An Roinn Oideachais agus Eolaíochta

Department of Education and Science


Subject Inspection of Mathematics



Greenhills College

Limekiln Avenue, Greenhills, Dublin12

Roll number: 70130I


Date of inspection: 20 January 2009






Subject inspection report

Subject provision and whole school support

Planning and preparation

Teaching and learning


Summary of main findings and recommendations





Report on the Quality of Learning and Teaching Mathematics



Subject inspection report


This report has been written following a subject inspection in Greenhills College, conducted as part of a whole school evaluation. 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, deputy principal and subject teachers.



Subject provision and whole school support


Timetabling provision for Mathematics in Greenhills College is very good. All classes have five periods of Mathematics per week with an additional class being provided for those taking higher level in senior cycle. All lessons are forty minutes long. Each class group is timetabled for at least one period of Mathematics each day and the balance of provision in Mathematics between morning and evening is also very satisfactory.


The timetable is designed to enable students to study Mathematics at the level most appropriate to their abilities: an additional class group is provided in each year in order to support students experiencing difficulties with Mathematics. A small class group has also been created in sixth year to provide students with the opportunity to study Mathematics at higher level. Mathematics classes are banded in all years and this facilitates students in changing levels and allows them to avail of additional support when required.


Procedures for facilitating the transfer of students from primary schools are comprehensive, and inclusive. Prospective students are first informed about the school during visits to the feeder primary schools by members of the transfer team, which includes management, members of the teaching staff and a number of students. During these visits prospective students are informed about the curricular and extra-curricular programmes available in the school and are invited to attend the school’s open night in the company of their parents. The open night serves to allow the students to become familiar with the layout of the school, to experience the different subject areas and to meet with the teachers. In addition, the parents are presented with the school’s policies and procedures and can avail of opportunities to meet school management and the learning support team. At the meetings with the learning support team, the special educational or other needs of individual students can be discussed in private and the concerns of parents allayed.


The home-school-community liaison (HSCL) co-ordinator and the co-ordinator of the school completion programme (SCP) play a vital role in ensuring that the transfer programme meets the needs of the incoming students and they act as a valuable source of information regarding the students’ interests and aptitudes They also provide valuable insights into any particular behavioural, social or educational issues that may exist.


Following receipt of completed application forms, the students are invited to sit the entrance assessment tests, which are held in December. The mathematical abilities of the incoming students are ascertained using numerical reasoning tests. On the day of the test, every effort is made to make sure that students feel at home and a range of special accommodations are put in place to assist those students who may be experiencing difficulties. A number of the school’s senior students attend the assessment tests to provide assistance when the need arises.


Once the outcomes of the assessments are analysed, the relevant primary schools are contacted and the students with special education needs or in need of learning support are identified. Parents are invited to meet individually with a member of the learning support team. Completed psychological assessments are provided to the school at this time and applications for additional resources, for consideration by the Department of Education and Science, and are then submitted.


Learning support in Mathematics is provided through the formation of an additional class in each year group. The additional classes are timetabled concurrently with those in mainstream, to facilitate movement between levels and the provision of short-term focussed interventions if it is deemed necessary. First-year students are re-tested in November to determine if their performance in the original assessment correctly reflected their abilities and, if it is deemed necessary, additional assessments are arranged through the National Educational Psychological Service (NEPS) or through the Psychological Service of Co. Dublin VEC.


There is an active core team in the school, which supports the implementation of the school’s pastoral care programme. The core team collaborates with the year heads and the class tutors in identifying students who are struggling in Mathematics and a co-ordinated response is then put in place. Targeted additional support is provided according to a programme agreed with the class teacher and the learning support team. In order to inform teachers of the needs of the students in their care and to facilitate the development of coordinated responses, two in-service days are provided at the beginning of each year for the entire staff. A teacher pack is developed to assist them in dealing with the various categories of special education needs they may encounter and a register of students is distributed to relevant teachers.


All first-year students are supported by the school’s mentoring programme and there is a special transfer programme for those students with special education needs. As part of this programme the students attend the schools’ sports day and get to meet the students who will mentor them in first year. They are also given a tour of the school and meet the year heads, teachers and management. This is good practice.


The mathematics department is well resourced and while the department has no formal annual budget, management responds favourably to any requests for additional resources. A number of resources for use in teaching Mathematics in learning-support classes have recently been purchased and a range of resources for teaching Mathematics in mainstream classes are also available and are stored in an accessible location


The school has very good information and communication technologies (ICT) facilities. There are three computer rooms that are primarily used for teaching the post leaving certificate (PLC) classes. Additionally there is one ICT room in the second-level school which can be accessed by the teachers of Mathematics. The school has recently purchased two data projectors and two interactive whiteboards for use in teaching and learning. To build on the very good work already underway and to inform the purchase and deployment of suitable resources for teaching and learning in Mathematics, it is suggested that an audit of existing resources be carried out and that the resulting list be included in the subject development plan for Mathematics. Two members of the mathematics team should also be selected to identify additional resources, including ICT resources, that could be gainfully employed in mathematics classes and to identify suitable strategies for their integration in teaching and learning. Assistance in carrying out this work is available on the website of the second level support service at



Planning and preparation


Subject development planning in Mathematics is good: a co-ordinator is in place, regular meetings of the team are held and the minutes are available in the subject development plan for Mathematics. The mathematics department also engages in the very good practice of examining student uptake and attainment in the state examinations with reference to the statistics available from State Examinations Commission (SEC). The results of the analysis are then used to inform planning. The formation of an additional class grouping in sixth year to enable students to follow foundation level resulted directly from this process. This proactive and student-centred approach to planning reflects the willingness of management and staff to tailor mathematics provision to meet the needs of the students.


A comprehensive subject development plan for Mathematics is in place. The subject development plan includes a mission statement for the department, a statement of aims and objectives, arrangements for student access to classes and levels, a short note on classroom organisation, lists of textbooks and course materials, a section on special education needs, reference to cross-curricular planning, suggested effective teaching methodologies, and procedures in relation to homework, assessment and record keeping. In order to build on the existing good work in department planning, it is recommended that the school’s homework policy be customised for use by the mathematics team to specify: the frequency and type of homework assigned; the purpose of homework, particularly as a means of providing independent and collaborative learning experiences; and the responsibilities of students, teachers and parents in relation to setting and correcting homework. In addition, students should be encouraged to amend their own work and to include the amendments in their homework copies. The customised policy should be included in the subject development plan for Mathematics


Collaborative planning is an important component in effective curriculum delivery and in developing a co-ordinated approach to teaching and learning. With this in mind, it is recommended that the expertise in the department be harnessed to develop schemes of work which specify learning outcomes, agreed methods for carrying out core procedures and the underlying approach to be adopted to enhance students’ understanding of basic principles.


Individual teacher planning is good. Each teacher visited during the inspection made their individual planning materials available to the inspector. These included schemes of work and intended delivery schedules. In some cases, teachers had prepared curricular materials in advance of lessons. These included graduated worksheets, which facilitated independent learning and the successful integration of resources designed to engage the students in discovery learning.


Management strongly supports teacher attendance at continuing professional development (CPD) courses and have been proactive in providing whole-school training. Most recently, teachers and management participated in whole-school programmes relating to promoting positive student behaviour and in adhering to good practice in supporting children with special education needs.



Teaching and learning


The lessons observed during the inspection were well planned, proceeded at a suitable pace and were consistent with the subject development plan for Mathematics. The material covered was appropriate and in some cases very challenging. The teachers taught with enthusiasm and confidence and in a number of instances were very skilful in linking the lesson content to the students’ previous learning and to their everyday experiences. To enhance the good practice evident in lesson planning and delivery, it is recommended that in all classes lesson objectives be shared explicitly with the students at the outset, as a means of creating negotiated learning outcomes and that these outcomes be captured and discussed at the end of each lesson.


The teaching methods employed were mainly traditional, involving teacher exposition at the board followed by students working individually on assigned problems. However, there was some integration of differentiated worksheets, use of models and, in one instance, the students engaged in discovery learning when estimating and measuring the weight of a range of everyday commodities. The level of differentiation displayed in this lesson was very good and the student-centred approach was ideally suited to the needs and abilities of the students. It is recommended that, as part of ongoing department planning, a wider range of teaching methods be identified and strategies for their implementation be developed, in order to increase levels of differentiation, to reduce reliance on the text book, to present mathematical concepts in a more visually stimulating way and to actively engage students in their own learning.


In all cases, classroom management was very good. The students were positive in their approach to their work, they were very supportive of the teachers and offered ready responses to questions, and were constructive in helping with calculations and in completing exercises and assignments. For their part, the teachers treated the students with respect, were affirming of their efforts and worked hard to ensure that the lessons were inclusive and purposeful. Teacher questioning was very effective. Good use was made of directed questioning to elicit factual responses and to reinforce key points. In one instance, the students were encouraged to speculate and to explain the discrepancies between their answers and the expected outcomes: this use of higher-order questioning is very good practice.


The quality of student learning was good. In response to teacher questioning and in their interactions with the inspector, the students displayed a good knowledge of concepts and facts and were well able to recall material covered in earlier lessons. The quality of the students’ homework copies and their performance in class tests was also very satisfactory.





Ongoing informal assessment occurs through teacher questioning in class, through the assignment and correction of homework and through class tests. Homework is assigned and corrected regularly and class tests are provided upon the completion of each topic. The homework copies examined during the inspection were very satisfactory. In some cases very good practice regarding the correction of homework was evident. In such instances, the students’ copies were signed and dated regularly and contained teacher comments and corrections. In one instance, the very good practice of parents signing the homework was also in evidence. Procedures concerning the allocation and correction of homework should be standardised across the mathematics department and the examples of good practice evident in some instances should inform any decisions taken.


Details of short-term planning, student attendance and attainment in class and formal tests are recorded in the teachers’ diaries. Roll call was taken at the start of each lesson and the teachers were cognizant of students who were absent from earlier lessons and framed their approach to the delivery of the lesson content appropriately. Furthermore, a number of teachers responded to student performance in assessments and homework by amending lesson content and teaching methods. Such reflective practice is indicative of a caring and student-friendly attitude and is very good practice.


Formal examinations for non-examination classes are held at Christmas and again prior to the summer holidays. Common papers, corrected in accordance with an agreed marking scheme, are provided where appropriate. Students in examination classes are continually assessed in the first term and a composite report recording their overall performance issue to parents at Christmas. Mock examinations are held just prior to the mid-term break in the second term and students taking the same level sit common papers. Written reports issue to parents following formal and mock examinations.


Ongoing communication occurs through the use of the student diary, telephone calls to the home, and through informal meetings, which can be organised at any time. In addition there is one parent-teacher meeting per year for each year group and an awards evening is held each year to recognise student attainment and endeavour.



Summary of main findings and recommendations


The following are the main strengths 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 teachers of Mathematics and with the principal and deputy principal, at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.





Published, January 2010