An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Trá Lí, Contae Chiarraí
Roll number: 70560K
Date of inspection: 25 March 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection conducted as part of a whole-school evaluation in Gaelcholáiste Chiarraí. 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/subject teachers.
Gaelcholáiste Chiarraí provides education through Irish for boys and girls from the town of Tralee and its hinterland. A majority of students come to the school from an Irish-language-primary-school background. The Junior Certificate, an optional Transition Year (TY) programme and the Leaving Certificate programme are on offer to its 253 students. The mathematics team consists of four teachers, two of whom teach the majority of classes in the school.
Each year has two class groups with the exception of sixth year which has three divisions for Mathematics. First-year, second-year and TY students are taught in mixed-ability groups. This is good practice as it allows students to study Mathematics at the highest level for as long as possible. In third-year, fifth-year and sixth-year classes are divided into higher and ordinary levels and timetabled concurrently. Students wishing to change level are accommodated following parental consultation with their class teacher.
Teachers are assigned to classes and levels by school management. It is practice within the school for teachers to remain with the same class groups from first to second year and from fifth to sixth year, where possible, thus maintaining high levels of continuity. Currently Leaving Certificate higher level is the responsibility of two member of the teaching team while at junior cycle higher level is rotated among a wider group of teachers.
The time allocation to Mathematics is good. All junior cycle mathematics classes have five periods per week. Fifth-year and sixth-year classes receive six periods each week. Three class periods are allocated to TY Mathematics. In line with accepted good practice, mathematics classes are generally distributed evenly throughout the school day and the school week. However one of the TY classes has two of its three mathematics lessons on the same day. This should, if possible, be avoided in future timetabling to ensure that all classes enjoy the benefits of an even spread of classes.
While there is no specific budget for mathematics equipment, requests for resources have been favourably considered by management. A number of resources have been purchased and are available to all members of the team. These include overhead projectors and drawing instruments for the boards. A computer room and mathematical software packages along with a number of ICT resources provided by the Mathematics Support Service (MSS) are also available for use by the mathematics teachers. Teachers’ attendance at continuous professional development (CPD) courses is facilitated by management and teachers have availed of courses offered by the MSS in recent years. These developments are praised.
Students in Gaelcholáiste Chiarraí have an opportunity to participate in a range of co-curricular activities connected to Mathematics. In recent years students were involved in the Team Maths competition for Leaving Certificate students and the Irish Junior Mathematics competition organised by the Irish Mathematics Teachers Association (IMTA). They have also been involved in the Problem Solving for Irish Second-Level Mathematicians (PRISM) competitions, organised nationally as part of Maths Week Ireland held in October each year. Other involvements include a range of Maths Week and World Maths Day activities. Such activities help to engage students, raise the profile of the subject and provide an opportunity to experience Mathematics outside of the classroom. All involved in the organisation of these activities are praised.
The mathematical abilities of all incoming first-year students are assessed following entry into the school. There is also contact with the local primary schools and consultation with parents. This assessment and contacts, along with ongoing monitoring and observation by the teacher during first year, help to identify students who find the subject particularly challenging. Support for these students is provided in the form of extra tuition through withdrawal for small group or one-to-one tuition. Students are withdrawn at times that do not coincide with their timetabled mathematics classes. This support is sometimes provided by a member of the mathematics team. It is recommended that the current model of support should be reviewed and the opportunities offered by in-class support and team teaching be assessed in the context of this review.
The team should not overlook the good practice of conducting an analysis of the school’s performance in the certificate examinations in Mathematics. This analysis should include a focus on achievement, uptake levels and comparisons with national norms. An analysis of results in recent years indicates strengths in these areas. Such analysis is useful in informing future planning and provision for the subject.
The task of co-ordination of the mathematics team is undertaken on a voluntary basis and the position rotates annually between the two members of the team most involved in the teaching of the subject. There is a sense of collaboration and co-operation within the team. This is supported by the good practices of rotation of levels, following of similar programmes of work and having common formal assessments at the end of first year, second year and TY.
Formal planning and review meetings are held at the beginning and end of the school year. Other regular informal meetings also take place. The good practice of record keeping of these meetings is in place.
A written plan for Mathematics has been prepared. The plan contains syllabus documents, overall aims and objectives for mathematics education within the school, outline programmes of work for each year group and level, organisational details and reference to a variety of resources. This is in line with good practice and is commended. The long-term plan for the subject consists of programmes of work for year groups and levels in the form of an outline of sections of the syllabus at junior cycle and senior cycle. Ideally a range of methodologies and differentiation strategies should also be listed and linked to specific learning outcomes for students. The plan should also contain a breakdown by term of the recommended time to complete the sections of the courses.
There is also a plan for the TY programme for the school. This is positive. Within this plan there is a balance between topics that consolidate the prior learning of students, some content that introduces elements of the Leaving Certificate programme and commendably details of non-curriculum materials as well as cross-curricular aspects of Mathematics for delivery in TY.
Irish was the language of communication and instruction, in all lessons visited. The exchange of information through Irish and the use of mathematical terminology in Irish by teachers and students were evident in lessons and formed a natural part of all classroom interactions. This is positive.
The mathematics lessons in Gaelcholáiste Chiarraí were well structured, purposeful and appropriate to the syllabus. In all cases, lesson content was appropriate and teachers’ explanations and instructions were clear. In lessons observed, the topic of the lesson was communicated to the students at the beginning of the lesson. This is good practice. Optimum benefit from this strategy occurs when the lesson content is presented as a learning objective for the students and when there is a checking strategy at the end of the lesson. This process is worthwhile because it increases students’ motivation and involvement in the lesson and leads to a sense of accomplishment on achieving each day’s learning goal.
Lessons generally began with the correction of homework from the previous lesson. A variety of strategies was used to ensure that this was dealt with efficiently and effectively. It is good that efforts were then made to review work previously done and to create connections to new material being presented, thus helping to develop new ideas and reinforce learning. Lessons progressed at an appropriate pace with good use being made of time.
The textbook and board were the main resources used in lessons. There were also good examples of the use of worksheets and some pair work in lessons. Teachers also effectively related students’ own life experiences to learning in lessons.
The predominant methodology used in lessons was traditional whole-class teacher-directed teaching. This consisted of the teacher modelling a procedure to the class, by doing examples on the board. The students then worked alone on similar problems from the textbook or worksheet while the teacher assisted individuals. Within this structure the teaching was caring and effective. The teachers were busy but students were passive and reliant on the teacher. More use of strategies such as working on student-generated problems, pair work, group work, investigation, consolidation activities, practical work, discussion, group work, quiz activities, the use of ICT and the use of concrete materials would have enhanced learning. Such methods should have the effect of encouraging students to become more engaged in the lesson and active in their own learning. It is therefore recommended that teachers build on current methodologies used in lessons and adopt greater variety in their teaching approaches.
Classroom interactions generally took the form of brief answers to questions posed by the teacher to individual students or to the class group on finding the next steps in a solution. There was good practice with regard to variety in the addressing of questions to individual students and whole class groups. This was an effective means of checking students’ levels of understanding of particular concepts. The questioning generally took the form of “next step” or “fill in” type questions. It is therefore recommended that teachers should engage in the posing of more open questions to challenge students and probe new material being presented.
The relationships between students and teachers were observed to be mutually respectful creating a positive working environment and classroom management was good. Teachers set appropriately high standards of expectation for their students and students responded to these expectations. In interactions with the inspector, students were able to answer questions asked of them in a confident manner using appropriate mathematical terminology and justified solutions to problems posed to them. Commendably students also demonstrated a good understanding of concepts engaged with during the lessons and were able to apply then to a range of similar problems from the textbook or worksheet.
In some classrooms visited the good practice of using displays of students’ work and student produced mathematical posters to enhance the visual learning environment had been adopted. Displays of posters and students’ project work are effective in reminding students of key mathematical concepts, formulae or terminology and should feature in all mathematics classrooms where it is practical to do so.
Students’ ongoing progress is assessed through observation during class, questioning and the assignment and correction of class work and homework. To add to this, regular topic tests are set. Teachers retain records of the results of these assessments. Formal examinations for those students who will be participating in the certificate examinations are organised at Christmas and they also sit mock examinations later in the school year. All other year groups sit formal tests at Christmas and at the end of the school year. Parents receive two reports regarding students’ progress following these formal examinations. The students’ journal is also used as a means of two-way communication by teachers and parents. There are two parent-teacher meetings per year organised for first-year and second-year students and one for the other year groups.
Teachers cooperate in the common testing of students where appropriate. First-year, second-year and TY students all sit common assessments during the school year. This is good practice. Appropriate homework was assigned in lessons providing students with an opportunity to practise and strengthen mathematical concepts engaged with during the lesson. Students’ copies and journals revealed that regular homework is assigned, which is good. An examination of a sample of mathematics copybooks and notebooks revealed work that was appropriate, relevant and reasonably well presented. There was also evidence that teachers are monitoring students’ copies. In some instances students’ monitoring of their own work could have been more evident. Students should be encouraged to regularly monitor and correct their own work in order that their copybooks become a template of good practice and a resource for their revision and study within the subject.
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 at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published, April 2010