An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Mount Temple Comprehensive
Malahide Road, Dublin 3
Roll number: 81002K
Date of inspection: 16 September 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Mount Temple Comprehensive. 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 acting principal, deputy principal and a number of 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.
Mount Temple Comprehensive has a current enrolment of 845 students studying the Junior Certificate, Transition Year (TY), Leaving Certificate, Leaving Certificate Applied (LCA) and Leaving Certificate Vocational (LCVP) programmes. The time allocation for Mathematics in each of these programmes is good, indicating a strong commitment to the subject in the school. First year, second year and third year have five periods per week, TY has four periods, fifth year receives six periods, sixth year five periods and LCA has four periods of Mathematical Applications. Lessons are generally well spread throughout the week, facilitating, for most classes, daily progress in a subject in which new learning builds to a great extent on previously developed skills and prior learning.
Mathematics is concurrently timetabled in second year, third year, fifth year and sixth year, making it possible for students to study the subject at the level most suited to their abilities and interests, and allowing their movement between levels during the course of their studies. The significant restrictions this arrangement places on the timetabling process should not be underestimated and reaffirms the importance given to the subject by the school.
First-year students are taught all subjects, including Mathematics, in mixed-ability groups. This allows them appropriate time to settle into the school and display their mathematical aptitudes prior to any decisions being made regarding their level of study. This year, TY students are also taught in mixed-ability groups – an arrangement that can be very well accommodated within that programme and is encouraged.
The levels taught by the mathematics teachers are rotated following discussion among the members of the teaching team. Continuity from second year to third year and from fifth year to sixth year is a priority. At Leaving Certificate, the higher-level course is currently rotated among a group of three teachers and there is a commendable openness to including others interested in teaching at this level over time.
Students in need of numeracy supports are primarily identified through standardised testing as part of the school’s incoming assessment process, through information received from parents or feeder primary schools and through the observations of teachers in mathematics classes, all of which are appropriate. A referral form allows teachers record their concerns and is followed up by a member of the educational support department. The needs of identified students are then addressed in a number of ways; small groups that will be withdrawn from the mainstream timetable and taught by a member of the educational support department are currently being formed according to level of ability; an additional class grouping has been formed in both third year and fifth-year mathematics ‘sets’ to support specified students; finally, in-class support is taking place in the LCA class, targeting the students most in need of assistance in the area of numeracy.
Currently, the educational supports team includes an insufficient number of mathematics specialists. While some steps have recently been taken to address this situation, it is recommended that the numbers of such personnel be further increased so as to enable numeracy support to be provided by teachers who have specialisms in Mathematics.
There is a good range of materials available in the school to enhance the teaching and learning of Mathematics, including demonstration geometry sets, set rings, probability pack, two dedicated data projectors, overhead projectors, class sets of geometry equipment and scientific calculators. All teachers are aware of the location within the school of this equipment and all have ready access.
Teachers are facilitated in engaging in continuing professional development (CPD), and have attended in-service courses offered by the Mathematics Support Service and the Irish Mathematics Teachers’ Association (IMTA). One of the teaching team has taken part in a Project Maths rehearsal day, providing feedback on presentations developed for nationwide delivery. Teachers have also participated in CPD activities taking place in the evening time, an indication of a strong commitment to their subject and their students. Currently, no member of the team holds membership of the IMTA and therefore it is recommended that membership be taken out so as to keep in touch with issues and changes occurring at this very important time in mathematics education.
Co-curricular mathematics activities, including the celebration of Maths Week, are strongly promoted and supported by members of the teaching team. Students have participated in the first-year mathematics quiz and Team Maths competition organised by the IMTA, the Hamilton Maths Challenge and training sessions for the Irish Mathematics Olympiad. In addition, a school award has recently been introduced to recognise outstanding achievement in Mathematics.
The mathematics department has experienced significant changes in personnel in recent years and the current team of eleven teachers is making progress in establishing collegial and collaborative practices. The work of the mathematics team is ably co-ordinated by the senior mathematics teacher who took over the role at the beginning of the last school year. It has been agreed among the team that the role will rotate every two years, allowing each member contribute to and gain experience from conducting the business of the department. The role of co-ordinator, as indicated in documentation, is to co-ordinate and chair department meetings, to relay information to other mathematics teachers and to oversee the movement of students between classes and levels. Informally, the role also includes the encouragement of new ideas from younger staff members and the building of a team spirit within the mathematics department.
Meetings of the mathematics team are facilitated by school management with the full team, or teachers common to a year group or programme, meeting, on average, once a month. The minutes of meetings from the 2008-2009 school year and from the beginning of the 2009-2010 school year were included in the department plan. The discussion and collaboration indicated in these minutes on areas such as assessment, TY and resources is commendable and should be continued. As an addition, agendas for future mathematics meetings should include a slot for feedback from continuing professional development activities. This will be particularly important in light of changes being introduced under Project Maths.
Significant work has gone into developing an informative department plan, which includes subject organisation details, data on certificate examination results, programme syllabuses, cross-curricular links, a list of resources available in the school and information on co-curricular activities. The mathematics teachers are congratulated on the collaborative work engaged in on the development of medium to long-term work programmes for each distinct year group and level. To further enhance the good work already undertaken, it is recommended that programmes of work be expanded, identifying and linking specific methodologies as well as supporting materials with course content and objectives.
Almost all mathematics teachers made personal planning and preparation materials available for inspection. Extensive banks of student handouts and worksheets, TY-specific materials, games, puzzles and ‘real-life’ documentation were of particular note and were indicative of thorough preparation and superb organisation by some teachers.
School management provides data on results in certificate examinations for discussion at subject department meetings. Therefore, there is awareness of the school’s standing in terms of achievement and up-take in these examinations. The mathematics team is encouraged to compile and analyse such data over a three or four-year period with a view to identifying the school’s strengths and areas for improvement, thus contributing more fully to team planning and review.
In each of the eight lessons observed, teachers had prepared well for their teaching, with lesson plans, worked examples, homework solutions, student activities, digital and overhead projector presentations and worksheets each contributing to the enhancement of the learning experience. A number of teachers began lessons by sharing the learning objective with students. It is recommended that the team of mathematics teachers makes it its policy and practice to explicitly state the learning objective at the beginning of each lesson, bringing a certainty and focus to students’ work.
The majority of lessons were structured around the teacher presenting work at the board followed by the assigning of exercises for student practice. While recognising the usefulness of this ‘traditional’ approach to mathematics teaching, it is recommended that teachers explore ways in which to include alternative student activities into class work. In two lessons observed, group activities generated enthusiasm and led to student enjoyment, clear evidence of the positive effect of such activities on the learning experience.
There was good and appropriate use of mathematical terminology and notation by teachers and some instances where this was also the case for students. Generally, however, teachers need to encourage greater use of the correct mathematics terms and expressions in students’ contributions. Simple ways of achieving this are asking students to accurately explain their workings to questions, to suggest next steps in solutions presented on the board or to identify the nature of errors made in written work.
In almost all lessons, teachers had appropriately high expectations of students’ capabilities. Students responded accordingly, underlining clearly the importance of teachers setting such high standards. Equally important is the pace at which lessons are conducted; an appropriately brisk passage through class work should be adopted by all teachers so as to maintain students’ motivation and to uphold their interest in the subject. Lesson content was not generally linked to students’ ‘real life’ experiences, in some cases missing opportunities to increase the relevance of the subject matter. Teachers should work together to identify appropriate links between class work and everyday life and to avail of every opportunity to exploit these links in class.
In all lessons observed, students were attentive and engaged in the work at hand. Mutual respect between teachers and students was clear. Teachers were affirming of students’ efforts and the classroom atmosphere was positive. Students were comfortable answering teachers’ questions and putting forward their own questions, providing evidence of a supportive learning environment. There was a small number of examples of probing questions being asked, challenging students’ understanding of the work in hand. A concerted effort should be made by all teachers teaching Mathematics to make “why”, “why not” and “explain” questions an integral part of all mathematics lessons.
In some classes, before the end of the lesson, teachers conducted a brief review of material covered. This good practice should be adopted by all mathematics teachers as a means of further reinforcing learning.
The very good practice of administering common end-of-term examination papers in all year groups is in place. First-year students sit common papers at the end of Christmas and summer terms, supporting them and their parents in making decisions regarding the level at which to study Mathematics in second year. From second year onwards, common assessments within levels are used, confirming choice of level and maintaining standards across class groups. Those and other assessment procedures have been discussed by the mathematics team, but a common practice to be followed by all teachers, in particular in relation to class tests, has not yet been established. It is recommended that a consistent approach to the ongoing and regular testing of student progress be agreed and implemented.
The assigning and marking of class work and homework is also used by teachers to assess progress made in Mathematics. A review of a random sample of students’ copy books indicated such work to be relevant to programme and syllabus and, in most cases, clearly monitored by teachers. In addition, a number of teachers had provided written feedback for students, in line with the principles of assessment for learning (AfL). All members of the mathematics team are encouraged to investigate further AfL strategies with a view to including them in their classroom practices. In some cases, students’ standards of presentation and correction of written work were less than expected. In these cases, closer monitoring is required, and generally all students should be reminded of the importance of presenting and marking their work in a structured and orderly fashion so as to increase the likelihood they will achieve their potential in the subject.
Transition Year assessment modes have been broadened this year, indicating a praiseworthy openness to new ideas on the part of the teaching team. Students will now receive grades for their portfolio of work, for the project they will undertake and for their achievements in their Christmas and summer term examinations.
Teachers keep records of students’ achievements in work assignments, building a profile of progress made. This progress is reported to parents in formal written reports issued twice in the school year and at parent-teacher meetings that take place once in the school year for each year group.
The following are the main strengths identified in the evaluation:
· The good time allocation for Mathematics and the concurrent timetabling of mathematics classes indicate a strong commitment to the subject in the school.
· First-year students are taught in mixed-ability groups, allowing them time to settle into the school and display their mathematical aptitudes prior to any decisions being made regarding their
level of study of the subject.
· The higher-level Leaving Certificate course is currently rotated among three teachers and there is an openness to including others interested in teaching at this level over time.
· Co-curricular mathematics activities, including the celebration of Maths Week, are strongly promoted and supported by members of the teaching team.
· The mathematics department has experienced significant changes in personnel in recent years and the current team of teachers is making progress in establishing collegial and collaborative practices.
· Teachers prepared well for their teaching; there was evidence of thorough individual preparation and superb organisation by some teachers.
· Mutual respect between teachers and students was clear. Teachers were affirming of students’ efforts and the classroom atmosphere was positive.
· The very good practice of administering common end-of-term examination papers in all year groups is in place. In addition, Transition Year assessment modes have been broadened.
· A number of teachers provided feedback for students on their class and home work, in line with the principles of assessment for learning (AfL).
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· An increase is recommended in the numbers of teachers with a mathematics background who work with the educational supports team, so as to enable numeracy support to be
provided by teachers who have specialisms in Mathematics.
· It is recommended that long-term schemes of work be expanded, identifying and linking specific methodologies as well as supporting materials with course content and objectives.
· Certificate examinations data should be compiled and analysed over a three or four-year period with a view to identifying the school’s strengths and areas for improvement.
· It is recommended that the team of mathematics teachers makes it its policy and practice to explicitly state the learning objective at the beginning of each lesson.
· Teachers need to explore ways in which to include a range of student activities into class work. In addition, probing questions that challenge students’ understanding should be an
integral part of all mathematics lessons.
· It is important that teachers maintain high expectations of students’ abilities and that lessons are conducted at an appropriately brisk pace.
· It is recommended that a consistent approach to the ongoing and regular testing of student progress be agreed and implemented.
A post-evaluation meeting was held with a number of the teachers of Mathematics, the deputy principal and the acting principal at the conclusion of the evaluation, when the draft findings and recommendations of the evaluation were presented and discussed.
Published February 2010