Peer Learning and Paired Maths

Peer tutor status and outcomes in primary mathematics

This evaluation explored the role that tutor status plays in determining cognitive and affective outcomes during peer tutoring in primary school mathematics. The project was supported by an award from the ESRC (Economic and Social Research Council), which ran from 18 months from May 2009.

The aims and objectives of the study were:

  1. To develop successful pedagogical approaches in peer tutoring in mathematics for use with 10-12 year-old pupils.
  2. To ascertain whether status of tutor influences tutoring discourse, cognitive and affective outcomes (self-esteem, social relationships and self-concept of pupils) when using reciprocal role tutoring techniques in primary school settings.

The peer tutoring technique used in this evaluation is called Paired Maths, a form of structured interaction between pupils. Research took place in 20 primary schools spread throughout Falkirk, Stirling and Dundee City Councils, and a pre-post design recorded changes and tracked outcome measures and variables. Control groups did not form part of this study. This was the first study to examine the predictive nature of tutor status on outcome measures. It was conducted jointly with Professor Keith Topping (University of Dundee), and was funded for 18 months from May 2009.

What is Peer Learning?

A very important part of school and later life is working with and helping other people. Peer Learning calls for children to help other children learn. Pupils work together in pairs with a child as the tutor and another as the tutee. It is important that Peer Learning is set up so that the tutor benefits, as well as the tutee. To tutor in a subject, it is necessary to gain a sound understanding and be able to explain it. So helping helps the helpers learn faster too.

Pupils should benefit from peer learning through:

  • Raised attainment in literacy and/or numeracy
  • Improved motivation and self-esteem
  • Increased confidence
  • Enhanced interpersonal skills
  • Greater awareness of the needs of others
  • Further opportunities to encourage responsible citizenship in a caring, supportive and tolerant environment
  • Better social, communication and teamwork skills.

A wide range of subjects have been developed for peer tutoring, including reading, mathematics, spelling, writing, languages and science. There is no doubt that peer tutoring ‘works’. There is a large body of research evidence showing that in peer tutoring projects, the tutors improve as much, if not more than, the tutees. Many studies show that peer tutoring also improves how both tutor and tutee feel about the subject. Also, in many cases the tutor and tutee grow to like each other more, and get on better. There are many reports of both tutor and tutee showing more confidence and better behaviour. The research clearly shows that peer tutoring is one of the most effective ways of using school time.

Some projects have tutors and tutees of the same age, and some have older children as the tutors. If the tutors and tutees are not too far apart in age and ability, there may be even more chance of the tutor gaining as a result. Some schools are also now tutoring with pairs of the same ability, where the job of tutor switches from one to the other.This form of tutoring seems to have the best effects overall as both children get the boost to confidence and status benefit of acting as tutor and tutee.

Like any other way of effective teaching or managing learning, setting up peer tutor projects needs enthusiasm, careful planning and hard work on the part of the teacher. It would be a mistake to think of peer tutoring as an easy option.

Paired Maths

This programme focuses on maths and employs the method of Paired Maths. This method relies on a dialogue between two pupils about a mathematical question. The interactions are structured in order for the tutor to help the tutee gain a clearer understanding of the solution and the path to the solution.  The tutors will employ strategies such as questioning, thinking out loud, praising, questioning and summarising and generalising. The concept is to highlight the different methods that can be employed when doing maths for both the tutee and tutor.

Paired Maths focuses on pairs of pupils working together and solving maths questions in three main steps:

  1. Understanding the question
  2. Finding an answer to the question
  3. Finishing the question by asking themselves what have they done and how it links to things they have done in the past

To facilitate this discussion, we propose the following strategies:

Understanding the question

  • Read: Your tutee might be having trouble reading a word question. If so, read it for them.
  • Identify: Make sure that your tutee understands what the question is askingTo help this happen encourage them to use fingers, counters, cubes, sticks or any other objects to show the reality of the question;Or have them draw dots, a picture, a list, table, diagram, graph or map; Useful things to help might 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 your tutee think of what they have learned before or questions they have solved before, relevant to the current question;

    Work through a similar but simpler question;

    How can this question be related to people, places, events and experiences in the life of the tutee? (or those of someone they know or have seen on television);

    Make up a similar question using the pupil’s own name;

    Try to use everyday language.

  • Listen: Give your tutee time to think about the question and then ask them to explain how they might solve it.Do not just jump in to fix what you assume the problem is.

Finding an answer to the question

  • Question: Ask helpful and intelligent questions that give clues, to stimulate and guide your tutees thinking. Challenge things that you think are wrong.However, 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?”;
    • Answering your own questions;
    • Indicating the “difficulty” of any step.

    Examples of questions you may want to ask are:

    • “What kind of question is this?”
    • “What are we trying to find out here?”
    • “Can you state the question in different words or a different way?”
    • “What important information do we already have?”
    • “Can we break the question 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?”
  • Praise: Give your tutee praise and encouragement very often, even for a very small success with a single step in solving a question. Keep their confidence high.
  • Think out loud: 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 also need time to think! If you are not sure, say so. You are not supposed to know everything.

Finishing the question by asking themselves what have they done and how it links to things they have done in the past

  • Check: Check that your tutee eventually gets the right answer. But remember there is probably more than one “right” way to solve the question.If the answer is wrong read the question over and try again. Only if all else fails show your tutee how you would do it (while you think out loud).
  • Sum-it-up: Have your tutee summarise the key steps in doing the maths question. Point out any errors or gaps, then summarise the key steps to yourself.
  • Link-it-up: The tutor and tutee should talk about how the learning might be used to do another similar question (generalise it to another maths question) or how the learning might be useful in a wider context.

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