An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
St Dominic’s High School, Santa Sabina
Sutton, Dublin 13
Roll number: 60380C
Date of inspection: 21 October 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in St Dominic’s High School, Santa Sabina, 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. In the junior cycle, four class periods of Mathematics per week are provided for first and second year groups. Third-year classes are timetabled for five mathematics lessons per week. The Transition Year (TY) group receives four mathematics lessons per week. In fifth and sixth year students are allocated five mathematics lessons per week. The level of provision is in keeping with syllabus guidelines. It is good that lessons are evenly distributed across the day and week; this is particularly important since morning lessons are five minutes longer in duration than afternoon lessons. It is recommended that mathematics lessons continue to be distributed in this way.
The mathematics department comprises ten teachers. The teachers themselves decide on teacher allocation to levels. Levels at junior cycle are rotated between all mathematics teachers. Since some members of the mathematics department do not teach senior cycle Mathematics, levels for senior cycle are rotated across a smaller team of teachers. This approach to the rotation of levels is very good practice as it will help the school to retain the high level of expertise necessary to teach higher level Mathematics and to meet the changing needs of the mathematics syllabuses in the coming years. It is department policy that teachers retain the same class group from second to third year and from fifth to sixth year. This continuity is also good practice.
At the beginning of first year, students are assigned to one of three mixed-ability classes. In each of the remaining year groups there is an ordinary level band and a higher level band; students are assigned to a class in one of these bands on the basis of achievement. The abilities are mixed within the level bands. Concurrent timetabling of Mathematics occurs from second year through to sixth year. This is good practice as it provides students with a high degree of flexibility in changing levels and enables the mathematics department to adopt a student-centred approach to level choice.
Students in need of learning support are facilitated through individual or group withdrawal from subjects other than Mathematics. In-class support is also provided in mathematics lessons, through team teaching. There are plans to increase the team teaching provision for Mathematics in the future. This was encouraged during the inspection visits since team teaching is a proven effective approach to the delivery of learning support. Reassessment takes the form of end-of-topic tests and ongoing teacher observation. There is a high level of learning support provided to students who are identified as needing it in Mathematics and the school endeavours to provide the support that best suits the individual needs of each student from the range of options available.
Teachers make use of a wide range of teaching resources for teaching and learning in Mathematics. These are kept in a central location and are shared between mathematics teachers. They include resources from the Junior Certificate Mathematics Support Service and the Irish Mathematics Teachers’ Association (IMTA), geometry sets, metronome, a class set of Voyage 200 graphing calculators, mathematics-related computer software, and scientific calculators for the overhead projector. There is a diverse collection of mathematics reference books and mathematics-related novels that are suitable for all age groups and abilities. These books are used to provide mathematics teachers with ideas for making mathematics lessons more relevant and enjoyable for students and for encouraging students to take an interest in Mathematics outside of the classroom. In addition, teachers have produced models to be used in the teaching of junior cycle geometry and in the solving of 3D trigonometric problems at Leaving Certificate higher level. An extensive and impressive range of mathematics resources has been built up over time by the mathematics department in the school.
The school is very well equipped with information and communications technology (ICT). There are a number of interactive whiteboards, fixed data projectors, mobile data projectors, and laptop computers. Two demonstration rooms are fitted with interactive whiteboards and there are two computer rooms. Most of the school has wireless broadband internet access. Within the mathematics department there are a number of mathematics teachers who have expertise in the use of interactive whiteboards and further training is to take place in the near future for all mathematics teachers. One teacher of Mathematics has a dedicated data projector in the classroom. In addition, mathematics teachers have access to ICT through a booking system. It is recommended that the organisation of access to ICT for teaching and learning in Mathematics be formalised to enable the mathematics department to optimise the value of the ICT resources that are available within the school.
Students of Mathematics participate in a wide range of extra-curricular activities that are organised in the school. Each year students enter the Irish Junior Mathematics Competition and in previous years they have attended the Hamilton Mathematics Workshop. Students are encouraged to take part in the mathematics activities organised for the annual celebration of Maths Week. This year’s events included a poster competition, a daily mathematics puzzle and participation in the PRISM Maths Challenge. The highlight of this year’s Maths Week was the visit to the school by a magician who specialised in mathematics-related tricks; this event was reported to be great fun for all who took part. It is clear from the articles printed in the school’s newsletter that Maths Week and other mathematics-related activities are significant events in the life of the school. It is evident that students are given every opportunity to experience Mathematics for pleasure and this is highly important in promoting a sound mathematics education for students.
Formal planning time is allocated at the beginning of the year as part of the whole-school planning process. Records are maintained and minutes are kept. Mathematics teachers also frequently meet on an informal basis to discuss day-to-day issues that arise. There is currently no co-ordinator for the mathematics department although there is clearly close co-operation and collaboration and a high level of collegial support among members of the mathematics teaching team. It is recommended that a mathematics co-ordinator be appointed to oversee the planning process for Mathematics. This position should rotate among all members of the mathematics department so that everyone can gain expertise in this area.
A mathematics plan has been developed as part of the school development planning process. It contains the aims and objectives of the mathematics department, department policy on student access to levels, provision for students who experience difficulty with Mathematics, homework and assessment procedures, resources available and extra-curricular mathematics activities planned. The plan also contains schemes of work for each year group that consist of chapters of the text book to be covered within given timeframes. It was clear from the range and diversity of resources used for teaching and learning in Mathematics and from the observation of classroom activity during the mathematics inspection that the wide variety of methodologies and teaching strategies actually used in practice is not reflected in the mathematics plan. The plan needs to be further developed over time so that it accurately reflects the day-to-day work of the mathematics department. Through ongoing revision and review, the mathematics plan should become a living document that reflects and informs classroom activity, puts the student at the centre of planning and provides the mathematics department with a forum for the sharing of experience and expertise.
In keeping with good practice, all teachers maintain individual plans. One of the plans reviewed, included a section for teacher self-evaluation. This involved the teacher maintaining a record of the teacher’s own assessment of particular lessons and a record of student assessment of the lessons. Teacher self-evaluation also takes place in TY to which students are expected to contribute comprehensive feedback on their experience of project work. This level of teacher self-evaluation and in particular the inclusion of student feedback is an indication of openness to the ongoing development of a dynamic learning environment. This is an example of very good planning practice.
The TY plan observes the spirit of the underlying principles of a good TY programme. Every opportunity is provided for students to experience Mathematics on an interactive and enjoyable level. Students are exposed to a wide variety of learning experiences, such as, project work, Maths Week activities, practical work, logic games, and ICT. TY students complete projects on everyday Mathematics, for example, ‘How Mathematics can be used to explain coincidence’ or ‘How Mathematics can be used to detect fraud’. The teacher provides the students with all the information they will require for the project, this is intended to encourage students to focus on the inferences they make and the conclusions they draw from the information rather than the sourcing of the information itself. Commendably, this strategy came about as a result of reviewing past practice. Students put forward the proposal for their project and on completion present their findings to the rest of their class group. ‘The Leprosy Project’, for example, involved students analysing population data using statistical analysis. The resulting projects are proudly displayed on classroom walls. In TY, teachers avail of every opportunity to incorporate non-traditional methodologies in the teaching and learning of any Leaving Certificate course material that is on the TY programme. All of this is very good practice.
It is recommended that the mathematics department undertakes an analysis of the certificate examination results each year and compares the school’s performance to the national norms. This analysis should then be used to inform future planning for Mathematics. It is evident from the inspector’s analysis of the results that there are a high number of students achieving very high grades in Junior Certificate Mathematics at ordinary level. It is recommended that this be kept under review in order to ensure that all students study Mathematics at a level appropriate to their ability.
High quality teaching and learning were evident in all of the lessons observed. Teacher explanations and instructions were clear and lessons were well structured in all cases. Teachers were careful to relate current work to the work of previous lessons. This is important as it helps students to situate new ideas and to understand the interconnections between concepts and procedures in Mathematics. Where it was appropriate, teachers chose examples from students’ own personal experience to explore difficult concepts. This is good practice as it helps students to identify with their course material and to appreciate the relevance of Mathematics in everyday life. At the beginning of some of the lessons teachers shared the learning objectives with the students. It is suggested that the learning objectives of the lesson be written on the board at the beginning of all lessons, where practical, and that the achievement of these objectives be checked at the end.
The pace of the lessons observed was lively and also, appropriate to the ability level of the students. A good mix of teacher-example and student-exercise was used to involve students and to keep lessons interesting. The level of student participation and engagement was very high in all of the lessons observed. In some cases students were expected to attempt previously unseen problems with teacher support where necessary. This was particularly valuable in a higher level Leaving Certificate lesson where students were expected to derive a general formula that was unfamiliar to them. After students had been given ample time to work it out for themselves, the teacher wrote the derivation on the board. This is very good practice as it helps students gain an appreciation of mathematical endeavour and can lead to a great sense of personal satisfaction on the successful solving of the task.
Teachers made good use of questioning to engage students and to assess learning. There was frequent use of open, higher-order questions to help students explore difficult concepts and ideas. This is good practice as it provides students with opportunities to develop the problem-solving and critical thinking skills that are essential for success in Mathematics.
In addition to teacher-led methodologies, teachers integrated a variety of learning experiences into their lessons. These included discovery methodologies, practical work, pair work, group work, and project work. In one TY lesson observed, students were revising geometry theorems using the Voyage 200 calculators. The lesson was very easy to follow for the students as they were provided with a comprehensive pack of instructions and were guided through the exercises by their teacher. This revision was intended to pave the way for them to go into first-year classes to help the students study the theorems on their course. This experience has potential to benefit the first-year students by enabling them, through guided discovery, to explore the concepts involved in a concrete way before they go on to study the theorems proper and also, to benefit the TY students by giving them opportunities to gain an alternative insight into the learning process. The use of innovative approaches such as this is both appropriate and desirable as they are effective means of promoting students’ understanding of Mathematics.
The effective use of ICT in teaching and learning in Mathematics was demonstrated during the inspection visit. Teachers also demonstrated the cross-curricular nature of mathematics in some lessons. For example, a TY project to investigate the relationship between the period and the length of a simple pendulum, and then the calculation of the acceleration due to gravity, provided links to History, Science, Music, Geography and ICT. The students investigated this relationship experimentally then used Excel software to graph the result. The acceleration due to gravity was calculated from the graph. Presentations of the completed projects were then made using PowerPoint. The handout used to support this project was clear and comprehensive allowing students to follow the step-by-step instructions with ease. The style of the questions on the handout encouraged students to come to their own conclusions and form their own opinions, the questions also expected students to engage in self-evaluation and self-reflection. The handout provided an interesting piece on the historical background of the pendulum, designed to capture student interest. This exemplary practice arises out of a genuine interest in and enthusiasm for Mathematics.
In some of the lessons observed it was evident that teachers are careful to differentiate the learning experience to suit the range of abilities present in the class groups. This was achieved by choosing a methodology that allowed students to work at their own pace or by providing exercises for students that ranged in difficulty. It is suggested that teachers create a bank of challenging exercises for each topic, so that if the situation arises where some students have achieved success at a certain task while others still need further explanation the additional material will be available to give to students as required.
There was an excellent rapport between students and their teachers. Teachers were encouraging, affirming and supportive of student effort and all interactions were characterised by a high level of mutual respect. This resulted in the creation of learning environments where students could engage with Mathematics with confidence.
All class groups are continuously assessed throughout the year. First, second and fifth-year students sit formal examinations in May. ‘Mock’ examinations are held in February for students in third and sixth year. TY students are assessed in a variety of ways including regular end-of-topic tests, an assessment of the quality of the presentations of their projects and on participation in class. This variety of assessment in TY is in keeping with very good assessment practice. Reports are sent home at Christmas and in May and parent-teacher meetings take place once a year.
It was evident from the inspector’s review of students’ copybooks that the standard of student work is high and that the majority of students are making steady progress in Mathematics. All teachers model good presentation in their work on the board, and this is reflected in student work. Teachers routinely monitor students’ work in class and assess learning through oral questioning on an ongoing basis. In one case it was reported that students are expected to make a written signal on their copybooks to alert their teacher to any difficulties that they may be having. The teacher monitors the copybooks throughout the lesson; the indications written by students enable the teacher to tailor the lesson to match student needs. Homework is regularly set and usually corrected as part of the next lesson. This close monitoring of student work is commended.
It is clear from the school’s assessment policy contained within the mathematics department plan that some assessment for learning (AfL) principles are used in the setting and correction of tests. Teachers are careful to use comment-based marking to provide students with constructive feedback that encourages self-correction. It is also department policy to include positive, motivational comments on examination papers. All of this is good practice and its continuation is encouraged.
The following are the main strengths identified in the evaluation:
· Concurrent timetabling of Mathematics from second year to sixth year allows students great flexibility in changing levels.
· A high level of learning support is provided to students who are identified as requiring it.
· There is an extensive range of resources, including ICT, available for teaching and learning in Mathematics.
· The TY programme for Mathematics is very good.
· High quality teaching and learning were evident in the lessons observed.
· Independent learning opportunities were provided for students to help them to develop critical thinking and problem-solving skills.
· Teachers use a variety of teaching methodologies in mathematics lessons to encourage student participation and to make learning interesting.
· Teachers take a learner-centred approach to the assessment and monitoring of student work and AfL principles are used to encourage and motivate students.
· An excellent rapport exists between students and their teachers.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· It is recommended that the organisation of access to ICT for teaching and learning in Mathematics be formalised to enable the mathematics department to make optimum use of the ICT resources that are
available within the school.
· The mathematics plan needs to be further developed so that it accurately reflects the day-to-day work of the mathematics department. A co-ordinator should be appointed on a rotational basis to oversee the
· The mathematics department should undertake a yearly analysis of the certificate examinations results and compare the school’s performance to the national norms. This analysis should be used to inform
planning for Mathematics.
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 June 2009