An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Killucan, County Westmeath
Roll number: 71430C
Date of inspection: 10 March 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Columba 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, deputy 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.
Columba College maintains close ongoing contact with its feeder primary schools, which ensures that the transfer of students into first year takes place in an effective and student-centred fashion. Prospective students are provided with a comprehensive taster programme, delivered over two afternoons where they meet with the teaching staff, sample the different subjects they will encounter in first year and interact with the school’s existing students. An open night is held in January each year at which parents are informed about the school’s policies and procedures and enrolment forms are distributed. Once the incoming cohort has been identified, they are invited to the school for an afternoon where they are paired with an existing first-year student with whom they can identify, and they engage in a range of activities designed to make them feel at home in the school. An induction day is held in September each year for all first-year students. The induction day provides opportunities for the incoming students to become familiar with the school’s policies and procedures and to meet with school management and their class tutor. A mentoring programme, in which fifth-year students are paired with individual first-year students, is also set in train during the induction day.
Timetabling provision for Mathematics in junior cycle is very good. There is one mixed-ability class group in first year and they are provided with five classes of Mathematics per week. There are two mathematics classes in second year and one mixed-ability class group in third year. In each case they are provided with five periods of mathematics per week. All class periods are forty minutes long. The distribution of mathematics classes throughout the week is, in most instances, very good and there is a good balance of provision between morning and afternoon. However, the five mathematics classes in first year are spread over only three days with two single periods on Mondays and Wednesdays. It is recommended that, in framing future timetables, criteria are set to ensure that all classes are provided with a balanced timetable.
Timetabling provision for Mathematics in senior cycle is good. There are two mathematics classes in both fifth and sixth year and they are provided with five periods of Mathematics per week. One class group, in each year, follows higher-level Mathematics while the other is mixed-ability, with the majority of students following ordinary level and a small number taking foundation level. The commitment of management to providing students with the opportunity to follow higher-level Mathematics is highly commended. Mathematics classes are timetabled concurrently within each year group, which facilitates movement between levels and enables students to follow the highest level possible for as long as possible.
Students in need of learning support or with special education needs (SEN) are initially identified as part of the school’s enrolment processes. Comprehensive profiles of incoming students are developed through ongoing contact with the feeder primary schools and through their performance in a range of appropriate standardised tests. The school’s guidance counsellor administers the tests and the results are discussed with the staff at the first staff meeting of the year. Incoming students who have had their learning or other needs formally assessed by the National Educational Psychological Service (NEPS) while in primary school are identified and applications for extra resources are then submitted by the school to the Department of Education and Science for consideration. If it is deemed necessary, additional assessments for some students are also arranged through NEPS.
Language development provides the main focus of the existing learning-support provision, while learning support in Mathematics is limited. It is recommended that work should begin on the development of a learning-support plan for Mathematics and that this should include strategies to support teachers who are delivering the Mathematics curriculum in a mixed-ability setting. Assistance in carrying out this work is available from the special education support service www.sess.ie.
The mathematics department is comprised of five teachers. The qualifications profile of the department is very good and the teachers are assigned to classes and levels by rotation. Furthermore, it is school policy that teachers retain the same class group from second to third year and from fifth into sixth year. This is very good practice as it helps to ensure continuity in curriculum delivery and facilitates effective planning.
The mathematics department is very well resourced. There is ready access to the school’s extensive information and communication technologies (ICT) facilities and there was evidence of effective ICT integration in the lessons observed during the inspection. The teachers have also produced a range of resources to enhance teaching and learning. In order to fully exploit the potential of the school’s ICT facilities and to facilitate enhanced collaboration in resource development, it is recommended that the mathematics department undertake an audit of existing skills and resources, and that responsibility for procuring, producing and sharing additional resources be appropriately assigned.
School development planning is well established in the school. In the last year the focus has shifted to subject development planning and co-ordinators have been appointed to the different subject departments. The mathematics department is very ably co-ordinated, regular meetings are held and the minutes of these meetings are contained in the subject development plan for Mathematics. Analysis of the performance of students in the state examinations using data provided by the State Examinations Commission is also underway. This is very good practice and should continue to form an integral part of ongoing department planning.
A subject-department plan for Mathematics is in place. It includes the mission statement for the department, a statement of aims and objectives, arrangements for student access, lists of agreed textbooks and the schedule for curriculum delivery. The schedule is very detailed and gives the content to be covered in the programme for each year group in the form of chapter lists.
In order to build on existing good practice in planning, it is recommended that the delivery schedule be amended to include agreed learning outcomes and strategies to integrate different areas of the syllabus routinely in the teaching and learning of Mathematics. The agreed delivery schedule should then be circulated to each member of the department to inform individual planning.
Individual teacher planning was very good. The teachers were well prepared for class and, in almost all cases, due cognizance was given to the needs and abilities of the students in setting out and delivering the lessons. A range of resources including worksheets, acetates for use with the overhead projector, and a dictionary of mathematics terms were effectively integrated into lesson delivery. This served to reduce reliance on the textbook and facilitated lessons that were student-centred and challenging.
Management encourages and facilitates teachers to attend continuing professional development (CPD) courses and a number of whole-school courses have been provided in the recent past. These were designed to facilitate subject development planning and to discuss co-operative learning in mixed-ability classes. Management also encourages the teachers to participate in professional associations such as the Irish Mathematics Teachers’ Association. Newly appointed teachers meet with the principal on an ongoing basis and are provided with a mentor from the established teaching staff during their first year in the school.
The lessons observed during the inspection were well planned. The teachers took great care to ensure that the students saw the relevance of material being covered and were very skilful in relating it to the students’ prior learning and to their everyday experiences. The teachers were clear and knowledgeable and the lessons were delivered with purpose and enthusiasm. In a number of instances the teachers shared the lessons objectives with the students at the outset and provided a review of the lesson just prior to its conclusion. This very good practice should be adopted as an integral part of lesson delivery.
Many of the lessons were delivered in a mixed-ability setting. In one such instance, an innovative seating arrangement was utilised to facilitate group work and to enable the teacher to manage a mixture of levels. The lesson was supported by the very effective integration of ICT, excellent teacher movement and peer tutoring. There was very little reliance on the textbook, the students were enabled to progress at their own pace and the level of differentiation in evidence was very impressive. This model of classroom management and lesson delivery should be adopted in all of the mixed-ability mathematics classes.
Student engagement with the lessons was, in all cases, very good. This was due to the excellent use of teacher questioning which served to elicit factual responses, to encourage the students to explain their reasoning and to pursue alternative solutions to problems. In one case, the students were invited to work through revision problems at the board. Under the supervision of the teacher they illustrated their approach to solving a number of different problems and explained the appropriateness of the approach in each instance. Positive student engagement was also encouraged by the use of clear and robust procedures for carrying out mathematical operations. For example, an innovative approach to teaching linear transformations ensured that this very complex concept was accessible to the students and that they were well equipped to deal with even the most difficult problems they might encounter.
Positive student behaviour was evident in all of the classes visited. The lessons were conducted in an atmosphere of mutual respect, where the teachers were affirming of the students’ efforts and the students carried out their assigned tasks with diligence and enthusiasm. Very good teacher movement and a proactive approach to differentiating lesson content facilitated positive student behaviour and ensured that the lessons were inclusive and student centred.
The quality of student learning was good. The students responded confidently when questioned by the teachers and during their interactions with the inspector. The students displayed a good knowledge of concepts and facts and were well able to recall material covered in earlier lessons. The quality of the students’ homework copies and their performance in class and formal tests was also satisfactory.
Homework is regularly assigned and corrected. In many instances the homework copies were monitored appropriately and there was evidence of teacher corrections and comments. Student sit class tests upon completion of individual topics and ongoing assessment also takes place through teacher questioning during class. Practices regarding the assignment of homework are in line with the school’s draft homework policy. However the policy should be customised to reflect the subject’s particular requirements. In particular, emphasis should be placed on the role of homework in providing opportunities for independent and collaborative learning and to allow students to develop competence in key mathematical operations. Furthermore, the role of the students in amending and correcting their own work should also be specified.
Very good practice in relation to recording student attainment and attendance was evident. Roll call was taken at the beginning of each class and recorded in the teachers’ diaries. In addition the teachers’ diaries contained comprehensive records of the performance of students in class and formal tests.
Formal examinations for non-examination classes are held at Christmas and again prior to the summer holidays. Common papers, corrected in accordance with an agreed marking scheme, are provided where appropriate. Students in examination classes sit a formal examination in November and sit the mock examinations in February each year. Written reports issue to parents following formal and mock examinations.
Very good use is made of the student diary as a vehicle in ongoing communication with parents. The students record homework assignments in their diaries and the teacher checks the diaries before they leave the classroom at the end of each lesson. Ongoing communication also occurs through telephone calls to the home, and through informal meetings, which can be organised at any time. In addition there is one parent-teacher meeting per year for each year group and an awards evening is held each year to recognise student attainment and endeavour.
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 and deputy principal, at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published, October 2009