An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Saint Clare’s Comprehensive School
Manorhamilton, County Leitrim
Roll number: 81013P
Date of inspection: 17 January 2007
Date of issue of report: 23 October 2007
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in St Clare’s Comprehensive School, Manorhamilton. 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 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 Clare’s Comprehensive School is committed to meeting the learning needs of the community it serves. Its open enrolment practice seeks to ensure there is a place for every young person, regardless of abilities and talents. The importance for students of reaching their potential in the core subjects, including Mathematics, is emphasised through the allocation of additional teacher resources in five of the six year groups. This facilitates the formation of supportive class groupings where students study higher, ordinary and, when necessary, foundation levels. In addition, the time allocation to Mathematics is in line with, or slightly above syllabus recommendations, at five periods per week for junior cycle and six for fifth and sixth year classes.
Concurrent timetabling, which can present significant challenges for school managements, is widespread in the subject. All year groups with the exception of Transition Year (TY), where there is only one class grouping, are concurrently timetabled. This represents a solid commitment to Mathematics and ensures that students have every opportunity to access their required level of study.
All first-year mathematics classes follow a common programme of work, allowing students a ‘settling-in’ period prior to any decisions being made regarding level of study. At the beginning of second year, and largely on the basis of results achieved in the previous summer-term examinations, higher and ordinary-level groups are formed. Care is taken, however, to ensure that every student is allowed the fullest opportunity to access the highest appropriate level. Teachers, in consultation with school management, agree to rotate levels, with two teachers currently sharing the workload of Leaving Certificate higher level.
Students identified as finding Mathematics particularly challenging are offered support through participation in small class groups formed within each year group. Assignments are made by the learning support coordinator in conjunction with school management, following parental agreement. It is school policy and practice for students in such groups, each of which has a group education plan, to follow the ordinary-level course. For each student in receipt of mathematics support, individual development targets are drawn up by their teacher in collaboration with the learning-support/resource teachers and school management. Such practices are commendable. The mathematics team has a commendable commitment to more able students also, with additional voluntary classes being offered, as required.
Links between St Clare’s and feeder primary schools have been established over a number of years. It is now recommended that subject-specific links be created with teachers of sixth classes. Members of the mathematics team should use the opportunities provided by such links to share information with their primary counterparts on course content, methodologies, approaches and issues. As well as contributing to better mutual understanding among teachers it will be a valuable measure in easing the transition for students from primary to post-primary level.
Resources available within the school to support the teaching and learning of Mathematics include overhead projectors, geometry equipment, posters and charts, and mathematics computer software. Co-curricular mathematics activities promoted within the school include participation in the annual Young Scientist and Technology Exhibition. Projects submitted, and awarded, in the 2007 competition were, at the time of the inspection visit, on prominent display in the main hall area. Teachers are commended for realising the benefits and enjoyment for students in partaking in such activities, and in celebrating their successes so publicly.
School management encourages teacher professional development, facilitating attendance at in-service courses. Commendably, information gained at such courses is disseminated to all relevant teachers, on an informal basis, on return to school.
The school’s development plan for the period 2004-2007 centres on raising standards of teaching and learning. Two strands of this, subject planning and the use of learning outcomes, have been identified as key elements. In the mathematics department, subject planning is led by the coordinator, a post-holder and senior teacher. The department plan is being developed along School Development Planning Initiative (SDPI) guidelines, with aims and objectives for the teaching of Mathematics, organisational details, resources, and programmes of work for each year group and level. Commendable additions to the plan include a teacher’s personal evaluation of effectiveness, and curriculum and pastoral statements. Programmes of work would benefit from the inclusion of teachers’ active lesson ideas and materials, and appropriate cross-curricular links. In the longer term, and in line with developments in the National Council for Curriculum and Assessment (NCCA), consideration should be given to presenting agreed programmes in terms of learning outcomes for students. Syllabus documents, guidelines documents and resources for TY mathematics teachers should assist in this exercise.
The meetings held by the mathematics department are mainly informal; formal meetings are facilitated by school management twice or three times per year with the main business being the organisation and/or restructuring of class groupings. The preparation of an agenda for each meeting would enhance the effectiveness and efficiency of the meeting, as would the appointment of a chairperson. An agenda could also be a mechanism for broadening the focus of meetings to include overarching mathematics issues such as common teaching strategies or policies such as calculator usage. In addition, the keeping of minutes to record discussions and decisions would add to progress being made and assist the follow-up process.
Given the workload involved in team planning and review, it should be given a higher priority and moved to a more formal level. With this in mind, consideration should be given to further developing the role of the coordinator and, with an eye to the future, possibly moving to its rotation among team members.
All teachers made individual planning/preparation materials available during the inspection. These included student worksheets, wall charts, examination documentation, daily class diaries, in-service materials, a student-developed theorem-teaching package and some extensive teacher notes. Teachers are commended on engaging in high levels of preparation for their teaching.
In all seven lessons visited, lesson content was appropriate and in line with syllabus requirements. Teachers’ presentations were made using the chalk board, white board or overhead projector and work was presented clearly. A significant proportion of student-teacher interaction took the form of brief answers to questions focused on finding the next steps to a solution. There were some very good examples, however, where teachers built on students’ answers, probing and extending students’ understanding and encouraging them to explain and justify their thinking and methods. This helps students to consolidate their learning and maintain engagement with the topic at hand and it is important, therefore, that a range of questioning strategies be incorporated in all lessons.
Classroom management was fittingly relaxed and effective, creating an atmosphere in which students were attentive and working. In line with good practice, student effort was, in all cases, affirmed by teachers. The pace of work was, in most cases, appropriately challenging, sustaining students’ interest, and progress was being made. An atmosphere of mutual respect between teachers and students was present in all interactions observed.
In line with the school development plan 2004-2007, all teachers explicitly shared lesson objectives with students. This practice, which ensures clarity regarding the expected outcomes of lessons, is highly commended. Its effectiveness was optimised in cases where the lesson concluded with a review of students’ achievement.
Teaching observed was, for the most part, traditional in style, with new work being presented by the teacher and followed with individual student practice. It is recommended that teachers explore a broader range of methodologies, with a particular focus on developing expertise in strategies that actively involve students in the learning process. Support and assistance in this regard is available from the Mathematics Support Service whose website address is www.mathssupport.ie.
There were many examples of good practice in mathematics teaching. These included relating class work to ‘real life’, employing clear methods and explanations, making time for individual students, and communicating high expectations of mathematical attainment to students.
A random sample of students’ copy books revealed relevant, appropriate, and in one instance, particularly extensive work. Presentation, however, was of variable quality, in some cases displaying 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 real potential in the subject.
Ongoing student progress is assessed informally through the monitoring of homework and oral questioning in class. With the exception of the TY class, the typical formal assessment consists of chapter or topic tests and term examinations. It is suggested that teachers explore a broader range of assessment strategies, either through links with approaches taken in TY or through the assessment for learning programme. Teachers keep records of students’ achievements and report to parents/guardians via twice-yearly written reports and annual parent/teacher meetings.
For the purposes of planning and review, school management makes available to staff data on students’ achievements in the Certificate Examinations and in the mock examinations. The mathematics team is now encouraged to engage fully with this data by discussing and analysing trends as discussed during the inspection visit.
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.