Leaving Cert examiners have expressed concern at the lack of basic skills of some students sitting the higher level maths paper.
In a report published on Thursday by the State Examinations Commission, it says a significant minority of candidates are struggling to complete simple procedures.
“It is clear that the proportion of the candidature for whom this is a significant difficulty has increased since 2011, and that a significant minority of candidates now struggle to complete multi-step procedures accurately,” the chief examiners’ report states.
The changes broadly coincide with the introduction of Project Maths, a reformed curriculum aimed at promoting a broader understanding of maths and increasing the numbers sitting the higher exam. Maths has also benefited from bonus points since 2012.
The commission’s report says candidates who in previous years might not have sat the higher level “need to be better prepared” in their application of skills and procedures.
In general, results at higher level between 2011 and 2015 show a decrease in the so-called honours grades – A, B and C – and a slight rise in failure rates.
Clearly unfamiliar
The report says this is not surprising given the changes in syllabus and increases in the number of students sitting the exam. It gives the example of students who were asked to solve a cubic equation.
Many candidates who were well prepared for the question had no difficulty with it, but a significant minority (almost 20 per cent) were “clearly unfamiliar with the procedure, as they were not able to produce work of sufficient merit to be awarded any marks”.
On a more positive note, it found the highest-achieving candidates at higher level showed a good depth of understanding of the whole syllabus, along with an ability to be both flexible and accurate in their work.
These candidates were generally able to express themselves clearly and coherently, and to engage with questions with which they were not likely to have been familiar.
“They clearly invested considerable time and effort in engaging with the syllabus objectives and achieved high grades in the examination as a result,” the report states.
Overall, it states there is no doubt that the shift of many of the more able candidates from ordinary to higher level has had consequences for both levels.
At higher level, the numbers achieving a grade C or below has shown a marked increase.
“When such candidates achieve a C or D grade, one might regard this choice of level as having been a good one, as these candidates have clearly benefitted from being exposed to a higher level of mathematical reasoning and problem-solving, which will stand to them in the future,” the report states.
Optimum choice
“However, such benefit is much less clear in the case of candidates achieving an E grade or below, and an E/F/NG rate of about 5 per cent does indicate that not all of those who opt for the higher level are necessarily making the optimum choice.”
At ordinary level, the report states that the proportion of candidates achieving a grade B or above has declined significantly.
“It is clear that many of the candidates who might previously have fallen into this category are now opting to study mathematics at higher level,” the report states.
Examiners found many ordinary level candidates displayed a lack of knowledge of standard procedures, basic competence in algebra and perseverance.
“In light of the migration of candidates from ordinary level to higher level, these observations are not necessarily surprising, but they are a cause for concern,” the report states.
It says the majority of these skills should be acquired at junior cycle and should have been consolidated and improved during the senior cycle.
What the examiners said
Physics & Chemistry
An increase in numbers sitting the higher-level exam last year was accompanied by a decrease in the proportion candidates achieving A, B and C grades.
The shift in people moving from ordinary to higher level may account for these changes, the report suggests.
At higher level in the Leaving Cert, good knowledge and understanding of basic physics and chemistry facts and concepts was demonstrated by most candidates.
At ordinary level, however. many candidates had evidently placed “insufficient emphasis on acquiring the fundamental knowledge of facts underlying the subject”.
Business
Participation rates in Leaving Certificate business have fallen from 37 per cent in 2007 to 31 per cent per cent last year.
There has been a slight decrease in A, B and C grades and a slight increase in failure rates over the past five years at the higher level, while the grades at the ordinary level accord closely with those of previous years.
This may be linked to an increase in numbers sitting the higher-level exam. In general, candidates at both levels engaged well with all aspects of the examination papers, which proved sufficiently challenging to provide the necessary level of discrimination.
Maths (Junior Cert)
At Junior Cert level, the top-achieving candidates at higher level showed a good depth of understanding of the whole syllabus.
However, concerns were expressed regarding many candidates’ lack of basic competency in algebra and in particular in algebraic manipulation.
A number of examiners observed that many of these candidates would struggle with aspects of the Leaving Certificate ordinary level mathematics syllabus as a result.
Vocational Programme
The number of Leaving Cert candidates undertaking this two-year programme has been falling in recent years, down from almost 16,400 in 2011 to 14,900 last year.
This may be linked to staffing issues. Suspected plagiarism cases have been steadily declining from 60 cases in 2011 to 31 cases in 2015.
The portfolio of coursework was generally well completed and of a much higher standard than the written examination
The two-year programme was introduced in the late 1980s to promote the development of enterprise, technology and vocational skills at senior cycle.
Agricultural Science
Almost 7,700 students sat the Leaving Cert exam, or 14 per cent of all candidates.
While more than 70 per cent of candidates were male, females have consistently outperformed them.
Overall, 11 per cent of candidates in the higher exam received an A grade, while 28 per cent received a B and a similar number received a C.
Arabic
Just more than 120 students sat the Leaving Cert Arabic exam last year.
Fewer candidates achieved an A grade in 2015 than in previous years.
The number of candidates scoring B and C grades remained relatively stable; the decline in the number of candidates awarded an A grade in 2015 was the main contributing factor to the decline in the combined A, B and C rate (79 per cent).
