GCSE Coursework AssessmentAuthor(s): Peter StockwellSource: Mathematics in School, Vol. 17, No. 1 (Jan., 1988), pp. 12-13Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30214420 .

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Searching for fora

Silver Lining by Brian Tytherleigh

It has been recognised for many years that the mathematics curriculum has been straitjacketed by the demands of the external examinations. This in itself was a good enough reason to demand a change, but, when it came in the form of GCSE some of us, looking perhaps for a radical alternative to the present system, were somewhat disappointed. GCSE, heralded as the greatest curriculum development since red "biros", appeared to be a simple exchange of one set of external criteria for another even flimsier set. It fell, not so neatly, into the no-mans-land between the notional object- ivity of external exams and pupil-teacher negotiated assess- ment. As our questions were left unanswered and the perceived future demands upon teachers increased, a sense of despondency and rancour arose.

However, beyond this, it is possible to detect some tiny glimmers of hope. Recently, an INSET course for teachers in Buckinghamshire focussed on coursework for GCSE. The first session of the two day course was an opportunity, initially as individuals, for us to reflect on the following question. "What are the issues relating to GCSE and coursework for you at the moment?" The written responses of those teachers were collected and below is a small section in no particular order whatsoever!

How do I achieve pupil involvement? What teaching aids will be needed? How do I prepare for this? How do I evaluate it? Clear presentation of work is essential but is their interest/ creativity suppressed by giving set methods of presentation?

Attitudes and approaches are all important as they will rub off on pupils. How do we stretch the brighter ones beyond the limits of the syllabus? What are we doingfor the pupils who find it difficult to write in words? What is meant by practical? Making an object, reading information, ... How do I persuade pupils that some activities are not just about finding the right answer? How do we assess the level of difficulty of a task? What mathematical tools do we wish to develop [in children]? Teaching strategies must be open-ended and be prepared to

follow lines suggested by the pupils and so change a lesson plan completely if necessary. Starting places - Do the ideas have to be theirs or mine? Does a particular teaching style help or hinder the promotion of coursework, reasoning skills, communication and independence? How do I cope with the wide spread of abilities in my classes? Am I giving too much away? When do I give hints? When do I let go? Each classroom needs to be resourced to encourage new initiatives. Is the right mathematical atmosphere being generated by the arrangement of the room, presentation of the task, .. How do we record what went on in the classroom? How do we effectively prepare the lower school? What about coordination of mathematics with other sub- jects? How does maths overlap with say, physics, business studies, music, ... How do we establish a departmental approach towards INSET, team teaching, observation/assessment, etc.

The remarkable thing about this sample of the responses is that in essence none of them are pertinent only to GCSE, but they have always been concerns of teachers of mathema- tics. Now whether or not it was intentional on the part of the Gurus of education or merely a happy by-product that we should use this initiative to reflect on the fundamentals of our craft is immaterial. What is important, is that this opportunity is seized. At the very least, teachers who are questioning their own practice deserve the time, space, and support to realistically explore the issues that concern them.

by

Peter Stockwell,

GCSE

Education Department,

Loughborough University

Coursework Assessment The assessment of GCSE coursework in Mathematics is currently of major concern and interest to teachers. This small study of forty coursework items compares the assess- ment results of their seven teachers with that of twenty secondary assessors. The pupils were from a mixed 11-18 comprehensive school in Northamptonshire. I wanted to investigate if the board's criteria and scheme of assessment' made a difference to the outcomes.

The "particular coursework involved" consisted of a two week investigational study undertaken by two hundred fourth year pupils setted into two top sets, two second sets, two third sets and two fourth sets. Pupils were given a

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choice of work (out of two), a brief, teacher led, explanation of each and a written sheet of open ended questions about the investigation. They were also given written information concerning which aspects of their work were being sought in the assessment. Pupils could help each other and seek advice from the teachers during the two week period, which also included two homework periods.

The teachers had a sheet of criteria from the examination board2 which involved making decisions to see if no evidence, some evidence or good evidence had been shown. Based on the types of criteria exhibited a grade (A, B, C, D, E, F, G or U) was awarded. The group of teachers had

Mathematics in School, January 1988

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discussions about interpretation of criteria before, during and after the pupils undertook the investigation. They also used internal (to the school) moderation procedures after- wards, in order to check their grade awards. It needs to be added that initially the teachers found some difficulty in interpreting the criteria in relation to the pupils work (something that the board has subsequently rectified).

By chance, some weeks later, I found myself working with a group of twenty non-specialist teachers of mathema- tics on an in-service course designed to improve their mathematics teaching3. Two days had been spent on con- sideration of GCSE and they wished to consider the problems of assessing coursework. Very few were presently involved with this but most knew that they would be in the not too distant future. They were given the information that the pupils had received and asked to assess their coursework folders. They were not shown any of the board's instruc- tions for assessing the coursework and were only given a limited amount of time to award the grades, they did, however, have the opportunity to discuss the grade awards amongst themselves.

Out of two hundred pupils who had completed course- work, a random sample of forty was chosen for this secondary assessment. They were presented with three groups of course- work targetted at higher, intermediate and founda- tion levels, it was explained that any grade could be awarded regardless of target group.

The secondary group did not have:

(a) Knowledge of the actuality of the work but only the written outcome. They could not, therefore, make assess- ments based on: Peer help, teacher help, independence of work, asking quality questions. (Nor is it likely that any form of moderation could provide this.)

(b) Knowledge of the criteria employed, their grading was based on what the pupils had been asked to do and their own assessment of how well it had been achieved.

(c) Very much time, compared to the first group of assessors. (d) Very much expertise in this type of grading.

On such a small sample interpretation of results must be made with caution. The most certain interpretation is that larger studies of similar "lax" moderation procedures could show whether the assessment of GCSE coursework is as difficult as many teachers currently believe it to be. This matter is returned to later.

The sample size is small; this is due to two factors. Firstly, it is difficult to persuade teachers involved with coursework (many teachers are not yet actively involved) to part with the results for secondary assessment. Where teachers are using coursework type projects only those currently involved with GCSE coursework have to use specified assessment criteria and only these are relevant to this form of enquiry. Photo- copies of coursework are not adequate due to poor quality, lack of colour, etc. It is only the actual folder, complete with imperfections, that lends any validity to the exercise. Secondly in the current climate it is not easy to find willing and suitable secondary assessors. Most teachers are finding the burden, or potential burden, of assessing their own coursework consi- derable. Having found such a group it was felt necessary to limit the workload to maintain their interest in the task.

The detailed criteria were held back from the secondary assessors for two reasons. As mentioned above, achieving sufficient familiarity with the criteria prior to assessment would have lengthened the exercise and risked lack of cooperation. The hypothesis that teachers have little need of such criteria, that they are, through their own experiences in teaching, capable of grading such work accurately was of interest.

The following coding system has been used to help analyse the results: where grades were identical a score of 0 is awarded, where original grade is one higher than secondary grade + 1 is awarded, where one grade lower - 1 and so on.

Mathematics in School, January 1988

Frequency of GCSE Grade Comparisons

Score Frequency Percentage

0 18 45 +1 17 42.5 +2 1 2.5 +3 1 2.5 -1 3 7.5 -2 0 0 -3 0 0

Taking the original awards as standard the following conclu- sions are evident:

7.5% were "kind" awards by the secondary group. 47.5% were "harsh" awards by the secondary group. 45% provided agreement. 5% (one in twenty) gave a difference of more than one grade.

The average difference grade was +0.475 (i.e. the original awards were nearly half a grade higher, on average, than the secondary awards). The correlation coefficient was +0.76 (two significant figures).

Only two results (five percent) differ by more than one grade. It would be of value to know if teachers using the same coursework scheme would achieve better than ninety-five per cent agreement within one grade or greater than forty-five per cent total grade agreement. Comments from the teachers involved in the original assessment suggest that they feel an improvement on these figures would be unlikely.

Of greater concern is the award of higher grades given by the original assessors. The motivation of this group will have been towards the achievement of high grades (not only were they assessing their own teaching groups but were aware of being involved in new procedures and anxious that their pupils should not suffer because of this). A study of CSE mode three moderation procedures4 reveals that they are designed to deal with exactly such a bias, positive or negative, on the part of school assessors (if the bias is found to emanate from the original rather than the secondary assessment). Adjustments are made by raising or lowering the marks awarded to the complete school based course- work rather than rearranging the order or marks of individual candidates. This particular problem, and its solution is not, therefore, new to GCSE coursework but has existed, to- gether with contingencies for correction, for some time.

This small study is based on the earliest of GCSE course- work assessments, the work was undertaken in October and November 1986. As more results become available it will be possible to produce further studies and involve larger samples. This study may help in the formulation of questions for such future work:

Are the criteria distributed by examination boards too detailed and time consuming given the level of teacher expertise in accurately grading and marking coursework? Many teachers are concerned about responding to such criteria. If they are reliable assessors the criteria may have little influence on the outcome of the assessment but will make the assessors initial task more difficult and time consuming. Should the criteria be simpler and fewer? The answers to these, and related questions, will require

further study and feedback from teachers. Any readers who have further information in these matters are invited to contact the Editor with a view to sharing experiences.

References 1. School Mathematics Project GCSE Mode 2 with Coursework. 2. Midland Examination Group. 3. Post Experience Vocational Education - Lincolnshire LEA in conjunc-

tion with LUT. 4. For example - East Midlands Regional Examinations Board CSE

Mathematics with Coursework.

Editors Note We are sorry to have to report that Peter Stockwell died prior to the publication of this article.

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