Two units of the fourth year mathematics curriculum were chosen for the experiment, each of which needed from five to six weeks of teaching. The first unit was about fractions and the second unit was about decimals. These units were clearly related to each other.
There were two reasons for determining the focus of the curriculum units used in the project:
two units would require twelve consecutive weeks of teaching, which was a reasonable ‘dose’ and length of ‘treatment’ for the experiment;
the complementary relationship between the units made them a good choice for the experiment and the timing of the study meant that these units could be covered during the time frame of the intervention in terms of teaching and chronological position in the school year.
In the control group and manipulatives group, the student’s partner was the student sitting next to him in the mathematics class. The researcher asked the teachers in these groups to ensure that each student had the same partner throughout the intervention period.
109 3.2.1 The manipulatives group
A 12-week programme guideline was developed to guide the teachers in the manipulatives group through their teaching, and the teachers were asked to use the programme at least once a week for 30 minutes. Two classes (one each from a government and an ARAMCO school) were taught using manipulatives in the pilot study and six classes (three each from a government and an ARAMCO school). The guideline included the following suggested process:
First, the teacher needs to explain to the students the value of using mathematical manipulatives in helping them learn mathematics. Although this explanation is important for the first time of using manipulatives, it is important to refresh the idea to remind the students about it. This process can be done by giving the students an opportunity to explore the manipulatives, start a discussion around what they already noticed and then introduce the subject of the lesson. Then, teachers should explain to the students the similarities and differences between using manipulatives in the maths class and playing with toys or games. They should explain to their students that with manipulatives they are required to use them to find out a solution to a maths problem and their activities and talk with manipulatives should be concerned with this problem, however, they are free to be creative and suggest new ideas.
Teachers should be aware of students’ arguing with each other and they should be aware of how they can interact with such issues to get the class back on track. They need to give the students time for free exploration of the manipulatives when introducing new material. This process will engage the students with the manipulatives and give them a chance to be free to use these manipulatives in their learning as they should use the manipulatives themselves to gain the most advantages from their use. It is also important to satisfy the students’ curiosity so they do not become distracted from the assigned tasks. After the free exploration, the teachers
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should find out what students have discovered and write their answers on the board to share the ideas around the class. After the students become familiar with the lesson’s concept, it the time to test their understanding by giving them the class task (even the questions from the maths textbook or from the worksheets provided by the researchers as required) to work with it individually and giving them a chance to use the manipulatives and share them around to help them to find the answers.
Manipulatives are usually provided to Saudi schools by the Ministry of Education. However, as there were some schools which did not have them, the researcher provided them where necessary. Two kinds of manipulatives were used in this study. The first was the fraction bars which were used to teach the fraction unit and the second was the base ten blocks which were used in the decimal unit. Fraction bars are among the manipulatives that teachers can use to teach the concept of fractions and mathematical operations with them. It has been reported that the use of fractions bars can enhance students’ understanding of both the concept of fractions and operations using them.
Base ten blocks are another mathematical manipulative that can be used to teach and learn a number of mathematical concepts. One of the concepts that base ten blocks can be used for is that of decimals. The individual place values of base ten blocks when they are used to teach and learn decimals are as follows: flats (representing number 1), longs (representing tenths), and units (representing hundredths).
The researcher did his best to ensure that there were enough manipulatives in each class for students to use them individually. However, this proved impossible and there were occasions where the students had to share these manipulatives. The researcher ensured that the manipulatives were passed around the class and the students remained in their places.
111 3.2.2 The peer tutoring group
A 12-week programme pack was developed to guide the teachers in the peer tutoring group through their teaching, and the teachers were asked to use the programme at least once a week for 30 minutes. Two classes (one each from a government and an ARAMCO school) were taught using peer tutoring in the pilot study and six classes (three each from a government and an ARAMCO school). The teachers who taught these classes were provided with a guideline containing the processes they should follow when using peer tutoring. The pack provided contained full details of the pedagogies and experiments, the tests and questionnaires.
The author of this present research was part of Professor Allen Thurston’s group at the University of Stirling in a joint project between the University of Stirling and the University of Dundee on the use of peer tutoring in primary school mathematics. This project was funded by the United Kingdom Economic and Social Research Council and was carried out in schools in Stirlingshire and Falkirk. The peer tutoring materials used in this project were translated from English into Arabic by this present researcher, and adapted from the manual used by Thurston and Topping (2009). The same-age peer tutoring mathematics programme is a method of learning in maths in which discussion between two students (tutor and tutee) is used to solve maths questions. In this research, it was decided to pair the students of similar ability in the peer tutoring group and have them alternate tutoring roles, which is sometimes referred to as reciprocal peer tutoring. Same ability matching would allow the researcher to suggest an effective method of learning to the class that could help to minimise the teaching changes. This would thus make them more acceptable to the teachers who had never been involved in research and had been never asked to change their teaching methods. It is important to minimise these changes to ensure the teachers’ willingness to make the changes in their teaching methods. The
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reciprocal process in this method improved the ability of both of the pairs to take advantages of the learning process, which increased the students’ engagement in the learning process and helped to make them feel they were playing an important role in the learning process. Each student should have the same partner for the two units in all periods of the intervention.
The role of the tutor is to provide support and mediate the learning processes for the tutee. In order to do this the tutor will try to ensure that the tutee attempts to answer maths questions using a structured approach. It is the job of the tutor to keep the tutee working within this structured framework. It is the job of the tutee to do the actual working out to arrive at an answer to a maths question.
The following is a description of the peer tutoring technique and thus is taken directly from the Stirling University website. Peer tutoring focuses on pairs of pupils working together and solving maths questions in three main steps:
Understanding the question
Finding an answer to the question
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, the tutee uses the following strategies: Understanding the question:
Read
Identify
Listen
Finding an answer to the question:
Question
Praise
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The tutor should finish the question by talking about what have they done and how it links to things they have done in the past:
Check the process and the answer
Sum-it-up
Link-it-up
3.2.3 The peer tutoring and manipulatives group
A 12-week joint manipulatives guideline and peer tutoring programme pack was provided to guide the teachers through their teaching in the peer tutoring and manipulatives together group, and the teachers were asked to use the programme at least once a week for 30 minutes. Two classes (one each from a government and an ARAMCO school) were taught using manipulatives in the pilot study and six classes (three each from a government and an ARAMCO school). The researcher explained to the teachers who taught these classes how they should apply peer tutoring and manipulatives together in the class. It was explained that the students should support their peer by applying peer tutoring using manipulatives and sharing the manipulatives around the class.
3.2.4 The control group
The control group was taught normally and had ‘treatment as usual’. The usual teaching method in Saudi Arabia is that the teachers control the class and all students are silent when the teachers explain everything to them.