An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Coolock, Dublin 5
Roll number: 60871V
Date of inspection: 16 May 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Mercy College, Coolock. 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 three 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, and the response of the board will be found in the appendix of this report.
Mercy College, Coolock caters for 446 girls and timetable provision for Mathematics is very good. In the junior cycle, five lessons per week are allocated to first, second and third year groups. Students following the Junior Certificate School Programme (JCSP) are timetabled for seven mathematics lessons per week in first and third year and for six mathematics lessons per week in second year. Transition year (TY) students are timetabled for three class periods of Mathematics per week. For the Leaving Certificate, ordinary-level students are allocated five mathematics lessons per week and higher-level students have six lessons. The school strongly encourages students to study the highest level possible for as long as possible and the extra lesson per week provided for higher-level Leaving Certificate students contributes to the achievement of this aim. Mathematics lessons are evenly distributed across the week, which is good practice. Concurrent timetabling of Mathematics occurs from second year through to sixth year. This is very good practice as it provides students with a high degree of flexibility in changing levels and enables the mathematics department to adopt a very student-centred approach to level choice.
In first year there are two bands, one consisting of four mixed-ability classes and the other made up of two smaller classes containing students who need additional support in Mathematics. Students are assigned to a class group in one of these bands on the basis of pre-entry assessment and information from feeder primary schools. In second year and third year there is a higher-level class, an ordinary-level band and a small ordinary-level class. Students are divided according to achievement and assigned to one of these groups. For the Leaving Certificate there is a higher-level class and an ordinary-level band. A foundation-level class group is created in fifth and sixth year if it is required. Abilities are mixed within level bands. Concurrent timetabling facilitates change of level where necessary. All of this is good practice.
The mathematics department comprises eight teachers. School management decides on teacher allocation to classes and levels in close consultation with the teachers themselves. It is mathematics department policy that classes retain the same teacher from year to year for the duration of a cycle, which is good practice. At senior cycle, higher-level Mathematics is rotated between two members of the mathematics teaching team. It is recommended that more members of the mathematics department become involved in teaching higher level class groups. This measure would enable the mathematics department to retain the high level of expertise that currently exists and to meet the challenges of the forthcoming revisions to the mathematics syllabuses.
Teachers make very effective use of the wide variety of teaching resources that is available. The mathematics department has access to three interactive white boards and a number of laptops and data projectors. The computer room is regularly used for teaching and learning in Mathematics, where students can gain access to the internet. In keeping with good practice, the computer software that is used to enhance teaching and learning in Mathematics has been chosen to suit students who find Mathematics difficult as well as students studying higher-level Leaving Certificate Mathematics. An extensive range of teaching aids is also used, such as posters, playing cards, dice, geometry equipment, geostrips, 3-D solids, overhead projectors, DVDs and videos of mathematical interest. These are all used to enhance student experience in the classroom. Throughout the school year, students of Mathematics occasionally engage in field work. Trundle wheels, clinometers, measuring tapes, flags and stopwatches have been provided for this purpose. Mathematics is very well provided for in the school.
Students who are in need of learning support are identified through pre-entry assessment and information from feeder primary schools. Support is provided through the creation of smaller class groups and small group withdrawal or individual withdrawal from subjects other than Mathematics. Teachers routinely monitor progress through ongoing class observation and class tests. Individual education plans (IEPs) are maintained for JCSP students. This is to ensure that learning is designed to specifically suit student individual needs. All of this is good practice. A very high standard of learning support is currently provided for students who find Mathematics challenging. It is suggested that team teaching, where two teachers share the responsibility for teaching each lesson, or in-class learning support, where the learning support teacher provides individual attention during the lesson to students experiencing difficulty be considered as further approaches to the delivery of learning support. Incorporating these additional modes of delivery would provide the school with the option of efficient and unobtrusive learning support provision. In this way students who would not usually require support could also benefit from the extra individual attention available in class and students who would normally be withdrawn for help with Mathematics could receive that help alongside their peers.
Formal planning time is allocated to Mathematics in September and May as part of the whole-school planning process. In addition, planning meetings occur on a bimonthly basis. Records are maintained of all formal planning meetings and minutes are kept. There are also frequent informal planning meetings among members of the mathematics teaching team. The position of co-ordinator of the mathematics department rotates every two years. It was reported that teachers new to the mathematics department benefit from the support of their more experienced colleagues. It is evident that collaboration around classroom activities and teaching methodologies takes place. The extent to which expertise is shared throughout the mathematics department has contributed to the extensive use of active and creative methodologies. All of this good practice has enabled the members of the mathematics teaching team to operate within a culture of collaboration and co-operation and this has contributed to a strong spirit of collegial support.
It was evident from the review of planning documentation that school development planning has progressed to subject areas and there is an excellent mathematics department plan. The plan contains details of department policy on cross-curricular activities, planning for students who need additional support in Mathematics, homework, a variety of effective teaching methodologies and student allocation to levels. The plan also contains schemes of work with defined timeframes for the topics to be covered. Each individual plan identifies aims, learning outcomes, resources necessary, and modes of assessment. It is clear from the plans that a wide range of active and creative methodologies is used to encourage students to engage fully with the core mathematical concepts in the lessons. Details of in-service courses attended are also included in the plan. In keeping with best practice, awards won and acknowledgements of student achievement are rightly included in the planning document. It is clear from the minutes of the mathematics department formal meetings that the plans are subject to regular review and revision. This is good practice as it ensures that the plan is a living document that informs the day-to-day activities of the mathematics department. It is recommended that this good progress be maintained by the continuation of the comprehensive work that is currently taking place on planning for Mathematics in the school.
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 study topics in Mathematics that do not form part of the Junior or Leaving Certificate courses. For example, a module of Applied Mathematics is taught to the higher-level group and other groups engage in the study of codes and ciphers, patterns and Fibonacci sequences. Where Junior or Leaving Certificate material is included in the TY programme it is taught using a variety of active, investigative, and project work methodologies. The plan for a project on budgeting, where students are expected to investigate salaries from a recruitment website on the internet and use this information to inform their study of arithmetic, provides an example of best practice in this regard. It is a clear aim of the TY programme to challenge students’ attitude to Mathematics by exposing them to the practical applications of Mathematics and to encourage them to engage with their course material in a positive way. TY students can also avail of the opportunity to take part in a combined initiative between the schools mathematics department and the home-school-community liaison officer, where a group of TY students provide help to local primary school pupils with Mathematics. This involves the TY students playing mathematical games with the primary school children. It has reportedly proven very beneficial to all concerned since it has helped to improve numeracy in a fun way and also provides the TY students with an insight into how Mathematics is taught. TY students also take part in Maths Lecture Week in Dublin City University (DCU) and on their return are encouraged to enter the follow-up competition by attempting the competition questions. Through careful planning and the sharing of expertise and ideas the mathematics department have created a programme for TY that encourages students to experience the relevance of Mathematics in a positive and pleasurable way.
High quality teaching and learning were evident in the lessons observed. Lessons had a clear focus and were well structured in all cases. At the beginning of each lesson observed the teacher shared the learning objectives with the students. Best practice in this regard occurred where the teacher wrote the aims of the lesson on the board at the beginning of the lesson and then checked at the end that these have been achieved. In order to increase motivation throughout the lesson and to provide an opportunity for a sense of achievement on reaching the lesson aim it is recommended that the learning objectives be shared in this way.
The pace of the lessons observed was lively yet appropriate to the ability level of the students in all cases. In most cases lessons began with the good practice of the correction of homework. Since the inspection visit occurred close to examination time, most of the class groups visited were engaged in revision, as is appropriate for the time of year. A good mix of teacher-example followed by student-exercise was used to involve students and to keep lessons interesting. Teachers made good use of questioning to engage students and to assess learning. Teachers routinely used higher-order questions, requiring reflection and consideration to help students explore difficult concepts and ideas. This is good practice since it helps students to develop the problem-solving and critical-thinking skills that are essential for success in Mathematics. In all cases teacher instructions and explanations were very clear.
Teachers integrate a variety of methodologies into their lessons. For example, in a lesson on probability the students participated in a number of activities designed to help them understand the different ideas in the lesson. The lesson opened with the students working in pairs to organise a deck of cards into suits, in order. The teacher then worked through some examples at the whiteboard. The students were then expected to work on a handout of probability exercises. The teacher then produced a bag of coloured lollypops, the students stood around the teacher’s table to count the number of each colour in the bag. The students were then asked to close their eyes, choose a lollypop and to state the probability of picking their favourite colour. Following this, the students worked in groups on choosing items on a restaurant menu; this was to prepare them for questions on the number of different possible meal combinations. This is an example of good practice because each activity was designed to explore a different concept and the subsequent handouts reinforced the ideas very well. Furthermore the students thoroughly enjoyed all the activities and engaged enthusiastically with the Mathematics involved.
Teachers demonstrated their effective use of ICT during the inspection visit. In one case the teacher demonstrated a lesson on algebra using the interactive whiteboard. One aspect of this lesson involved the use of cartoon characters to illustrate the grouping of like terms. In another lesson, higher-level Leaving Certificate revision software was demonstrated. These are examples of good practice in regard to ICT and it is recommended that the mathematics department explores further opportunities to incorporate ICT into teaching and learning in Mathematics.
In general, very good relationships exist between students and their teachers. The mutual respect that was evident in most of the classrooms visited has contributed to very high standards of student behaviour. Teachers are in general very encouraging of student effort and relate to their students with great sensitivity and patience. The majority of teachers have created caring, supportive learning environments where students can gain confidence in their own ability in Mathematics. Where this was in evidence students responded positively to the affirming manner of their teachers. However, this was not universal practice among the lessons observed; in one instance the tone of the classroom interaction was overly negative and critical. It is therefore recommended that the positive, affirming, supportive and encouraging practices evidenced in most of the lessons observed be adopted by all teachers. This applies equally to the correction of student work and the acknowledgement of student effort, particularly in a whole-class context. Where an answer is almost correct save one small mistake it is appropriate that individual students be given some praise for their good efforts and that the mistake be corrected with sensitivity. It is also important where a student answers a question correctly in class that the effort be rewarded by some positive feedback.
All students are formally assessed at Christmas. Summer examinations are held in May for first, second, fourth and fifth year groups. Students taking the certificate examination sit ‘mock’ examinations in February. Common examination papers are set within levels which is good practice. Reports are sent home on foot of these formal examinations and parent-teacher meetings are held annually. Learning is routinely assessed through oral questioning in class and students sit class tests at the end of each topic studied. A variety of additional modes of assessment is used for assessing TY students. These include continuous assessment and project assessment where students can receive credit for their application to the task and for their participation in discussions around the conclusions to be drawn from the results of their project work. All of this is good practice.
It is evident from the review of student copybooks that the standard of presentation of student work is high and that students are making good progress in Mathematics. Teachers routinely monitor student work and encourage students to adopt a well-organised, logical approach to the layout of their work. In keeping with good practice, homework is set regularly and is usually corrected as part of the following lesson. Most teachers are engaging in assessment for learning (AfL) practices by using comment-based marking in the correction of homework and tests. This is valuable as it provides students with feedback that can be a source of positive reinforcement. In the case of one first year class visited the teacher used stickers with encouraging messages to affirm student work. The students responded very positively to this type of feedback. The extension of the use of AfL practices is therefore recommended. Further information on AfL is available on the National Council for Curriculum and Assessment website (www.ncca.ie).
Prizes are awarded at the end of the school year for achievement in Mathematics in each class group. The student, or students, who achieves the highest result in Mathematics in the Leaving Certificate examination receives the Sister Gonzales Perpetual Trophy, an award that commemorates a late member of the mathematics department at Mercy College. Students are encouraged to take part in the mathematics activities that are organised for the annual celebration of Maths Week. The mathematics quiz that is held for the duration of Maths Week is enjoyed by students and teachers alike. It is clear from articles printed in the school’s newsletter that Maths Week and Mathematics related field trips are significant events in the life of the school. Mathematics clearly enjoys a high profile within the school.
The following are the main strengths identified in the evaluation:
· There is a high level of whole-school support for Mathematics and the mathematics department has access to a wide range of teaching resources.
· A very high standard of learning support is provided for students who find Mathematics challenging.
· The extent to which expertise is shared throughout the mathematics department has contributed to the extensive use of active and creative methodologies and to the creation of a strong spirit of collegial support.
· Significant progress has been made on planning for Mathematics.
· The mathematics department have created a programme for TY Mathematics that encourages students to experience Mathematics in an active and positive way.
· High quality teaching and learning were evident in the lessons observed.
· In the lessons observed, the teachers routinely used higher-order questions, requiring consideration and reflection to help students to explore difficult mathematical concepts.
· Teachers are, in general, very encouraging of student effort and relate to their students with great care and sensitivity.
· The standard of presentation of work in student copybooks is high and good progress is being made in Mathematics.
· It is clear from the prizes awarded for student achievement, the whole school celebration of Maths Week, and the mathematics articles in the school newsletter that great pride is taken in the work done in Mathematics in the school and that Mathematics enjoys a high profile position.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· The numbers of teachers with responsibility for teaching higher-level mathematics should be increased to enable the school to retain the expertise that exists in the mathematics department and to meet the challenges of the forthcoming revisions to the mathematics syllabuses.
· The positive, affirming, and supportive practices evidenced in the majority of the classes visited should be adopted by all teachers.
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.
Submitted by the Board of Management
Area 1: Observations on the content of the inspection report
The Board of Management of Mercy College welcomes the very strong and positive findings of the inspection report. It wishes to congratulate all involved, and to thank the Inspector for the professional and encouraging manner in which the inspection was carried out.
Area 2: Follow-up actions planned or undertaken since the completion of the inspection activity to implement the findings and recommendations of the inspection
The number of teachers with responsibility for higher level mathematics has already been increased for 2008/09 and will be increased further in subsequent years.