An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
Palmerstown, Dublin 20
Roll number: 91302F
Date of inspection: 7 October 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Pobalscoil Iosolde. 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 studentsí work, and had discussions with the teachers. The inspector reviewed school planning documentation and teachersí 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.† 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.
The time allocated to Mathematics in Pobalscoil Iosolde is very good. All junior cycle students, including those participating in the Junior Certificate Schools Programme (JCSP), have five periods of Mathematics per week. Four periods are timetabled for Mathematics in Transition Year (TY). Students taking the ordinary and foundation levels in Mathematics at Leaving Certificate have five periods each week, and those following higher level have six periods. Students taking the Leaving Certificate Applied programme (LCA) have four classes of Mathematical Applications per week. Class periods are forty minutes long except on Wednesdays when they are thirty five minutes.
A small JCSP cohort is established upon entry to the school in first year. They have one period of Mathematics each day and follow a programme designed to equip them with life-skills and with mathematical skills to increase their confidence in dealing with numbers. Many of these students then go on to take foundation level Mathematics in the Junior Certificate. The remaining first year mathematics classes are mixed ability. These are timetabled concurrently and follow a common programme with common assessments.
Mainstream mathematics classes are banded in second and third year and are timetabled concurrently within each year group. This is very good practice, as it facilitates student movement between levels and provides them with opportunities to study Mathematics at higher level for as long as possible.† The second year mainstream classes have one period of Mathematics per day. The corresponding classes however, in third year have one double period on Tuesdays and have no mathematics class on Wednesdays. It is recommended that this element of the timetabling provision be kept under review with the intention of providing each class group with at least one period of Mathematics each day.
Students participating in JCSP in second and third year have a separate mathematics timetable from the remainder of other classes in the year groups. This practice however is reviewed each year, and if it is deemed appropriate the JCSP classes are timetabled concurrently with the mainstream mathematics classes to enable students to sit ordinary level mathematics in the Junior Certificate. This proactive and reflective approach to timetabling of Mathematics is very good practice.
Upon completion of junior cycle, students intending to follow the established Leaving Certificate programme enter TY, while the remainder go directly into LCA. The mathematics programme in TY is traditional in its structure, content and delivery modes. Students choose higher or ordinary level and follow a curriculum that is very similar to the established Leaving Certificate. It is recommended that a review of mathematics provision and delivery in TY be undertaken with a view to aligning the provision more closely with the Transition Year Programmes, Guidelines for Schools.
Mathematics classes in fifth and sixth year are streamed and the classes are timetabled concurrently within each year group. Students following higher level are provided with an additional class period per week. This is a very welcome intervention as it actively seeks to enhance uptake and attainment in higher-level Mathematics.
Teachers are allocated to classes by rotation and following consultations held with the principal. It is school policy that classes retain the same teacher from second to third year and from fifth to sixth year. The mathematics team currently comprises seven teachers and each member teaches Mathematics to at least two different class groups. This is good practice, as it facilitates teachers to have more frequent contact with the curriculum, and enhances opportunities for them to interact with other team members.
The school and its main feeder primary schools are participants in the School Completion Programme (SCP), thus ensuring that strong links with the primary schools are maintained and developed. This, supported by the activities of the schoolís deputy principal, the home-school-community liaison co-ordinator and the schoolís learning-support co-ordinator facilitates the smooth transfer of students from primary to post-primary. The needs, interests and talents of incoming students are established during ongoing contacts maintained with the feeder schools. The very good practice of providing feedback to primary schools on the progress being made by students following their transition to post primary school also takes place and this is to be commended. In addition, the school holds an open night in early November each year and invites the parents of prospective students to attend. At this meeting, parents are informed about the schoolís policies and practices and the range of programmes available to students. Application forms and the arrangements regarding the assessment of incoming students are distributed. An induction day for incoming students is held shortly after the open night. The incoming students are invited to participate in a range of curricular and extra-curricular activities and to become familiar with the layout of the school. Entrance assessments are held for prospective incoming students towards the end of November each year.
Students in need of learning support or with special education needs (SEN) are identified as part of the schoolís enrolment process. All incoming students sit a range of standardised assessment tests to determine their verbal and numerical reasoning. The schoolís learning-support co-ordinator visits the feeder primary schools prior to and then following the entrance assessments. The purpose of these visits is to develop a more complete profile of each prospective student. Particular attention is paid to students with identified special education needs, those already in receipt of extra resource hours in the primary schools and to individuals whose performance in the entrance assessments raises questions about their needs.† Formal assessment reports which have been already completed for incoming students by the National Educational Psychological Service (NEPS) are sought from parents, and applications for extra resources are then submitted by the school to the Department of Education and Science for consideration. If it is deemed necessary, additional assessments for some students are also arranged through NEPS.
Learning support in Mathematics is provided through team teaching and by withdrawal in small groups from classes other than Mathematics. The learning support model to be implemented in the case of individual students is discussed in detail with the studentís parents and their crucial role in supporting the implementation of the model is explained. The progress of each student who is in receipt of learning support is tracked by monitoring their performance in class tests and in the formal examinations. In addition, each studentís learning-support teacher prepares ongoing reports. The reports are used to measure the suitability of the support being provided for each individual, and to inform the development of new schemes of work and learning-support models. Use is also made of in-school referral forms, which enable teachers to inform the learning-support co-ordinator about students who are not already in receipt of learning support, but who are having difficulty coping with the material being covered in class.
Students with exceptional abilities in Mathematics are also identified as part of the enrolment and ongoing assessment procedures. The schoolís guidance counsellor, in collaboration with the mathematics teacher and the studentsí parents, identifies the most suitable course of action. Typically such students are enrolled in the Centre for Talented Youth of Ireland (CTYI) in Dublin City University or participate in the Trinity Access Programme (TAP), which operates under the aegis of Trinity College Dublin.
The school has good information and communication technologies (ICT) infrastructure. Mathematics classes have access to one of the schoolís three computer rooms and to an interactive whiteboard. Interactive solutions to the Leaving and Junior Certificate examination papers are also available to students on the schoolís computer network.† Additional resources for teaching Mathematics are limited however, and no mention is made in the planning documentation of how ICT or other resources might be integrated into the teaching and learning of Mathematics. It is therefore recommended that the mathematics team carry out an audit of skills and resources. The audit should identify the key resources to be purchased or developed and any training needs of the team members. Assistance in carrying out this work is available from the second level support service www.slss.ie.
Subject development planning in Mathematics is underway. A co-ordinator has been appointed and frequent meetings of the mathematics team take place. The minutes of these meetings are contained in the subject-development plan for Mathematics. Responsibility for co-ordinating the mathematics department rotates between the team members. This is very good practice as it ensures that each team member gains experience of the challenges associated with subject planning and contributes to the development of the subject in the school.
Work is also underway in producing a subject-development plan for Mathematics. The current draft of the plan consists of very detailed schemes of work and a comprehensive delivery schedule for each year and level. In order to build upon the work already done, it is recommended that the mathematics team collaborate in developing the plan to address: the integration of different areas of the syllabus, the choice of teaching methods, the use of ICT and other resources in teaching and learning, the use of homework and assessment, and the challenges inherent in teaching Mathematics in mixed ability settings.
Individual planning for Mathematics is good. All the teachers made their individual planning materials available to the inspector. In all cases it was found to be relevant and comprehensive. Best practice was evident where the teacher had identified the individual strengths and weaknesses of the students in the class and modified the teaching strategies to be applied accordingly. Almost all of the teachers had prepared additional materials in the form of graduated worksheets in advance of the lessons observed during the inspection. These worksheets were most beneficial when they facilitated differentiation and enabled a range of interactions and learning opportunities and were not simply a substitute for the textbook. In addition, the teachersí diaries were used to record attendance, homework completions and performance in class tests.† The very good practice of developing, recording and updating student profiles was also evident in one case.
Management supports the continuous professional development (CPD) of the mathematics teachers. The majority of the teachers of Mathematics have postgraduate degrees and, an impressive range of CPD courses, particularly in relation to the integration of children with SEN in second-level schools, has been made available to the staff in recent years. It is suggested that the list of courses attended by the teachers be included in the subject development plan for Mathematics and that it be updated annually. †The majority of the mathematics team are members the Irish Mathematics Teachersí Association (IMTA) and one member of the team is chairperson of the local branch.
Newly appointed and PGDE teachers attend an induction day arranged each year where they are briefed on the operation of the school and are introduced to the schoolís ethos, its policies and procedures. Teachers joining the mathematics team are provided with a mentor from the team in their first year, and a full briefing regarding the profile of each of their classes is provided. In addition, every newly appointed teacher meets the learning support team to be appraised of policy and practice in catering for students in receipt of resource hours or with SEN.
Examination of uptake rates and studentsí performances in the state examinations suggests that that there is close collaboration between the mathematics team and the schoolís guidance counsellor in advising students of the most appropriate level of Mathematics to follow in both junior and senior cycle.
The lessons observed during the inspection were well prepared and had a well-defined structure. Homework was corrected at the outset, the learning objective for the lesson in question was then shared with the students, new material was introduced and links to earlier learning were discussed. Students worked on material assigned by the teacher and a summary of the lesson was delivered prior to assigning homework at the end of the lesson. The material covered was relevant and included: natural numbers, rational numbers, integration, the circle, indices, trigonometry and long division in algebra.†
The teaching methods employed were mainly traditional and involved teacher exposition at the board followed by students working individually on assigned problems. There was however, some integration of differentiated worksheets and in one instance the overhead projector was used. While the teachers taught with enthusiasm, were very knowledgeable and delivered the material in a very clear fashion, the lessons would benefit from the use of a wider range of teaching methods and resources to facilitate differentiation and more student-centred activities.
In one lesson where students explored natural numbers, an excellent worksheet supported by teacher intervention and guided student discussion facilitated a very worthwhile learning experience for the class. They were encouraged to explore ideas, to share their opinions with their peers and were enabled to proceed at a pace that suited their individual needs and abilities. The level of differentiation achieved in the lesson was very impressive as was the use of material, prepared by the teacher, in enabling a range of learning experiences.
Studentsí engagement with the lessons was very good. The lessons proceeded in an atmosphere of mutual respect, discipline was excellent and a sense of fun was pervasive. The quality of the studentsí written work was very good, their homework copies were well maintained and they responded readily when questioned by the teacher. In some instances students were invited to the board to share their solutions to more exacting problems. This is very good practice as it affirms innovation and achievement, deepens the selected studentís understanding of the material at hand and enriches the learning experience for the entire group.
The integration of different areas of the mathematics syllabus was evident in one lesson where the teacher introduced equations and the idea of the root. Great care was taken to draw on the studentsí earlier experiences and they were enabled to extrapolate general principles regarding the number of possible solutions to different equations and the implications that this has for the graph of the related function. This very welcome approach towards identifying and exploiting links between different areas of the syllabus should form a central part of the schoolís subject development planning in Mathematics and inform future classroom practice.
Ongoing assessment is achieved through the use of teacher questioning in class, homework assignments, class tests at the end of each topic and formal written examinations. Teacher questioning in the lessons observed during the inspection was very good. While it was primarily used to elicit factual responses, it also served to encourage speculation and deepen studentsí understanding of the subject matter under consideration. In one instance, students were asked to prepare questions. These were then used to teach students who had been absent the previous day when the material was originally covered. This process required reflection and initiative on behalf of the students and contributed to a very lively and enjoyable class.
A homework and assessment policy is in place and is being implemented. Homework is assigned and corrected each day. The studentsí homework copies are well maintained and they are monitored regularly by the teachers and, in some cases, there was evidence of students amending their own work. To build upon the existing good practice it is recommended that the process of correcting homework in class be promoted. This provides greater opportunities for students to engage in shared learning. It is further recommended that the homework policy be amended to specify the studentsí role in correcting and amending their own homework.
All students sit formal examinations at Christmas and again just prior to the summer holidays. First year students take common assessments in Mathematics, which are corrected according to an agreed common-marking scheme. The results of these assessments are collated and are used to inform student choice of level at the end of first year. This is very good practice as it enables students to determine their performance relative to the other students in the year group and provides a guide as to the most appropriate level they should follow.
Mock examinations are held early in the second term and students taking the same level sit common papers. The mock examinations are corrected by the teachers themselves and this has proved to be very beneficial in gauging studentsí readiness for the state examinations, and when giving feedback to students on their performance.
Reports issue to parents following the formal and mock examinations and ongoing communication with parents occurs through the student diary, telephone contacts and through the use of formal letters. In addition, each year group has one parent-teacher meeting per year and less formal meetings can be arranged if required.
The school holds an awards evening each year which celebrates student achievement and their contribution to school life. An award for outstanding performance in Mathematics, presented by NUI Maynooth, is presented at the awards evening. The school also promotes positive attitudes to Mathematics through its association with TAP, CTYI and by facilitating participation in the annual regional table quiz organised by the Irish Mathematics Teachersí Association.
The following are the main strengths identified in the evaluation:
∑ The quality of teaching and learning in the school is good.
∑ Good timetabling provision for Mathematics is in evidence.
∑ The school has very good procedures in place to facilitate the smooth transition of students from primary to post primary school.
∑ Good procedures are in place for supporting students who are in need of learning support.
∑ Good ICT facilities are provided.
∑ School development planning is underway.
∑ Teachersí individual planning and preparation for class is good.
∑ Student engagement, behaviour and attitude to Mathematics are very positive.
∑ Management is proactive in supporting the continuing professional development of the teaching staff and the majority of the teachers of Mathematics have postgraduate degrees.
∑ A homework and assessment policy is in place and is being implemented.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
∑ It is recommended that the timetabling provision for Mathematics be kept under review with the intention of providing each class group with at least one period of Mathematics per day.
∑ It is recommended that the mathematics team carry out an audit of skills and resources. The audit should identify the key resources to be purchased or developed and any additional training needs of
the team members.
∑ It is recommended that the mathematics team collaborate in developing the plan for Mathematics to address, in the first instance, integration of different areas of the syllabus, teaching methods, the use
of ICT and other resources for teaching and learning, the† deployment of homework and assessment, and the challenges inherent in teaching in the mixed-ability setting.
∑ It is recommended that the process of correcting homework in class be promoted to provide greater opportunities for studentsí shared learning. It is also recommended that the schoolís homework policy
be amended to specify studentsí role in correcting and amending their own homework.
Post-evaluation meetings were held with the teachers of Mathematics and with the principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published March 2009