An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
Patrician Secondary School
Newbridge, County Kildare
Roll number: 61681V
Date of inspection: 3 November 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Patrician Secondary 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 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.
Timetabling provision for Mathematics in the Junior Certificate (JC) is good. Mathematics classes are mixed ability in first year and are banded for the remainder of the Junior Certificate. There are four mathematics classes per week in first year and five classes per week in second and third year. Class periods are forty minutes long. Mathematics classes are timetabled concurrently within the bands. This is very good practice as it provides students with access to the highest appropriate level and facilitates ease of movement between levels.
Timetabling provision for Mathematics in senior cycle is very good. Transition year (TY) is optional and students are provided with three classes of Mathematics per week. There are five classes of Mathematics per week in fifth and sixth year while those students taking higher-level Mathematics in sixth year are provided with an additional class period each week. Students in fifth and sixth year following the Leaving Certificate Applied (LCA) programme are provided with four classes of Mathematical Applications per week. Applied Mathematics is also provided as part of the option bands in fifth and sixth year.
Procedures for facilitating student transfer from primary schools are very good. Application forms are freely available from the school and are also distributed at the schoolís open night, which is held each November. Following the closing date for receipt of application forms, the schoolís guidance counsellor visits the relevant primary schools to meet with the class teachers and to discuss the needs, strengths and interests of the incoming students. Each incoming student is invited to meet with the school principal and the guidance counsellor. This meeting is also attended by the studentís parents and affords an opportunity to further develop the studentís profile and discuss any special educational needs (SEN) or resource requirements. Completed psychological assessments can also be provided to the school at this stage. Assessment tests are held in February or March each year. Finally, an information evening, attended by parents and students, is held in May to allow the students to meet with their class group and to provide information on the schoolís policies, procedures and practices. Feedback on individual incoming students is provided to the teaching staff by the schoolís guidance counsellor. The parents of each first-year student meet with the appropriate class tutor in November and further feedback is then provided to staff.
Students with SEN or in need of learning support are identified as part of the schoolís enrolment process. The mathematical aptitudes of incoming students are determined using a diagnostic test, designed by the schoolís learning support co-ordinator, and the Norman France numerical reasoning test.† It is recommended that the testing arrangements be reviewed in order to include the class teachers in the feeder primary schools in the design of the diagnostic tests. It is further recommended that the school refer to Circular 0008/2007 www.education.gov.ie to ensure that the standardised tests currently being used are included in the list of approved tests contained therein. Incoming students who have had their learning or other needs already formally assessed by the National Educational Psychological Service (NEPS) in primary school are identified, 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 and resource teaching in junior cycle is provided through the withdrawal of students, in small groups, from subjects other than Mathematics and following consultations with parents. Team teaching is used to provide learning support in senior cycle. Individual education plans (IEPs) are prepared for each student in receipt of learning support and from these, and following collaboration with the class teacher, agreed and detailed schemes of work are developed. Student performance is tracked through the schoolís normal assessment procedures and the learning support co-ordinator monitors the results achieved in class and formal tests. The learning support team gives feedback to parents at parent-teacher meetings and also attends the schoolís information evenings. The learning support co-ordinator liaises with the mathematics team during departmental meetings, through regular informal meetings and through the use of referral forms, which are used to advise the learning-support team of students who are encountering difficulties with the subject matter being covered in class.
The work of the learning support team is strongly supported by management and a superb customised learning-support facility has been recently developed. This facility consists of a central meeting area for small-group work, with a number of smaller rooms that can be used for individual tuition or for private meetings. The facility is very well resourced; it provides the learning-support team with a focus for their activities and enables teachers and students to employ a variety of teaching and learning strategies.
Students with exceptional abilities in Mathematics are also identified as part of the enrolment procedure. They are encouraged and facilitated to participate in the programmes operating under the aegis of the Centre for Talented Youth of Ireland (CTYI) in Dublin City University.
The mathematics department is comprised of ten teachers and they are deployed in line with their qualifications. It was evident, from the outset of the inspection, that a strong sense of teamwork permeates the department and that there was admirable leadership within the department. The commitment of all of the team members in promoting positive attitudes to Mathematics and in enabling their students to achieve to the highest level possible was equally obvious. Teachers are assigned to classes and levels by rotation and ongoing capacity building has ensured that a large number of the team teach higher-level Mathematics in senior cycle. Furthermore, it is policy that teachers retain the same class group from second to third year and from fifth to sixth year. This is very good practice as it ensures continuity of approach and facilitates long-term planning.
The mathematics department is very well resourced and a central storage area that can be accessed by all of the teachers is in place. The school has recently embarked on a process of distributing information and communication technologies (ICT) into individual classrooms and the majority of the rooms now contain a computer and data projector. In response to these developments, the mathematics department has chosen one of its members to identify suitable ICT resources, to recommend strategies for their integration into teaching and learning and to source appropriate training. This proactive approach in responding to, and planning for, ongoing developments is very good practice.
School development planning is well advanced and subject planning in Mathematics is very good. The department is very ably co-ordinated, regular meetings are held and a comprehensive subject development plan for Mathematics has been developed. The schedule of department meetings, together with the minutes of the meetings, is included in the subject development plan. The members of the mathematics department meet every August to review and amend the subject development plan. The department also analyses the performance of students in the state examinations with reference to the statistics supplied by the State Examinations Commission. This informed and enlightened approach to subject planning is very good practice.
The subject development plan includes a mission statement for the department, a statement of aims and objectives, resource lists, teaching and learning styles, a comprehensive section on SEN, policies on assessment and recording studentsí attendance and achievement, and procedures for monitoring and reviewing the plan. The plan also includes very detailed schemes of work for each year and level.
In order to build on the existing very good practice in planning, it is recommended, in framing the schemes of work further, that emphasis be placed on identifying key learning outcomes and that methodologies to achieve these outcomes be identified. It is further recommended that the strategies to integrate different areas of the course, already being employed in some instances, be detailed in the subject development plan and be adopted as common practice by all members of the department.
Separate plans are in place for LCA and TY. In both cases, the plans were found to be comprehensive, with the TY mathematics plan being particularly praiseworthy. The TY mathematics class is mixed ability and emphasis is placed on remediation and confidence building. A refreshing range of approaches to teaching and learning is advocated and the course content is ideally suited to equipping the students with the key skills they will need in successfully tackling whichever Leaving Certificate mathematics programme they choose upon completion of TY.
Individual teacher planning is excellent. All of the teachers made their personal planning materials available to the inspector and it was evident that collaboration in preparing for lessons and in integrating resources in lesson delivery is a fundamental part of teacher planning. There was ample evidence that the resources listed in the subject development plan are actually used to enhance teaching and learning and that the teachers are skilled in integrating a range of resources in lesson delivery.
Management is very accommodating in facilitating attendance at continuing professional development courses. The subject development plan for Mathematics lists the courses attended by the different team members, details of upcoming courses and the materials presented at those courses attended by a member of the team. All of the mathematics team are members of the Irish Mathematics Teachersí Association (IMTA) and the school management pays the cost of membership. Correspondence from the IMTA is stored in the subject development plan for Mathematics.
A comprehensive induction programme is provided for all newly appointed teachers. The teachers meet with the principal at the beginning of the year to become appraised of the schoolís policies and procedures and to discuss the most effective approaches to classroom management, assigning and correcting homework and implementing the schoolís code of discipline. A senior teacher from the appropriate department is appointed to act as mentor for the first year and regular meetings are held with the principal throughout the year.
The lessons observed during the inspection were very well planned and in line with the schedule outlined in the subject development plan for Mathematics. In most instances, the lessonís objectives were shared with the class at the outset and every effort was made to create links to the studentsí prior learning and to their everyday experiences. The material covered was appropriate and included: geometry, rearranging formulas, sequence and series, area and volume, coordinate geometry of the line, simple equations, counting and probability. The lessons proceeded at a good pace, were inclusive of all the students and there was excellent adherence to correct procedures in relation to core mathematical operations. In addition, the sequencing of the material presented was very good and best practice was in evidence when a review of the material covered was conducted towards the end of the lesson.
A range of teaching methods was observed during the inspection and, in each case, these served to enhance the studentsí involvement in and understanding of the lesson. In one instance, models were used to illustrate that when a body changes shape, its volume is unaffected and in another the students were actively engaged in constructing bisectors of lines and angles, and in verifying their work through measurement.
ICT was very effectively integrated in one lesson where the students were engaged in very challenging material in algebra. The ICT was used to reinforce good practice in approaching the material, by presenting the material in a systematic and structured fashion. Great care was taken to ensure that there was consistency in approach and that the students were provided with an effective and robust procedure for solving the problems in hand. Time and again, the teacher insisted that the students explain their reasoning and that they adhere to procedure when attempting the problems themselves. Furthermore, as the problems became more intricate, the adherence to correct procedure became even more pronounced. The resulting lesson was characterised by great student engagement, lively discussion and reflective learning.
Differentiated worksheets were successfully used in a number of lessons, to underline the material being covered, to facilitate discussion with individual students, to enable peer tutoring and to challenge the more able students. It was clear that the worksheets were designed with particular learning outcomes in mind and to meet the needs of the individual class groups, rather than as a mere substitute for the textbook.
Student behaviour and engagement was of the very highest standard. The lessons proceeded in an atmosphere of mutual respect, the teachers taught with enthusiasm and in a manner that made the material being covered accessible to as many students as possible. The teachers had high expectations of the students and matched this with the quality of their own preparation, presentation and classroom management. The classrooms were bright and cheerful and the walls were decorated with bespoke and locally produced posters describing relevant formulas and mathematical principles.
The quality of learning was also very high. The students responded knowledgeably when questioned by the teachers and responded confidently during their interactions with the inspector. Analysis of uptake and student attainment in the state examinations provides further evidence of the high standards expected of, and achieved by, the students in the school.
The schoolís homework policy is contained in the subject development plan for Mathematics and details the amount of homework to be given each day. It takes due cognizance of the abilities of the students to which the homework is being assigned. While the purpose of homework in reviewing the work done and in providing opportunities for independent learning is clearly stated, it would be worth amending this section of the policy to also include the role of homework in providing shared learning opportunities. The homework policy also details the procedures to be followed and the responsibilities of the various stakeholders regarding the correction of homework. It is suggested that this element of the policy should be extended to include the studentsí role in amending their own work and to promote the adoption of assessment for learning as a key assessment vehicle when correcting studentsí work.† Analysis of a sample of the studentsí homework copies suggested that the majority of the mathematicsí teachers are implementing the homework policy and that the standard of the work being done by the students is very good. In order to build upon existing good practice in this area, it is recommended that the policy in relation to assigning and correcting homework be implemented consistently by all members of the mathematics team.
A comprehensive assessment policy is also in place and it details the arrangements for formal and informal assessments for all programmes and levels. First-year students are provided with four formal common assessments in Mathematics. The results of these assessments are collated and serve to inform student choice concerning the level they will follow for the remainder of junior cycle. However, the assessment policy states explicitly that students are facilitated in following higher-level Mathematics for as long as possible and that a poor performance in the first-year tests does not necessarily mean that higher level is not an option for any given student. The remaining non-examination classes sit formal examinations at Christmas and, again, prior to the summer holidays. Common papers, corrected in accordance with agreed marking schemes, are provided in all formal examinations.
Students in examination classes sit formal examinations at Christmas and sit mock examinations during the second term. The teachers, themselves, correct the mock examinations and this practice has proved very useful when providing feedback to students upon their performance, and in advising them as to the most appropriate level to sit in the upcoming state examinations. Reports issue to parents after the formal and mock examinations and students in examination classes also receive an additional progress report in November each year.
Ongoing communication with parents occurs through the use of the student diary and telephone contact, and formal letters are also issued if the need arises. In addition, each class group has one parent-teacher meeting per year. An assembly is held for parents and students at the beginning of each year. Other, less formal meetings can also be arranged if required.
Positive attitudes towards Mathematics are promoted by facilitating studentsí participation in the annual regional table quiz organised by the IMTA and by the provision of a range of in-school activities to celebrate Maths Week. An awards evening is also held each year to recognise attainment and endeavour.
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, October 2009