An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Roll number: 71980O
Date of inspection: 10 October 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in O’Carolan College. 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 was given an opportunity to comment in writing on the findings and recommendations of the report; a response was not received from the board.
O’Carolan College offers a full range of programmes for junior and senior cycle students; Junior Certificate, Junior Certificate School Programme (JCSP), Transition Year (TY), Established Leaving Certificate, Leaving Certificate Applied (LCA) and Leaving Certificate Vocational Programme (LCVP) cater for its current enrolment of 415 students. The time allocated to Mathematics is appropriate to the needs of the subject with five periods per week for all junior cycle classes, five periods for TY, Established Leaving Certificate and LCVP classes, and three periods per week for classes following the LCA programme. The arrangement of class periods, occurring in all but one case, on separate days of the week, is also suited to the way in which Mathematics learning builds on previously developed skills and prior learning.
In both first and second year, two classes out of four are concurrently timetabled, or ‘set’, for Mathematics. Mathematics classes in third, fifth and sixth years are concurrently timetabled across the complete year group. Commendably, this timetabling strategy helps to facilitate students’ access to the different levels of the subject, and to allow movement of students between levels, when necessary. Students wishing to change level follow a formal procedure developed by the school, which involves teachers, parents and school management as well as the students themselves. In first year one of the ‘sets’ of two classes has been further divided to include a third grouping for students who need additional support in numeracy. Fifth year also includes a third teaching group to try to ensure all sixty students within the year group can study the subject at a level and pace most suited to their abilities and needs.
First year students are taught Mathematics in mixed-ability classes, with the exception of those being taught in the additional class grouping referred to above. This, commendably, allows the students follow a common programme of work and settle into the college prior to having to make choices regarding their level of study of the subject. Division into levels begins in second year and continues into third year. Students are encouraged to and supported in studying Mathematics at the highest level possible for as long as possible and commendable progress has been made in this area in recent years.
Teachers are assigned to mathematics classes by school management, taking into account the benefits for students of continuity through programmes of study, the need to rotate levels among members of the mathematics team, and teachers’ individual workloads. It is a sign of good curriculum management and of solid commitment to the subject that there has been no difficulty, even within the relatively small seven-person team, in identifying teachers who are willing to teach the Leaving Certificate higher-level course.
The identification of students in need of learning support in numeracy takes place through the entrance assessment process including a standardised testing element, information received from feeder primary schools and information offered by parents. Following entry into first year, observations are also invited from mathematics teachers, who can refer students for additional support. The needs of these students are addressed on a withdrawal basis for small group teaching or individual assistance. In keeping with good practice, all students attend regular mathematics class with their peers and there is close linking between the mathematics teacher and the teacher providing supplementary support.
The educational support department has recently prioritised the purchase of numeracy materials, which include concrete materials, numeracy games and worksheets. It is recommended that a comprehensive list of concrete resources available in the school to support the teaching and learning of Mathematics, including those available in the educational support department, be drawn up. In addition, a system for the sharing of these resources among the mathematics teachers should be agreed and implemented. Having applied to participate in one of the Junior Certificate School Programme (JCSP) numeracy initiatives, it is planned that targeted students will soon be involved in a cross-curricular numeracy project. Improvements in students’ numeracy levels are currently identified through tests administered in regular mathematics class. However, in line with good practice, there are plans to test students prior to engaging in numeracy support activities and again on annual completion of such activities.
O’Carolan College has made significant investment in information and communications technology (ICT) resources for the teaching and learning of Mathematics. Each member of the mathematics team has the use of a “Tablet” personal computer (PC) on which notes and diagrams can be handwritten and drawn. In addition, each classroom has a networked PC, internet access and data projector, meaning that high-quality enhanced presentations can be easily made for any group of students on any topic. The challenge for teachers now is to make sure that the capacity of this technology is exploited to the full and that it is contributing in a positive way to students’ learning.
Continuing professional development courses attended recently by the mathematics teachers include Leaving Certificate algebra and trigonometry and TY Mathematics. All members of the team are informed about upcoming courses with attendee/s decided by school management, based on the courses and levels team members are involved in teaching at the time. Currently two teachers are members of the mathematics and/or applied mathematics subject teachers’ associations. The school supports this important professional connection by funding the cost of membership.
Co-curricular activities engaged in by students at the school have included mathematics puzzles with junior students for Maths week, the first-year Mathematics competition promoted by the Irish Mathematics Teachers’ Association (IMTA), the Problem Solving for Irish Second-level Mathematicians (PRISM) competition promoted by University College Galway (NUIG) and the International Mathematics Olympiad. It is suggested that efforts be made to strengthen the ‘whole school’ profile of Mathematics, extending competitions outside the classroom and promoting mathematics activities through poster displays and intercom announcements.
Members of the mathematics teaching team work together with the aid of a co-ordinator whose duties, carried out on a voluntary basis, include calling and chairing meetings, disseminating information, coordinating planning and maintaining the ‘red book’ of minutes of meetings. In principle, the co-ordinator post is rotating, but in practice, circumstances on the ground have meant the same person has acted in the post for a number of years. Prior to the inspection, a new co-ordinator took over and is being inducted into the role.
Formal team meetings are facilitated by school management at the beginning of the school year and during Christmas and summer term examination periods. In exceptional circumstances, additional meetings can be requested and team members released from class to attend. Informal meetings take place on an ongoing basis between subgroups of the team, for example, teachers teaching within the same year group or level. Minutes of formal meetings are recorded and those for past and current years, going back to August 2005, were made available for inspection. This excellent practice of the maintenance of long-term records gives clear evidence of collaborative working among team members and indicates a wide range of relevant discussions taking place through the years. Laudably, the system in place within the school ensures this will continue to be the practice.
Significant work has been done on developing a mathematics department plan that includes a department mission statement, planning guidelines, long-term programmes of work for each year group and level, relevant Department of Education and Science (DES) and State Examinations Commission (SEC) documentation, school homework policy, and certificate examination results for the past two years. Of particular note are the written programmes of work for mathematics support classes in first, second and third years, and the clear evidence of periodic programme review. Team members are congratulated on their commitment to and understanding of the importance of the planning process. To further support the planning and review process, it is recommended that long-term work programmes be expanded and that student activities and web resources that enhance the learning experience be identified. Similarly, the TY programme, which appropriately introduces students to traditional mathematics topics, hands-on activities and a practical project, should be written to more fully reflect this reality.
As a next step in the mathematics department planning work, it would be appropriate for its focus to move to teaching methods. It is easy to understand the benefits for students if teachers agree consistent approaches to teaching core elements of the syllabus, for example ‘percentages’ or ‘factors’. Such approaches should be agreed, not only among the mathematics team, but, in the longer term, across those aspects of the curriculum where mathematics plays a role.
Some teachers made personal preparation and planning documentation available during the inspection. These included teacher notes, student notes, revision sheets, work sheets, student homework, behaviour and assessment records, and records of work given in class.
Data on students’ participation and achievement in certificate examinations is analysed and discussed among members of the team. The result has clearly contributed to planning and review activities within the department including modifying timetabling arrangements and targeting work programmes on specific areas.
Eight lessons were observed by the inspector during the evaluation. In all cases, teachers were prepared for their teaching and the content of lessons was in line with syllabus recommendations. However, there was scope for lesson content and delivery to be planned more carefully, taking into account students’ levels of ability and the importance of allowing them achieve the lesson objectives. The explicit statement of the learning goal, either orally or in writing, as part of the normal classroom routine would greatly assist in this.
There were instances when the pace of lessons was not sufficiently challenging for students or there was too much focus on the mathematics content being ‘difficult’. These can lead to students losing interest in the subject or feeling there is no point in trying to achieve something that is outside their reach. To counteract this, teachers should maintain an appropriately brisk pace throughout lessons and not only hold, but also communicate, on an ongoing basis, high but realistic expectations for all students.
In all lessons observed, teachers made good use of subject-specific terminology, helping students become familiar with mathematics vocabulary and expressions. Students’ use of such terminology would increase with their more active involvement in lessons and continued teacher support. Specific examples observed of good practice in mathematics teaching included the use of cut-outs to liven up a topic, the encouragement of students to work in pairs, students demonstrating work at the board, the use of questioning as a means of including students in the work of the class, and the communication of high expectations of students’ abilities and attainment in relation to particular tasks.
Teaching observed was, however, predominantly conducted through the presentation of work via the Tablet PC followed by the setting of exercises for individual student practice. To complement this ‘traditional’ approach, it is recommended that a broader range of teaching methodologies and materials be explored and developed. Their incorporation into lessons recognises students’ different preferred learning styles and exploits a richer variety of learning opportunities. Some appropriate suggested strategies can be found in National Council for Curriculum and Assessment (NCCA) documents and through the Second Level Support Service (SLSS) mathematics support team. The use of mathematics-specific software packages might also be considered, as a means of gaining full advantage of ICT hardware currently being used by teachers.
Classroom management was, in all cases, relaxed and effective and students were supported in asking questions and affirmed in their learning. Mutual respect between teachers and students was evident. Also, the classroom environments which were in some cases enhanced with poster displays were found to be conducive to learning.
It is commendable that the college’s homework policy is complemented by agreed procedures for the assigning and marking of homework that apply in mathematics classes. It is noteworthy that these policies and procedures were implemented in almost all lessons visited during the inspection.
Students’ progress in Mathematics is assessed through participation in classroom activities, homework, class tests and term examinations. A review of a random sample of students’ copy books showed relevant and appropriate work with evidence of teacher monitoring. However, there was considerable variety in the standards of presentation; in some instances, the copybooks displayed undisciplined working techniques that can lead to errors being made. Teachers should impress on students the importance of presenting their work in a structured and orderly fashion as a means of assisting them in achieving their potential in the subject.
Parents/guardians are kept informed of progress on a regular basis, through student journals, student diaries, at scheduled parent/teacher meetings and through written reports. It is notable that third and sixth-year classes have two scheduled parent/teacher meetings during the school year and from third year onwards, students are invited to attend such meetings with their parents/guardians. Commendably, parents of fifth and sixth-year students receive reports of progress on a monthly basis, indicating a considerable commitment by school management and teachers to the continued advancement of students at senior level in the college.
The following are the main strengths identified in the evaluation:
· The timetabling strategy for Mathematics is appropriate; it facilitates students’ access to levels and allows for movement between levels.
· First-year students are taught mainly in mixed-ability groupings, allowing a settling-in period prior to decisions regarding level of study having to be made.
· Commendable progress has been made in encouraging students to study Mathematics at the highest level possible for as long as possible.
· A cross-curricular numeracy project has been planned for students with numeracy difficulties.
· There has been significant investment in ICT resources to enhance the teaching and learning of Mathematics.
· Members of the mathematics team work together with the aid of a department co-ordinator. Formal meetings facilitated by school management take place at least three times in the school year. Informal
meetings take place on an ongoing basis.
· It is excellent practice that minutes of meetings going back to 2005 are maintained within the school.
· Highly commendable work has been done on developing a mathematics department plan.
· Data on students’ participation and achievement in certificate examinations is analysed and discussed and contributes to planning and review activities.
· Teachers made good use of mathematics terminology, helping students become familiar with the subject’s vocabulary and expressions.
· Classroom management was relaxed and effective and students were supported and affirmed in their learning. Mutual respect between teachers and students was evident.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· Long-term work programmes should be expanded to include the identification of activities and web resources that enhance the learning experience for students.
· The mathematics team should work towards the development of consistent approaches to teaching core elements of the syllabus.
· Lesson content should be carefully planned, taking into account students’ levels of ability and the importance of allowing them experience success in Mathematics.
· The pace of lessons should be appropriately brisk, in line with high but realistic expectations of students’ capabilities.
· A broader range of teaching methodologies and resources should be explored and developed.
· As a means of assisting students to achieve their full potential in the subject, teachers should impress on them the importance of presenting their work in a structured and orderly fashion.
A post-evaluation meeting was 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 March 2009