An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Saint Mogue’s College
Bawnboy, County Cavan
Roll number: 70360C
Date of inspection: 12 December 2006
Date of issue of report: 21 June 2007
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in St. Mogue’s College, Bawnboy. 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 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 to the 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.
St. Mogue’s College is in a period of transition, with the appointment of a new principal in September 2006. Provision for Mathematics, as for all other subjects, in this the 2006-2007 school year, was determined prior to the changeover at senior management level. It is noted that the current timetabling arrangements in the school fall short of what is required to ensure that all students have access to twenty eight class-contact hours. School management has indicated it will be addressing this matter and making adjustment to the timetable for future years or seeking additional resources to address the matter if this adjustment would compromise essential course provision.
The time allocation to Mathematics, at five thirty-five-minute periods per week for each year group, is broadly in line with syllabus requirements. Valuable time, however, could be gained if it was decided to organise the school’s timetable in forty-minute periods. Students studying the subject at higher level, in particular, could have the pressure of course coverage reduced if this were the case. Alternatively, it was suggested by teachers that Leaving Certificate higher-level classes might have an allocation of six thirty-five-minute periods each week.
The organisation of class time sees many students having class contact with the subject on only four days. It is recommended that, in preparing the timetable for the coming school year, efforts be made to schedule Mathematics on each of the five days of the week, enabling teachers and students to make best use of the time available.
Concurrent timetabling of mathematics classes occurs mainly in groups of two; first and fourth years have one set of two classes concurrently timetabled and a class standing alone. Third and fifth years have two sets of two classes concurrently timetabled, and the two second-year class groups run concurrently. This relatively complex arrangement has been undertaken to try to ensure access for all students to the level of the subject most suited to their abilities and interests, and is commended. However, a possible alternative—stand-alone classes in first year followed by across-the-board concurrent scheduling from second year onwards—might be considered by teachers and management in their search for more effective and efficient arrangements.
The allocation of additional teachers to Mathematics is evidence of the school’s commitment to the subject; one additional teacher has been scheduled in each of first, second and fourth years, and two additional teachers in third and fifth years. The school has a strong commitment to students identified as finding the subject particularly challenging, with the creation of small, supportive class groupings and the provision of learning support. In addition, teachers are commended for their dedication to meeting the needs of all students with the offer of additional lessons, outside of timetabled hours, to ensure course completion or reinforce topics or concepts.
Teachers are assigned to specific mathematics class groups by school management, in consultation with the relevant teachers. It is normal practice for continuity to be maintained, in so far as possible, within junior and senior cycles. Currently one teacher takes responsibility for Leaving Certificate higher level.
School management facilitates teacher attendance at in-career development courses. It is recommended that contact be made with the Mathematics Support Service and the Irish Mathematics Teachers’ Association in order to keep up-to-date on courses available and trends and developments in mathematics education.
Resources available to support the teaching and learning of Mathematics in St. Mogue’s College include geometry equipment, three-dimensional shapes, sets rings, trundle wheel and quizzes. The mathematics team are encouraged to become proactive in identifying and seeking further resources to be used with classes across the range of abilities and interests. The possibility of the allocation of a subject budget, under consideration with school management, may help to define and clarify this process.
Mathematics is ably coordinated by a senior teacher, in a voluntary capacity, and the small mathematics team works closely together as a cohesive group. Team meetings are held approximately once per term. Although meetings are currently organised on an informal basis, it is commendable that records are made and maintained.
Significant progress has been made on the subject department plan. Aims and objectives for the teaching of the subject, reports of meetings over the past two years, and agreed programmes of work for each year group and level have been documented. Planning would be enhanced with the inclusion of additional elements such as a long-term vision for the development of the subject, cross-curricular links and strategies for the promotion of Mathematics within the school. The team might also consider agreeing policies and practices on generic issues, for example, calculator use among students.
All teachers made individual planning and preparation materials available during the inspection. These included lesson plans, revision programmes, student worksheets and handouts, examination-related materials and a commendable example of extensive teacher notes. Teachers are congratulated on this level of preparation for their teaching.
In the four classrooms visited, students showed a positive attitude towards Mathematics; they were attentive, interested and engaged in their work. Mathematics posters were used in classrooms to create a stimulating setting in which to study the subject and teachers are encouraged to continue to enhance the learning environment in this way.
Teachers’ classroom management was appropriate and effective, and an atmosphere of mutual respect between teachers and students was in evidence. Small numbers in classes, which ranged from two to thirteen students, offered clear opportunities for individual attention which were availed of by teachers. Questioning techniques used saw questions being directed to individual students, maintaining engagement with and inclusion in the work at hand.
A random sample of students’ copy books revealed relevant and appropriate work. Presentation, while generally very good, in some cases displayed undisciplined working techniques that can lead to mistakes being made. Teachers, in monitoring students’ written work, should continue to stress the importance of presenting their work in a structured and orderly fashion as a means of assisting them in achieving their potential in the subject.
In 2005-2006, the mathematics department engaged in a team-teaching project. This saw two teachers working together with a second-year class on a particular area of the Junior Certificate course. Following the project, an evaluation was conducted and plans for extending the use of this methodology to other classes and areas were outlined. Such innovative practice is highly commended, as is the use of active methodologies reported by teachers.
During the inspection visit, however, teaching observed was traditional in style, with teacher presentation at the board followed by individual student work. It is recommended that teachers include a broader range of methodologies in their normal classroom practice, with a particular focus on the continued development of expertise in strategies that actively involve students in the learning process. Support and assistance in this regard, if required, is available from the Mathematics Support Service and/or other Second Level Support Services.
The many examples of good practice in mathematics teaching observed in St. Mogue’s College included the affirmation of student effort, the appropriate use of mathematical language, the explicit statement of the lesson objective, and the maintenance of high expectations for students’ achievements in the subject.
Teachers assess students’ progress through regular monitoring of homework, which is assigned and corrected each day, chapter or topic tests and two end-of-term examinations. There is some informal liaising between teachers teaching in the same year groups and this is commended. In the final year of the Leaving Certificate programme, progress is closely monitored through the continuous assessment of past-examination questions carried out on a weekly basis. In line with the philosophy of assessment for learning, consideration might be given to other options for assessment. Further discussion and examples can be accessed on the website www.ncca.ie
There is currently no formal monitoring of examination results and uptake rates by the mathematics team. It is recommended, for the purposes of review and planning, that ongoing monitoring of examination data forms a normal and regular part of mathematics department activities.
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 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.