An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Loreto High School, Beaufort
Rathfarnham, Dublin 14
Roll number: 60340N
Date of inspection: 29 February 200
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Loreto High School, Beaufort, conducted as part of a whole school evaluation. 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.
Timetable provision for Mathematics is good. Five mathematics lessons per week are allocated to first, second, third, fifth and sixth year groups. The Transition Year (TY) group receives four class periods of Mathematics per week. There are plans to increase the fifth and sixth year allocation to six lessons per week and to reduce the transition year allocation to three lessons per week. The planned increase for fifth and sixth year groups will bring the allocation for Mathematics in line with optimal provision and is commended. Mathematics lessons are evenly distributed throughout the school day and across the week and this is good practice.
Students are assigned to one of four mixed ability classes in first year. Throughout the year, students sit regular common assessment tests. Students are then set at the beginning of second year into one of five classes in order of ability on the basis of the results from common end-of-topic tests and more formal Christmas and summer examinations. All students then follow a common course, with common assessments and a common Christmas examination. Following this, students select the higher or ordinary level course and classes are again set within levels. At the beginning of TY, which is compulsory, students are divided for the senior cycle, according to ability, into one of five class groups. Students are encouraged to study the highest level possible for as long as possible, and this is good practice. Change of level is facilitated by concurrent timetabling and is accommodated in consultation with parents and the career guidance service. However, it is recommended that class formation for Mathematics be reviewed to accommodate varying rates of student development and to maintain teachers’ and students’ expectations of high levels of achievement. It is recommended that students be divided into higher and ordinary level groups and then assigned to mixed ability classes within these levels. This would allow for the highest possible expectation for the maximum number of students.
School management is commended for the provision of a wide variety of teaching resources. Most teachers have been assigned their own classrooms. All mathematics classrooms have been recently equipped with Information and Communications Technology (ICT). All mathematics teachers’ classrooms have broadband internet access and ceiling-mounted data projectors. All teachers have laptop computers and the mathematics department has recently acquired three interactive white boards. It has also been provided with a wide range of teaching aids such as sets of log tables, geometry instruments, 3-D solids and commercial posters to enhance the physical learning environment. Teacher Continual Professional Development (CPD) is fully facilitated. Teachers are encouraged by management to attend in-service courses. The school funds membership of The Irish Mathematics Teachers’ Association and relevant further education courses. Although there is no set budget for the mathematics department, requests for resources and equipment are favourably considered.
Students who find Mathematics particularly difficult are identified through discussions with feeder primary schools, pre-entry assessment, regular in-house common testing, and teacher observation. Support is provided through the creation of small groups for extra tuition and occasionally through the provision of individual tuition during withdrawal from subjects other than Mathematics. Learning support can continue throughout the school life of the students if necessary. Mathematics learning support is provided by members of the mathematics department and teachers of other subjects. There are very close informal links between the mathematics department and the members of the learning support team. They consult each other on a regular basis to ensure that uniformity of content and approach is observed. This high level of collaboration is commended.
The mathematics department consists of eight teachers and most are subject specialists. The school provides an induction programme for new teachers and there is a strong culture of support among the members of the mathematics teaching team, which is warmly commended. Classes are allocated to teachers through consultation with management. It is department policy that, where possible, classes retain the same teacher from year to year. This is good practice. Levels are rotated between some members of the teaching team, and the full rotation of teachers in the junior cycle is commended. In order to extend the high level of expertise necessary for teaching higher level Leaving Certificate Mathematics, it is recommended that more teachers become involved at this level and that a move towards more rotation of teachers in the senior cycle be considered. This will enable the school to meet the changing needs of the curriculum in the coming years.
Formal planning time is allocated three times per year as part of the whole school planning process. To facilitate teachers who teach more than one subject, the meeting schedule on school planning days is split to ensure attendance of all members of the mathematics teaching team at the planning meeting. This is very good practice. Mathematics teachers also meet regularly on an informal basis. Records are maintained and minutes are kept. The position of mathematics co-ordinator is rotated between members of the teaching team. The mathematics department operates within a culture of collaboration and co-operation and this has led to a strong spirit of team work and collegial support. This is highly commended.
It was evident from the inspectors’ review of planning documentation that school development planning has progressed to subject areas. However, planning for Mathematics mainly consists of schemes of work in the form of chapters to be covered within set timeframes. The planning initiated here needs to be developed over time. Within levels, mathematics teachers teach the same topic at the same time. This has facilitated the administration of common assessment tests. It has also made it possible for students to change level mid-year. While this has led to a planned cohesive approach and is commended, it is important that the subject plan be regularly amended to reflect more accurately the day-to-day teaching and learning activities in the classroom. At the beginning of all of the lessons observed the learning intention was shared with the students. It is suggested that a record of these daily learning intentions be maintained and collated at the end of the year. This would form an accurate plan that would reflect classroom activity more closely. The department plan should also reflect the way in which the mathematics team work together to create an environment of openness, where a sharing of resources and experience is possible. It should also contain a list of resources available and in-service courses attended.
The focus of the TY plan is on Leaving Certificate material and the plan mostly consists of a list of chapters to be covered for the year. It is strongly recommended that this plan be extended to incorporate a wider range of mathematical experience in keeping with the spirit and intention of the TY programme: placing the emphasis on teaching different Mathematics or on Mathematics taught differently. It is commended that a project on famous Mathematicians had been completed by most TY groups and it is suggested that a module be created to study some of the Mathematics that made them famous. A module on the Mathematics of Fibonacci or Euler for example would be ideal for TY. It is also suggested that a module of Applied Mathematics be considered for TY. This could be beneficial for two reasons: firstly, it would help develop problem solving skills that can be applied to other areas; secondly, it would appeal to the substantial number of very able students in the school who might consider taking it as a Leaving Certificate subject. Although Leaving Certificate material can form part of a TY plan, TY should be seen above all as a valuable opportunity to encourage students to engage with Mathematics on an enjoyable level and to help them gain a greater appreciation for the subject. The planned increase in timetable allocation for fifth and sixth year will provide the extra time necessary to meet all syllabus requirements for the Certificate Examinations.
All the lessons observed were well planned. Teachers keep records of topics to be covered and homework given. Teacher resources that were available for inspection included revision sheets, tests, formula sheets, handouts and puzzle sheets. These were all appropriate and were designed to support learning. Teachers reported that they share these resources on a regular basis; this is good practice.
The quality of teaching and learning in Mathematics was generally good, and in many instances students were observed to be very competent and interested in mathematical ideas and applications. Teaching predominantly consisted of teacher example followed by student exercise. Within this traditional approach, teaching was effective. However, it is suggested that the range of teaching and learning methods be extended to support more active learning and a greater engagement with mathematical concepts.
The lessons observed were purposeful, appropriate to the syllabus, very well planned and all the necessary resources were utilised. In all cases, teachers’ explanations were very clear and learning intentions were shared with the students. Best practice in this regard occurred when the teacher wrote the aims of the lesson on the whiteboard and then checked at the end of the lesson to see that these had been achieved. This practice is commended because it increases motivation and leads to a sense of accomplishment on achieving the day’s goal. Revision work was well handled and linked to new material being presented, thus helping to reinforce learning and to place new ideas in context. Some teachers have used real life examples to help make Mathematics more relevant, and this is good practice. For example, in copybooks from one lesson observed, Simpson’s rule had been used to estimate the area of the Shannon Estuary from the Ordinance Survey map.
In all lessons observed, teachers made effective use of the wide range of resources at their disposal. Teachers’ work on the white board was very clear and in all cases teachers were very careful to model good presentation. This was of particular note where the high level of student ability necessitated a very fast pace and where teachers were careful to include all the relevant steps of worked solutions. Appropriate use of ICT was observed in the classes visited. In the classrooms where they were installed teachers used interactive white boards to recall previous examples and to save current work. They also reported their usefulness in the teaching of graphs and geometry. In many of the classes visited good use was made of power point presentations particularly in the lessons on volume and area. There are plans to increase the integration of ICT in teaching and learning over time.
Teachers made good use of questioning, both global and directed, throughout the lessons observed. Best practice was seen when more open and probing questions were used to encourage students to think for themselves. Since this type of questioning is so beneficial to learning in Mathematics, it is suggested that it be incorporated into lessons more frequently. In one lesson observed, a number of students were invited to correct homework on the whiteboard. This simple but effective methodology enabled students to become active participants in the lesson and they were able to demonstrate their understanding with confidence. In another lesson observed, the student-led solving of a problem using a non-traditional method was affirmed by the teacher writing the steps taken onto the whiteboard. This very good practice is commended as it rewards student innovation and helps students develop an appreciation of Mathematics.
The relationships between students and teachers were observed to be mutually respectful. This has led to the creation of a working environment where high expectations are set for students and where students respond accordingly. The very high standard of student behaviour and the excellent working atmosphere that exists in each classroom enables students to contribute to and participate fully in lessons with absolute confidence. In interactions with the inspector, the students were able to demonstrate understanding of the concepts taught and could display clear, solid mathematical knowledge. They were also quite fluent in the use of appropriate mathematical language. The high level of student ability observed at the time of the evaluation, would suggest the need for students to be sufficiently challenged in order to reach their full potential. Strategies for the provision of such challenge should be explored by the mathematics department and the introduction of more student-led, active methodologies is recommended. Organising students to work on unseen problems with little teacher intervention provides a simple but effective example of this approach.
It was reported to the inspector that an experiment to team-teach some aspects of the geometry elements of the Junior Certificate course proved to be very successful. It was also reported that some teachers regularly use the table quiz format to assess learning. Active methodologies such as these are commended as they help students engage with Mathematics in a positive way. Almost all teachers have been allocated their own base classrooms. They have made considerable effort to enhance their physical working environments with a wide range of commercial posters and student generated work. This is commended as it has created a visually stimulating mathematical environment.
Students are formally assessed twice a year at Christmas and summer. Common examination papers with common marking schemes are set for first year and Christmas of second year and within levels for subsequent year groups. Third-year and sixth-year groups also sit mock examinations. Reports are sent home on foot of these formal examinations and assessment reports for first, second and fifth year groups are sent home at Easter. Parent teacher meetings take place once a year.
Learning is routinely assessed through oral questioning and students sit common end-of-topic tests within levels. In most cases, students are expected to keep separate copybooks for tests, class work and homework and on inspection the standard of presentation was found to be very high. Excellent records of student achievement are kept by all teachers. Homework is set regularly, corrected promptly and is monitored carefully in all cases. Students are expected to write corrections into their copybooks and to indicate when their own answers are correct. This is very good practice as it ensures the creation of the copybook as an excellent study resource.
The Mathematics department are planning to participate in World Maths Day and posters advertising the event are displayed on the mathematics notice board. Activities have also been arranged for Maths week. The school has previously been involved in Team Maths and has taken part in Irish Junior Mathematics Competitions. This very good practice is highly commended as it raises the profile of the subject within the school, gives students the opportunity to enjoy Mathematics and allows them to have an interest in Mathematics outside of the classroom.
Prizes are awarded at prize giving for academic and non-academic achievement. In Mathematics achievement within each class group is acknowledged. Prize-giving for Mathematics is good practice as is provides recognition and reward for excellence in the subject and encourages a healthy sense of competition among students. The school is justifiably proud of its high uptake rates for higher level Mathematics in the Certificate Examinations and the achievement in Mathematics of all its students in the Certificate Examinations.
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 with the principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published December 2008