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close this bookTutoring (IAE - IBE - UNESCO, 36 p.)
View the document(introduction...)
View the documentThe international academy of education
View the documentSeries preface
View the documentIntroduction
View the document1. Real-life goals
View the document2. Question and prompt
View the document3. Check and correct errors
View the document4. Discuss and praise
View the document5. Reading: support and review
View the document6. Writing: map and edit
View the document7. Mathematics: make it real and summarize
View the document8. Recruit and match partners
View the document9. Provide training and materials
View the document10. Monitor and give feedback
View the documentConclusion
View the documentReferences and further reading
View the documentBack cover

7. Mathematics: make it real and summarize

Questions, make it real, check, summarize and generalize in mathematics

Research findings

The research evidence suggests that tutoring can be particularly effective in mathematics (e.g. Cohen, Kulik & Kulik, 1982). Britz (1989) reviewed studies of tutoring in mathematics published from 1980-89. Findings indicated the effectiveness of peer tutoring in promoting significant gains in mathematics performance for both the tutor and the tutee, including with low achievers, mildly handicapped or socially disadvantaged children. Heller & Fantuzzo (1993) have demonstrated the effectiveness of combining peer tutoring with parent tutoring in mathematics with 10-11-year-old students.

Tutoring in mathematics should not be just supervised mechanical drill. Tutors must not just do the problem for the tutee, or give them the answer. It is important that the tutee has time to talk and feels able to disclose their misunderstandings.

Mathematics is much more than just arithmetic. Its scope is so wide that some tutoring projects have used mathematical games (or other structured materials) to support the tutoring (e.g. Topping & Bamford, 1998a, 1998b). Designing a single tutoring procedure that could apply to all kinds of mathematics and requires no special materials is difficult. However, this has recently been done, based on principles of instructional design and the study of one-to-one interactions between professional teachers and students in mathematics. The resulting method is known as Duolog math (Topping, 2000a), on which the advice given here is based.

Practical applications

· Listen. Give your tutee time to struggle to explain what their difficulty is. Do not just jump in to fix what you assume their difficulty is.

· Read. Your tutee might be having trouble reading a word problem. If so, read it for them and check their understanding.

· Question. Ask helpful and intelligent questions which give clues, to stimulate and guide student thinking, and challenge their misconceptions. Examples: ‘what kind of problem is this?’; ‘what are we trying to find out here?’; ‘can you state the problem in different words or a different way?’; ‘what important information do we already have?’; ‘can we break the problem into parts or steps?’; ‘how did you arrive at that?’; ‘does that make sense?’; ‘where was the last place you knew you were right?’; ‘where do you think you might have gone wrong?’; ‘what kind of mistake do you think you might have made?’. Do not say ‘that’s wrong!’ - ask another question to give a clue. Ask ‘why?’. Try to avoid: closed questions which require only a ‘yes’ or ‘no’ answer; questions which just rely on memory; questions which contain the answer; the question ‘did you understand that?’. Try to avoid answering your own questions. Avoid indicating the ‘difficulty’ of any step.

· Pause for think-aloud. Give your tutee some thinking time, before expecting an answer. Encourage them to tell you what they are thinking all the time. Then you will find out where and how they are going wrong. Remember tutors need time to think, also! If you are not sure, say so. You are not supposed to know everything.

· Make it real. Try to make the problem seem real and related to the life of your tutee. Ask the tutee to try to imagine what the problem would look like in real life. Encourage them to use fingers, counters, cubes, sticks or any other objects to show the reality of the problem. Or have them draw dots, a picture, a list, table, diagram, graph or map. Useful charts include a number line, a multiplication matrix and a place-value chart. With your tutee’s permission, mark their written working out with lines, arrows, colours or numbering to help them. Have the tutee think of what they have learned before or problems they have solved before, relevant to the current problem. Work through a similar but simpler problem. How can this kind of problem be related to people, places, events and experiences in the home/community life of the tutee? Or those of someone they know or have seen on television? Make up a similar problem using the student’s own name. Try to use everyday language.

· Check. Check that your tutee eventually gets the right answer. But remember there is probably more than one ‘right’ way to solve the problem. Only if all else fails show your tutee how you would do it (while you think aloud).

· Praise and encourage. Give your tutee praise and encouragement very often, even for a very small success with a single step in solving a problem. Keep their confidence high.

· Summarize and generalize. Have your tutee summarize the key strategies and steps in solving the problem. Point out any errors or gaps, then summarize the key strategies yourself. Talk about how these might be applied to another similar problem (generalized).

The next three chapters (8 to 10) give principles and advice on how to organize tutoring.