An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
Firhouse Community College
Firhouse, Tallaght, Dublin 24
Roll number: 70140L
Date of inspection: 11 May 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Firhouse 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 and deputy principal. The board of management of the school was given an opportunity to comment in writing on the findings and recommendations of the report, and the response of the board will be found in the appendix of this report.
The systems in place to facilitate the transfer of students to Firhouse Community College and for assessing their mathematical capabilities are very good. Students who enrol in the college are provided with a wide range of supports to ensure that they feel at home in the school and are familiar with the additional demands they will encounter as second-level students.
All incoming students sit appropriate standardised tests prior to entry to the school. Once the results of these tests have been analysed, and following consultation with the sixth-class teachers in the feeder primary schools, mixed-ability mathematics classes are formed. Mathematics classes are mixed ability throughout first year and follow a common programme in Mathematics. In order to ensure that the common programme followed in first-year addresses the identified needs of the students, it is advised that all incoming students sit a competency test in Mathematics and that the outcomes are analysed and used to inform the content of the programme. Furthermore, the duration of this programme should be reviewed with the intention of completing it in the first term.
Mathematics classes are set in second and third year. The composition of the mathematics classes formed at the end of first year is determined by student performance in a series of common assessments provided throughout the year. This is very good practice. In order to provide additional time to tackle the junior cycle programme in Mathematics, consideration should be given to setting the classes from January of first year upon completion of the common programme.
Timetabling provision for Mathematics in junior cycle is in need of review. All junior cycle classes, with the exception of those following higher level in third year, are provided with four periods of Mathematics per week. Students taking higher level in third year have five periods of Mathematics per week. While it is acknowledged that all classes are forty-five minutes long, the provision for Mathematics is less than ideal. The distribution of classes throughout the week in second and third year is poor. Except in third year at higher level, all students are provided with one double period and two single periods per week. It is recommended that the number of mathematics classes in second and third year be increased and that the provision of double classes be avoided, particularly in situations where there are just four periods per week.
Timetabling provision for Mathematics in senior cycle is good. Upon completion of the junior cycle students enter transition year (TY) or opt for the Leaving Certificate Applied programme (LCA). There are three periods of Mathematics per week in TY and five periods per week in fifth and sixth year. Students following LCA are provided with four periods of Mathematical Applications per week.
Arrangements for providing students with access to the most appropriate level of Mathematics and for facilitating them to change level are very good.† The school is a participant in the Junior Certificate Schools Programme (JCSP) and one JCSP class is formed in first, second and third year. These classes are taught Mathematics by teachers with expertise in special educational needs, are small in size and follow an adapted curriculum. The remaining mathematics classes in each year are timetabled concurrently with the JCSP classes. Concurrent timetabling of mathematics classes is also a feature of the timetable in senior cycle. This is very good practice as it enables students move between classes if the need arises and ensures that all students can access higher-level Mathematics if appropriate.
Procedures for identifying and supporting students with special educational needs or in need of learning support are comprehensive, student centred and timely. Following the analysis of assessment tests, the parents of incoming students whose performance gave cause for concern are contacted and invited to meet with the learning-support teacher and the year head. The purpose of this meeting is to access existing completed psychological assessments, facilitate any eternal assessments that may be thought necessary and to agree the most appropriate support model to be implemented. Additional support in Mathematics is provided through the formation of the JCSP classes and through small-group withdrawal from subjects from which the students are exempt. In some instances targeted individual withdrawal also occurs.
The mathematics department comprises nine teachers all of whom have an appropriate qualification in Mathematics. Teachers are assigned to classes and levels by rotation, which serves to develop capacity within the department and to familiarise the members of the department with the issues involved in delivering the different syllabuses. Teachers retain the same class group from second to third year and from fifth to sixth year. This facilitates consistency in curriculum delivery and supports long-term planning and is very good practice.
The mathematics department is very well resourced. The school has been proactive in developing its information and communication technologies (ICT) infrastructure and mathematics classes have access to the schoolís two computer rooms and to a laptop and data projector. A large variety of resources to facilitate group and pair work and to engage the students actively in their own learning are also available. The available resources are listed in the subject department plan for Mathematics and are stored centrally. In order to build on the very good work in sourcing and procuring resources and to enhance the integration of ICT in lesson delivery, it is recommended that a member of the department be chosen to identify suitable ICT resources, to propose strategies for their integration into teaching and learning and to source appropriate training. The second level support service www.slss.ie is available to assist in this work.
Management actively supports the continuing professional development (CPD) of the staff of the school. The members of the mathematics department have attended a number of relevant in-service courses and two whole-school training programmes of particular relevance to teachers of Mathematics have been delivered in the last two years. The details of the CPD courses attended by members of the department are contained in the subject department plan for Mathematics. Newly appointed teachers attend an induction programme provided by Co. Dublin VEC and a member of the department is appointed to act as mentor to them in their first year in the school.
Subject department planning is well established in the school. Responsibility for co-ordinating the activities of the mathematics department is shared between two of the teachers. The co-ordinators are appointed by rotation with each pair remaining in place for one year. Regular meetings are held, the minutes of which are kept in the subject department plan. Subject development planning in Mathematics is informed by ongoing analysis of the studentsí performance in the certificate and in-house examinations. This progressive approach to subject planning is very good practice.
A subject development plan for Mathematics is in place. The plan includes resource lists, a comprehensive section on special educational needs, policies on homework and assessment and details regarding the composition of the mathematics classes and the deployment of teachers. The plan also includes detailed schemes of work, in the form of chapter lists, for each year and level. In order to build on the existing good practice in planning and to extend the scope and relevance of the schemes of work, it is recommended that clearly defined aims and objectives be developed and that these inform the further development of the schemes of work. It is further recommended that the new schemes of work include key learning outcomes and methodologies to be adopted in achieving them.
Separate plans for TY and LCA are in place. Both plans are in keeping with the aims and objectives of the respective programmes. The TY mathematics programme is designed to consolidate prior learning and to relate the subject to the studentsí everyday experiences. The TY plan for Mathematics details a number of innovative approaches to curriculum delivery. For example, each TY student is expected to carry out a significant assignment as part of the mathematics programme and is supported in this work by the provision of a project brief, a description of the assessment criteria and suggestions as to how the assignment might be successfully completed. This structured approach to promoting and supporting research and project realisation is very good practice.
Individual teacher planning is very good. Almost all of the teachers made written planning documentation available to the inspector and it was evident that a great deal of care had been taken in matching the lesson content and teaching methods to the needs and aptitudes of the students. Planning for the use of resources in lesson delivery is underway and in a number of instances very creative use of teacher-produced materials was in evidence. It is recommended that the integration of resources, including ICT, in teaching and learning in Mathematics be adopted as a targeted area for development in both individual and subject department planning.
The lessons observed during the inspection were well prepared. The teachers were knowledgeable and taught with enthusiasm. The lessons proceeded at a suitable pace and were well structured. In one instance, the lessonís intended outcomes were outlined at the beginning of the lesson and provided the focus for a review of the lesson just prior to its conclusion. This very good practice should be adopted as standard across the department.
Teacher exposition at the board followed by student activity carried out under the supervision of the teacher was the primary teaching method in evidence during the inspection. The textbook was widely used as the primary teaching and learning resource. There was very good insistence on the correct use of procedure in carrying out calculations and in solving problems. The teachers carefully explained the theory underlying the work at hand and as a result the studentsí understanding of the material was greatly enhanced. The existing practice would be further improved by utilising a wider range of teaching methods, particularly the use resources to facilitate group and pair work and by the appropriate integration of ICT.
A lesson introducing sets and set notation was greatly enhanced by the use of pair work, supported by resources produced in advance of the lesson by the teacher. The teacher distributed an envelope containing numbered squares to each pair of students. The students then used set notation to describe the contents of the envelope. The overhead projector was used to record the outcomes of the studentsí deliberations and to provide a focus for ensuing discussions. The students proceeded to create Venn diagrams and to investigate the common set operations. Skilful teacher questioning ensured that the students reflected on the outcomes of their deliberations and could defend any conclusions they had drawn.
Differentiated worksheets and revision handouts were combined very effectively to review simultaneous equations and to investigate how such equations are applied in solving real-life problems. The use of the worksheets allowed the teacher to move around the classroom to support individual students when the need arose and to identify any questions that were proving particularly problematic. In such instances, the teacher returned to the marker board and discussed with the entire class how the questions should be tackled. This meant that any difficulties encountered during the lesson were addressed immediately and that any novel approaches to problem solving adopted by the students could be shared and analysed.
Classroom management is very good. Teacher questioning served to reinforce the lessonsí objectives and to include as many students as possible in the lesson. The students were very engaged and contributed to the lessons by proposing solutions to problems and by asking insightful questions. The rooms were decorated with posters, produced by the teachers and students, which helped to generate an atmosphere conducive to teaching and learning Mathematics.
The quality of student learning is good. The students carried out the work assigned to them during class with confidence and the quality of their written work in their homework copybooks is very good. The percentage of students taking higher-level and ordinary-level Mathematics in the state examinations is in line with national norms and the performance of the student in these examinations is also very satisfactory.
Practices regarding the assignment and correction of homework are very good. An extensive homework policy is in place and, in almost all cases, is being implemented assiduously. The homework policy contains details of how Assessment for Learning (AfL) should be employed in the ongoing assessment of studentsí work and it was evident from the studentsí homework copybooks that the majority of teachers of Mathematics have adopted AfL in the correction of homework. In the instances where AfL was used, the quality of the written feedback provided to the students was of the very highest quality. It is advised that all members of the mathematics department adopt this very good practice when correcting and monitoring homework.
The subject department plan for Mathematics details the assessment practices followed by the members of the department. All students sit class tests upon completion of each topic, and formal examinations are held in November and just prior to the summer holidays. Common papers with agreed marking schemes are provided where appropriate and the examination papers and marking schemes are differentiated to take account of the needs of the students sitting the examinations. This is very good practice. Interim classroom-based examinations take place on a regular basis and the studentsí performance in these examinations informs an interim report that issues to parents in March each year. AfL practices are employed in correcting formal and informal examinations. Student performance is also assessed through teacher questioning in class, through the use of worksheets and project work. This progressive and comprehensive approach to assessing student performance in Mathematics is commended.
Practices pertaining to communication with parents are very good. Regular contact is maintained though the student diary and telephone calls to the home. Written reports also issue to parents three times per year. Each class group has one parent-teacher meeting per year and additional time is made available each November for parents to meet with the appropriate class tutor.
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 principal and deputy principal, at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published, December 2009
Submitted by the Board of Management
Area 1†† Observations on the content of the inspection report†† ††
The Board of Management would like to thank the Inspector for the professional and courteous way he conducted the Inspection.
The Board welcomes the very positive report and believes that it recognises and affirms the very fine work of the teachers in the Mathematics Department.
It is the policy of the teachers and management in this College to constantly reflect on our practices and all recommendations will be addressed in due course.