An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Mercy Secondary School
Inchicore, Dublin 8
Roll number: 60872A
Date of inspection: 23 March 2006
Date of issue of report: 26 October 2006
This Subject Inspection Report
This report has been written following a subject inspection in Mercy Secondary School, Goldenbridge. 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 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.
Mercy Secondary School, Goldenbridge is a single-sex girls’ school that offers the Junior Certificate, the Junior Certificate School Programme (JCSP), an optional Transition Year programme, the Leaving Certificate Applied (LCA) programme and the established Leaving Certificate to its 185 students.
Five teachers teach Mathematics in the school. The teaching of programmes and levels is generally allocated on a rotating basis among all Mathematics teachers. This is good practice as it develops the expertise within the subject department. Teachers whose main specialism is Mathematics are assigned higher-level classes on a rotational basis which is appropriate. In general, teachers retain the same class groupings through each cycle. There is good allocation of teachers to Mathematics. For example two extra teachers are assigned to first-year Mathematics class groupings with one extra teacher assigned to second, third 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.
Prior to entry into Mercy Secondary School all students sit an assessment test. This assessment and other information received by the school from the primary schools in the catchment areas and relevant psychological reports assist in the assignment of students to first-year classes. Generally, one foundation-level class, containing students in receipt of learning support, is arranged in first-year. The remaining first-year students follow a common programme until October. Following a common assessment and teacher observation students are then arranged into either a higher-level or ordinary-level class grouping. However, movement between levels is permitted.
At senior cycle, generally one higher-level class and one ordinary-level class are formed. However, in fifth-year there is only one class grouping of Mathematics which is an ordinary-level class. As a special measure, management and staff have facilitated one student to follow the higher-level Mathematics programme. This has been arranged by concurrently timetabling the student for Mathematics classes alongside the sixth-year higher-level class. These efforts to ensure that students have an opportunity to follow an appropriate level in Mathematics are highly commended.
Time allocated to Mathematics is good and classes are distributed evenly throughout the week. 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.
Teachers have been facilitated in attending inservice courses on the Junior Certificate School Programme, the Leaving Certificate Applied and the revised Junior Certificate Mathematics syllabus. While there is no specific budget allocated to Mathematics it was reported by teachers that any reasonable request for resources has been provided. Resources purchased include calculators and geometry sets. Mathematical resources are retained centrally and all teachers have access to them for the teaching and learning of Mathematics in the classroom. This is good practice.
Work in the area of school planning is ongoing and currently the school is focusing on subject planning. The school will be progressing work in this area in conjunction with a regional coordinator from the School Development Planning Initiative (SDPI) who will shortly be visiting the school.
There is evidence to suggest that the Mathematics department works as a cohesive team collaborating on issues that arise. Staff are facilitated by management to meet formally throughout the year. Such support is to be commended. It was reported that issues such as the selection of common textbooks and the setting of common assessments for first-year classes are discussed at these meetings. However, it is recommended that the Mathematics department retain minutes of these meetings. This will ensure that all teachers are fully informed of decisions taken and of agreed policy on issues pertaining to Mathematics.
Currently, the Mathematics department does not have a long-term plan for the subject but work on the preparation and development of one is in hand. It is therefore recommended that this long-term plan for Mathematics should outline the aims and objectives of the Mathematics department; 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 teaching. The development of a common plan for Mathematics will give teachers an opportunity to identify and share good practice. The plan should outline the general organisational details of the department and the system of allocating students to Mathematics classes and levels. This will ensure that all newly-appointed or substitute teachers have relevant and important information and are aware of the customs and practices of the department. The SDPI website, www.sdpi.ie has useful resource material that may assist in this regard in conjunction with the input from the regional SDPI coordinator. The plan should be reviewed annually and any necessary amendments made accordingly.
The school’s Transition Year Mathematics module is reviewed annually and includes a good variety of material for students. Students have the opportunity to engage with Mathematics through the use of problem solving exercises, puzzles and games.
In most classes visited, lessons were well structured and purposeful and there was evidence of good short-term planning. Topics such as algebra, geometry, and statistics featured in the lessons observed. In all lessons teachers used Mathematics terminology appropriate to the relevant topics and students’ ability. In general, lessons began with the teacher correcting homework from the previous night. Teachers circulated the classrooms to check each student’s homework and this enabled students to receive individual and immediate feedback on their work. Such good practice is commendable.
In general, the main methodology used 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. Good practice was observed where students were given the opportunity to use investigation to consolidate the topic being taught through the use of prepared work sheets. This methodology had the effect of ensuring that students were fully engaged in the topic and developed an understanding of the concepts encountered. As not all students benefit from traditional whole-class teaching it is recommended that all teachers vary the methodologies used in lessons. Some examples could include investigation, consolidation activities, practical work, discussion, group work and quiz activities as outlined in the Junior Certificate Mathematics Guidelines for Teachers.
In most lessons observed, interaction between teacher and students generally took the form of brief answers by the students to closed questions by the teacher. Oral exchanges focused mostly on finding steps in the solution to a problem. In some lessons, teachers’ skilful questioning encouraged students to build on their answers thus probing and extending the students’ understanding and encouraging them to explain and justify their thinking and methods. Such good practice is to be commended and should be extended to all lessons. It is recommended that a varied range of questioning strategies be employed in order to help consolidate learning and maintain student engagement with the topic.
Textbooks and examination papers were the main resources used in lessons. However there were some good examples where differentiated worksheets were developed and used in lessons. On occasion the use of an overhead projector would have been beneficial in lessons in order to highlight important points and provide a variety of examples.
Classroom management was effective and students were attentive and appropriately behaved. The principal frequently visited classrooms and used the opportunity to ensure that all behaviour was appropriate. In all lessons observed a good teacher-student rapport was evident and students were attentive and generally interested. Inputs from students were welcomed and encouraged, generating a comfortable secure environment where all students were respected. Individual attention was given in a sympathetic and professional manner. Students in general answered questions put to them by the inspector in a confident manner. It was obvious that most students had a clear understanding of the work being undertaken in the lessons.
Homework assigned was appropriate in terms of its quantity and relevance. It was clear that teachers monitor students’ copies. Some teachers write commendations and suggested areas of improvement in students’ copies which is good practice. Students should also be encouraged to correct their own work and make any necessary amendments.
In some classes visited walls had displays of students’ mathematical work or mathematical posters. This good practice is to be commended and should be extended to all classes.
Students are assessed in a variety of ways such as questioning in class, written examinations following the completion of a topic and homework. Formal examinations for non-examination year groupings take place at Christmas and summer with examination years sitting ‘mock’ examinations in the second term.
The school maintains good communication with parents. For example, reports are issued following formal examinations. Parent-teacher meetings are convened for all year groups. Those parents who are unable to attend meetings are invited to make an appointment to attend at a later date.
The school provides teachers with diaries which were generally used effectively to record attendance and assessment details. All teachers should record daily attendance. Through observation of teachers’ records it was apparent that on occasion there have been difficulties for some students in the area of attendance. However, it was reported that the school is proactive in ensuring that good attendance is maintained.
Students are encouraged to follow either higher or ordinary-level in both the Junior and Leaving Certificate examinations. Teachers are to be commended for the practice that has been developed whereby teachers aim to keep the number of students taking foundation-level to a minimum.
The school is involved in the Trinity Access Programme (TAP) that operates in conjunction with Trinity College Dublin. It was reported that a very high percentage of students proceed to further education following the completion of their Leaving Certificate in Mercy Secondary School. Such links with third level and the encouragement of students to continue with their education is to be highly commended.
Students have been given the opportunity to participate in the Junior Certificate School Programme Mathematics poster competition and have also attended the Hamilton Institute table quiz, which was held in Trinity College Dublin. “Maths for Fun” has also been introduced to the school. These initiatives are to be commended as they provide students with opportunities to engage with the subject while experiencing Mathematics in a different learning environment. Mathematics teachers are commended for their availability to meet students after school to give extra help as needed.
The following are the main strengths and areas for development identified in the evaluation:
There is very good support for Mathematics in the school in terms of teacher allocation to Mathematics classes, time allocation and in providing resources and opportunities to attend inservice.
In general, teachers have developed good short-term plans for their subject.
Teachers are keen to promote Mathematics and are commended for aiming to keep the uptake of foundation level to a minimum.
Students have opportunities to experience Mathematics through co-curricular activities.
The school has developed links with Trinity through its access programme.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
The Mathematics department should retain minutes of meetings.
The Mathematics department should collaborate and develop a long-term plan for Mathematics.
A variety of methodologies should be included in all lessons.
A varied range of questioning strategies should be employed in all lessons.
Post-evaluation meetings were held with the 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.