An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
Confey Community College
Leixlip County Kildare
Roll number: 70691C
††††† Date of inspection: 13 October 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Confey Community College. 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.
Very good timetabling provision for Mathematics in junior cycle is in place. In first year, classes are mixed ability until Christmas and then follow a programme designed to consolidate and develop the studentsí mathematical skills. This is very good practice, as it ensures that any shortcomings can be identified and addressed and that a synchronized approach can be adopted in developing competency in core mathematics operations. A number of first-year classes were visited during the inspection where it was evident that the programme was being delivered in a uniform and co-ordinated fashion, and that each class group was progressing through the programme at a similar rate. Following common assessments and discussions with class teachers and parents, the classes are separated into bands and are banded for the remainder of junior cycle.
Mathematics classes are timetabled concurrently in each year group in junior cycle. This facilitates ease of movement between levels, supports the co-ordination of planning and lesson delivery and enables students to continue with higher-level Mathematics for as long as possible. The distribution of classes throughout the week is good and the balance of provision in Mathematics between mornings and afternoons is also very satisfactory.
Upon completion of junior cycle, students can go directly into the established Leaving Certificate programme, enter Transition Year (TY) or opt to follow Leaving Certificate Applied (LCA). There are four periods of Mathematics per week in TY and the classes are timetabled concurrently. The TY mathematics programme, as it is currently constituted, is in need of review. It is recommended that it be amended to reflect more closely the programme objectives as outlined in the Transition Year Programmes, Guidelines for Schools www.transition.ie and the classroom practices observed during the inspection. It is further recommended that the programme address any identified deficiencies in the studentsí mathematics skill and knowledge, that it enables them to develop competence in key procedures required to successfully tackle the Leaving Certificate programme, and gain an appreciation of the scope and breadth of the subject. The amended programme should also identify appropriate teaching methods, cross-curricular links, strategies for the integration of information and communication technologies (ICT) and project work.
Provision for Mathematics in fifth and sixth year is also very good. Students taking ordinary level are provided with five periods of Mathematics per week, while those taking higher level have six. Vertical movement between levels is facilitated by the concurrent timetabling of Mathematics classes and it is school policy that students are encouraged to take higher-level Mathematics for as long as possible. In addition, LCA students in fifth and sixth year are provided with three single periods of Mathematical Applications per week.
Students in senior cycle can also take Applied Mathematics as an additional subject. It is currently timetabled outside the normal subject-option bands. The inclusion of Applied Mathematics in the schoolís curriculum is evidence of the commitment of management to nurturing positive student attitudes to Mathematics amongst the schoolís student body and is highly commended
Prospective students are informed about the school during visits by the principal to the feeder primary schools and through advertisements placed in the local media. An open night is held each November and this affords students the opportunity to visit the different departments and to participate in a number of activities including a mathematics challenge. This innovative idea serves to promote positive attitudes to mathematics and is very good practice. Application forms are distributed at the open night and entrance assessments are held each February.
Students with special education needs (SEN) or who are in need of learning support are identified as part of the schoolís enrolment procedures. The incoming studentsí cognitive skills are established using the Drumcondra Reasoning Test (DRT1998) as part of the schoolís entrance assessment. Following an analysis of the results of these assessments the schoolís learning support co-ordinator visits the primary schools to meet the pupils and the learning-support teachers. These meetings are intended to give feedback on pupilsí attainments in the entrance assessment and establish their individual talents, needs and interests. 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 are also arranged through a special initiative funded through Co. Kildare Vocational Education Committee.
Learning support is mainly provided through team teaching, with a small number of students being withdrawn in small groups from classes other than Mathematics, where appropriate. Formal planning meetings are held with the mathematics team to establish the most appropriate support model and to agree schemes of work. Parental approval is sought in writing if a student is to be withdrawn from class and ongoing communication with parents is maintained through telephone calls, parent-teacher meetings and informal face-to-face meetings. Students in receipt of learning support sit the normal class tests and formal assessments. Their performance is subsequently analysed by the learning-support team and the analysis is used to inform the development of schemes of work and student profiles.
The learning-support team is proactive in identifying students who present with difficulties in Mathematics as they progress through the school. An additional class group is created after Christmas in third year in which extra support in Mathematics is provided. This year a mathematics specialist has been released by the school to attend a postgraduate course in SEN teaching. Upon completion of the course this teacher will then join the learning-support team. The inclusion of a mathematics specialist as part of the learning-support team is a very welcome development.
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 by the Centre for Talented Youth of Ireland (CYTI) in Dublin City University and regular contact is maintained with parents regarding additional challenging activities, initiatives and competitions that are identified during the course of the year.
The mathematics team is currently composed of eight teachers, many of whom have been recently appointed to the team. This presents a great opportunity regarding the ongoing development of the subject in the school. Each team member has an appropriate qualification in Mathematics, this is in keeping with the managementís objective of maximising uptake and attainment in Mathematics and Applied Mathematics, and this is very good practice. One of the team has only one class group for Mathematics this year. †This is unsatisfactory as it reduces this teacherís contact with the curriculum and lessens opportunities to interact with the other team members. It is therefore recommended that each member of the mathematics team should be timetabled for at least two class groups of Mathematics each year.
Teachers are assigned to classes and levels in junior cycle by rotation and following consultation with the principal. This is very good practice as it gives all members of the mathematics team the opportunity to gain experience in teaching at higher, ordinary and foundation levels and of encountering a wide range of learning styles. It is also policy that teachers retain the same class group from second to third year thus ensuring continuity of curriculum delivery. Higher-level Mathematics in senior cycle is presently taught by just one of the teachers. It is intended that the model being used at junior cycle will also be adopted in senior cycle as the team settles into their new roles in the school.
The mathematics department is well resourced and there is ready access to ICT. Teachers have access to laptops and data projectors and the integration of resources, including ICT, was evident during the inspection. In light of the composition of the mathematics team, and in order to streamline the management and integration of resources, it is recommended that an audit of existing resources be undertaken. It is further recommended that the resource list in the subject development plan be updated and that all mathematics resources be stored in an agreed convenient location.
Subject-development planning in Mathematics is very good. A co-ordinator has been appointed and responsibility for co-ordinating the department rotates between the team members. Regular meetings of the mathematics team take place and the minutes of these meetings are contained in the subject-development plan for Mathematics. A very detailed analysis of the performance of students in the state examination using the data supplied by the State Examinations Commission is carried out annually and a meeting is held with the principal at the beginning of each school year to discuss the outcomes of the analysis and to identify any implications for planning, teaching and learning and in-school assessment.
A comprehensive subject-development plan for Mathematics is in place and this is subject to regular review. The plan outlines the provision for Mathematics in the school, including access to levels, the grouping of students, the timetabling of classes and details about staffing for the subject. The plan also contains the mission statement for the department, the role and responsibilities of the subject co-ordinator, a statement of aims and objectives, schemes of work including the expected learning outcomes in each case, lists of resources, the schedule for curriculum delivery, suggested teaching methods, planning for students with special needs, homework and assessment procedures, and cross-curricular links.
The existing very good practices in planning could be further enhanced by detailing how different areas of the syllabus could be integrated during lesson delivery and how the resources listed in the plan could be incorporated to enhance teaching and learning. For example, a lesson investigating the solution of simultaneous equations in two variables might make reference to the co-ordinate geometry of the line and how dynamic geometry software could be deployed to illustrate the geometric nature of the solution.
Separate plans for TY and LCA are in place. Both plans are very comprehensive and while the LCA plan is appropriate to the aims and objectives of the programme, the TY plan needs to be rewritten to reflect the changes recommended earlier in this report.
Individual teacher planning was, in almost all cases, very good. This was evident from the seamless fashion in which resources such as worksheets, ICT and the overhead projector were integrated into the lessons observed during the inspection. Teachersí individual planning documents were comprehensive and in a number of cases were of the very highest quality. There was extensive use of ICT in preparing worksheets, posters and presentations and the very good practice of adhering to the precise meaning of mathematical terms in preparing the resources was also evident.
The mathematics teachers have attended a wide range of continuous professional development (CPD) courses and a number of whole-school professional development events, including ICT integration, differentiated learning and inclusion of students with SEN, have also been organised in the recent past. Details of the CPD courses attended by staff members are contained in the subject development plan for Mathematics. A number of the teachers are members of the Irish Mathematics Teachersí Association (IMTA) and management covers the cost of membership.
The induction programme for newly appointed teachers is very well managed. The principal and deputy principal meet newly appointed teachers at the beginning of the school year to discuss the schoolís policies and procedures and a number of follow-up meetings with the principal take place during the year. A mentor from the relevant subject department is also assigned to each newly appointed teacher during their first year in the school.
The lessons observed during the inspection were, for the most part, very well planned. The learning objective was shared with the students at the outset of each lesson. The material covered during the lessons was in keeping with the subject development plan for Mathematics, it was relevant, in line with syllabus requirements and, in some instances, quite challenging. The material covered included fractions, simultaneous equations, sequences and series, compound interest, complex numbers, statistics and algebra. Planning for the inclusion of resources was also very good. Differentiated worksheets, ICT, the overhead projector, posters and other graphic material were skilfully integrated into classroom activities and contributed to very stimulating lessons.
Effective planning and teacher collaboration were evident from observing two separate classes where fractions were being introduced in a mixed-ability setting. The resources, language, and student-centred approach utilised in each case was identical. The lesson content was delivered in a confident and accessible manner and this, combined with very good differentiated worksheets, contributed to a worthwhile and invigorating learning experience. A particularly impressive feature of the lessons was that the resources created by the teachers did not merely replace the textbook, but enabled a range of interactions and activities to realise the lessonsí objectives.
There was extensive use of ICT in preparing resources and in lesson delivery. In one instance, a commercial software package, based on a popular television game show, had been customised to present a series of graduated questions on factors and the solution of quadratic equations and to track the progress of the class in solving them. The software, supported by a worksheet and good teacher movement, facilitated a lesson that was student-centred, purposeful and fun. In another case a series of PowerPoint slides was utilised to illustrate the correct procedure to be followed in drawing histograms. The animations created by the teacher supported the lessonís objectives very effectively and helped to deliver a visually stimulating, productive and enjoyable lesson.
The teaching of Mathematics in context was also evident during the inspection. In order to explore the idea of compound interest, a higher-level Junior Certificate class was presented with a number of investment options and was asked to identify the one that provided the best rate of return. The resources, prepared in advance by the teacher, were beautifully presented and served to engage and challenge the students. The interactions between the teacher and students contributed to an atmosphere of mutual respect where achieving the lessonís objective remained in focus throughout.
Positive student behaviour and engagement were evident in almost all of the lessons visited during the inspection. Where positive student engagement and behaviour were observed they were achieved through effective teacher questioning, appropriate seating arrangements and the deployment of student-centred teaching methods. It is important that the good practice employed in so many of the lessons be adopted by all members of the mathematics team, and that the highest standards of behaviour and engagement are expected and realised in all classes, irrespective of their level.
The studentsí written work examined during the inspection was of a very good quality. Furthermore, their responses to teacher questioning and their confidence when interacting with the inspector offered ample evidence of the quality of studentsí learning. Very good practice in sharing learning outcomes was manifest from the practice of discussing alternative solutions and approaches to problems encountered by students in class or while doing homework. Analysis of the uptake rates and student attainments in the state examinations provided further evidence of the high quality of learning.
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. A homework policy is in place and is being implemented. The schoolís parent handbook outlines the practice regarding the assignment and correction of homework. It also specifies the contribution parents can make in encouraging compliance with the schoolís homework policy, and in assisting students in completing their homework in a satisfactory manner. Good practice was also evident in the consistent and effective use of the studentsí journal in recording homework assignments and in alerting parents to any issues that may arise.
Excellent practice was in evidence in a number of instances concerning the monitoring, amendment and annotation of studentsí homework. In such cases, the studentsí homework copies contained positive teacher comments and suggestions as to the correct procedures to be followed in solving problems. Students were also exhorted to greater effort when the need arose. It is recommended that all members of the mathematics team adhere to this practice and that the schoolís homework policy be amended to include assessment for learning as one of its key assessment vehicles.
Non-examination classes have formal examinations at Christmas and just prior to the summer holidays. Students taking the same levels sit common papers, which are corrected using common and agreed marking schemes.† Examination classes sit formal examinations in November and again at Christmas and the mock examinations are held early in the second term. Students in receipt of reasonable accommodation in the state examinations are also provided with appropriate facilities and support during house examinations.
Reports are issued to parents after each formal assessment and ongoing communication occurs through the use of the student journal, parent-teacher meetings, the parentsí handbook and the schoolís excellent website. Each class group has one parent-teacher meeting per year.
In addition to the mathematics challenge presented to the incoming students at the open night, positive attitudes towards Mathematics are promoted in a number of ways. Maths Week is promoted enthusiastically each year, challenging mathematics problems are posted in the school at different times during the year and students are facilitated in participating in the prism competition and the Mathematics Olympiad. Close contact is also maintained with the CTYI in DCU.
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 †March 2009