An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
REPORT
Saint Mary’s College
Knockbeg, County Carlow
Roll number: 61130H
Date of inspection: 12 December 2006
Date of issue of report: 21 June 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. Mary’s 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 and subject teachers. 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.
Subject provision and whole school support
St.Mary’s College is a single sex all boys’ school which offers the Junior Certificate, optional Transition Year, Leaving Certificate Vocational Programme and Leaving Certificate to its 379 students. The school has a large catchment area and has approximately one hundred boarders. The school has forty-five class periods per week and classes are either thirty-five or forty minutes in duration.
The Mathematics department comprises eight teachers. In addition, a higher diploma teacher shares in the teaching of some Mathematics classes. Teachers generally retain the same class grouping from year to year within cycles. At junior cycle the teaching of levels is rotated among Mathematics teachers. However at senior cycle the practice has developed that one teacher generally teaches higher-level Mathematics. It is planned that in future at senior cycle the rotation of the teaching of higher level among Mathematics teachers will occur. This is desirable as it will further enhance the current subject expertise while ensuring that no one person is associated with the teaching of a level.
First-year students are assigned alphabetically into one of three mixed-ability class groupings. In second year, students are reassigned for Mathematics and are generally divided into two higher-level and one ordinary-level class groupings. In fifth and sixth year generally one higher and two ordinary-level class groupings are arranged.
Time allocated to Mathematics varies. First, fifth and sixth-year class groupings each have five Mathematics class periods per week. Transition Year students have three class periods and second and third-year students have four Mathematics class periods per week. In addition, some second and third-year students are timetabled for four class periods per week of ‘extra’ Mathematics. This results in some students having two teachers for Mathematics and inequity in terms of class period provision. This issue was raised with previous management in a whole school evaluation and present management is currently addressing the matter. Time allocated to first-year Mathematics has increased from four to five class periods per week. It was also reported that over the next two years all junior cycle class groupings will have five class periods of Mathematics per week, thus the ‘extra’ Mathematics classes as they currently exist will be phased out, which is commendable.
Two of the four class periods assigned to second-year Mathematics are timetabled as a double period one day of the week so that students have no Mathematics on two days of the week. It is recommended that a review of timetabling should be undertaken to ensure that Mathematics classes are distributed more evenly throughout the school week.
Teachers are facilitated in attending inservice pertaining to Mathematics. Current resources available for the teaching of Mathematics include overhead projectors and some access to Information and Communication Technology (ICT). To further enhance current resources, management intends introducing a new system for requisitioning resources in the near future. This is commendable and it is therefore timely that teachers should develop and acquire a prioritised list of resources for the teaching of Mathematics.
Students are given opportunities to participate in co-curricular activities such as competing in the sixth-year TeamMath quiz and the first-year Mathematics competition arranged by the Irish Mathematics Teachers Association (IMTA). Some students have also been invited to the Irish Mathematical Olympiads. Participation by students in such competitions is commendable as it presents opportunities for students to engage with Mathematics in different settings.
Prior to entry to the school, first-year students take an assessment, an open day is convened and primary schools are visited. A profile of each student is gathered and this helps in ascertaining students’ numeracy needs. In so far as is possible numeracy support is provided at a time when students have an exemption in Irish or during one of a student’s ‘extra’ Mathematics class.
Planning and preparation
School development planning is ongoing. Current work involves developing a homework policy for the school.
Mathematics teachers have a minimum of two formal meetings per year with many other informal meetings taking place on a needs basis. The Mathematics department has two coordinators, one for junior cycle and one for senior cycle. The department records minutes of formal meetings, which is good practice. Issues discussed include class arrangements, feedback from inservice and an agreed agenda for future meetings.
The Mathematics department has collaborated and developed a long-term plan for Mathematics in the school. In its current format the yearly plans for junior and senior cycles are presented as individual documents. Each plan includes the aims and objectives for the subject and a yearly programme of study with suggested timescales for each topic. There is evidence that teachers have reviewed and refined the yearly plan for senior cycle, which is commendable practice. Such planning has allowed teachers to share best practice. In addition the planning has allowed for common assessments to be used among teachers. In future planning, consideration could be given to combining the junior and senior plans into one plan for Mathematics to ensure continuity and, as is the current practice, regular reviews and updates should continue.
The Transition Year plan is generally based on the Leaving Certificate syllabus. However, although not observed, it was reported that other topics form part of the Mathematics Transition Year plan. It is therefore recommended that the Mathematics department review the Transition Year plan for the department to ensure that all topics are included while ensuring that there is a clear distinction between Leaving Certificate material and the Transition Year Mathematics programme.
Individual planning for lessons was good and many teachers had developed additional materials for use in lessons. Supplementary materials and resources are centrally located and can be accessed by all teachers within the department.
Teaching and learning
Topics observed included linear programming, trigonometry and arithmetic and were appropriate to syllabus requirements and student level. Teachers presented lessons in a confident and purposeful manner. Time was used effectively and steady progress was made in all lessons due to good preparation.
Terminology used by teachers during lessons was very good. Effective linkages were made between topics and sections of the syllabus which reinforced the concept of Mathematics being an integrated programme rather than a range of topics being taught in isolation. In this way students engaged with their learning.
In general, teaching was of a high standard. The predominant teaching methodology used was traditional whole-class teaching. This method includes teachers demonstrating a method and students typically practising this by completing a series of exercises. It is recommended that a greater range of methodologies be used in the teaching of Mathematics thus ensuring that the preferred learning styles of all students are catered for.
In many lessons a range of questioning strategies was used. Generally, individual questioning of students was used to good effect and took the form of recall type questions. This allowed for the initial establishment of student understanding and for making connections with previous lessons. In addition, best practice observed in some lessons included the use of higher-order questioning. This ensured that students developed secure understanding of Mathematics and competency in the subject. As this was not always the practice it is recommended that a varied range of questioning strategies be used in all lessons to ensure that all students participate.
Textbooks and examination papers were used to good effect in lessons observed. In addition the use of differentiated worksheets encouraged students to achieve at a level appropriate to their needs while extending and challenging their understanding in Mathematics.
Teachers had developed a good rapport with their students and interactions between teacher and students were positive. Classroom management was appropriate and ensured that all students were encouraged to strive to achieve and to attempt all work assigned. Teachers generally circulated the classroom to assist students and provide necessary advice. However, in some lessons this practice should be used more frequently to ensure that students are given opportunities to become participants in their own learning.
There were no mathematical posters or evidence of students’ displays in classrooms. It is therefore recommended that teachers collaborate to develop materials in this area, as this will enhance the learning environment for students while providing teachers with an opportunity to use such displays as a resource in lessons.
Students answered questions capably and often used appropriate mathematical terminology. Through observation of State examinations results there is evidence that student uptake in terms of levels and achievement is very good. The majority of Junior Certificate students take higher or ordinary level. Foundation level is offered on a needs basis.
Assessment
Ongoing assessment takes many forms including class questioning and end-of-topic examinations. Formal examinations take place for all year groupings excluding Transition Year students three times per year. School reports are issued following formal examinations. First, second and fifth-year students receive four school reports per year and examination year groupings receive three school reports. Transition Year students receive four progress reports per year, based on continual assessment and project work undertaken throughout the year. Parent-teacher meetings are convened for each year grouping and an awards night is arranged in May for Transition Year students and parents. Further communication is maintained if necessary by phone.
The student diary is an effective means of communication between the school and home and vice versa. For example, teachers can include comments on students’ participation and achievement on a daily basis. Parents are expected to review their son’s progress and sign this weekly record.
Management provides teacher diaries to all staff. Most, teachers record student attendance, assessment and, on occasion, daily records of work undertaken or homework assigned are recorded. However, there was evidence to suggest that not all teachers are recording students’ attendance in classes. It is suggested that this matter be addressed so that teachers are fully cognisant of the implications of student attendance and absence on their learning and progress.
Homework assigned in lessons was appropriate and provided students with an opportunity to develop mathematical concepts engaged with during the lesson. The monitoring of students’ work varied from teacher to teacher. Management reported that work on the area of formative assessment would be undertaken in the near furture. It is recommended that written feedback should be used in all assessment of students’ copies thus providing students with a clear indication of how to improve and learn from their mistakes.
Summary of main findings and recommendations
The following are the main strengths identified in the evaluation:
· The Mathematics department has a minimum of two formal meetings per year. Records of meetings are kept. Mathematics teachers have collaborated and developed a common plan for junior and senior cycle programmes.
· In general, teaching was of a high standard with lessons presented in a confident and purposeful manner. Good linkages were made between topics and sections of the syllabuses.
· Student participation and achievement in state examinations is very good.
· Teachers had good rapport with their students and good classroom management skills. They encourage students to strive to achieve in their work.
· Communication between parents and school is good and it is maintained in a variety of ways.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· Work on the timetabling of Mathematics should be continued to ensure that time allocated to second and third-year classes is increased. This work should also facilitate a more even distribution of Mathematics class periods throughout the week.
· The Transition Year Mathematics programme should be reviewed.
· A greater range of methodologies should be used in lessons.
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.
Appendix
School Response to the Report
Submitted by the Board of Management
Area 1 Observations on the content of the inspection report
In relation to the findings of the report we are happy to note the acknowledgement of our students’ results in state examinations and the work done by staff towards achieving this. We are also happy to note that the good relationship between teachers and students was commented upon as well as communications between parents and school.
Area 2 Follow-up actions planned or undertaken since the completion of the inspection
activity to implement the findings and recommendations of the inspection.
In September 2007 1st and 2nd year classes will have 5 periods of Maths per week and from September 2008 the previous practice of having 4 periods per week will be phased out entirely for all Junior cycle classes. The T.Y. programme is being reviewed and staff members have already begun analysing Formative Assessment as an additional methodology.