An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Bóthar Nangor, Cluain Dolcáin, Baile Átha Cliath 22
Roll number: 70100W
Date of inspection: 27 March 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Coláiste Chilliain, 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 acting principal and subject teachers.
The mathematics team, which has seen a number of changes in personnel in recent years, currently consists of six teachers, the majority of whom are subject specialists. Presently, two members of the team teach Mathematics to only one class group. It is recommended that, where possible in future timetabling, each member of the team would have more contact time with the subject.
First-year students are taught in three mixed-ability groups. This is good practice as it allows students to adjust to the pace and content of the mathematics syllabus at post-primary level. In the context of the school, it also allows for the introduction and use of mathematical terminology in Irish. This structure also facilitates the minority of students, who do not come to the school from an Irish language primary school background, to adapt to Irish language instruction in the subject.
The distribution of mathematics lessons within the timetable is good. In second, third, fifth and sixth years, and in Transition Year (TY), mathematics classes are timetabled concurrently. This allows for the creation of one higher-level and two ordinary-level classes in each year group. This structure also encourages students to follow the highest appropriate level for as long as possible while still retaining the option of changing level. For students wishing to change level, parental consultation with their class teacher is required before the change is permitted.
The current practice in the school at ordinary level is that the two classes are created based on the ability levels of the students. To take account of varying rates of student development and to take advantage of the correlation between levels of teacher expectation and levels of student achievement, class formation for ordinary level Mathematics should be reviewed. It is recommended that, after first year, students be divided into higher-level 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
It is practice within the school for teachers to remain with the same class groups from second to third year and from TY to sixth year, where possible, thus maintaining high levels of continuity. Teachers are assigned to classes and levels by school management. Currently, Leaving Certificate higher level is the responsibility of two senior member of the teaching team while at junior cycle, levels are rotated among a wider group of teachers. To take advantage of the experience built up over the years, it is suggested that more rotation of levels at senior cycle be gradually introduced.
The time allocated to Mathematics at both junior cycle and senior cycle is good. Junior cycle classes have five periods, generally of forty minutes duration, each week. TY classes have three periods and fifth-year and sixth-year students have six periods of Mathematics each week. In keeping with accepted good practice, mathematics classes are generally distributed evenly throughout the school day and the school week. However, the TY classes have all their mathematics lessons in the afternoon. This should, if possible, be avoided in future timetabling to ensure that all students enjoy the benefits of an even spread of classes.
While there is no specific budget for Mathematics, all reasonable requests for purchase of resources are granted. The team has access to a mobile laptop, data projector and a well-equipped computer room with mathematics software installed. There is also a room available with a fixed computer and data projector where classes may be conducted if information and communication technology (ICT) is required in the course of a lesson. The classrooms, which are generally teacher based, have overhead projectors and whiteboard drawing equipment available.
Teachers’ attendance at continuous professional development (CPD) courses is facilitated and teachers have availed of courses offered by the Mathematics Support Service in recent years. Details of courses attended, the names of teachers who have attended along with the topic covered, and any resources resulting from the course should be included in the subject plan.
The mathematical ability of all incoming first-year students is formally assessed prior to entry to the school. These assessments, along with contacts with the primary schools and ongoing teacher observation and monitoring, identify students who find the subject particularly challenging. Support in the form of extra tuition for these students is provided in first year through withdrawal from classes, other than mathematics classes in most instances, for small-group and one-to-one tuition. The resource teacher or learning-support teacher maintains informal contact with the mathematics teacher. Students in receipt of support are re-tested at the end of first year.
There is a mathematics department within the school. Two experienced members of the mathematics team share the role of subject co-ordinator on a voluntary basis and this is positive. However, it is recommended that this arrangement be reviewed by the team and possibly altered so that the role of co-ordinator is rotated within the mathematics department on an annual basis. This will serve to ensure that a wide leadership skills base develops within the department. Ideally the team should agree the duties attached to the role of co-ordinator and include these in the subject plan.
Management facilitates formal mathematics team meetings each term as part of the school development planning process. In the current year records of formal meetings have begun to be kept. This is positive and should be continued. In addition, informal meetings take place on a needs basis. It is recommended that future team meetings should allow time for sharing teaching methodologies, discussion on procedures used in various topics, feedback from CPD courses attended, review of resources, and other issues relevant to the teaching of Mathematics within the school.
A written plan for Mathematics has been prepared. The plan contains syllabus documents and published teacher guidelines at Junior Certificate level. The department plan includes overall aims and objectives for mathematics education within the school, outline programmes of work for each year group and level, organisational details and reference to a variety of resources. The schools homework policy is included. This is in line with good practice and is commended. The long-term plan for the subject consists of a list of chapter headings from the textbook to be covered in the course of the year at each level. To build on this solid foundation, a review of programmes of work for year groups should see these programmes expanded to include not just lists of chapters from the textbook, but also an outline of sections of the syllabus at junior cycle and senior cycle and the recommended areas of study under each of these sections. This would allow a range of methodologies and differentiation strategies to be listed and linked to specific learning outcomes for students. The plan should also contain a breakdown by term of the recommended time to complete the sections of the courses. This collaboration should provide mathematics teachers with the opportunity to identify and share good practice.
There is a plan for mathematics in TY. The plan contains the same aims and objectives as the main plan. The general focus of the TY plan is on Leaving Certificate material, along with a module on aspects of the history of Mathematics. It comprises a list of chapters to be covered for the year along with details of the module. Circular M1/00 The Transition Year Programme states that: “A Transition Year programme is not part of the Leaving Certificate programme, and should not be seen as an opportunity for spending three years rather than two studying Leaving Certificate material.” It is therefore recommended that aspects of the Transition Year programme for Mathematics be reviewed to ensure compliance with the circular. Possible sources for this might be the Project Maths Development team’s website www.projectmaths.ie and the Mathematics Support Service website www.slss.ie/maths.
It was reported that some discussion and review of uptake rates, as well as results, are conducted within the school. This is good practice and should be used as a regular and natural part of the planning activities of the mathematics department, in particular in relation to addressing any weaknesses that become apparent during the process.
The school provides some opportunities to participate in co-curricular activities associated with Mathematics. Students have competed in a competition organised by the Hamilton Institute in the National University of Ireland, Maynooth and have attended lectures there. Those involved in the organisation of these events are praised. Future planning should not ignore the availability of other competitions and activities which are available to engage and motivate students. Among these are the Team Math and Junior Mathematics competitions, organised by the Irish Mathematics Teachers Association (IMTA). There are also the Problem Solving for Irish Second Level Mathematicians (PRISM) competitions, organised nationally as part of Maths Week Ireland held in October and World Maths Day activities.
The lessons observed in Coláiste Chilliain were generally well structured, purposeful and appropriate to the syllabus. In all cases, lesson content was appropriate and teachers’ explanations were clear. In lessons observed, the topic of the lesson was shared with the students. This is positive. Best practice in this regard, however, occurs when the lesson content is presented as a learning objective for the students and when there is a checking strategy at the end of the lesson. This practice is worthwhile because it increases students’ motivation and involvement in the lesson and leads to a sense of accomplishment on achieving the day’s goal. It is commendable that effort was made to review work previously done and to create connections to new material being presented, thus helping to reinforce learning and to develop new ideas. The pace of the lessons, while challenging, was matched to the ability levels of the students. Time management within lessons was generally good.
The textbook and whiteboard were the main resources used in lessons. In a number of instances ICT and the use of concrete materials enhanced the learning process. There was also effective use of worksheets, pair work, group work and relating learning to the experience of the students evident in lessons.
Teaching in the main consisted of teacher example followed by individual student exercise. Within this traditional approach, teaching was effective but students tended to be passive and over-dependant on the teacher. It is therefore recommended that teachers review current methodologies, with a view to adding greater variety to their teaching approaches. More use of a variety of learner-centred and active methodologies could enhance learning. Strategies for the use of such approaches should be explored by the mathematics department.
Teachers made use of questioning, both global and directed, throughout the lessons observed. Questioning focused mostly on finding the next steps in the solution of a problem. Best practice was observed when some more open and probing questions were included to encourage students to think for themselves. As this type of questioning is so beneficial to learning it is recommended that it be incorporated into lessons more frequently.
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. They were able to provide answers and justify solutions to questions posed to them and were able to make relevant connections between topics. Learning was also evident as students were able to apply procedures, taught in class, to similar type problems set during lessons.
The relationships between students and teachers were observed to be mutually respectful and classroom management was good. Teachers set appropriate high standards of expectation for their students and, in the classes where this was observed, students responded to these expectations.
In many classrooms visited, the good practice of using displays of students’ work and student-produced mathematical posters enhanced the visual learning environment. The display of such posters and project work is effective when used to remind students of key mathematical concepts, formulae or terminology.
The school’s homework policy is implemented by the mathematics team. Appropriate homework was assigned in all lessons observed, providing students with an opportunity to consolidate and practise mathematical concepts engaged with during the lesson. Students’ copybooks and journals revealed that regular homework is assigned, which is good practice and in line with the policy. An examination of a sample of mathematics copybooks and notebooks revealed work that was appropriate, relevant and reasonably well presented. There was evidence that teachers are monitoring students’ copies.
Students’ progress is monitored on an ongoing basis through questioning in class, homework and written examinations following the completion of a topic. Students are assessed five times during the course of the school year as well as having formal examinations at Christmas and summer. All first-year classes are commonly assessed at Christmas and summer and common assessment within levels also occurs in other year groups. This is good practice.
Teachers keep a record of the achievement of their students in these assessments and the school has put positive mechanisms in place to communicate these results to parents. Parents of first-year and second-year students receive a report, containing a comment on their child’s progress, immediately following each of these assessments. For students in third, fifth and sixth year, a results sheet is sent home to be signed and returned to the school. Further reports are also issued to all parents at the end of the first term and following the ‘mock’ examinations or following the summer exams as appropriate. This system ensures that parents are regularly updated.
Communication between parents and the school is good. A parent-teacher meeting is held for each year group during the school year. Individual meetings between teachers and parents are arranged as appropriate during the year. The student journal is also used as a means of two-way communication between home and school.
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 acting principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published, March 2010