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5: DUOLOG MATHS: METHOD

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Just as Paired Reading is a set of generalised tutoring behaviours for reading which can be applied to any book (Topping, 2001b), there was a need for a set of generalised tutoring behaviours which could be applied to any mathematical problem. Mathematics is a very wide ranging area, and this proved considerably more difficult for mathematics than for reading.

However, after a study of successful tutoring behaviours by professional teachers, a set of (much simpler and complementary) tutoring behaviours suitable for use by non-professionals was designed. This system was termed "Duolog Maths". A duologue is a dialogue between two people, and the title was selected as the preferred name by a large group of teachers in the USA - hence the American spelling.

A flowchart indicating the coaching behaviours identified in the study of teacher behaviour will be found below. The behaviours are arranged here in a logical and strategic order. The behaviours indicated by an asterisk (*) were those considered appropriate for inclusion in a system designed for use by non-professionals. (The definition of the others need not concern us here.)

The resultant flowchart for the Duolog Maths system (see below) includes only these behaviours, again arranged in a strategic and sequential order. It is intended that this flowchart be used in training tutoring pairs and then a copy be given to each pair in order to remind them of the interactive flow required of them. The following page then gives more detail concerning the definition of each tutoring behaviour. It is intended that this be photocopied onto the back of the flowchart, for reference by tutoring pairs.

A listing of "More Tips for Tutors" is included below. Teachers will need to use this with considerable care, given the dangers of information overload for the participants. However, this forms a useful list for reference by professionals, who might select single items from this list for discussion with participants in the light of particular problems which seem to be emerging from the monitoring of the interaction between the pairs.

Duolog Maths - Tips for Tutors

Two additional more detailed prompt Sheets are provided, one for the "Questions" behaviour and one for the "Make It Real" behaviour. These would not be issued at initial training, but could be used subsequently as necessary at the teacher's discretion. They could also be printed back-to-back as required.

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DUOLOG MATHS Questions Prompt Sheet

Remember:

Example Questions

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DUOLOG MATHS Make It Real Prompt Sheet

Remember:

Ways to Make It Real

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DUOLOG MATHS More Tips for Tutors

Your aim is to help your tutee:

Remember:

How did your tutee go wrong? Was it because:

When your tutee goes wrong, you might want to:

If all else fails:

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About

Evaluation of the Duolog procedure at the time of writing has been with parents rather than peer tutors. This was a controlled study in Glasgow with P4 to P7 pupils who were weaker mathematicians. Pre-post curriculum-based mathematics tests showed the experimental group made significantly greater gains than the control group (Topping, Kearney, McGee & Pugh, 2001 - see section 7 of this manual).

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