The State Examinations Commission has warned that a small proportion of Junior and Leaving Certificate students are sitting Higher Level examination papers when the Ordinary Level may be more appropriate.
In reports published today on performance in the 2015 Leaving and Junior Certificate Mathematics examinations, the SEC Chief Examiner says about 5% of Leaving Certificate candidates who received an 'E' or lower in the Higher Level Leaving Cert paper did not necessarily make the "optimum choice".
The Chief Examiner's Leaving Certificate report raises concern around the overall performance of "some" Higher Level candidates regarding their ability to apply basic skills appropriately and accurately.
It says the proportion of students for whom this is a "significant difficulty" has increased over the past four years, and that "a significant minority" of Higher Level students now struggle to complete what it calls "multi-step" procedures accurately.
There has been a dramatic rise in recent years in numbers opting to sit the Higher Level Maths papers.
This has been attributed largely to the introduction of bonus CAO points for the Higher Level paper at Leaving Certificate level.
Last year more than 27% of candidates were examined at Higher Level. That compares to just under 16% four years earlier.
The Chief Examiner's subject reports, by their nature, focus on areas where there are concerns or room for improvement.
At Leaving Certificate Ordinary Level the report finds that many candidates display a lack of what it calls "basic competence" in algebra and in algebraic manipulation in particular.
It also finds that many candidates are prone to what it calls "a lack of perseverance". It says that these issues are a cause for concern.
Referring to the Junior Certificate maths papers, the examiner says that a small proportion of candidates are studying the subject and taking the examination at a level that is too high for them.
There are three exam levels at Junior Cycle; Higher, Ordinary, and Foundation. The examiner's report says it remains to be seen how such candidates will fare as the new Project Maths syllabus 'beds in'.
The Junior Certificate report also expresses concern regarding a "lack of basic competency in algebra" at Ordinary and Foundation level.
It says that many of these candidates would struggle with aspects of the Leaving Cert Ordinary Level Mathematics syllabus as a result of this.
The report also identifies concerns around algebra at Junior Certificate Higher Level. It said the standard in basic algebraic manipulation showed "some decline", with most candidates struggling to complete multi-step procedures accurately.
Both the Junior and Leaving Certificate Chief Examiner reports find that candidates are generally successful in navigating the new Project Maths papers - on which the order of topics is no longer predictable.
However they found that students had more difficulty drawing on multiple strands of the syllabus at once in order to answer questions.
The Chief Examiner has concluded from this that students' skills and knowledge remain too "compartmentalised".
The reports found improvements in the performance of students in the years since the new Project Maths syllabus was introduced.
The Leaving Certificate report, for instance, remarks that in 2015 candidates showed an improvement compared to preceding years in their answers to questions that required an explanation or justification.
It concludes that students are becoming more used to explaining and justifying their reasoning and understanding and calls this "a very positive development".
The Examiner's reports include recommendations for students and for teachers.
The two maths reports are among a number published today (Thursday) on the State Examinations Commission website. Reports on Leaving Certificate Agricultural Science, Latin, Ancient Greek, Business, Pysics and Chemistry, as well as the Leaving Certificate Vocational Programme are also published.
They are available at www.examinations.ie
