The Teacher's Role
Many teachers have erred on the side of too much intervention, and 'learned dependency' is common. All too often students successfully play the game 'If I look confused for long enough she'll eventually feel guilty and tell me the answer.'
For the purposes of discussion let us characterise the range of teacher - student interactions by a continuum.
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3 |
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Teacher
Withdrawal |
Interactive
Teaching |
Teacher
Intervention |
Hinting |
Explanation |
- Teacher Withdrawal. The teacher leaves the group of students completely to their own devices. The teacher observes them but does not interact with them.
- Interactive Teaching. The teacher does not give out information but helps the group to clarify their thinking. 'Tell me what you know already'. Or asks general questions. Have you tried a range of strategies?' 'Have you worked independently on the problem as well as cooperatively?'
- Teacher Intervention. The teacher gives specific suggestions, or raises questions, about useful mathematical processes. 'Have you tried solving a simpler problem?' 'Why don't you draw a picture?' 'But, if that's true won't this happen... ?'
- Hinting. The teacher gives specific suggestions, or raises questions, about useful content 'It's got something to do with adding consecutive numbers' 'Draw a right-angled triangle and look at ratios' 'Have you tried multiplying the length by the width'.
- Explanation. The teacher explains how to solve the problem or complete the investigation.
Where do you sit on this continuum?
Perhaps you can best represent your practice by allocating a percentage weighting to each category. Needless to say, if hinting or explanations are disproportionately represented, the likelihood is that the students will be teacher dependent and not developing their capacities to think mathematically. Let us explore interactive teaching and teacher intervention further.
Broadly speaking there are three types of teacher interaction and intervention:
- Those used when students get stuck
- Those used when students 'think' they have the solution
- Those used to help students extend a problem further
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