An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Coláiste Naomh Cormac
Kilcormac, County Offaly
Roll number: 72520I
Date of inspection: 11 February 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Coláiste Naomh Cormac. 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 was given an opportunity to comment in writing on the findings and recommendations of the report; a response was not received from the board.
Timetabling provision for Mathematics in junior cycle in Coláiste Naomh Cormac is good. There are four classes of Mathematics per week in first year and five periods per week thereafter. Upon completion of junior cycle, students can enter transition year (TY) or opt to follow the established Leaving Certificate programme. Classes are mixed ability in TY and are provided with three classes of Mathematics per week. There are five classes of Mathematics per week in fifth and sixth year. It is evident that students are encouraged to study Mathematics at the highest level possible for as long as possible. This is facilitated by the concurrent timetabling of mathematics classes within each year group and the provision of higher-level mathematics classes even in situations where the numbers of students in the classes are small.
Mathematics classes are mixed ability in first year and are banded in second and third year. A series of common assessments with common and agreed marking schemes are provided at regular intervals throughout first year. The results of these assessments, together with recommendations from class teachers and the learning-support team, inform the level the students will follow once the classes are banded at the end of the year. The final composition of the bands is only agreed following consultation with parents and management. These procedures are thorough and student-centred. The length of time devoted to mixed-ability in first year should, however, be reviewed as part of whole-school development planning. Consideration should be given to formation of banded classes in January in first year following common assessments in September, November and prior to the Christmas holidays.
The TY mathematics programme is very good. It is designed to enhance the students’ appreciation and understanding of Mathematics. It also provides the students with opportunities to develop the key skills and competencies to enable them to successfully tackle the material they will encounter during the leaving certificate programme. The mathematics programme in TY is delivered in a series of modules. The students provide written evaluations upon completion of each module. This is very good practice.
Students with special educational needs or in need of learning support are identified as part of the school’s enrolment procedures. Ongoing contact with the feeder primary schools ensures that the attributes, interests and special needs of the incoming cohort are identified at an early stage. The school’s enrolment procedures clearly outline the parents’ responsibilities regarding the provision of completed psychological assessments and other relevant reports. The comprehensive nature of these procedures ensures that incoming students, who have had their learning or other needs formally assessed by National Educational Psychological Service (NEPS) while in primary school, are identified. Where appropriate, the school makes applications for extra resources to the Department of Education and Science for consideration.
All incoming students are assessed during the second week of September using appropriate standardised tests. Following an analysis of the outcome of these assessments and consultation with teachers and parents, the learning-support cohort is identified. If it is deemed necessary, additional assessments for some students are also arranged through NEPS. Learning support in Mathematics is provided by withdrawal in small groups from subjects other than Mathematics. Ongoing, informal, contact is maintained between the learning-support team and the mathematics teachers to ensure that the material being covered during withdrawal is in line with the work being done in mainstream classes. This is very good practice. In order to formalise this process, it is recommended that the procedures proposed in the school’s draft SEN policy in relation to liaison between the class and learning support teachers be adopted in their entirety.
The mathematics department is comprised of five teachers who work as a very effective team. They are ambitious for the students in their care and have been proactive in developing the profile of the department and in encouraging the students to be positive about Mathematics. The qualifications profile of the department is very good. The teachers are assigned to classes and levels by rotation in junior cycle, but only one of the teachers currently takes higher-level classes in senior cycle. It is recommended that, in order to build capacity and to ensure continuity and uniformity of provision, additional teachers from the department be identified and assigned to higher-level Mathematics in senior cycle in the coming years. Mathematics teachers retain the same class groups 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. A wide range of resources, to facilitate active teaching and learning, has been accessed and are freely available to the members of the department. The school has also been proactive in developing its information and communication technologies (ICT) facilities. Mathematics classes have ready access to the school’s computer room and data projectors have been installed in a number of classrooms. ICT integration was evident in lesson delivery and preparation, a variety of software titles have been procured and useful websites have been identified. An e-learning committee was formed in October 2008 and an e-learning plan has been drafted. A key element of the plan is the deployment of a virtual learning environment to facilitate collaboration in resource development and subject planning. This progressive and innovative approach to ICT integration and resource development is very good practice.
Subject development planning is well established in the school. A co-ordinator, who is appointed by rotation, facilitates the planning work. The department operates in a collaborative environment and planning is informed by the desire to provide the students with a wide-ranging and fulfilling experience of Mathematics. Regular meetings of the mathematics department take place and detailed minutes are taken. The minutes of the department meetings are kept in the subject development plan for Mathematics. To further enhance the planning process and to provide an additional vehicle to inform planning, it is recommended that the mathematics department meet annually with management to review the performance of its students in the state examinations with reference to the statistics available from the state examinations commission.
A comprehensive subject development plan for Mathematics is in place. It includes a mission statement for the department, a statement of aims and objectives, resource lists, arrangements for student access to levels, detailed schemes of work, procedures for monitoring and reviewing the plan, and details of continuing professional development (CPD) courses attended by members of the department.
In order to build on the existing very good practice in planning, it is recommended that, in framing the schemes of work, more emphasis be placed on identifying key learning outcomes and suitable methodologies to achieve them. Strategies to integrate different areas of the course and agreed procedures for carrying out core mathematical operations should also be identified and included the subject development plan for Mathematics.
A separate plan for TY Mathematics is in place. The plan is appropriate to the aims and objectives of the TY programme and outlines a range of teaching and learning strategies where the emphasis is on constructivist methods and collaborative mentoring. The content outlined in the plan provides opportunities for students to develop key skills and understand key concepts. The material is ideally suited to facilitating cross-curricular links and for developing an appreciation of the role of Mathematics in everyday life.
Individual teacher planning is excellent. All of the mathematics teachers prepare extensive schemes of work and produce a variety of resources to enhance teaching and learning. Planning for the inclusion of resources is also very good. Worksheets and ICT resources were seamlessly integrated into the lessons observed during the inspection and, rather than merely acting as a substitute for the textbook, served to enhance the students’ understanding of the material being covered.
Practice in relation to the ongoing professional development of the mathematics teachers is very good. Management actively supports and facilitates teacher attendance at relevant CPD courses. Members of the mathematics department have attended a large number of courses, the details of which are contained in the subject development plan for Mathematics. Materials presented at CPD courses were contained in some of the teachers’ individual planning folders. In addition, a large number of whole-school training programmes have been provided in recent years. All of the mathematics team are members of the Irish Mathematics Teachers’ Association (IMTA) and the school management pays the cost of membership. In addition, newly appointed teachers avail of a structured induction programme managed by the school’s deputy principal. The teachers are familiarised with the school’s policies and procedures and get advice on classroom management strategies. All newly appointed teachers also attend a specially tailored training course, which is provided in the local Education Centre.
The lessons observed during the inspection were well planned and in line with the schedule outlined in the subject development plan for Mathematics. The material covered was appropriate to the requirements of the syllabus and included co-ordinate geometry, trigonometry, timetables and arithmetic. The lessons proceeded at a good pace, were inclusive of all the students and there was very good adherence to correct procedures when carrying out the various operations and calculations. The sequencing of the material presented was, in most cases, very good and best practice was in evidence when the lesson’s objectives were shared with the students at the outset and a review of the material covered was conducted towards the end of the lesson. However, the time allocated to correcting homework varied and it is suggested that the amount of time allocated to correcting homework at the beginning of class be agreed and specified in the subject development plan for Mathematics.
A number of approaches to teaching were observed during the inspection. In one instance, ICT was very successfully used to illustrate solutions to problems in co-ordinate geometry. The ICT served to enhance the students’ involvement in, and understanding of, the lesson and reduced the time needed to investigate different approaches to the problems in hand. The teacher did not need to spend time at the board and was free to deal with problems encountered by individual students. The clustered seating arrangement in the room also facilitated student interaction and collaborative learning. The lesson was very focused, purposeful, and marked by an impressive range of interactions.
Graduated worksheets were also used to reduce the amount of teacher exposition, to engage students in problem solving and to facilitate differentiation. For example, a worksheet on trigonometry not only illustrated the correct formulae to use when solving different types of problem but prompted discussions as to the appropriateness of different approaches and enabled students to work at a pace appropriate to their abilities. The teacher was free to support those encountering difficulties and to challenge those who found the material less taxing.
A lesson arising from the students’ difficulties in interpreting train timetables while on a recent trip provided an ideal opportunity for teaching the twenty-four hour clock and for using the calculator in solving problems in this area. The relevance of the lesson was evident from the outset and the student engagement with the material was very good. The students worked in pairs, facilitated by an excellent worksheet, very good teacher movement and effective teacher demonstrations using the overhead calculator.
Student behaviour, in all of the lessons observed, was very good. They approached the tasks assigned to them diligently, responded to teacher questioning with enthusiasm and supported the work of the teacher by asking good questions themselves. The teachers were affirming of the students’ efforts and were skilful in ensuring that the lessons’ goals remained in focus while maintaining a warm and interactive atmosphere.
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.
A draft homework policy is in place and it was evident that it is being implemented. Homework is regularly assigned and corrected. The student’s homework copies were very well maintained, and were appropriately monitored. In some instances the copies also contained written feedback from teachers. This very good practice is in line with the homework policy and should be uniformly adopted. The homework policy should also specify the responsibility of the students in correcting and amending their own work. The homework policy also refers to the need to differentiae homework to take account of the special needs of individual students. This is very good practice.
Students’ progress is also monitored through the use of teacher questioning in class, through their ability to complete assignments in class and through peer assessment. Class tests are provided upon the completion of each topic. Students in TY are also expected to complete a portfolio detailing all the work completed in the different modules. Students in non-examination classes sit formal examinations at Christmas and just prior to the summer holidays. Common papers are provided for first-year students and these are corrected using an agreed common marking scheme. Students in third and sixth year sit a formal examination in November each year and sit mock examinations early in the second term. The examination papers provided in the November assessments are similar in style and content to those the students will encounter in the state examinations and are designed to reinforce the students’ knowledge and to affirm their progress.
Students in receipt of reasonable accommodation in the state examinations receive appropriate support in class and formal tests.
Practice in relation to recording student attendance and attainment in class and formal tests is very good. Roll call is taken at the beginning of class and is noted in the teacher’s diary. Student compliance with homework completion and their performance in class and formal tests are also recorded.
Reports are issued to parents after each formal assessment and ongoing communication occurs through the use of the student diary, parent-teacher meetings, telephone calls to the home, and other less formal means. Each class group has one parent-teacher meeting per year.
The school promotes positive attitudes to Mathematics by encouraging students to take part in a range of extra-curricular activities pertaining to Mathematics. Junior cycle students participate in Problem Solving for Irish Second Level Mathematicians (PRISM) competitions, organised nationally as part of Maths Week Ireland, while senior cycle mathematics students participate in Team Maths.
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 at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published, November 2009