Findings of the study

The findings of this are summarised here in response to the two guiding research questions.

5.5.1 How does peer tutoring shape the mathematical experience of the participating tutors?

The mathematical experiences of participating tutors are summarised here in relation to emerging themes.

Self-confidence: The peer tutors who participated in this study reflected in their responses that the peer tutoring programme had a positive influence on their self-confidence. This improved self-confidence was manifested in different forms for different tutors. For one tutor the self-confidence generated through the tutoring programme manifested in a desire to help others achieve well in mathematics. For another tutor, increased self-confidence resulted in an improved sense of personal autonomy. For most tutors, the tutoring programme was very helpful in terms of building their own mathematical understanding and reinforcing their mathematical confidence, while at the same time impacting on their affective wellbeing beyond the confines of the tutoring programme itself.

Better understanding of mathematics: The peer tutors who participated in this programme indicated that the peer tutoring process helped them improve their own mathematical understanding, highlighting that it was the process of teaching others, and the preparation that went into it, that had the positive effect of building their mathematical understanding

Prospects of improving mathematics examination results: All six tutors shared the sentiment that peer tutoring afforded them an opportunity to potentially improve their examination results. For some tutors there was a development in the belief that if one works hard there is a good chance of improving one’s results. The tutors saw their

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participation in the peer tutoring programme as having a positive impact on their drive to succeed and thus ultimately on their mathematics examination marks.

Feeling good, happy and appreciated by peer: All six peer tutors indicated that being a peer tutor made them feel happy and appreciated by their peers. For all six tutors, helping other learners was a positive personal experience. Tutor 4 summed up her feelings as follows: “teaching my fellow learners mathematics was really great, that feeling of knowing you are

sharing your knowledge with others is a most wonderful feeling” (lines 530-531).

5.5.2 How does peer tutoring shape the mathematical disposition of the participating tutors?

The following table provides descriptions of the categories (and subcategories) of the various dispositional functions (Beyers, 2011) along with observed changes in the mathematical disposition of the group of tutors taken as a whole, as tracked by the MDFI instrument. Taking the six tutors as a group, the cognitive mode increased from 0.64 to 0.80. The affective mode increased marginally from 0.70 to 0.73, while the conative mode also showed only a marginal improvement, from 0.75 to 0.77.

Table 5.1 Dispositional functions based on Beyers (2011)

Scale

Subcategory of Dispositional

Function

Description of

Subcategory Observed change

Cognitive Connections

A tendency to try and connect with or cross mathematical topics.

The average score for this subcategory increased from 0.65 to 0.81. Specifically, tutors were able to connect their understanding of fractions to ratio and proportion.

Argumentations

A tendency to evaluate the mathematical correctness of statements, make

mathematical arguments, justify mathematical statements, etc.

The average score increased from 0.62 to 0.80. This indicates an increase in critical reasoning. Affective Nature of Mathematics

A belief about mathematics being more procedural or conceptual in nature.

The average score increased from 0.57 to 0.64, indicating a slight increase in an

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conceptual aspects of mathematics.

Usefulness

A belief about the usefulness of mathematics for meeting current or future needs in or out of school.

The average score

increased marginally from 0.66 to 0.68.

Worthwhileness

A value judgement that the work put into learning mathematics has been worth it to the student.

The average score increased from 0.72 to 0.90. This represents an increased appreciation for the value of time and effort put into learning mathematics.

Sensibleness

A belief that mathematics is composed of ideas that can be made sense of.

The average score increased from 0.65 to 0.70, indicating a slight increase in the belief that mathematics as a subject can be made sense of. Mathematics Self-

Concept

What the student believes about him or herself as a learner of mathematics

The average score decreased marginally from 0.76 to 0.74. Attitude

The respondent’s emotional reactions to mathematical activity in or out of school.

The average score increased marginally from 0.87 to 0.89. Maths Anxiety

Whether or not the student experiences anxiety in relation to mathematics.

The average score decreased marginally from 0.83 to 0.80. Conative Effort/Persistence A tendency to persist or _{exert effort if necessary.}

The average score increased marginally from 0.75 to 0.77.

In terms of the individual tutors, all six tutors saw an improvement in the cognitive mode – the biggest increase being that of Tutor 2 from 0.48 to 0.86. In the affective mode the overall scores suggested little change, but the subcategories showed some interesting shifts. The conative mode saw an increase for Tutor 1 and 6, a slight decrease for Tutor 2, while the scores for Tutors 3, 4 and 5 remained essentially constant.

Tutor 1 saw a change in his view of mathematics through his participation as a peer tutor.