and explicit and give a time constraint
Hold students accountable for completion or at least productive effort
Praise effort and good ideas at least as often as you criticise noise or off-task behaviour
Pay attention to the work students have completed and praise what they got right even if they did not do well.
Consider asking groups in advance to be ready to show their work to other groups as well as the teacher
If students are not completing the task give them assistance
If students still do not complete the task, ask them why they have not managed it.
There is not space here to address the issue of classroom management fully. Consider separate staff development events on classroom management. You could use the LSDA pack Aint Misbehaving by Carole Mitchell. If it is not just classroom management then consider also following up the issues raised with appropriate staff, e.g. learning support; initial guidance; etc.
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