Deputy FitzGerald gave notice that he would raise the following matter: the pass mathematics papers which have been the subject of protest by six educational bodies.
Adjournment Debate: Examination Papers.
I raise this matter because, while every year there are complaints about some questions on the papers, and this can be regarded as inevitable, what has happened on this occasion in regard to the pass paper is on a different scale and is of a different character from what has happened previously. It is unique to have a situation in which six teaching bodies involved either in a specialist or general way with the teaching of mathematics have protested in the strongest terms about the paper. As the Minister is aware, the bodies concerned are: the Irish Mathematics Teachers' Association; the Association of Secondary Teachers of Ireland; the Conference of Convent Secondary Schools; the Catholic Headmasters' Association; the Federation of Irish Secondary Schools and the Teaching Brothers' Association.
All these bodies have protested and have sought a new paper. They have not done this without a good reason. There will always be some degree of conflict on the appropriateness of a particular paper but when all these bodies protest in such strong terms and demand a new paper I think the Minister ought to take the matter seriously. He cannot simply dismiss it because his Department who are responsible for the papers say they are all right. Education is a co-operative business. It is not something to be run bureaucratically from above without consultation on or consideration of the expert views of the people concerned and the Minister ought to be prepared to listen to such views when they are expressed by a responsible body, or bodies, in a responsible way when it is a matter of public import. The Minister will appreciate, from his own experience as a teacher, how easily it is for pupils to become demoralised and frustrated when faced with something they regard as unfair, something outside their experience, something with which they cannot cope and, in the middle of this examination which they are undergoing at present, the repercussions of this paper can be very considerable. Not alone will the failure rate be very high, unless the marking is completely distorted, but the impact on the students must overflow into their other work because the frustration and demoralisation it has created for them is bound to have its impact elsewhere in the leaving certificate.
A number of points have been made about the paper by the people concerned. Mr. Buckley, chairman of the Irish Mathematics Teachers' Association, has said that the content of the paper is too theoretical. I quote from today's Irish Press:
Its content requires deep theoretical knowledge. It was unjust, we think, and there was a complete change of format from the previous four years; this year is the end of a five year cycle ... next year there will be a new programme and a new syllabus. We also think that it will discourage future pupils from taking mathematics.
He added that:
... he did not know why the paper had been set in the first place. It was very difficult because, besides the format change, the language in which the questions were couched was new, in the sense that it suggested to him that this particular paper could have been set for what he would call mathematicians.
Normal Leaving Cert. pupils, however, who were doing maths at a pass level could not be expected to be mathematicians.
They could only be expected to be able to reach a certain standard of maths at a practical level. "This paper, we think, was not a paper for pass standard".
That is the view of Mr. Buckley, a man of whose view account must be taken because this is an organisation of experts in this particular area, mathematics teachers, and this is their voice through their chairman. What he has said must be taken seriously.
The fact that his view has been supported and endorsed independently, or in consultation with him, by all the other teaching and managerial bodies must also be taken account of and now I have just been handed a letter which has come in to a member of our party on this subject:
I refer in particular to No. 2 paper in pass mathematics on which all the adjectives in the English language have been used and I honestly believe that Questions Nos. (2) to (6) are not on the pass syllabus, but it is impossible for students to understand them let alone answer them. It is grossly unfair to candidates whose whole future depends on this examination and the strain and tension is increasing daily as each successive paper comes.
That is the view of someone who has written in on the subject today. I have been talking to a mathematics teacher within the last hour and discussing the paper with him. In fairness, I should say that I am not qualified to speak on the details of the paper. It is a long time since I studied mathematics and mathematics were never a good subject with me. I am necessarily speaking at secondhand in a matter of expertise. I claim no expertise. It is not the function of Members of this House to be experts in everything. It is rather our function to represent the views of people who are experts in their own area when these views have validity and seem to be worthy of consideration.
Let us look at the paper in the light of the comments. The Minister will see that the complaints are not necessarily that there are a large number of things not one of which should appear on any paper and in such a form; there are some things which should not appear on a pass paper and other things which should not appear in the form in which they appear, with a theoretical bias, but almost all the questions are in some degree too difficult or too theoretical and that makes the paper unacceptable. On any paper in which there is a choice there can be two or three questions outside the competence of the normal student. Students have to answer six out of ten and, from the point of view of choice, they can take them in their stride. When there is virtually no question which does not contain a difficulty of the kind I have mentioned and the pupil finds he can answer nothing fairly readily within the course he has covered, then he becomes completely demoralised.
I understand the first question is acceptable as regards (a) but, as regards (b), I am told the ordinary pass mathematics pupil, even though taught by someone experienced in teaching honours mathematics, as is this particular teacher who was speaking to me today, would not understand the question. This is not something he would normally do; it was never on a paper before. It would probably frighten most students. Question No. 2 is mesmerising in its length. May I mesmerise the House with it? This is what the pupil is supposed to take in when he sits down in front of the paper. I think the question could quite validly have been asked without going so far as this:
(a) p and q are two numbers which can be written as non-terminating decimals with patterns as follows:
p=
2.10110111011110111110111110 ...
q=
2.020120112011120111120111112, ...
Say whether each of the numbers is rational or irrational.
(b) is a theoretical question:
Give an example which shows that the sum of two irrational numbers can be a rational number.
Can the product of two irrational numbers be rational? Explain your answer by giving an example.
Pass pupils do not study mathematics in that way. This is too theoretical for pass pupils. The questions on a pass paper are meant to be practical questions within the competence of a pass student. The ordinary pass student would find it difficult to put down examples.
Part (c) of question No. 2 has not been asked since 1950—20 years ago. It has been resurrected this year with all the other impossible things in this paper.
Question No. 3 is too generalised and theoretical and, in regard to (b), 14 sets are needed to answer the four questions under (b), which is also, I am told, unduly theoretical.
This is 4 (a):
The numbers1/n, n and (—1)n are the nth terms of the sequences S(¹), S(²) and S(³) respectively.
Then there are questions asked about that. I have been told the ordinary pass pupil would have knowledge of 1/n but no knowledge of the square root of n and the sequences S(¹), (²), and (³) he would never have seen before. This notation is not used in the teaching of pass mathematics in the ordinary way.
Question No. 5 as asked is one which the pupil would not recognise as a normal formula of logMn. With regard to (b) it would be necessary to pursue this to infinity, which is not normally done, and it is, in fact, doubtful if this is on the course.
There is a slight difficulty in 6 (a) but it is one which would be acceptable if it were in isolation on the paper; (b) involves the drawing of a graph, which is unusually difficult, and the rest of the question is regarded as too difficult and involved. It would frighten away the pupil, quite apart from its content. Question No. 7 is more for honours than pass. It has never been on a pass paper except in the form of an equation, but it is not in that form here. Pass pupils might be able to manage the first part of 8(a), but they would not be able to manage (b). It is an honours question and should not appear on a pass paper. Question No. 9, the ordinary pupil will read and pass on, not knowing what it is all about. This kind of question is not normally done in the class. There is a minor difficulty in that the last part is:
Solve the equation g(x)=4.
There is no reference back to "g" earlier on. An honours student would know enough to look back but a pass student would not. Question No. 10(a) is all right. The second part is too theoretical; (b) is all right; (c) is a totally different question unrelated to 10(a).
There is no question on that paper in respect of which questions cannot be raised from the point of view of validity and appropriateness. It is no good the Minister saying that this is all on the course. With mathematics anything can be on the course, but this is a pass course and pupils are prepared to deal with questions capable of a simple or elementary approach. There is a clear distinction between honours and pass and no one question on this paper falls clearly into the pass category. In every question there is a difficulty. With such an indictment as that, coming from such an authoritative source and with such support from all the teaching interests concerned, the Minister really ought to reconsider this.
Indeed, in the Irish Press of today's date, there is an excellent editorial headed “Maths Paper Crux”. The Irish Press is frequently to be complimented on its editorials on subjects like this, particularly in the field of education in which it shows a great interest. The editorial reads as follows:
The Irish Mathematics Teachers' Association is a responsible body, and not one in the habit of making complaints about the examinations set by the Department of Education. For that reason its statement yesterday attacking the pass maths paper in the current Leaving Certificate examination should merit careful attention. The teachers' condemnation of the paper has been strong and unqualified, and the bland rebuttal of the charges by the Department will do little to assuage the considerable public disquiet which the teachers' statement has raised.
The Department did have expert advice in the setting of the papers and presumably the normal care was taken. But quite clearly there either exists a serious conflict of interpretation between the teachers and the Department as to the content of the course or else the Department is setting standards not normally attainable at Leaving Cert. level. In the final analysis the people best qualified to judge the capabilities of the students, and those most familiar with the courses done by the students are the teachers, and the extent of their dissatisfaction with the papers clearly indicates a breakdown or lapse of some sort.
If the Department goes ahead and refuses to yield to the teachers' request there are two possibilities, neither of which will do any good to the public image of the Department. If the failure rate is no higher than usual, the suspicion of a "ready up" within the Department will not easily be removed, and doubt may be cast on the credibility and reliability of the whole examination system. If, on the other hand, there is a high failure rate, all the indications will be that the Department's refusal to admit the possibility of an error resulted in many students failing, who would otherwise have passed.
That is a responsible and reasonable approach to the problem. I trust the Minister will take account of what is said in that editorial in the Irish Press. His Department's statement, as reported in today's newspapers, about choice in the paper is, I understand and I have evidence in the form of the paper for 1968—untrue. The Department is quoted as saying:
In regard to the Leaving Certificate Maths (Pass) it was stated that the paper this year contained a far wider selection of questions than in previous years.
This is an incomprehensible statement for the Department to make. If they know so little about their own papers, I do not think their judgment on the content of the paper should be taken seriously.
What was referred to there was, previous to this particular syllabus coming into operation.
What relevance has that to the complaint that this paper is totally different in character to the last four papers within the syllabus? If the Department meant that then somebody was simply trying to dodge the issue and to raise a red herring here. The syllabus is not at issue. We know that four papers have been set on this syllabus. So far as I am aware, they did not give rise to any similar dissatisfaction. However, in the fifth and final year of the syllabus, a totally different kind of paper has been set. It may be appropriate to the syllabus for next year if the pupils and teachers are told what to expect. We can raise standards all the time—gradually—but people must be given time to adapt to them. The teachers must be given time to understand the new approach. To introduce, in the fifth year of a five-year cycle, a totally different kind of paper and at a level completely inappropriate to pass, and to try to justify it by the red herring of a bigger range of questions is disreputable.
The Minister is in a difficulty. I, also, should be in a difficulty if I were in his position. In going over this paper, not being a student or a teacher of mathematics, my own knowledge of mathematics does not enable me easily to judge whether or not the allegations are true. The Minister may well be in the same position. Perhaps he is—I hope he is—better qualified mathematically than I am. Before taking a final decision on this matter, however, the Minister ought to see the people concerned. If he is not in a position to give a positive reply this evening to my request to set another paper—he may be in difficulty about deciding it on the spot—I would urge on him to receive a deputation from the Irish Mathematical Teachers' Association and any other bodies who want to see him on this matter, to listen to them as I have listened to them and then, having listened to them and having got the views of his Department, to make up his own mind. I would urge on the Minister not to take a negative decision unilaterally on the basis of the only advice given to him by people who inevitably have an interest in defending the paper for the setting of which they are responsible.
If there is a difficulty, because of the technical complexity of the problem, the Minister will require to think about it and he will require advice from a wide range of sources. He has open to him the advice of these bodies. If he is not able to state positively that he will agree to set another paper, he should agree immediately to meet these associations and to be briefed on both sides of the case. The demoralising effect of this paper on students is causing great concern.
A difficulty has arisen in some centres due to the absence of a sufficient number of log tables. There are two schools within a few hundred yards of this House who complain that, at the centre which they share, there were simply not enough log tables and students had to wait their turn for them. That meant that the students were not able to tackle the paper as they would have wished to tackle it and to do the questions in the order of their choice. They had to wait their turn for the log tables. The Minister knows the tension that exists at examinations. He should be sympathetic in this matter. Quite apart from the main problem here today, I would ask him to ensure that adequate sets of log tables will always be available at the various examination centres throughout the country and that a situation will not occur again of the type that has occurred this year where there was a scarcity of log tables.
On the main issue, if the Minister has not a positive answer tonight in relation to the protest over this year's leaving certificate maths (pass) paper, I urge him to see the experts involved and then to make up his own mind.
I want to say a few words——
Deputy FitzGerald spoke for 20 minutes. The debate started three minutes before 5 o'clock.
Very briefly may I say a few words? I assumed that Deputy FitzGerald started at 5 o'clock and that I had three minutes in which to speak. It is fitting and proper that this rather anomalous situation should be raised on the Adjournment this evening and I rise to support the points made by Deputy FitzGerald. I think the basis of the complaint is quite legitimate, in the light of the information we have received. There does seem to have occurred a rather serious error of preparation in the setting of the pass maths paper, leaving certificate, and, arising from this, there is a very urgent need for the Minister to give the public reassurance, to resolve the situation and to get rid of the confusion and concern.
While Deputy FitzGerald and myself are quite well aware of special pleading that does occur in relation to some examination papers, on this occasion, in the light of the reputable information conveyed to us by the mathematics teachers themselves and by their association, it would be fitting and proper that the Minister should meet them, consult with them, rather than rush into the precipitate, defensive reply which we may anticipate from him this evening. We believe, therefore, he should have these consultations and, having heard all the evidence from all sides, make up his own mind and relieve the current rather serious confusion and distress that has occurred which is damaging——
The Minister to conclude.
First of all, I may say that I have very carefully considered this matter. Not only did I discuss it with the officials of my Department— which was obvious—but, for the reasons stated by Deputy FitzGerald, I also discussed it with various mathematics teachers. Having considered the matter very carefully, I cannot accede to the request to set a new paper.
Let me deal first with the technical side of the matter. This paper was set out in accordance with the syllabus for secondary schools for the leaving certificate issued to secondary schools, pass course. I want to emphasise that fact. Some reference was made to the possibility of some of the questions being based on the honours course. So far as I am aware, nobody has suggested otherwise.
The main cause of the complaint appears to be that the format of the questions was not the same this year as it was in previous years. All I can say about this is that the format of some of the questions this year was not the same as in previous years but this is normal procedure. Each year some changes are made in the format of some of the questions. In many instances the format of the questions was the same as it was in previous years.
I do not want to go into detail in relation to the papers here, as Deputy FitzGerald did, except to say that I discussed some of these questions with mathematics teachers and I found that in many of the instances where Deputy FitzGerald suggested the questions were too difficult the teachers concerned accepted that they were not too difficult. I might also add, of course, that all the teaching organisations concerned were involved in the framing of the syllabus. This is the syllabus, as I said before, from which these papers did not depart.
The information given to me personally from a number of sources indicates that a high proportion of the schools would be disturbed, in fact very disturbed, if there were any question of setting another paper. I want to emphasise that. I was also assured by these schools and teachers that where students read the questions the average student was able to reach the same degree of success in answering the paper as he would in previous years.
I am sure Deputies are aware of the position in relation to mathematics. The pass and honours courses are entirely different. Only about 12 per cent take the honours course. The pass papers, therefore, must cater for a very wide range of student ability and in the process they must provide the standard necessary for university entrance, for entrance to the Civil Service, for entrance to teaching and the various other professions and occupations.
There is one other aspect of this of which Deputies are not perhaps aware. This paper has to satisfy the collaborating examiner from the university. There are two papers in mathematics, paper 1 and paper 2. Paper 1 consists mainly of the traditional material and paper 2 deals with the more modern aspects of the syllabus. Candidates' marking will be based on their answering of both papers. Taking the two papers jointly, I am satisfied, as are many others with whom I spoke, that they provide a fair test in mathematics for the average leaving certificate student.
We should not lose sight of the fact that what we are dealing with here is the leaving certificate. If we do not seek a sufficiently high standard for that examination—and might I add, if we are not seen to seek a sufficiently high standard—then our educational system will be devalued.
As both Deputy FitzGerald and Deputy Desmond mentioned, there is nothing unusual in representations being made to the Department in relation to individual examination papers. Very few years have elapsed in which there have not been representations in relation to one subject or another. These representations have always been borne in mind in relation to the marking of the papers. This course will be followed in the case of the mathematics papers, 1 and 2, this year.
As I say, I am satisfied from the very careful consideration I have given to this paper that it would not be the right course to set another paper and this view has been backed up by the schools and by the teachers with whom I have spoken.
Can the Minister say why he is prepared to accept these private representations rather than those of the relevant representative bodies?
It is not just a matter of accepting one representation rather than another. I have to face up to a number of difficulties in regard to this matter. Having considered the representations made by those bodies and having also satisfied myself in regard to the discussions I had with other teachers and schools and my own Department, I feel that I am adopting the course which is most acceptable to all the schools.
Did the Minister have discussions with these bodies?
I had not but I was aware of the representations.
Why did the Minister have discussions with unrepresentative bodies and not with representative bodies?
I felt it necessary to get information from various parts of the country.
Unrepresentative views.
Not necessarily unrepresentative.
Non-representative views.
Not necessarily.
Will the Minister convey to those marking the papers the representations, public and private, and will he recommend to them that they should bear those representations in mind in marking the papers?
I have already mentioned that I most certainly will.
The Dáil adjourned at 5.30 p.m. until 3 p.m. on Tuesday 23rd June, 1970.