An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Carrigaline Community School
Carrigaline, County Cork
Roll number: 91388S
Date of inspection: 14 November 2007
Date of issue of report: 17 April 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Carrigaline Community School. 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 the 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 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.
The commitment of Carrigaline Community School to providing a high-quality mathematics education for all its students is evident from the concurrent timetabling of all year groups from second year on and the creation of two concurrent bands of mixed-ability classes in first year. This allows students access to all levels and facilitates transfer between levels. Furthermore, an extra teacher is allocated to each first-year band to allow for the provision of in-class support during some of the lessons. This extra allocation is commended. It is policy and practice within the school for teachers to remain with the same classes from second to third year and from fifth to sixth year where possible, thus maintaining high levels of continuity.
Students who find the subject particularly challenging are identified through pre-entry assessments, contact with local primary schools and teacher observation and assessment during first year. These students are supported through a system of withdrawal from classes other than mathematics class, for one-to-one or small-group tuition by a member of the mathematics team qualified in learning support. In the current year the school has changed to allocating first-year students to classes on a mixed-ability basis. There are seven class groups in first year. In an effort to provide support to those students who are finding the subject difficult, while at the same time allowing them to experience the subject on a similar basis to all the other students, two bands, one of three classes and one of four classes, have been created. All classes within each band are concurrently timetabled and an extra teacher is assigned to each band to allow for in-class support to be provided as required. Management and mathematics teachers are commended for adopting this innovative approach to supporting students. These arrangements underline the commitment of management and the mathematics team to encouraging students to follow the highest level possible for as long as possible while at the same time providing an appropriate mathematical education for all students.
Time allocated to Mathematics is good. All junior cycle classes are allocated five periods per week. Transition Year (TY) is optional within the school. However a majority of pupils choose to avail of the programme. Four class periods are allocated to TY Mathematics. Six class periods are allocated to fifth-year classes and sixth-year classes have five periods each week with the exception of those following the higher-level course who have one extra period each week. The Leaving Certificate Applied (LCA) class in fifth year has four periods of Mathematical Applications each week and the sixth-year group has three periods.
In a number of instances, due to reported timetable constraints, classes have a different mathematics teacher for one of their lessons each week. It is suggested that this practice be avoided, if possible, in future years as this does not facilitate continuity of approach. All first-year classes have one double period of Mathematics each week resulting in classes not having daily contact with the subject. In another instance, the second-year LCA class has two of its three mathematical applications classes on the same day. Every effort should be made in future timetabling to ensure that mathematics lessons are well distributed throughout the week.
Senior cycle students wishing to study Applied Mathematics are not accommodated within the timetable. However they are catered for as part of the school’s Adult Education programme. The support of the school for this subject is commended.
A budget for mathematics resources and materials is agreed each year as part of the school’s overall expenditure. Requests for specific materials are also favourably considered. Information and communication technology (ICT) is currently most commonly used in the preparation of materials for mathematics classes rather than as a teaching aid in class. The school has recently opened a state-of-the-art computer room which will be available for use in the teaching and learning of subjects across the curriculum. All teachers are currently receiving training in the use of this facility. The mathematics team and school management are confident that this will result in the greater use of ICT in mathematics teaching. All involved in this project are commended.
The mathematics department at Carrigaline Community School is co-ordinated on a formal basis. The current co-ordinator, a senior member of the mathematics team, has held the position for a number of years. It is reported that the position will be reviewed in the current year with a view to having the duties of co-ordinator rotate among members of the team as had been the case previously. This is good practice as all mathematics teachers should be aware of the issues involved in the running of the subject department.
As part of the school’s commitment to teaching and learning, mentioned earlier, regular meetings of teachers are scheduled to allow for the sharing of methodologies and for providing feedback from outside continuous professional development (CPD) courses attended. This is good practice and all involved are commended.
Two formal meetings for planning and review are scheduled for the beginning and end of the school year. Subject departments have meeting time within this structure. Records are kept of these meetings and a report is made to the principal on issues discussed. The mathematics team meet outside timetabled hours on other occasions during the school year. The high level of co-ordination and planning is commended and provides evidence that the department works collaboratively.
Clear progress has been made on the mathematics plan. The current plan contains organisational details of classes and teachers, records of previous meetings dating back to 1999, details of in-house teaching and learning meetings, in-service training and feedback from CPD courses attended. The plan also contains a copy of a previous mathematics inspection report, a record of student activities during Maths Week and suggestions for challenging more able students. Programmes of work for each year group, in the form of chapter headings to be covered each term, have been agreed and are being implemented. To enhance the good work already accomplished it is recommended that a future review of the plan include a list of key topics to be covered and key skills that students should master. This would serve to further the sharing of and implementation of sound professional practice among mathematics colleagues. The publications Junior Certificate Mathematics Guidelines for Teachers and Calculators: Guidelines for Post Primary Schools could make a significant contribution in this area. The plan should also include a list of the resources available in the school for the teaching of Mathematics and their locations and a section on ICT use to complement the work of the teachers in increasing their own skill in this area.
There is a TY mathematics plan. The current plan consists of a list of chapters from the textbook to be covered. It is recommended that this plan be reviewed to reflect the innovative teaching methodology observed and the reported use of project work, in which two classes work together, and the use of assessment by portfolio, as well as the reported active nature of the teaching of statistics and probability.
A majority of mathematics teachers made individually prepared planning and preparation materials available for review during the inspection visit. Included in these were detailed weekly and monthly work plans, prepared worksheets and transparencies, homework records, students’ attendance and assessments records and mathematics support-service material. In some cases extensive amounts of relevant material were presented and the high levels of preparation are acknowledged and commended.
In lessons observed, teachers’ preparation for teaching was evident and presentation of work was clear. While classroom activities were generally of a passive nature students were attentive to their work and on occasion enthusiasm for and interest in the subject were apparent. Classroom management was good and students were kept on task. There was a sense of mutual respect between teachers and students, creating an atmosphere that was conducive to learning.
The predominant methodology used in lessons observed was whole-class teacher-directed learning. This involved presentation of work at the board followed by the setting of work for individual student practice. Within this traditional structure, lessons were generally purposeful and content and pace were appropriate to syllabus and level. In line with good practice, some teachers explicitly shared the lesson objective with students. Where this was done it had the effect of increasing the students’ motivation and sense of accomplishment. It is suggested that all lessons should have a clearly defined objective that appropriately challenges students of all abilities and that this objective is explicitly stated to the learners. Best practice would then see each lesson end with a review of the attainment, or otherwise, of the objective.
Teachers had good knowledge of their students’ abilities and there was evidence that where teachers set appropriate high standards, students generally strove to achieve them. In some instances students were asked to read and analyse questions, identify areas of difficulty and propose methods of solution. Other examples of good practice in mathematics teaching observed in Carrigaline Community School included the use of clear methods in arriving at solutions, the appropriate use of mathematical language by both teachers and students, ongoing review of terminology and concepts, high levels of attention to individual students, acknowledging and drawing on previous learning and experience of students, and some use of concrete materials.
Generally lessons began with the correction of homework. Board work, textbooks and worksheets were the main resources used during lessons, although there were commendable examples of teacher-prepared ‘loop’ cards and puzzles being used to engage the students and reinforce concepts taught. In one lesson, where students were writing notes in their copies, the class worked through some examples and they decided on the ‘best’ wording of the note to be inserted into the copybook. This commendable practice is in line with the principles of ‘assessment for learning’ and is an effective means of getting students more involved in their own learning. It is recommended that these strategies and other teaching methodologies such as investigation, consolidation activities, practical work, discussion, pair work, group work, quiz activities, use of concrete materials and relating learning to students’ own experiences should be appropriately incorporated into current classroom practice. Some classrooms visited had displays of mathematical posters and students’ project work, enhancing the learning environment and reminding students of key mathematical concepts or formulae.
Interaction between teacher and students generally took the form of brief answers by the students to ‘fill-in’ or ‘next-step’ type questions from the teacher. There were some good examples where teachers built on their students’ answers and encouraged them to explain and justify their thinking and methods. This is good practice as it helps students to consolidate their learning and maintain their engagement with the topic. It is recommended, therefore, that a range of questioning strategies be employed in all lessons.
Appropriate learning was evident from an examination of the written work being done by students, during the lessons inspected. The quality of this work and their justification of it to the inspector indicated that, in almost all instances, they had understood the procedures taught during the lessons and were able to apply them to similar problems set by their teachers. In interactions with the inspector, it was evident that, in most cases, students had a clear understanding of the work in which they were involved and could relate it to other areas of Mathematics. In almost all lessons students were able to discuss solutions to questions posed to them in appropriate mathematical language.
Students’ progress is assessed through the monitoring of class work and homework. Students also receive regular end-of-topic tests and end-of-term tests. Staff members are supported through the provision of teachers’ diaries and these are used by teachers to record the results of students’ assessments and their attendance.
All the mixed-ability first-year classes sit common examinations at Christmas and summer. This is good practice as the students’ mathematical ability at the end of first year is the main criterion for placement in second-year classes and this process ensures that all students are similarly assessed. It is reported that from first year on, some other common class tests and formal tests, within levels, also occur. This good practice is commended and should be expanded where possible. For example, teachers could agree on some common questions to appear on tests.
Reports are issued to parents twice a year following formal assessments for non-examination classes at Christmas and summer. Students in third and sixth year are assessed through Christmas tests and ‘mock’ examinations in February. Each year group also has a parent-teacher meeting during the school year.
The performance of students in the state examinations is reviewed each year and is used to inform planning. There has been a gradual increase in the uptake rates at higher level over recent years at both junior and senior cycle. Among the ongoing efforts to increase the uptake levels in the current year is the creation of two higher-level classes in fifth year. One of these classes is composed entirely of students who have completed the optional TY programme and the other contains students who have completed their junior cycle. The effects of this process will be monitored. All concerned are commended for their willingness to be innovative in the pursuit of their goals.
Homework was assigned in lessons. It was appropriate, in line with the syllabus and provided students with an opportunity to develop mathematical concepts engaged with during the lesson. A review of a sample of students’ copybooks at Carrigaline Community School revealed relevant work, reasonably well presented by students and generally monitored by teachers.
To recognise students’ success, the school organises an awards ceremony which acknowledges academic and non-academic achievements within the school. Students have the opportunity to participate in a range of extra-curricular activities pertaining to Mathematics. In previous years students have participated in the Problem Solving for Irish Second Level Mathematicians (PRISM) competitions, organised nationally as part of Maths Week Ireland. TY students have attended lectures in UCC organised as part of this week and lecturers have visited the school to talk to students. Students have participated in the Irish Mathematics Teachers Association (IMTA) organised Irish Junior Mathematics Competition during first year. Students from the school have been selected for training for the international Maths Olympiad competition on the basis of their performance in the Junior Certificate mathematics examination. All involved in providing support for students in such activities are commended.
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: