An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Coláiste Na Sceilge
Caherciveen, Co. Kerry
Roll number: 76068N
Date of inspection: 12 December 2007
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Coláiste na Sceilge, Caherciveen. It presents the findings of an evaluation of the quality of teaching and learning in Mathematics and Applied Mathematics and makes recommendations for the further development of the teaching of these subjects 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 acting principal and 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.
The support for Mathematics in the school is excellent. With the exception of first year, all classes are timetabled concurrently within the different year groups. This is commendable as it enables students to study at the highest level possible for as long as is feasible and affords the opportunity for teachers to agree common programmes and prepare common assessments.
Allocation of time to Mathematics is very good. Junior certificate classes have five periods per week while in third year, higher-level students and those who find the subject particularly challenging are provided with one additional class per week. Time allocation in senior cycle is also very good with six periods provided per week in both fifth and sixth year while an additional plenary session is provided to those sixth-year students who do not participate in the Leaving Certificate Vocational Programme (LCVP). All periods have a duration of forty minutes.
The school has an all-Irish stream (an Aonad lán Gaeilge) and Mathematics is taught through the medium of Irish to one class group per year up to Junior Certificate. One of the ordinary level groups in sixth year is also taught through Irish.
Transition year (TY) is available to all students and is optional. Currently, there are two periods of Mathematics per week in TY and, despite the very good provision for Mathematics in senior cycle, it is suggested that the school revert to three periods of Mathematics in TY as soon as is feasible. Furthermore, it is suggested that students currently in TY engage in cross-curricular projects with Mathematics as a central theme to offset the effects of the reduced allocation.
The school offers the Leaving Certificate Applied Programme (LCA). Due to the small numbers opting for the programme, the first and second year groups are taught together in a single class. In the current year, the sequencing of modules as outlined in the programme’s objectives, is proving difficult to implement. It is recommended that the programme be reviewed and a plan developed to enable the school to continue providing the LCA while complying with the sequencing requirements of the programme.
Students wishing to study Applied Mathematics are accommodated within the timetable and are provided with five periods per week in both fifth and sixth year. This provision is commended.
Teachers are assigned to classes in first year; thereafter, they are assigned to year groups and allocate class groups by agreement. Typically, teachers continue with their classes from second to third year and from fifth to sixth year. Students are encouraged to follow the highest level possible for as long as possible and parental consent is sought should a student wish to change level. First year classes are mixed ability and second year classes are streamed for higher and ordinary level at the end of September. This allows time for teachers to assess students’ abilities and for students to make an informed decision regarding the most appropriate level to follow.
The school makes very good provision for students in need of learning support and for those who may find Mathematics particularly challenging. Some students are identified from assessment in primary school, and following monitoring in first year, others are recommended for assessment. Close informal links are maintained between the learning support teacher and the class teachers. Students identified as being in need of support are withdrawn from classes and receive tuition in small groups. In addition, a mathematics class with reduced numbers, is created in third year and the students in this class are provided with an additional period per week compared to their peer group. Assessed students receive learning support until they complete their education in the school.
The school facilitates teacher attendance at continuous professional development courses (CPD). Teachers have availed of such such opportunities, sometimes outside of school time. Furthermore, some teachers are members of their subject association and their membership is paid by the school’s management. There is no formal budget for the mathematics department but requests for resources and equipment are favourably received. Resources are centrally located and available to all members of the mathematics team. There is an induction programme for new teachers and the school participates in the mentoring programme provided by the Kerry Education Service. Furthermore, the school has representatives attending the mentoring programme being provided by Dublin City University. The school’s positive approach to ongoing teacher professional development is commended.
Subject development planning in Mathematics is well established and is coordinated on a voluntary basis. The position of coordinator is reviewed annually and is allocated on a rotational basis. This is good practice as it enables all team members to experience developments in mathematics teaching and learning and to become aware of the issues that arise in organising a subject department. Subject planning is facilitated by the school’s management and involves one group meeting at the start of each year and an additional meeting with the principal where a detailed analysis of student performance in the Certificate Examinations is undertaken. Additionally, portions of staff meetings are allocated to subject planning during the course of each year.
The mathematics department plan is at an advanced stage. It contains a mission statement for the department and includes organisational details, resource lists and long-term plans for each year group and level in the form of topics to be taught, details of class work and homework assignments. The plan also outlines differentiation strategies, learning support materials, links to resources and appropriate written materials. A separate plan is in place for TY and while its structure is similar to that for the other programmes it, commendably, also contains materials from outside the mainstream syllabus. Similar planning has taken place for Applied Mathematics and for mathematics teaching in the Aonad. This good practice relating to planning can be further enhanced by including a list of those teachers who have attended CPD and the topics covered on these courses. This will enable more effective dissemination of resource materials and it is recommended that feedback from these courses be given during planning meetings. It is further recommended that the long-term plans be divided into half yearly portions to allow for more coordination within levels and to enable more common assessment or common questions during assessments.
Most teachers made personal planning materials available for review during the inspection and in some cases these were extensive and most commendable. These materials included both long and short-term schemes of work, attendance records, records of work completed, assessment materials and teaching resources.
Positive student behaviour was evident in all of the lessons observed. Students were engaged with the lesson at all times, responded readily to questioning and participated productively in the various activities undertaken during the lessons. Teachers were very knowledgeable regarding their subject matter. Lessons proceeded at a suitable pace. Classroom management was good and students were given good individual attention. Teachers were affirming of students’ efforts. Continuity from previous lessons was generally good and new information was well linked to previous learning. Teachers had high expectations of students and the students responded to this.
Teaching was, in almost all cases, traditional in style. In most cases the teachers relied on the markerboard, textbooks and worksheets in delivering the lesson. Typically lessons involved teacher demonstration to the full class group with the students then working on assigned tasks while the teacher assisted individuals. In some classes there was commendable use of materials other than textbooks and good practice was observed when teachers used appropriate mathematical language, clear board work and methodologies and used the students’ own experiences to engage them in their own learning.
In one lesson students were actively involved in experimental work to investigate a particular formula. They worked in small groups and their enthusiasm for the task in hand was very obvious. The integration of this active methodology was seamless and it is recommended that these and other methodologies, including the integration of information and communication technology (ICT), paired work and investigations be extended to all classes and levels.
Good use was made of directed questioning in most classes, however not enough emphasis was placed on higher-order questions which would encourage the students to hypothesize, to speculate and to explain their reasoning. It is recommended that a greater range of questioning strategies be incorporated into lessons to increase student engagement and to give them a role in directing their own learning.
In the classroom where students were being taught through Irish, effective use was made of teacher and student-prepared posters and charts which were displayed on the walls. In other classrooms, the teching and learning environment would be greatly enhanced by incorporating displays of students’ work and other relevant printed materials on the walls. The school should consider extending the number of base rooms for teachers which would, in turn, facilitate the development of a more print-rich environment.
Students demonstrated a positive attitude towards Mathematics as evidenced by the level of engagement and interest observed during the lessons visited. Students displayed a very good level of knowledge, understanding and skills during interaction with the inspector. They were able to make connections between related topics on the course. They also demonstrated a range of mathematical knowledge, were able to answer questions in a confident manner and justified solutions to questions posed to them in appropriate mathematical language. Formative assessment of students is carried out on an ongoing basis by questioning in class, through correction of classwork and homework and through monitoring of students during lessons.
Formal assessment for non-exam classes takes place in December and again just prior to the summer holidays. Examination classes have informal class tests at Christmas and sit the ‘mock’ examinations in February. Reports are issued to parents twice per year. A parent-teacher meeting is held for each year group during the school year while the sixth-year group have two such meetings. Additional communication with parents is achieved through the use of the student diary and in some cases through parents signing the students’ work. To enhance this good practice it is suggested that the school should arrange a greater number of common assessments within year groups and levels or include common questions within the current assessment model.
There was evidence of record keeping by teachers, covering such areas as student attendance, assessment records, student behaviour, work done and homework. This is good practice. However, in one instance, while topic tests were regularly checked, no homework was being reviewed. Recorded information can be very useful in developing student profiles and can form a valuable evidence base in communicating student progress to parents and in advising both students and parents on choice of subjects at senior level and on what level of examination paper to choose in certificate examinations. It is recommended that, as part of a wider homework policy for the school, the mathematics team agree on the level and modes of review across all years and levels.
The school’s management and teachers undertake a detailed analysis of the school’s performance in the Certificate Examinations in Mathematics in relation to achievement and uptake levels and compare them with national norms. This analysis is then used to inform planning. This good practice should be used to review the school’s policy regarding the provision of the subject at foundation level in junior and senior cycle.
The school has participated in co-curricular and extracurricular activities including the Team Maths competition organised nationally by the Irish Mathematics Teachers Association and the Young Scientist Exhibition. In addition, speakers have been invited to speak on relevant mathematics topics to the TY cohort. To further support these activities it is suggested that the team should investigate the range of national mathematics competitions available for students and decide on an appropriate level of engagement.
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 Applied Mathematics and with the acting principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published, October 2008