Effective teaching combines a number of techniques so that the experience of the student is varied and the different learning styles of students can be catered for.
Whole class teaching is an effective way of introducing a topic and to assess quickly where a class has reached and how well they understand the current work.
Group work promotes discussion and interaction. Students can learn from one another and develop the skill of expressing mathematical concepts in their own words.
Individual work is necessary to hone the skills of the student and ensure that they address weaknesses, learn facts and formulae for later use and prepare for exams.
Whole class teaching
Effective whole class teaching is no different at AS and A2 to teaching in the lower school. To teach effectively you need to prepare so that you know your subject and can present it in a stimulating and interesting way. Using ICT to enhance your presentation helps and it is easily stored and adapted for the next time that you choose to present the topic from the front of the class. Whole class teaching also gives you the opportunity to place the mathematics within an historical or work-related context. There are a number of high quality websites (see below) that can be used to show that mathematics has meaning in and relevance to the real world.
Another factor in effective whole class teaching is your style of questioning. You need to know whether you have succeeded in getting your ideas across and you need to ensure that everyone is onboard.
Finally, appropriate timing of your presentation, your interventions and your final plenary can make the difference between a good lesson and an ordinary one. Whole class teaching will always be part of a lesson and will form a structure within which group and individual work can take place and will direct the talking that occurs in the classroom.
Group Work
Managing group work effectively is probably one of the most difficult aspects of teaching mathematics. You have to design a task that ensures that all students are involved and that one talented or forceful individual does not do all the work. You also want to avoid failing groups and encourage reticent individuals to get involved.
To establish good group work you have to use it often so that students are used to doing it in mathematics lessons. Talking in pairs is also an effective way of initiating discussion.
The effectiveness of groupwork is discussed in this Bibliography from the standards web site.
It is good practice to establish base groups which you use regularly. These are established groups of three or maybe four students which you have selected soon after the beginning of term. These groups should be mixed in every way - by ability, gender and ethnicity. Whenever you then work in groups you can say Get into your base group" and students know immediately what is expected of them. On other occasions you may wish to group students according to their ability to complete extension work and support slower learners.
When working in groups, ensure that each member has a definite role. For example, each group will need a note taker and a chair to ensure that all members contribute.
Design tasks so that they cannot be done by individuals. For example, this task is designed for three groups of three students each:
Each group receives a different exam question and are given 15 minutes to ensure that everyone within the group understand the question and can produce a solution. They then split into a different set of three groups that contain one student from each of the original groups. Each student then ensures that each member of the new group understands the question that they have brought to the group.
Individual work
For many students, individual work is getting through an exercise without making too many mistakes. Some talented individuals will absorb the ideas and others will flounder. We as teachers need to support individual work effectively both in the classroom and when the student is completing homework.
To support homework, you could adopt some or all of the following strategies:
When setting an exercise, make the learning aims explicit. For example, say that the purpose is to ensure that a student can solve any quadratic that has one or two real solutions and to recognise when they can be factorised.
Insist that the student writes a summary of the points learned at the end of every exercise and that at least one of the questions contains detailed commentary on how the solution has been reached.
Provide students with a list of useful websites that provide help and advice.
Consider setting up an online course forum using Moodle. More and more schools are now using Moodle to support learning and establishing forums where students can ask questions and discuss their work is a simple task for the Moodle coordinator. Having a forum can prevent students from getting stuck and is especially useful if you only see your class once a week. They can also see other students' questions and your responses.
Useful websites: