An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
REPORT
St Brendan’s College, Woodbrook,
Bray, County Wicklow
Roll number: 61790D
Date of inspection: 22 January 2007
Date of issue of report: 6 December 2007
Subject provision and whole school support
Summary of main findings and recommendations
Report on the Quality of Learning and Teaching in Mathematics
Subject inspection report
This report has been written following a subject inspection in St Brendan’s College conducted as part of a whole school evaluation. It presents the findings of an evaluation of the quality of teaching and learning in St Brendan’s College and makes recommendations for the further development of the teaching of this subject in the school. The evaluation was conducted over one day 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.
Subject provision and whole school support
St Brendan’s College is an all boys’ school that offers the Junior Certificate, Transition Year, Leaving Certificate Vocational Programme and Leaving Certificate to its 392 students.
The Mathematics department comprises five teachers and, in addition, a higher diploma teacher shares in the teaching of some Mathematics classes. At junior cycle the teaching of levels and programmes is rotated among all teachers. Two teachers rotate the teaching of higher-level at senior cycle. This ensures that subject expertise is developed and maintained within the Mathematics department. Teachers generally retain the same class grouping from second to third year and from fifth to sixth year, which is good practice. Management is commended for the allocation of extra teachers to Mathematics classes in senior cycle.
On entry to the school students are assigned to one of three mixed-ability, first-year classes. In second year students are reassigned into class groupings depending on their ability. This results in one higher and two ordinary-level class groupings of Mathematics being formed. However, some students are being taught higher level in an ordinary-level class setting. As this is not an ideal situation for students, it is recommended that a review of the practice of assigning students to class grouping in second year be undertaken to ensure that all students have access to an appropriate level. In fifth and sixth year generally one higher and two ordinary-level groupings are arranged for Mathematics.
Time allocated to Mathematics is good with each junior and senior cycle class allocated five class periods per week. Transition Year students have four class periods per week. In addition, some Transition Year students have a fifth Mathematics class period during the week, resulting in these students having two Mathematics teachers, which is not good practice as it disrupts continuity in learning. It is recommended that the rationale underpinning such timetabling be reviewed. In general, Mathematics classes are distributed evenly throughout the week. However, one class grouping in third year has two of its five Mathematics class periods on one day of the week with none on another day. It is recommended that a review of such timetabling be undertaken to allow for daily contact with the subject for all year groupings.
Mathematics classes from Transition Year onwards are concurrently timetabled. This facilitates students in studying Mathematics at a level appropriate to their ability, while permitting movement between classes of different levels. During a discussion with management it was reported that attempts to provide concurrent timetabling of Mathematics at junior cycle have not been possible. However it is recommended that, in conjunction with a review of the practice of student assignment to class groups in second year, renewed efforts be made to concurrently timetable Mathematics classes at junior cycle, which would facilitate greater student access to an appropriate level while allowing movement between levels.
Teachers are facilitated to attend inservice pertaining to Mathematics. In this regard opportunities to attend upcoming inservice in Mathematics should be availed of by teachers. Reasonable requests for resources for the teaching of Mathematics are granted. In general resources are retained by individual teachers within their own classrooms. It is therefore recommended that Mathematics teachers collaborate to document the current resources available for the teaching of Mathematics. This collaboration should also allow for the creation of a prioritised list of resource requirements for the department. Furthermore, consideration should be given to maintaining a shared resource bank for access by all teachers.
Students have, in the past, been invited to participate in the Irish Mathematics Olympiads, which provides opportunities to encounter Mathematics in different learning contexts. Teachers are commended for their availability to meet students and provide extra help in Mathematics on a regular basis.
The reported practice of withdrawing students from Mathematics for numeracy support should be reviewed.
Planning and preparation
Teachers have approximately three formal planning meetings per year with many more informal meetings taking place on a needs basis. Minutes of meetings are not retained but it was reported that teachers’ discussions during these meetings include agreement on common areas of the syllabus to be taught for each year grouping. It is recommended that records of formal meetings be retained, as these will provide a valuable record of evidence of issues discussed and decisions taken.
Currently there is no convenor of Mathematics. Such a position would allow all teachers within the department to take responsibility for the coordination of the subject. Hence, it is recommended that the Mathematics department appoint a convenor on a rotational basis.
Subject department planning has recently begun and the Mathematics department has made some progress in the development of a long-term plan for the department. However, to further progress planning in Mathematics, it is recommended that the long-term plan should outline the sections of the syllabus at junior and senior cycle and the advised areas of study under each of these sections. The plan should also include a range of methodologies, resources and learning outcomes and planning for the integration of Information and Communication Technology (ICT) for Mathematics. Such collaborative planning should provide a guide to teachers’ day-to-day work in the classroom and promote continuity and progression in students’ learning.
Individual teachers provided an outline of the programme of work being studied by students in Transition Year. Topics encountered by students in this year include mathematical concepts from the Junior Certificate, project work and some Leaving Certificate material. Three aims for the teaching of Mathematics have been identified in the TY Mathematics programme but there is no outline of course content. It is therefore recommended that Mathematics teachers collaborate and develop a written Transition Year Mathematics plan. This programme should fully recognise the good work that is currently being undertaken by teachers in the Transition Year lessons observed. Consideration should be given to accessing “Writing the Transition Year Programme” and materials available on the website www.slss.ie.
Individual planning for lessons observed was good. For example, teachers had prepared handouts and other supplementary materials. In general, teachers develop such resources individually. Increased benefit would be derived from developing such resources more collaboratively as this would allow teachers the opportunity to identify and share good practice.
Teaching and learning
Classes generally commenced with the recording of attendance and proceeded with topics such as sequence and series, percentages and algebra. Lessons were presented in a confident and purposeful manner. In some lessons the aims and objectives of the lessons were clearly established from the outset. This is good practice and should be extended to all lessons.
Mathematical terminology used was appropriate to the relevant topics and students’ abilities and, where appropriate, teachers made connections between various sections within the syllabus. This has the advantage of allowing students to learn that Mathematics is an integrated programme rather than sections of a syllabus learnt in isolation. Furthermore, some teachers put Mathematics in context by referencing the historical facts about the Mathematics topic. This allowed students to become fully engaged and to develop a genuine interest in the topic. Such practice is commendable and should be extended to all classes.
Methodologies encountered in lessons varied. Some teachers used traditional whole-class teaching, which was a combination of the teacher demonstrating to the full class and students working alone on tasks. In other lessons the use of a group activity in the teaching of probability proved very positive for students. In another lesson investigative work was used in the preparation of Mathematics projects. Such methodologies are commendable and should be used more regularly as they encourage students to become actively involved in their own learning while catering for their preferred learning styles.
Many teachers used recall type questions in lessons observed. These were generally used to establish students’ understanding or to focus on the next steps in the solution to a problem. However, there were instances where effective and commendable use was made of higher-order questions, which involved building on students’ answers, while encouraging students to explain and justify their thinking and methods. Therefore it is recommended that a varied range of questioning strategies be used in all lessons to help consolidate the learning of students.
Textbooks and, to a lesser extent, handouts were the main resources used in lessons. In addition to such resources, consideration should be given to integrating a greater variety of resources in the teaching of Mathematics, such as the use of an overhead projector or ICT.
Classes were generally conducted in an environment of mutual respect. Teachers had good classroom management skills and used these in the event of some students becoming talkative. Many classrooms are teacher based but there were no displays of students’ mathematical work or Mathematics posters. As such displays could be used to enhance and promote the teaching of Mathematics, it is recommended that students’ work and other mathematically relevant displays should feature in classrooms.
Interactions with students during the inspection were generally positive. Many were capable of answering questions. Through observation of State examination results there is evidence that some students, particularly at Leaving Certificate ordinary level, are over ambitious in their choice of this level. It is recommended that such students should be encouraged to take a more appropriate level.
Assessment
Ongoing assessment of students is undertaken through class questioning, end-of-topic examinations and formal school examinations. Non-examination year groupings have Christmas and summer examinations and third and sixth-year classes have Christmas and ‘mock’ examinations.
Communication between home and the school is maintained with two reports issued following formal examinations and a minimum of two progress reports sent home during the school year. In addition parent-teacher meetings are convened for all year groupings. Student diaries are used primarily by students to record homework but also by parents to communicate with the school. A TY open night is arranged towards the end of the school year at which students display work completed during the year.
The standard of presentation of work was good in some classes but disappointing in others. There was evidence that teachers are monitoring homework copies and many provided oral feedback when returning copies to students. However, to ensure that students have a written reminder of areas for improvement, it is recommended that teachers include formative assessment when correcting students’ copies. This form of assessment, while providing students with guidance regarding their work, should also be used to encourage better presentation of work. Furthermore, consideration should be given to using the Transition Year open night to display students’ Mathematics copies and to apportioning some of the final Mathematics assessment grade for the presentation of students’ copies.
Management provides staff with teacher diaries, which are used to record students’ results and attendance. Many also use the diaries to record homework assigned in lessons. Through observation of teachers’ records there is evidence that some students have poor attendance. It is therefore recommended that a whole school strategy be adopted to address the absenteeism of some students. Furthermore during the course of the inspection a number of Transition Year students were absent from Mathematics lessons due to their involvement in the preparations for a school play. While acknowledging that such extra-curricular activities are an important component of the Transition Year it also raises questions about the continuity in the learning experience of Mathematics for students. It is therefore recommended that in the event of students being missing from lessons, due to school related activities, consideration should be given to the compilation of a list of such students, which should be made available in the staffroom thus ensuring that all staff are fully cognisant of students’ whereabouts.
Summary of main findings and recommendations
The following are the main strengths identified in the evaluation:
· Time allocated to Mathematics in St. Brendan’s College is good. In generally Mathematics classes are distributed evenly throughout the week.
· Teachers are given an opportunity to rotate the teaching of Mathematics levels and programmes.
· Teachers are facilitated by management to attend relevant Mathematics inservice and have opportunities to meet formally during the school year.
· Students are assessed regularly.
· Lessons were presented in a confident purposeful manner with many teachers using a range of methodologies.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· The Mathematics department should collaborate to progress work currently undertaken in the writing of a long-term plan for Mathematics. In addition the Mathematics plan for Transition Year should be updated.
· A review of the practice of assigning students to second-year classes should be undertaken.
· The timetabling of Mathematics should be reviewed to ensure that appropriate arrangements are made to facilitate students to access a level suitable to their abilities. This review should also address alternative times for the provision of numeracy support, which is currently offered on withdrawal from Mathematic classes.
· To cater for the preferred learning style of all students a greater range of methodologies should be used in lessons.
· Increased monitoring of students’ Mathematics copies should be undertaken and formative assessment should be included in copies.
· A whole-school approach should be undertaken to address the absenteeism of some students.
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.