An Roinn Oideachais agus Eolaíochta

Department of Education and Science



Subject Inspection of Mathematics




Portmarnock Community School

Portmarnock, Co. Dublin

Roll number: 91324P



Date of inspection: 24 February 2006

Date of issue of report: 22 June 2006




Report on the Quality of Learning and Teaching in Mathematics

Subject Provision and Whole School Support

Planning and Preparation

Teaching and Learning

Assessment and Achievement

Summary of Main Findings and Recommendations

Report on the Quality of Learning and Teaching in Mathematics



This Subject Inspection report


This report has been written following a subject inspection in Portmarnock Community School. It presents the findings of an evaluation of the quality of teaching and learning in Mathematics and makes recommendations for the further development of the teaching of this subject in the school. The evaluation was conducted over two days during which the inspector visited classrooms and observed teaching and learning. The inspector interacted with students and teachers, examined students’ work, and had discussions with the teachers. The inspector reviewed school planning documentation and teachers’ written preparation. Following the evaluation visit, the inspector provided oral feedback on the outcomes of the evaluation to the principal and subject teachers. The board of management of the school was given an opportunity to comment on the findings and recommendations of the report; the board chose to accept the report without response.



Subject Provision and Whole School Support


Provision for Mathematics in Portmarnock Community School is good; the weekly time allocation of five periods at junior cycle and five or six periods at senior cycle meets the subject requirements.  In addition, lessons are generally organised to take place on each of the five days of the week, thus taking account of the hierarchical nature of mathematics, where new concepts build upon previous knowledge, and the fact that students require time to assimilate new ideas.  The arrangement of Mathematics instruction time shows clear commitment to and understanding of the requirements of the subject, with Mathematics classes from fourth year onwards being concurrently timetabled across the board, third-year classes taking place concurrently within two bands and second-year classes arranged in a mixture of stand-alone classes and concurrently timetabled classes within two bands.  This arrangement, while appearing complicated in a school of this size, facilitates both the formation of classes at different levels and the movement of students between classes of different levels.


Additional teaching resources are allocated to Mathematics in four out of six year groups, in each case allowing for the formation of smaller or level-appropriate class groupings.   Supports targeting students identified as having particular difficulty with Mathematics are available and arranged in one of three ways—withdrawal from mainstream Mathematics class for individual or small-group tuition with the resource/learning support teacher, team teaching with a class group being taught by a mainstream Mathematics teacher together with the resource teacher, or the creation of an additional Mathematics group (currently happening in two year groups) to be taught by the resource teacher.  It is particularly commendable that such supports are being provided by a teacher qualified in Mathematics.


First-year Mathematics classes are mixed-ability within the banding structure operated within the school and remain as distinct units until the end of the year.  Second to sixth-year classes separate into higher and ordinary levels, with the possibility of a foundation-level class being organised if required.  Ongoing monitoring of student performance through class tests and term examinations, and ongoing teacher cooperation facilitate students in studying Mathematics at the most appropriate level.  This is evidenced in the discussions currently underway regarding the possible formation of a foundation-level class in one of the year groups at junior cycle.  Furthermore, to support students in making the correct decisions regarding the level at which to study the subject, it is commendable that term examinations have common papers within levels.  A student can change level on discussion with the teacher involved and with parental consent, and every effort is made in timetabling classes to ensure that space is available for such students.


Teachers’ professional development is supported by the school; documentation relating to in-career development in Mathematics is made available to the subject co-ordinator and there is a dedicated display area in the staff room where courses for teachers are advertised.   Since the revision of the syllabus for Mathematics at junior cycle, all teachers have attended seminars and workshops provided by the Junior Certificate Mathematics Support Service (JCMSS).  Current (optional) sessions being run by the JCMSS are attended by a nominee from among the Mathematics teachers.  In addition, a number of members of the team are members of the Irish Mathematics Teachers Association (IMTA) and, in this way, keep in touch with issues and discussions in mathematics education.  It is intended that the school will fund one membership to each subject association from the next school year.  Currently, feedback from seminars and workshops, and new information received is generally passed on informally to other teachers, as relevant.  It is recommended that a formal system of disseminating information received at in-career training or through the IMTA be developed, so as to keep all Mathematics teachers up to date on developments and issues in mathematics education.


Resources for the Mathematics department are allocated on request to school management and are stored in a dedicated press accessible to all Mathematics teachers.  Resources currently available within the school to support the teaching and learning of Mathematics include State examinations documents, syllabus documents, geometry equipment and a demonstration calculator.  


The school is embarking on a project to improve the physical learning environment within classrooms and Mathematics will be one of the first subjects to benefit.  This will mean that a number of rooms in which the subject is taught will be designed and decorated in a mathematics theme.  The motivational benefits that may accrue from a visually stimulating classroom setting should not be underestimated, and the school is commended on its foresight and vision in this regard.  Co-curricular mathematics activities promoted within the school include student participation in the Irish Mathematics Olympiad and the mathematics quiz for first-year students organised by the IMTA, as well as a Maths Club run by a member of the faculty on a voluntary basis.



Planning and Preparation


The Mathematics department is ably co-ordinated by a senior teacher and commendable effort goes into ensuring the smooth running of the department, as evidenced by the extensive organisational documentation supplied.  The team have two to three timetabled subject department meetings per year with additional meetings taking place outside of timetabled hours, as required.  It is recommended that records be kept of such meetings, with minutes to include reference to discussions as well as outcomes.


Team planning and collaboration is, nonetheless, evident.  Subject planning is being prioritised within the school and the Mathematics teachers have made inroads into policy development, programme planning and review, and the development of resources (particularly those related to examinations and assessment).  To build on the good work currently underway, it is recommended that programme planning be extended to include aims and objectives for mathematics education within the school and that these aims and objectives inform all future planning activities.  In addition, key skills within mathematics topics and key terms for students to know and understand should be identified.  Resources, including software packages, to assist students in acquiring such key skills should then be sourced and obtained by the Mathematics department.     


The Transition Year plan for mathematics is strongly academic, with little deviation from the Leaving Certificate programme, including the use of a standard Leaving Certificate textbook.  However, on discussion it is clear that, over a number of years, efforts have been made to provide students with a mathematical experience appropriate to the Transition Year Programme.  In light of this, it is recommended that planning for Transition Year should be refocused, possibly on the formation of a subgroup that could include members of the Mathematics team along with one or two teachers from other subject areas (possibly practical/technical areas).  Ideas for allowing students experience Mathematics in a different way to that for junior and senior cycle studies should then be reflected, along with suggested methodologies, in the department plan.


Teachers who made individual planning documentation available during the visit supplement department plans with their own notes and resources.  Among these were examples of impressive revision notes, student-motivating worksheets and mathematics games and quizzes.



Teaching and Learning


Lessons observed were purposeful and appropriate to syllabus and level.  The presentation of work observed was clear and preparation for teaching was evident.  It is suggested that teachers consider explicitly sharing the lesson objective with students, with a view to increasing student motivation and sense of accomplishment.  


Teaching was, in almost all cases, of a high standard, and was traditional in style; teachers presented work at the board and, typically, followed this with the setting of work for individual student practice.  To expand on this traditional teaching style, it is recommended that a range of teaching methodologies (for example pair work, field work, investigative learning) be explored and developed, with the aim of involving students more actively in the work at hand.  Resources and ideas available from the JCMSS and the Junior Certificate Mathematics Guidelines for Teachers should help in this process.


Examples of good practice in Mathematics teaching included the use of mathematical language, affirmation of student effort and success, the use of clear explanations and the acknowledgement and encouragement of alternative methods.  A positive working relationship between students and teachers was evident in all classes visited and classroom management was relaxed and effective.  Students, in most cases, showed an interest in achieving in Mathematics and were attentive to their work.


There were commendable levels of attention to individual students in all classes observed.  In addition, teachers used questioning as a means of involving students in the lesson.  There was varied and acceptable practice with regard to the addressing of questions to individual students and/or whole class groups, but in some cases the directing of questions to named students would have been more appropriate, both as a means of checking understanding and of keeping students on task.


Assessment and Achievement


Student progress is formally assessed in class tests and term examinations.  It is practice among the mathematics teachers for class tests to be administered on completion of a chapter or topic or on a monthly basis.  Some teachers teaching in the same year group at the same level collaborate with regard to common class tests; the continuation and possible expansion of this is encouraged.  All teachers retain records of results obtained by students.   It is in line with good practice that common examination papers are prepared for Christmas and summer term examinations, along with common marking schemes. 


It has been practice in Portmarnock Community School for a mid-term assessment to be carried out in the first term each year, where teachers complete reports on students based on their work during the settling-in period. However, the outcome of this assessment is communicated to parents only when the Christmas reports are issued.  In order to maximise the value of this assessment as a guide and encouragement to students’ progress, it is recommended that the results be forwarded to parents immediately on completion of the assessment.


Student copybooks provide ongoing insights into daily achievements in work covered in class and in private study.  An examination of student copybooks revealed work that was appropriate and relevant and in line with syllabus requirements, but was not always well presented.  In addition, students were not, as a rule, marking their own work, even when it had been corrected on the board by the teacher.  It is recommended that all Mathematics teachers prioritise the monitoring of student copybooks, checking that work has been presented appropriately, marked right or wrong and that relevant corrections have been noted.


An analysis of uptake rates in the State examinations for the last four years indicates very good participation at higher and ordinary levels.  Members of the Mathematics team displayed an awareness of levels achieved in the State examinations and the school’s standing in this regard.  


Summary of Main Findings and Recommendations


The following are the main strengths and areas for development identified in the evaluation:


As a means of building on these strengths and to address areas for development, the following key recommendations are made:



Post-evaluation meetings were held with the principal and with the teachers of Mathematics at the conclusion of the evaluation at which the draft findings and recommendations of the evaluation were presented and discussed.