A Peer-tutoring Scheme to Support Independent Learning and Group Project Work in Mathematics

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Database:

Record: 1

A peer-tutoring scheme to support independent learning and group

project work in mathematics. By: Houston, Ken; Lazenbatt, Anne.

Assessment & Evaluation in Higher Education, Sep96, Vol. 21 Issue 3,

p251, 16p, 4 Charts; Abstract: Discusses a peer-tutoring scheme

introduced to an undergraduate mathematics module. Provision of a

learning support for an independent learning program; Function as task

groups for group project work; Assessment of student attitude to peer-

supported independent learning programs; Students' acceptance of the

need to work in groups.; (AN 9609200206)

Academic Search Premier

A PEER-TUTORING SCHEME TO SUPPORT INDEPENDENT

LEARNING AND GROUP PROJECT WORK IN MATHEMATICS

ABSTRACT

A peer-tutoring scheme was introduced to an undergraduate mathematics module. This

was to provide a learning support for an independent learning programme. These student

support groups also functioned as task groups for group project work. In the independent

learning programme, students were directed to read selected passages of text, to attempt

certain exercises and to devise peer assessment tasks. For some of the sessions senior

students were present and functioned as additional peer tutors. To assess the students'

attitudes to the peer-supported independent learning programme, an Attitudes to Peer-

tutoring Questionnaire was constructed. The results show that the students readily

accepted the need to work in groups and to support one another. Overall, 78% felt that

they could work easily without pressure and that the sessions were not a complete waste

of time. However, 65% of the students did not appear to enjoy the independent learning

sessions and felt that they preferred to be responsible only for their own learning.

Introduction

In higher education, there has recently been a pronounced move towards student-centred

learning (Goldschmid & Shore, 1986; Goodlad & Hirst, 1989). Students are being asked to

take more responsibility for their own learning techniques and one way of enabling

students to do this is to offer them peer support. The strategy in education of training

students to help their peers learn is by no means new. The student help concept, termed

peer-tutoring, has been implemented in many undergraduate settings (Bruffe, 1988;

Collier, 1980; Goldschmid & Goldschmid, 1976; Nicholls, 1992; Saunders, 1992; Sims &

Metcalf, 1989). Indeed, many of the new teaching and learning strategies developed as a

result of the Enterprise in Higher Education Initiative, (Training, Employment and

Education Directorate, 1989) are designed to ensure that students develop personal

transferable skills such as teamwork, leadership, problem-solving and communication

skills. Few quantitative studies which measure the success of these programmes exist in

the literature (Goodlad, 1989). Indeed, much of the published literature in the field relies

on anecdotal reports of lecturing sessions and the subjective interpretation of case

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histories in order to show their success. The lack of objectivity based assessment of peer-

tutoring programmes has been explained by the need for:

better measures of outcomes, particularly, in the social area, than are now available.

(Klaus, 1985, p. 6)

The solution to this problem would require a balance between the experimental approach,

which utilizes programmes designed by researchers to examine microscopic aspects of

the tutoring experience in a laboratory setting, and a more in-depth qualitative approach in

a naturalistic setting.

A peer-tutoring scheme was introduced to an undergraduate mathematics module on

mathematical modelling. Primarily, the scheme was to be a learning support for an

independent learning programme through which the students would learn part of the

course and which was introduced at the same time. Students would also be involved in

group project work, and this activity, while new to these students was not new to themodule. It was intended that the peer-tutoring groups would function not only as learning

support groups but also as project task groups.

The module concerned is a first-year module for students on the honours and ordinary

Bachelor of Science (BSc) degrees in Mathematics, Statistics and Computing, and a

second-year module for students on the Higher National Diploma (HND) in Mathematical

Studies. It is an introduction to applied mathematics and attempts to familiarise students

with 'the way of life of an applied mathematician'. It covers three things:

(a) mathematical methods

(b) mathematical models

(c) mathematical modelling

(a) Mathematical Methods are 'tools' for doing things. For example, this module aims to

teach students to recognise and solve certain types of differential equations. There are

well-defined 'methods' for solving each type once it is recognised. Here a 'method' is an

algorithm or sequence of instructions which, when carried out, will solve the equation.

Before starting this module, students will have met some types of differential equations

and the corresponding methods of solution, so the ideas are not entirely new.

Generally, this topic would be taught by teacher exposition followed by pupil repetition. It

is fairly mechanical and it seemed to be an appropriate topic to include in an independent

learning programme Many textbooks give a clear exposition and lots of practical

examples, and reading a textbook on this topic seemed to be a more efficient way of

transferring knowledge to students than giving a series of lectures. What is missing, of

course, is the 'commentary' and the immediate presence of the lecturer. Peer-tutoring,

through learning support groups within the class and through postgraduate and senior

students giving tutorial support, was seen as a substitute.

There is support for these ideas from Boud (1981) who gives carefully reasoned

arguments for using peer-tutoring as a means of promoting the development of




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autonomous learning habits in students. He says 'It is desirable that students learn to

work with their peers' and that 'A preponderance of classroom teaching is [incompatible

with autonomy]'. 'Given suitable conditions [students] can facilitate and support each

others' learning'.

Furthermore, there are examples in the literature of this sort of activity being carried out in

school classrooms. For example Bloom (1984) found that students who were in peer-

tutored groups achieved significantly better than students who were only taught in the

conventional way. He states 'We believe that this solution is relevant at all levels of

education'. Harper et al. (1993) working with 7-year old children conclude that 'the results

of this investigation are supportive of the notion that Classwide Student Tutoring Teams

and Direct Instruction are useful adjuncts to teacher-led instruction'. 'Participants believed

the procedure beneficial and perceived few negative consequences of its use'. Fuchs et

al. (1994), again working with young children, researched the nature of student

interactions during peer-tutoring and concluded that it was important for tutors to provide

explanations as well as give directions as to what to do.

Learning new methods for solving mathematical problems by reading books or journals is

an essential part of 'the way of life of an applied mathematician' so it is a useful skill for

students to develop. Peer support comes first from one's colleagues through conversation

and, if that does not clarify everything, one can write to the author of the book and hope

that they are alive and well and willing to reply!

Formative assessment is an essential part of learning and the 'first line' assessors are

oneself and then one's peers. Learning mathematical methods by independent learningwith peer support seemed to be a suitable activity to enhance with a scheme for self and

peer assessment. Answers to many of the practice exercises are given 'at the back of the

book'.

In the next section on methodology, there is a description of the ways in which peer

support and self and peer assessment were introduced to enhance the learning of the

mathematical methods via this independent learning programme.

(b) Mathematical Modelling is a creative activity. It is the very essence of an applied

mathematician's work. Modelling is a process whereby a phenomenon in the world is

studied and a mathematical representation or model of the essential features of the

phenomenon is created. Thus a Mathematical Model is the product of the process of

mathematical modelling. It is a mathematical entity (such as a differential equation)

together with a 'map' or set of statements which describe how the modeller moved from

the phenomenon to the abstract representation. This map would include statements of

definitions and assumptions made in the modelling process and is a necessary and

important part of the model. A model is a mathematical description of a simplification of

the phenomenon.

Generally, someone will be asking questions about the phenomenon which has just been

modelled--'What will happen next year?' 'What if this value were different?' These




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questions can also be mapped into the model, and corresponding mathematical problems

can be created. These are solved using an appropriate mathematical method (which the

mathematician may already have in his or her tool bag, or which they may have to look for

in the literature, or they may have to invent one). The answers to the mathematical

problems then have to be interpreted as answers to the questions asked about the

original phenomenon. Through observation it may be possible to verify or validate themodel in some circumstances, thus giving modellers some confidence when they use the

model to predict the behaviour of the phenomenon in some other circumstances. The

modeller may find that the model is not very good and they will then need to revise the

model and start again. These activities--simplification, problem solution, interpretation,

validation, revision---comprise mathematical modelling.

Usually mathematical modelling is a team or group activity. There is discussion about the

phenomenon under consideration and the questions to be answered. The simplifying

assumptions have to be agreed and a suitable method of solution found and used. The

results must be interpreted and, if possible, validated. There may be a division of labour to

speed up the process and to make best use of the particular talents of the individuals in

the group. Those who participate in group based mathematical modelling must have good

interpersonal skills.

This method of learning mathematical modelling is well established and its use is

widespread. There have been six, biennial international conferences on the Teaching of

Mathematical Modelling and Applications, and the published proceedings of these

conferences give ample justification for its use. (Berry et al., 1984, 1986a and b; Blum et

al., 1989; de Lange et al., 1993; Nisset al., 1991; Sloyer et al., 1995.)

Mathematical modelling is a new activity for all the students taking this module. Working in

groups is a new activity for the BSc students taking the module; the HND students will

have had experience of this in Year 1 of their course. These activities have been standard

practice in this module for several years. Students are introduced to the ideas through

lectures and demonstrations (some on video); then task groups are formed, tasks

assigned and/or selected and work begins. At the end of the period (about four weeks)

each group presents a written report to the lecturer and gives a seminar presentation to

the class. Both of these are assessed, the latter by peer and lecturer assessment. Newtask groups are formed, new problems set and after another four weeks the group write a

report and give a poster presentation. Again the latter is peer and tutor assessed.

Not only do these students create their own mathematical models, they also study models

created by other people. Generally, when engaging in modelling, especially for the first

time, problems are set which can be solved using nothing more advanced than 'last year's

mathematics'. The purposes of the models part of this syllabus are to demonstrate to

students how the methods they are currently learning (i.e. differential equations) have

been used in modelling, and also to help give students insights into the modelling processas carried out by others. For example, population growth is studied. Simplifying




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assumptions and definitions are described and models obtained and used. This part of the

module is usually delivered by lectures and tutorials with the lecturer present.

The module is summatively assessed by written examination, which concentrates on

methods and models, by the written reports and oral and poster presentations, which

concentrate on modelling and interpersonal skills, and a comprehension test which, to

some extent, covers all three aspects of the course. (See Berry & Houston, 1995;

Houston, 1993a, b, 1995.)

Methodology

Development of the Task Groups

As described above, it was standard practice in this module to form students into task

groups for the purpose of engaging in mathematical modelling. These groups usually

consisted of three or four students and for this first task they were selected by the lecturer

to reflect, as far as possible, a mix of gender and ability. It was also felt that, at the

beginning of the course, students would not know one another well enough to select

groups for themselves. (This may not be an issue in the future because the module is now

a second semester module rather than an all-year course.) These task groups were also

asked to function as peer support groups for the independent learning aspects of the

module.

After four weeks, on the completion of the first modelling exercise, the groups were

reformed to tackle the second exercise. In the past, the lecturer reassigned the students

in an attempt to get them to meet and work with as many different people as possible. In

this experiment, since we were interested in exploring different ways of forming peersupport groups, the students were asked to form new groups which would tackle the

second modelling assignment and would function as peer support groups for the rest of

the semester. Again groups were limited to three or four (four being the desired size).

Some of the groups stayed the same. Others formed themselves into groups of friends,

some a mixture of men and women and others all of one gender. One student was left on

his own for a while; he was eventually taken in by a mixed group of three.

The class was timetabled for four, 2-hour slots in the week. The semester lasted for 12

teaching weeks followed by three examination weeks, with a 3-week break in the teaching

period at Easter. It was intended that one slot in the week be devoted to a lecture/tutorial

with the lecturer definitely present, one slot to modelling activity with the lecturer present

at the beginning and end of the four-week periods, and one slot to independent learning

with the lecturer not present most of the time. Students were expected to attend this

session and they took it in turns to record attendance on a register provided by the

lecturer. The remaining slot was available for whichever of these activities needed more

time that week. A classroom with moveable furniture was available.

The groups, whether assigned or self-selected, worked quite happily at the group

modelling project tasks. They had a common purpose with things to produce by a

deadline. These tasks lent themselves readily to group work. On rare occasions when a




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student does not cooperate, they usually incur the wrath of their peers who have to carry

the burden themselves.

For the peer-supported, independent learning programme, students were directed to read

certain passages from the set text and to attempt certain exercises each week. They were

to do this on their own outside class and also during the first hour of the slot devoted to

independent learning. During the second hour they were asked to get together in their

groups to discuss the material read, the worked examples in the book and the exercises

attempted. They were asked to explain to one another some aspect of the material they

had covered and to compare notes on their attempts at the exercises. If the whole group

was stuck on a particular problem, they were to ask another group and if the whole class

was stuck they were to ask the lecturer when he/she was next present. For some of these

sessions senior students were present and available to help.

Peer-tutoring Evaluation

Sample

A total of 39 mathematics students completed the Peer-tutoring Evaluation Questionnaire

and the Attitudes to Peer-tutoring Questionnaire (see Appendix l a & b).

Development of the Questionnaire

The questionnaire was designed to discover participating students' views on a number of

points. These included:

Willingness or otherwise to become involved in the group activity.

Adjustment to peer tutor authority and loss of academic staff authority.Assessment of increased motivation/interest.

Increase of creative/intellectual participation.

Greater degree of integration with students engaged in same activity.

Increased use of cognitive activities eg explaining, directing, responding, questioning,

organising, criticising, arguing, defining, presenting, reading, listening and giving opinions.

Increased use of affective activities e.g. problem-solving, leadership skills, taking group

control, directing others.

Assessment of increased or enhanced learning as results of participation in peer-tutoring

scheme.Student attitudes to peer-learning.

Evaluation of most and least helpful aspects of experience.

Recommendation of peer-tutoring schemes in the future.

As available information from other relevant studies is relatively sparse it is helpful to

combine the freedom and breadth of response which can be encompassed in open-ended

questions with the more objective indices by the use of a questionnaire. The Peer-tutoring

Evaluation Questionnaire was developed specifically for the project and contained two

sections (see Appendix la & b). Section one contained 18 questions and section two

contained 20 attitudes pertaining to peer-learning. Section two was factor analysed andresulted in three factors, namely: ambivalence, teaching and feelings. The concept of




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validity is a difficult one to interpret in this type of study, though the questionnaire

measures were of high face validity.

Development of the Attitudes to Peer-tutoring Questionnaire

To assess the students' attitude to the peer learning sessions, items for the initial

questionnaire were based on similar areas of enquiry in the literature (Keller, 1974;

Goldschmid & Shore, 1986; Goodlad & Hirst, 1989) and on observations gleaned from

students during informal conversations regarding the use of peer-tutoring in higher

education.

Using this material as a base, a 20-item questionnaire was compiled. Responses were

recorded on a yes/no, positive/negative scale. Once completed the questionnaire was

distributed to the 39 students in both the BSc/HND Mathematics groups.

Reliability Tests

When initial Principal Components Analysis was performed on all 20 items in thequestionnaire, the resulting factor analysis solution accounted for 48.5% of the variance.

The internal reliability of the questionnaire was found to be 0.2, based on Cronbach's

Alpha (Cronbach, 1951), suggesting only a fair degree of reliability. Four items for which

correlations with the total score were less than 0.3 were omitted from further analysis.

The remaining 16 items were subjected to Principal Components Analysis and Orthogonal

Varimax Rotation. Cattell's Scree Test (Cattell, 1966) was used as a guide to the optimum

number of factors to be extracted, and a three-factor solution was decided on as the one

drawing the greatest meaning from the data. This solution accounted for 42.3% of thevariance (see Table 1). Rotation resulted in three clearly-defined and meaningful factors.

Only those with loadings of 0.4 or higher were retained in the final questionnaire. Details

of the rotated factors and resulting scales are presented in Table 2.

The result of this procedure was a 16 item questionnaire having 3 factors, which was

entitled the Attitudes to Peer Tutoring Questionnaire (Appendix lb).

Internal Consistency

Measures of internal consistency based on Cronbach's Alpha (Cronbach, 1951) were

computed for the complete sets of scales. Overall Consistency was Cronbach's Alpha =

0.4402, suggesting a moderate level of reliability for the complete questionnaire.

Outcomes and Evaluation

The students readily accepted the need to work in groups and support one another in the

group project work on the modelling tasks. They organised their time and delegated

separate tasks to themselves. They cooperated in the writing of the report and in the oral

and poster presentations. They were happy enough working in assigned groups or self-

selecting groups, and the only disagreement that came to light was when one woman

from a group of three women dropped out soon after the start of the second exercise. Theother two had to do all the work themselves and were angry at the drop out.




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However, the students did not so readily accept the ideas associated with peer support

and peer assessment of the independent learning activity. They found the textbook too

hard to understand and preferred to work at their own pace and not to have to meet

weekly deadlines for reading and doing problems. They did not appreciate the value of

setting their own problems for peer assessment. They found it difficult to support one

another because they themselves had an inadequate knowledge of the subject matter.The independent learning sessions were generally noisy. They did, however, appreciate

the presence of senior students at some of the tutorials. They tended to seek the advice

of these tutors on all aspects of their work the 'modelling' problems as well as the

'methods' problems.

These attitudes were determined through conversation and the Peer Tutoring Evaluation

Questionnaire (see Appendix la). A more detailed report now follows.

Students did not enjoy the independent learning sessions (65%). They were equally

divided in their opinions about how easy it was to work collaboratively. They said that the

groups should be selected by the lecturer to reflect a mix of males and females and a mix

of abilities and not just social friendships. About 55% to 60% felt reluctant to join a peer

learning group and did not find it a valuable experience. The group sessions did not

reinforce (57%) or clarify (65%) their own personal learning, nor did this increase their

level of performance (85%) or level of ability (73%). They would not recommend this type

of learning to other students (65%) nor volunteer to act as tutors in the future (68%). They

felt that they learnt very little from their peers (80%), that they would not necessarily have

learnt more by working alone (47% with 25% unsure), but they were very sure (72%) that

they would have learnt more from conventional lecturing.

However, they did say that the independent learning sessions made them feel that they

could work easily without pressure (78%) and, surprisingly in the light of earlier

responses, that peer learning is not a complete waste of time (63%). About half the class

were bored by the activity and about half felt that they did not belong to a group that cared

for one another. They were divided on the value to learning of having the opportunity to

talk about their work.

Many felt that they had an inadequate understanding of the subject matter (43%) andmore felt uncomfortable within the group (70%). They did not believe that it enhanced

their communication skills (90%) although 60% felt that they could be a good teacher.

They said that they were pressurised for time (65%), and were embarrassed by the

activity (73%). They would prefer to have responsibility only for their own learning (65%).

An analysis of the attitudes questions shows that overall 15 students out of the 39 tested

had a positive attitude to the scheme (scored less than 30), with 12 of them being in the

BSc group. The negative attitude taken by the HND group may, perhaps, be understood

by recognising that these students were coming up to their final examinations, that they

had had a fairly dependent style of education up to now, and consequently were anxious




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that this new, independent style of learning might prejudice their ability to obtain a good

grade. They felt insecure and resented the innovation.

Discussion of the Factor Analysis Scales within the Attitudes to Peer-tutoring

Questionnaire

Factor 1 (Appendix 2, Table 4) Ambivalence. Of the 11 attitudes examined in this factor,

six proved positive while the remaining five were negative. The mathematics students

listed the most positive gains of peer learning as an extended range of transferable skills

deriving from teamwork, more efficient verbal transfer of information, more relaxed

attitude to work, greater familiarity with subject matter than was possible with a more

conventional style of teaching and finally increased levels of course performance and

achievement.

While the questionnaire elicited such positive reactions it also provided an opportunity for

students to register certain concerns about a new teaching technique. This may have

been sponsored more by concern regarding the immediate outcome of their present

courses, and a hesitancy to accept change. Nevertheless, it resulted in several more

negative reactions to the peer learning experience. These ranged from the overly hostile

view that peer learning is a complete waste of time, through criticism of classmates'

expertise in specific subject areas and inexperience with regard to communicating their

knowledge, to the general complaint that academic standards might fall by placing the

responsibility of teaching on those who traditionally saw themselves as learners.

These reactions can be explained by an understandable nervousness in the face of

innovation. Since the majority of students have spent their learning lives in a systemwhich promotes competition, several clearly found difficulty in adjusting to a new system

where yesterday's competitors become today's collaborators.

Factor 2 (Appendix 2, Table 4) Teaching. This factor addressed attitudes towards

teaching. All responses were very positive, with students feeling that they had developed

better communication skills as a result of the peer learning exercise, that they had

developed confidence enough to be good teachers and to demonstrate familiarity with the

subject matter in a classroom situation.

Factor 3 (Appendix 2, Table 4) Feelings. The factor dealing with feelings prompted two

different reactions. On some occasions students found the peer learning experience very

embarrassing and on other occasions confessed to being bored.

Reflection

The evaluation illustrates that these students were just not mature enough to take so

much responsibility for their own learning. They had been accustomed to conventional

teaching and lecturing through 'A' levels and their first semester modules. This reflection

is reinforced by the comments of the senior students who acted as tutors:

Only two group members appeared to ask pertinent questions.




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The class did not appear to enjoy this type of learning and used any excuse to either chat

among themselves or become involved in other ongoing projects rather than tackle the job

in hand.

The class should have been prepared to take more responsibility for their own learning.

The senior students felt that they themselves had benefited from the experience and now

had a deeper understanding of the subject matter. However, they would have liked more

training in the areas of group dynamics, teaching skills and communication skills.

Despite all their fears, 12 of the 14 HND students passed the module assessments, some

with very high marks, and 21 of the 26 BSc students passed, again some with high marks.

The mean and standard deviation of the scores in the written examinations are illustrated

in Table 3.

These results are similar to previous years, so the students did not suffer as a result of theindependent learning activity.

The fact that the students worked happily in groups on the modelling tasks suggests that

their discontent is more with the independent learning aspect of the course than with the

ideas of peer-tutoring and peer support. It is, we believe, worth persisting with an

independent learning scheme for all the reasons outlined in the Introduction. However,

students appear to need more 'expert' help than was available to this cohort. Better

written materials, which set clear goals for each week's learning, should be provided.

Also, there should be frequent testing to encourage regular study habits, perhaps with

less emphasis on the setting of peer assessment tasks. These tests could be quite short

and could be peer assessed using specimen solutions provided by the lecturer. (This

technique was used successfully by Catterall, 1995). Nevertheless, we believe that peer

assessment which involves the setting of assessment tasks as well as the marking of

them, while quite a difficult activity, is desirable, and is rewarding in terms of its value as a

learning aid. Perhaps the peer teaching aspects of the scheme could be more formally

structured with particular students selected each week to give a short seminar

presentation to their group on that week's topic. Students will always be embarrassed

when they give a presentation to their peers, but this tends to ease with practice and

maturity. It is our experience that final-year students, most of whom will have spent a year

on placement in industry, usually give very polished performances in seminars. The

'boring' aspect of the activity which some students confessed to, needs further

investigation. Are mathematical methods innately boring when decontextualised? Was it

all just too hard for them and they did not know what to do next?

Senior students who acted as tutors mentioned that they would have liked training for the

job. Such a training course is being prepared and should be available to student-tutors in

the future.

The competitive attitude adopted in particular by the HND students is a difficult one to

combat since it is not clear how to reward cooperation. This attitude is easy to understand




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when it is realised that these students are approaching finals and are competing with one

another for places in year 2 of the BSc course and for jobs. One way could be to make

admission to the BSc course dependent only on reaching a certain standard rather than

on both reaching the standard and gaining a high enough ranking in the class to be

offered one of the available places. The number of places available to these students

depends on other resource factors. Perhaps a policy change is called for! There may alsobe a reluctance on the part of brighter students to give up their time to help less able

students and thus hold themselves back. (This phenomenon was encountered by Curran,

private communication, in his unsuccessful attempts to introduce a peer support scheme

for engineering students.) They need to be persuaded of the benefits to themselves to be

obtained from teaching the subject to others.

Teaching strategies which could be adopted in the future include the following. A variety

of peer support mechanisms will be suggested and an investigation will be carried out at

the end of the semester to determine the extent to which the different mechanisms were

used. Project task groups will be formed and it will be suggested that these could function

as peer support groups. Another mechanism would be to pair off the students to give one

another 'front line' peer support. Friends will be encouraged to help one another prepare

for the tests. They will certainly be encouraged to help one another prepare for the

(summative) comprehension test.

The activities of 'independent learning' and 'peer support for independent learning'

became just one activity for the students. They did not like the former and therefore did

not appreciate the latter. The activities need to be separated.

TABLE 1. The attitudes to peer tutoring questionnaire. Rotated factors--eigenvalues

and percentages of variance

Factors 1 2 3

Eigenvalues 4.32442 1.38701 1.05369

% of variance 27.0 8.7 6.6

Total variance 42.3%

TABLE 2. Rotated factors of resulting scales for the attitudes to peer tutoringquestionnaire

Factor Scale Items

1 Ambivalence 11

2 Teaching 3

3 Feelings 2

TABLE 3. Mean and standard deviation scores obtained by the students in the

written examination

Mean Standard deviation(%) (%)




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BSc 51.5 19.4

HND 55.0 19.2

After resits in the autumn, another two BSc students passed.

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Appendix 1a: Peer-tutoring Evaluation Questionnaire

Peer-tutoring is a system of instruction in which learners help each other and learn by

teaching. As you have been involved in a peer-tutoring project in mathematics there are

listed below a number of questions asking how you felt during these independent learning

sessions and your attitudes to this type of study. Please answer each question as

honestly as you can as this information will help the University ascertain how valuable and

interesting this experience has been for you. Thank you.

Name:

Course:

Year:

This questionnaire relates to the Independent Learning from the

Set Texts.

1. Did you find the independent group learning sessions enjoyable?Yes/No

Why or why not? underbar

2. Did you find it easy to work collaboratively in the group?

Yes/No


3. Do you feel the groups should be selected:

(i) by the lecturer? Yes/No/Indifferent

(ii) by the students? Yes/No/Indifferent

(iii) to achieve a mix of males and

females? Yes/No/Indifferent

(iv) to achieve a mix of abilities? Yes/No/Indifferent

(v) to reflect social friendship groups? Yes/No/Indifferent





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4. Did you ever feel reluctant to become a member of a

peer-learning group? Yes/No


5. Did you find it a valuable learning experience? Yes/No


6. Did you find the group sessions (Please tick as many as you

wish)

(a) reinforced you own personal learning? underbar

(b) clarified your own personal learning? underbar

(c) increased your level of performance? underbar(d) increased your level of ability? underbar

7. How would you assess your peer group's ability to meet your

individual learning needs? (Please circle which applies)

Excellent Good Fair

8. What part of the group sessions was the most useful to you?

underbar

9. Which was the least helpful?

underbar

10. Do you feel that you will be a more capable student having

gone through this programme of learning? Yes/No


11. Would you recommend this type of learning to other students?

Yes/No


12. Would you volunteer next year to be a tutor for year 1

group? Yes/No





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13. Which of the skills listed below did you bring to the

learning session. (Tick as many as you wish)

Problem-solving skills underbar

Leadership skills underbarResearch skills underbar

Study skills underbar

Communication skills underbar

Technical skills underbar

Teaching skills underbar

Modelling skills underbar

Knowledge skills underbar

Skills in working effectively in a

team and cooperating with others underbar

14. How much did you learn from the other members of your group

in the discussions and group exercise?

(Circle which answer applies to you)

'I learnt a great deal 'I learnt a few things 'I learnt nothing

from collaborating of value through of value at all'

with others' collaboration'

15. In your opinion, would you have learnt more if you had worked

alone on this project?

(Circle which applies to you)

Yes No Don't know

16. In your opinion would you have learnt more from the moreconventional type of lecturing situation?

(Circle which applies to you)

Yes No Don't know

17. Cognitive Activities in Discussion Groups

When you were participating in your group sessions did you use anyof the activities listed below?




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Often Sometimes Never

Explaining ----- ----- -----

Questioning ----- ----- -----

Responding ----- ----- -----

Directing ----- ----- -----Organising ----- ----- -----

Criticising ----- ----- -----

Arguing ----- ----- -----

Giving opinions ----- ----- -----

Defining ----- ----- -----

Presenting ----- ----- -----

Reading ----- ----- -----

Listening ----- ----- -----

18. Did you value the presence of the year 2 and Postgraduate

Tutors at these sessions? Yes/No


Appendix lb. Attitudes to Peer-tutoring Questionnaire

Overall, did the independent learning sessions make you feel

1. that you could work easily without pressure? Yes/No

2. that peer learning is a complete waste of time? Yes/No

3. bored? Yes/No

4. that you belonged to a group that cared? Yes/No

5. that you had the chance to learn more by talking? Yes/No

6. that you had an inadequate understanding of the

subject matter? Yes/No

7. uncomfortable within the group? Yes/No

8. that you have developed better communication skills? Yes/No

9. that you could be a good teacher? Yes/No

10. that you could learn skills by working in a group? Yes/No

11. that you became pressurised for time? Yes/No

12. very embarrassed? Yes/No

13. confident enough to demonstrate how much of the

subject matter you really know? Yes/No

14. that you could get help without showing ignorance

to a lecturer? Yes/No

15. that you have insufficient ability/knowledge to

teach your subject? Yes/No

16. that you would prefer to be responsible for your

own learning and not that of the group? Yes/No

17. that you have developed better communication skills? Yes/No




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18. that your level of performance and achievement have

increased? Yes/No

19. that academic standards would fall if peer learning

became an established mode of teaching in Higher

Education? Yes/No

20. that you understood the subject matter better thanyou would have during conventional lecturing? Yes/No

Appendix 2. Attitudes to Peer-tutoring Questionnaires--3 factors

TABLE 4. Attitudes to Peer-tutoring Questionnaire--3 factors

Attitude Factor

loadings

Factor 1 Ambivalence

You had the chance to learn more by talking 0.73225

That peer learning is a complete waste of time -0.70063

That you could learn skills by working in a group 0.62164

That you had inadequate understanding of the

subject matter 0.60767

That you could work easily without pressure -0.58022

That your level of performance and achievement

have increased -0.57096

That you have insufficient ability/knowledge toteach your subject 0.54507

That academic standards would fall if peer learning

became an established mode of teaching in higher

education 0.54276

That you understood the subject matter better than

you would have with conventional lecturing -0.52212

That you could get help without showing ignorance

Factor 2 Teaching

That you have developed better communication skills -0.48435

That you could be a good teacher 0.47700

That you are confident enough to demonstrate how

much of the subject matter you really know 0.42625

Factor 3 Feelings

That you were very embarrassed 0.41392That you were bored 0.41103




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~~~~~~~~

By KEN HOUSTON and ANNE LAZENBATT, University of Ulster, Co. Antrim, Northern

Ireland

KEN HOUSTON was educated at Queen's University, Belfast, where he gained BSc

(Hons) and PhD degrees. He is Professor of Mathematical Studies in the School of

Computing and Mathematics. He is interested in the teaching, learning and assessment of

Mathematical Modelling and all else pertaining to introducing students to 'the way of life of

an applied mathematician'. This includes the development of 'enterprise' competencies,

the use of Information Technology and innovative teaching strategies like peer tutoring.

He is the editor of Innovations in Mathematics Teaching, SEDA Paper 87, 1994, and co-

author of Mathematical Modelling with John Berry. Correspondence: Professor Ken

Houston, School of Computational Mathematics, University of Ulster, Shore Road,

Jordanstown, Co Antrim, Northern Ireland, BT37 0QB. Tel: (01232) 366953. E-

mail:[email protected]

ANNE LAZENBATT was educated at the University of Ulster where she gained her BSc

(Hons) and DPhil degrees in Psychology. She is currently employed as Research Fellow

in the School of Health Sciences. Her main research interests include health education

and innovative teaching practice and she has published a number of articles in these

areas. The authors, with Sandra Griffiths, have recently published a resource pack

Enhancing Student Learning through Peer Tutoring in Higher Education, University of

Ulster, 1995, and are preparing a book on the subject. Correspondence: Dr Anne

Lazenbatt, School of Health Sciences, University of Ulster, Shore Road, Jordanstown, Co

Antrim, Northern Ireland, BT37 0QB. Tel: (01232) 368858. E-mail: [email protected]

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A Peer-tutoring Scheme to Support Independent Learning and Group Project Work in Mathematics

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