An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection in Mathematics
Castlecomer Road, Kilkenny
Roll number: 61570M
Date of inspection: 8 February 2006
Date of issue of report: 22 June 2006
This Subject Inspection report
This report has been written following a subject inspection in Kilkenny 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 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, 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.
Founded in 1538, Kilkenny College is a co-educational boarding and day school that offers the Junior Certificate, compulsory Transition Year, the Leaving Certificate Vocational Programme and Leaving Certificate to its 805 students.
The school operates a fortnightly cycled timetable with nine class periods per day of either a thirty-five or forty-minute duration. Ten teachers teach Mathematics in the school. The teaching of programmes and levels is allocated on a rotating basis among all Mathematics teachers. This is good practice as it develops the expertise within the subject department. In general, teachers retain the same class groupings through each cycle. There is good allocation of teachers to Mathematics. For example one extra teacher is assigned to first, second and Transition Year Mathematics class groupings with two extra teachers assigned to third, fifth and sixth-year class groupings. In this respect, management is to be commended for its deployment of Mathematics teachers at both junior and senior cycles, which facilitates the teaching of Mathematics in smaller class groupings.
On entry to Kilkenny College, six class groupings are formed each year. Initially, Mathematics students are assigned to mixed-ability classes. All classes follow a common programme of work for approximately the first eight weeks. First-year students then sit a common assessment and are arranged into set Mathematics classes. In general, at junior cycle three higher-level, three ordinary-level and one foundation-level class groups are formed. At Leaving Certificate, two higher-level, five ordinary and one foundation-level class groups are formed.
Time allocated to Mathematics is good. The concurrent timetabling of Mathematics allows students the opportunity to move between levels and the flexibility to study Mathematics at a level appropriate to their ability. Generally, there is a good distribution of Mathematics classes throughout the two week timetable. However, during week one of the two-week timetable third- year Mathematics classes are timetabled for two double periods. It is recommended that care be taken to avoid the re-occurrence of this in future years insofar as is possible.
The Transition Year programme is very broad due to the diverse curriculum available to students. It was reported that at times difficulties arise in the continuity in the teaching of Mathematics in Transition Year because of scheduling of other activities during Mathematics time for some students. It is recommended, therefore, that the scheduling of such activities should, insofar as is possible, take place at a time other than during Mathematics classes in order to minimise disturbance to teaching and learning.
The school has developed a very good support system for newly appointed and substitute teachers. For example, substitute teachers work-shadow the teachers that they will replace for two or three days and are provided with information regarding customs and practices of the subject department. Furthermore, ongoing support is available from all members of the Mathematics department. Such good practice is to be commended.
Teachers are facilitated to attend inservice and it was reported that some Mathematics teachers would soon attend inservice offered through a local education centre. Furthermore, it was reported that some teachers are or have been members of their subject association.
An annual budget is available for Mathematics and it was reported by teachers that any reasonable request for resources has been provided. Recent purchases included overhead projector, calculators and geometry sets. It was reported that the Mathematics department has not made many requests recently for resources. It is recommended, therefore, that the department collaborate and develop a list of appropriate teaching and learning resources that could be retained in a central location. Furthermore, consideration should be given to developing the resources available for Mathematics in the school library.
There is evidence to suggest that the Mathematics department works as a cohesive team collaborating on issues that arise. The Mathematics team has a subject convenor who facilitates subject meetings and informs teachers about mathematical issues. Staff members are facilitated by management to meet formally approximately three times per year. Such support for Mathematics teachers is to be commended. Further informal meetings take place as needs arise. Minutes of formal meetings are retained and issues discussed include curriculum planning. Agendas for further meetings are documented. This is good practice as it provides a focus and direction for these meetings.
While work on school development planning is ongoing, the Mathematics department is working on a plan for Mathematics. Currently, teachers have developed a number of draft “Custom and Practice” documents. These documents detail the general organisation details of the department and the system of allocating students to Mathematics classes and levels. Teachers have developed plans for Mathematics. However, plans vary in terms of content and detail. It is recommended, therefore, in the context of school development planning, that the Mathematics department collaborates to develop one common long-term plan for the department. In addition to the existing “Custom and Practice” documents this plan should outline the aims, objectives and the sections of the syllabus at junior and senior cycle, and the advised areas of study under each of these sections. It should also include a list of varied methodologies and a range of resources and learning outcomes to be achieved. Furthermore, consideration should be given to planning for the integration of Information and Communication Technology (ICT) into Mathematics. Such collaboration should allow for common assessments that exist currently for some year groupings to be extended to other years. The development of a common plan for Mathematics will give teachers an opportunity to identify and share good practice. The web site of the School Development Planning Initiative (SDPI) www.sdpi.ie has useful resource material that may assist in this regard.
The Transition Year programme is being updated at present. However, most of the programme is based on the Leaving Certificate syllabus. Circular M1/00 outlines that the Transition Year programme should not be seen as an opportunity to have a three-year Leaving Certificate programme. In this context it is recommended that the Mathematics team review and update the Mathematics programme to ensure compliance with the circular and to provide students with an opportunity to learn Mathematics in a different context. Furthermore, teachers should make reference to the suggested template for module writing, which is available in the brochure Writing a Transition Year Plan. To this end a useful support is available at www.slss.ie where teachers can access resources and newsletters, that outline teaching and learning strategies, interdisciplinary links and curriculum ideas pertaining to Transition Year Mathematics.
Teachers have developed good individual short-term plans for Mathematics as evidenced by the prior preparation of material such as handouts and other supplementary materials. In general teachers develop resources individually. It is recommended that consideration be given to the development and sharing of these resources, which should be easily accessible for use by all teachers in their classes.
In the classes visited, lessons were well structured and purposeful and there was evidence of good short-term planning. Clear objectives were set for lessons and the lessons progressed at an appropriate pace with good use being made of time. Topics such as algebra, geometry, and trigonometry featured in the lessons observed while other classes worked on examination papers. In general lessons began with the teacher correcting homework from the previous day in class.
The predominant methodology observed was traditional, whole-class teaching. This involved a combination of teacher demonstrations to the full group and the students working alone on tasks while the teacher assisted individuals. Less frequently, student-centred learning was observed. This was effectively done and is to be commended. Where there was evidence of too much teacher talk students became passive. In some non-examination years there was an over emphasis on preparation for state examinations. Therefore, it is recommended that all teachers vary the methodologies used in lessons. Some examples could include investigation, consolidation activities, practical work, discussion, group work, quiz activities as outlined in the Mathematics Junior Certificate Guidelines for Teachers.
Teachers used Mathematics terminology that was appropriate to the relevant topics and students’ ability. They also made relevant connections between various sections within the syllabus. Furthermore, some teachers created links between Mathematics and real life situations. This allows students to become engaged fully and to develop a genuine interest in the topic. Such practices are commendable and should be extended to all classes.
Interaction between teacher and students generally took the form of brief answers by the students to closed questions from the teacher. Questioning focused mostly on finding the next steps to the solution to a problem or on mistakes that had arisen. There were some very good examples where teachers built on their students’ answers, exploited the learning potential of ‘wrong’ answers, or probed, checked and extended the students’ understanding, and encouraged them to explain and justify their thinking and methods. This is good practice as it helps students to consolidate their learning and maintain student engagement with the topic. It is recommended, therefore, that a varied range of questioning strategies be employed in all lessons.
Textbook and examination papers were the main resources used during lessons observed. Teachers use the textbook as a source of examples and in some lessons good use was made of handouts. In some lessons very good use was made of the overhead projector (OHP) to illustrate a variety of examples. Sometimes the whiteboard was used effectively to record key words, and important formulae were denoted through the use of different coloured markers. However, there were instances where the appropriate use of other resources would have allowed for greater student input. It is recommended that greater use be made of class aids such as differentiated worksheets, to ensure that all students are encouraged to work to the best of their abilities.
Classroom management was very good. Where necessary, instructions were given in a clear and unambiguous manner. There was a strong sense of cooperation and mutual respect which led to an atmosphere conducive to learning. Inputs from students are welcomed and encouraged, generating a comfortable, secure environment. Individual attention was given in a sympathetic and professional manner without attention being drawn to the individual.
Students demonstrated a clear understanding of concepts engaged with during the lessons in interactions with the inspector. They were able to answer questions posed to them in a confident manner and justified solutions to questions posed to them.
In some classrooms walls had displays of students mathematical work or mathematical posters. The decoration of one room by students to demonstrate the integration of a mathematical project is to be commended. It is recommended that mathematical posters or student project work be displayed in all classes.
Assessment is carried out on an ongoing basis through questioning in class and written examinations following the completion of a topic and homework. Formal assessments take place for non-examination years at Christmas and summer. Examination years have formal examinations at Christmas and ‘mock’ exams. Students who will receive reasonable accommodation during state examinations are also offered similar facilitates by the school during formal in-house examinations.
The school maintains good communication with the students’ parents. Parent-teacher meetings are convened for each year grouping. Two school reports are issued for each student during the year. Additionally, an individual school report is issued following a parental request.
Staff members are well supported through the provision of teachers’ diaries. In general, teachers retain good records of their student’s attendance and use the diaries to record student assessments.
Homework has an important role in the learning process and was assigned in all lessons observed. In most lessons homework was appropriate in terms of the quantity and relevance to the work done during the lesson. Students’ copies revealed that regular homework is assigned which is good practice. There is evidence that some teachers are monitoring students’ copies. Good practice is evident where teachers encourage students to correct and amend their work as this encourages students to develop as independent learners. This practice should be extended to all classes. Teachers should monitor students’ work regularly and include commendations and suggested areas for development.
To recognise students’ success the school organises a prize-giving day which acknowledges the academic achievements and endeavours in each subject. Students have the opportunity to participate in a range of extra-curricular activities pertaining to Mathematics. Furthermore, students participate in a variety of co-curricular activities such as the ESAT Young Scientist exhibition.
More specifically, Mathematics students have been invited to participate in Mathematics Olympiads. Additionally, a number of students have participated in Scolastic Aptitude Tests (SAT) organised by the Irish Centre for Talented Youth (CTYI). Students have also participated in the Irish Mathematics Teachers’ Association Team Mathematics competition. Participation in Mathematics competitions promotes interest in the subject. Furthermore, it also allows students the opportunity to develop their interest and skills in Mathematics while experiencing Mathematics in a different learning environment. The teachers are to be commended for their promotion and encouragement of Mathematics and for their commitment through their availability to meet students after school to give extra help as needed.
Participation in Mathematics at higher level at both Junior and Leaving Certificate is high. Good practice by Mathematics teachers has been developed whereby teachers aim to keep the number of students doing foundation level to a minimum.
The following are the main strengths and areas for development identified in the evaluation:
As a means of building on these strengths and to address areas for development, the following recommendations are made:
Post-evaluation meetings were held with the principal, deputy principal and with the teachers of Mathematics at the conclusion of the evaluation at which the draft findings and recommendations of the evaluation were presented and discussed.