An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
CBS Secondary School,
James Street, Kilkenny, County Kilkenny
Roll number: 61550G
Date of inspection: 17January 2007
Date of issue of report: 8 November 2007
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in CBS Secondary School, Kilkenny. 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.
CBS Secondary School, Kilkenny is an all boys’ school that offers the Junior Certificate, Transition Year, Leaving Certificate Vocational Programme and Leaving Certificate to its 641 students. The school operates a forty class period week and classes are either forty, forty-five or fifty minutes in duration.
There are ten teachers teaching Mathematics in the school. In general, management endeavours to provide teachers with the opportunity to rotate the teaching of levels and programmes. This is commendable practice as it facilitates the continued development of subject expertise within the department. Teachers generally retain a class grouping from year to year within a cycle.
On entry to the school, first-year students are assigned to one of four streamed class groupings. In the first term, some first-year students are reassigned to a different stream. It is recommended that consideration be given to a more flexible arrangement for student placement to ensure that students are not assigned too early to a particular stream. Consideration could be also given to some concurrent timetabling of Mathematics at junior cycle to ensure optimal deployment of Mathematics teachers while allowing for all students to access an appropriate level. A second teacher has been allocated to one third year class grouping to facilitate the students who wish to take higher-level Mathematics. However, in another third-year class, higher and ordinary-level Mathematics is being taught within the one class. As this is not equitable, it is recommended that consideration be given to a review of such practice. From Transition Year onwards an extra teacher is assigned to each year grouping for Mathematics and this coupled with concurrent timetabling of Mathematics at senior cycle allows students to access a level appropriate to their ability. This is good practice.
Time allocated to Mathematics is generally good. All junior cycle Mathematics class groups have four lesson periods per week and senior cycle class groups have six lesson periods per week. Transition Year students have three lesson periods per week. Mathematics periods at junior cycle are, with one exception, evenly distributed throughout the week which is good practice. While fifth-year students have six periods of Mathematics per week, Mathematics is not timetabled on one day of the week. Although acknowledging the complexities of timetabling, a more even distribution of lesson periods across the week would be desirable.
Mathematics teachers are supported by management in their continued professional development and are therefore facilitated to attend inservice. Requests for resources to support teaching and learning are made to management and it was reported that reasonable requests are granted. Mathematics resources are retained centrally for ease of teacher access. Resources available include class sets of calculators and mathematical sets. In addition, although not used during the inspection, access to Graphmatica is also available to Mathematics teachers within the Information and Communication Technology (ICT) rooms.
Students are encouraged to participate in a variety of co-curricular and extra-curricular activities in Mathematics. For example, students have been invited to participate in the Irish Mathematics Olympiads and have also entered the Irish Mathematics Teachers Association (IMTA) TeamMath table quiz. In addition, many students have competed in the Prism competition organised in conjunction with the National University of Galway. To this end teachers are commended for encouraging and supporting students in such activities which enable students to encounter Mathematics in situations outside the classroom and promote independent learning.
Management facilitates Mathematics teachers to meet formally four times per year and many informal meetings also take place on a needs basis. The position of convenor of Mathematics is rotated at each formal meeting. Minutes of formal meetings are recorded on a school-designed template. This is commendable practice. Issues discussed include feedback from teachers who have attended Mathematics inservice and discussion about State examination results. Such meetings provide teachers with an opportunity to share best practice while ensuring that teachers are kept updated with regard to current practices in Mathematics.
In its current format the long-term plan for Mathematics outlines the aims and objectives for both junior and senior cycle. These aims are those of the Department of Education and Science syllabuses. In many cases two yearly schemes of work were presented for a single year grouping which was a duplication of work. Schemes of work presented were generally textbook rather than syllabus based. It is therefore recommended that the Mathematics department collaborate to refine the current work in subject department planning and develop one succinct plan for the subject. The plan should include one programme of study for each year grouping, grounded in the relevant syllabus. In addition the plan should include planning for greater inclusion of ICT in the teaching of Mathematics. Furthermore, the aims and objectives for Mathematics should relate to the aims of the school. In addition the plan should be regularly reviewed and updated. Such planning will also allow for the extended use of common assessment and for the sharing of ideas and best practice.
The Transition Year plan aims to consolidate material from the Junior Certificate and introduce Leaving Certificate material. Topics such as ICT also feature in the plan. However, teachers reported doing other activities with students including students developing Mathematics resources such as geometry shapes for use by teachers. Furthermore, some Transition Year students assist Mathematics teachers during some learning-support classes. It is therefore recommended that the Transition Year plan be reviewed and updated to include all aspects of Mathematics that are not currently reflected in the plan.
Individual planning for lessons observed was good. Planning usually followed the long-term plan for the particular year grouping. In addition teachers had developed supplementary materials for use in their classroom.
Lessons were presented in a confident and purposeful manner. Best practice ensured that teachers stated from the outset the learning objectives for the lesson. This had the effect of focusing students on the tasks to be completed during the lesson and as such should be extended to all lessons. In most lessons time was used effectively. However, on occasion teachers proceeded with new material with insufficient time available. Therefore, greater planning should be undertaken to ensure that a realistic amount of new material is covered during each lesson while being cognisant of the level and abilities of each student cohort.
Teachers used terminology appropriate to the level and ability of students. Commendable practice observed included making links between various topics in Mathematics. This allows students to understand that Mathematics is an integrated programme rather than a series of concepts to be studied in isolation.
Teaching methodologies varied from lesson to lesson. In some lessons traditional whole-class teaching was used. This is generally characterised by the teachers presenting work on the board and the setting of work for students to practise. It is recommended, where this is the dominant teaching strategy, that a greater range of appropriate methodologies be used to ensure that the learning styles of all students are catered for. In some lessons prior preparation of materials allowed for problem solving exercises and mathematical games to be encountered by students. Such methodologies provided students with an opportunity to become active participants in their learning and develop a genuine interest in the subject. Lessons that included these methodologies were generally characterised by an appropriate balance between teacher inputs and students’ work. In another instance effective use was made of higher and lower-order questions to allow students to become fully engaged in lessons. In such lessons students had an opportunity to justify their thinking when responding to the teacher’s questions.
Teachers generally used textbooks and supplemented these with differentiated worksheets. In one instance, while homework was being corrected, effective use was made of an overhead projector (OHP) to display relevant material for students. However, on other occasions the use of an OHP would have allowed for greater accuracy in the illustration of specific mathematical graphs and reduced the duplication of work for teachers. Therefore it is recommended that a range of resources be used in all lessons.
Students were attentive and appropriately behaved during lessons observed. Teachers had a good rapport with students and, when necessary, teachers moved around during the lesson to check work and provide immediate support. Students presented as being confident and capable when answering questions and frequently used appropriate subject specific terminology, which is commendable.
Some classrooms had mathematical posters or examples of students’ work on display. In some lessons, use was made of such posters to reinforce mathematical concepts, which is commendable practice. Therefore, to enhance and promote the teaching of Mathematics, it is recommended that students’ work and other mathematically relevant displays should feature in all classrooms.
Participation rates of students at higher and ordinary level in recent State examinations are appropriate. To address an emerging issue of a small cohort of students who are not achieving at ordinary-level Leaving Certificate Mathematics, management is commended for the allocation of an extra teacher to create a small class group.
Student assessment takes many forms including class questioning, end-of-topic examinations and formal school examinations. Non-examination year groupings sit examinations at Christmas and summer while examination year groupings have Christmas and ‘mock’ examinations. In addition first-year students have a formal examination in November to facilitate the aforementioned reassignment of some students into different class groupings. School reports are issued following formal assessments and parent-teacher meetings are convened for each year grouping.
Homework has an important role in the learning process and was assigned in all lessons observed. Through observation of students’ Mathematics copies and some of their end-of-topic assessments there is evidence that many teachers provide formative assessment to their students. This is good practice as it provides students with a constant reminder of suggested areas for improvement and as such should be used more often by teachers.
Management provides all staff with a teacher diary. Teachers retain good records of students’ attendance and assessment results and, in addition, many teachers use them to record daily homework assigned. Most students record their homework in their diaries and parents use the diaries as a means of communication with the school. However, there was evidence that some students are not as diligent as others in recording their assigned homework and consequently consideration should be given to a review of the use of the diary.
The following are the main strengths identified in the evaluation:
· In general, there is good whole school support for Mathematics as shown by the deployment of extra teachers to the subject, the facilitation of teachers’ attendance at in-service courses and the scheduling of formal department meetings on four occasions during the school year.
· Lessons were presented in a confident and purposeful manner and the content of lessons was appropriate to the range of abilities of the students. Homework was assigned in all of the lessons observed and lessons were conducted in a positive atmosphere.
· Students’ progress is regularly assessed and, in general, students were confident and capable of answering the questions put to them during the visit.
· Individual planning for lessons was good. Teachers had developed supplementary material for use in lessons observed.
· In some lessons a good range of methodologies was used and, in addition, questioning strategies were appropriate.
· Teachers are commended for their encouragement of students to participate in extra and co-curricular activities.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· A greater range of methodologies should be used in lessons.
· A review of the long-term plan for Mathematics should be undertaken to develop one succinct Mathematics plan for the department. In addition the written Transition Year Mathematics plan should be updated to fully reflect practices that are not currently acknowledged.
· Students’ Mathematics copies should include more formative assessment which should provide students with suggested areas for improvement.
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.