An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Lucan Community College
Lucan, County Dublin
Roll number: 70080T
Date of inspection: 15 May 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Lucan Community College, Lucan, Co. Dublin. 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 subject teachers. The board of management of the school was given an opportunity to comment in writing on the findings and recommendations of the report, and the response of the board will be found in the appendix of this report.
Timetabling provision for Mathematics is very good. There are five periods per week in junior cycle, six periods per week in fifth and sixth year and four periods per week in Transition Year (TY). The majority of mathematics classes are thirty-five minutes long while the remainder are thirty minutes. Additional provision is made in second and third year to accommodate students who wish to follow higher level Mathematics to the Junior Certificate. This proactive approach to supporting the uptake of higher level Mathematics is highly commended. There are four periods per week for mathematical applications in fifth and sixth year of the Leaving Certificate Applied (LCA). It is recommended that the distribution of classes for Mathematics throughout the week be kept under review, with the intention of providing at least one mathematics class per day to each class group in junior and senior cycles.
Mathematics classes are banded into two bands in first year. The top band is comprised of three mixed-ability classes while the remaining classes are arranged so that team teaching and withdrawal can be provided to those students identified as being in most need. All first year mathematics classes follow a common curriculum. In second and third year, mathematics classes are set within the top band and mixed ability within the lower bands. Students in both bands have the opportunity to follow higher level mathematics to the Junior Certificate. There is one learning-support group in the second band in first, second and third year. The students in these groups receive additional support in Mathematics or English at the level they follow in their base class. Common programmes for Mathematics with common assessments are followed within the bands and students are encouraged to follow the highest level for as long as possible.
Upon completion of the junior cycle, students opt for TY or the LCA. Classes are mixed ability in LCA. In TY, two of the periods for Mathematics are set and the remainder are mixed ability. Classes are set in fifth and sixth year. This approach is designed to facilitate students’ transfer between levels and to enable them to follow the highest level for as long as possible.
It is school policy that common and agreed procedures are employed in carrying out fundamental mathematics operations. This is very good practice, as it means that students are familiar with the classroom practices they encounter when they change levels.
Applied Mathematics is currently provided in senior cycle as an optional subject outside of formal provision. [d1] It is intended to improve upon this arrangement as soon as circumstances allow. The provision comprises the equivalent of three periods per week. The commitment to providing Applied Mathematics is commended.
Prospective students receive information about the school when application forms are distributed to the fifth-class cohorts in the feeder primary schools. Applicants and their parents are invited to a general induction meeting, which is held early in the school year prior to the students’ entry to the school. Meetings with individual parents are then arranged. The function of these meetings is to discuss the particular needs and interests of each incoming student, and collect any completed psychological assessments from parents.
Students who require additional support in Mathematics are identified as part of the school’s enrolment procedures. All incoming students sit standardised tests in verbal, numerical and perceptual reasoning. A group-reading test is also administered. In addition, the learning-support coordinator and the student pre-induction coordinator contact the sixth-class resource and learning-support teachers and consult with parents, and additional psychological assessments are arranged when deemed necessary. Learning support is mainly provided through team teaching, with a small number of students being withdrawn from classes where appropriate. The learning support team is proactive in identifying students who present with difficulties in Mathematics as they progress through the school. A flexible and inclusive approach is in place to provide them with the required supports. In addition, individual support in Mathematics is available to students in senior cycle.
The mathematics teachers have attended an impressive range of continuing professional development (CPD) courses. Materials presented at these courses were in evidence during the inspection, and the good practice of including the details of the CPD courses attended by staff members in the subject development plan for Mathematics was also being followed. Newly appointed teachers receive induction training from Co. Dublin VEC and directly from the school itself. A number of the teachers are also members of the Irish Mathematics Teachers’ Association (IMTA). The membership of teachers in this association is supported by school management.
Teachers are assigned to classes and levels on a rotating basis and by agreement with management. However, the teaching of higher level Mathematics to classes in senior cycle typically alternates between just two colleagues. It is suggested, as an integral part of the school’s CPD programme, that additional teachers be identified and assigned to higher-level Mathematics in the coming years. It is policy and practice within the school for teachers to remain with the same class groups from second to third year and from fifth to sixth year, where possible, thus maintaining high levels of continuity.
The mathematics department is very well resourced. Resources are stored centrally and can be accessed by all of the mathematics teachers. In addition, information and communication technologies (ICT) are readily available. ICT integration was in evidence during the inspection and a wide range of ICT resources are contained on the school’s local area network (LAN). These resources include revision notes, common syllabuses and agreed approaches to teaching particular topics. This collaborative approach to preparing and sharing resources is highly commended.
Subject-development planning in Mathematics is excellent. Responsibility for coordinating the department rotates between the colleagues and is currently jointly coordinated. A very comprehensive subject-development plan for Mathematics is in place and is updated regularly. One main planning meeting is held per year. This is supplemented by shorter meetings, which are held every two months. The minutes of all these meetings are contained in the subject development plan. A copy of the plan is available on the school’s local area network.
The current schedule for content delivery in the subject-development plan mentions the topics to be covered by each year group and level in a very general way. It is recommended that the delivery schedule be revised to specify the topics that are to be covered by each year and level each month. This would further support the excellent work already taking place in delivering common assessments and common revision programmes, and would form an invaluable resource for newly appointed and substitute teachers.
Separate, comprehensive plans are in place for TY and LCA. The TY plan provides many opportunities for the inclusion of active methodologies in teaching and learning and for self-directed learning. The plan also lists various project ideas together with a very innovative assessment scheme to grade the projects. A full plan for Applied Mathematics is also in place.
Individual planning documents were made available by all of the mathematics teachers visited during the inspection. It was very refreshing to observe that common approaches towards the teaching topics such as factoring the quadratic, solving linear and simultaneous equations were being adopted across the mathematics department. The use of common methodologies is very good practice, particularly in light of the movement of students between levels.
Informal planning is also taking place. It was clear that teachers within year groups collaborate effectively in relation to the progress of their students, the approaches to be adopted in preparing common assessments and in preparing common revision programmes. Wider collaboration across the mathematics department was also very evident from the shared resources that were made available during the inspection.
The lessons observed during the inspection were very well planned. Additional materials, to support the lessons’ learning objectives, were prepared in advance of the lessons and these helped to create a very inclusive and challenging environment. The lessons proceeded at a very appropriate pace, were well organised and placed the student at the centre of learning.
A range of methodologies was in evidence during the inspection and very good practice was observed in the use of ICT to support the revision of statistics for the Leaving Certificate ordinary-level examination. During an earlier lesson, the students had been assigned Leaving Certificate problems, and they were then able to compare their answers to the exemplar solution presented by the teacher. This approach facilitated the class to discuss any shortcomings or errors and to propose alternative approaches, and provided a very effective revision strategy. The students were then assigned to groups to work on more difficult examples while the teacher dealt with questions from individual students. The students in the different groups worked collaboratively in solving problems. It was very refreshing to observe the students discussing Mathematics and to see very effective peer tutoring taking place.
Positive student behaviour was observed during the inspection. The students were engaged with the material and contributed positively in all cases. In one instance, ICT, flash cards and a graduated worksheet contributed to a very enjoyable lesson in which the students were actively engaged throughout. ICT and flash cards were used independently to revise set notation and the students then worked through the worksheet supported by the teacher when the need arose. The lesson was fun and challenging and the subject matter was embraced enthusiastically by all of the students.
Classroom management and student discipline was very good. The atmosphere in the classrooms was warm, and the rapport between teachers and students and among the students themselves contributed to an open and enjoyable learning environment. Very good practice was observed in the involvement of students in self-directed learning at Leaving Certificate higher level. The students were assigned the task of preparing revision material on a particular topic and of presenting their work to the class group. The work produced by the students was very good and the innovative manner in which they approached their assignments was most commendable.
The students responded readily and knowledgeably when questioned by the teacher and during their interaction with the inspector. Good use was made of teacher questioning and the students sit regular tests. The results of these tests are collated by the teachers and were made available during the inspection.
Positive attitudes towards Mathematics are prompted and encouraged in the school. All of the classrooms were decorated with students’ work and appropriate teaching and learning materials. The students participate in a wide range of co-curricular activities and a ‘maths week’ is enthusiastically promoted each year. The commitment of management and staff to promoting Mathematics in the school is highly commended.
Practices relating to assigning and correcting homework in Mathematics are good. Homework is assigned during each lesson and, in some cases, teacher comments and student corrections were evident in the students’ homework copies, which were examined by the inspector. It is recommended that practices regarding the correction of homework be standardised across the mathematics department, and that the good practice of students amending their own work be included as a key assessment vehicle in the subject development plan for Mathematics.
Formal common assessments for first-year students are held at Christmas, and just prior to the summer holidays. These assessments are corrected using a common marking scheme and the results are collated centrally and are used to inform student decisions regarding choice of levels at the end of first year. Common assessments are set in second and third year within the bands, as needs and opportunities arise. Examination students sit formal assessments at Christmas and sit mock examinations at Easter. Students at the same level take common papers in the mock examinations.
Reports are issued to parents after each formal assessment and ongoing communication occurs through the use of the student diary, parent-teacher meetings and other, less formal, means. Each class group has one parent-teacher meeting per year.
Students participate in a range of extra-curricular activities pertaining to Mathematics. These activities include: the Junior Maths competition, the Hamilton competition, Team Maths competition, maths week and international maths day.
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 the principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published October 2008
Submitted by the Board of Management
Area 1 Observations on the content of the inspection report
We welcome the process of the inspection and the content of this inspection report and have a number of observations we wish to add.
1. Recommendation number 1 suggests working towards providing at least one mathematics class per day. While we understand the value of balancing the provision of Mathematics across the week, the Mathematics Department also see the value that a double period once a week can serve in the use of some of the more time-consuming but worthwhile active methodologies.
2. We wish to point out that our CPD programme within the Mathematics Department has already been actively encouraging teachers to consider taking on the Higher Level Leaving Certificate Mathematics course and some teachers have attended training courses to this end.
3. While we see the value of detailed planning, we also recognise the value of leaving a certain amount of planning to the discretion of the individual teacher. As such we feel there is merit in our approach to planning of having a 'bench-mark' of topics to be completed by a certain deadline while leaving the actual order of topics to be decided by the class teacher.
4. As mentioned to the Inspector at the oral feedback meeting, we feel that the observation of homework practices was not typical due to the timing of the inspection. Teachers were more focused on revision and preparation for examinations at this late stage of the year.
Area 2 Follow-up actions planned or undertaken since the completion of the inspection activity to implement the findings and recommendations of the inspection.
We commend the focus of the report on the teaching and learning observed in the school. We accept the spirit of the recommendations for further development and are already working towards achieving many of them. Our Mathematics Department meetings have already discussed the draft report and recommendations. We found the whole experience to be a positive and affirming one and commend the inspector for his clear focus on the teaching and learning of the subject and for the enthusiasm with which he carried out his task. The process left our Mathematics teachers feeling affirmed and ready for future challenges.