An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Saint Columba’s College
Whitechurch, Dublin 16
Roll number: 60320H
Date of inspection: 1 May 2009
REPORT ON THE QUALITY OF LEARNING AND TEACHING IN MATHEMATICS
This report has been written following a subject inspection in St Columba’s 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 and head of the Mathematics department. The board of management of the school was given an opportunity to comment on the findings and recommendations of the report; the board chose to accept the report without response.
Time allocated to Mathematics in St Columba’s College is very good. All Mathematics classes have an allocation of five periods per week of either forty or forty-five minutes. Mathematics classes are distributed throughout the six-day school week allowing for regular contact with the subject, and this is commendable practice. Applied Mathematics is also offered to students in St.Columba’s College and is, in general, offered outside the timetable. However, an introductory course which provides an opportunity to sample aspects of the syllabus is offered in Transition Year (TY) to students who intend taking Applied Mathematics.
The Mathematics department comprises five teachers who are subject specialists in the area of Mathematics. This year, a Postgraduate Diploma in Education student for Mathematics is being offered teaching experience in the school. The practice of sharing the rotation of teaching programmes and levels among members of the department is commendable. This allows for expertise to be developed and maintained within the department. Furthermore, teachers are facilitated to remain with a class throughout each of the cycles and this is also good practice.
On entry, first-year (Form I) students are arranged into mixed ability classes for the first term. A common assessment paper in Mathematics is administered and students are then placed in one of three ability groups for Mathematics. However, following regular monitoring of students’ attainment in subsequent assessments and classwork, movement is permitted between classes. This is facilitated through the concurrent timetabling of Mathematics. In general two higher-level and one ordinary-level Mathematics classes are formed following the division into ability groupings. The assigning of students to ability groupings at an early stage is likely to affect students’ expectations for themselves. This practice should be closely monitored to guard against a lowering of expectations. The school’s own stated policy of encouraging all students to take higher level should be borne in mind in matters of class formation.
There are four mixed-ability class groupings in TY. Teachers of TY Mathematics take responsibility for two class groups and complete a half-year module with each class group. This practice allows teachers to pursue topics that they find particularly interesting and to communicate these interests to students. Two higher-level and two ordinary-level classes are formed for Mathematics in the remaining two years of senior cycle. An additional teacher is allocated to sixth-year Mathematics to take a small class group of students who find Mathematics difficult. Management is commended on this provision.
The school offers support to students who find Mathematics a challenge and also to students who are termed “gifted”. Additional lessons are provided by the learning support team on a one-to-one basis or in small groups to support students in the study of Mathematics. Evening classes are also offered to support students at higher level. The supports offered to all students by the school in Mathematics are commended.
The school supports teachers to attend relevant continual professional development in Mathematics. Teachers are members of the Irish Mathematics Teachers Association (IMTA) and the American Mathematics Society. Involvement in such associations ensures that teachers are informed about the most up-to-date practices in Mathematics. Teachers disseminate materials and documentation received at such Mathematics in-service to colleagues, and this is commendable.
An annual budget is available to the department to obtain necessary resources for the teaching of Mathematics. The department has built up a very good range of shared resources which are kept in an office adjacent to the head of department’s classroom and are accessible to all. Teachers also retain individually sourced resources in their own classrooms. The college’s library also has mathematical books for use as reference aids for the learning of Mathematics. Management is currently phasing in Information and Communication Technology (ICT) in all classrooms. However, it is regrettable that although many of the Mathematics classrooms have access to PCs and data projectors they were used in a limited manner throughout the evaluation.
The school has established a mentoring system whereby the principal observes lessons and provides the teacher with an appraisal. The head of Mathematics also observes colleagues’ lessons and serves as a critical friend. This provides opportunities to observe and develop good practice in the teaching of Mathematics and to support and develop common practices within the department. The department handbook for Mathematics is an invaluable resource for all teachers and includes an overview of the aims and objectives of the department, the role of the teacher and information regarding the department’s policy on assessment and differentiation. All these practices to support professional development are commended.
Students are encouraged and supported to participate in Mathematics competitions and events such as the IMTA Team Maths competition, Problem Solving for Irish Second Level Mathematicians (PRISM) and Irish Mathematics Olympiads. The school also participates in events during Maths Week, and international Maths Day. In addition the school organises prizes for junior, TY and senior students based on performance in a school-based Mathematics exam. The promotion of Mathematics that affords students opportunities to experience the subject outside the classroom context is highly commended.
The Mathematics department is ably coordinated by a school-appointed permanent head of department. Specific duties associated with this position include: responsibilities in the assignment of students to classes; Mathematics planning and its development in the school; assessment; and budgetary and resource issues for the department.
Departmental meetings are convened on a monthly basis and more frequently if necessary. Minutes of meetings are retained and indicate that issues discussed include the arrangement for common assessments and review of student progress in Mathematics. In addition, the department has discussed and agreed common methods for the teaching of techniques for specific topics such as factorisation in Mathematics. Such collaboration is highly commendable as it ensures consistency in the teaching approaches encountered by students should they change level. Following departmental meetings the head of department meets with the principal to discuss issues arising. They agree on the action to be taken and the head of department communicates this to his colleagues. These procedures are sound.
A comprehensive Mathematics department plan has been developed. The plan includes schemes of work for each year group, detailing the topic and timeframe to complete each topic. A supplementary document provides a brief overview of topics to be studied and is grounded in the relevant syllabuses. The documents prepared are exemplary. In order to ensure that they are used to complement each other in supporting effective practice, it is recommended that the department collaborate to develop one succinct document. This combined document should include the learning outcomes to be achieved by each year group and level.
The TY plan is reviewed annually and aims to allow students to consolidate junior cycle material, and participate in project work while encountering Mathematics in real-life situations. The department has compiled a range of resources into a commendable TY Mathematics manual. The Mathematics programme offered to TY students includes a weekly lesson devoted to the application of Mathematics in careers such as engineering and construction. Projects completed by students based on these areas included ‘Engineering in Ancient Egypt’, ‘Astronomy’, ‘Famous Mathematicians’ and ‘The History of Mathematics’ and these were displayed in classrooms.
Individual preparation for lessons was very good. Teachers keep records of topics to be covered and of homework assigned. Supplementary materials available for the inspection included handouts, copies of previous ‘mock’ examination papers and common Mathematics assessments. There was clear evidence that teachers follow the department plan of work when preparing their lessons.
The Mathematics department analyses the students’ achievement in Mathematics in the certificate examinations and compares these results with the national averages. This analysis is used by the Mathematics department to plan yearly objectives for improvements in Mathematics. This is commendable practice. It is evident that students are achieving very well particularly at higher level. However, it is advisable that ongoing department planning accommodate an appropriate balance between the preparation of students for state examinations and the acquisition of lifelong skills in Mathematics.
Eight lessons were observed during the evaluation covering all years, level and programmes. The teaching observed was competent and largely traditional in style, with some examples of excellent and innovative practice. Students were generally engaged in the lessons and best practice was observed where students were given opportunities to reflect on their learning.
Lessons were conducted in an atmosphere of mutual respect. Teachers have established good rapport with their students and set high expectations for their students. Teachers circulated to ensure that students received individual assistance when necessary. The content of lessons visited included revision of material in examination year groups, calculations of taxation and algebra. Lessons were in general well paced and the objectives for the lesson were clearly established and explicitly stated.
In many lessons good use was made of the time available to allow for a balance between teacher and student work. In some instances students were given tasks without a timeframe or a clear understanding of what was expected from the task in hand. A specified length of time should be given to students for the completion of set tasks during a lesson, and the procedures to be followed should be outlined to them in advance. Properly managed tasks will also provide teachers with an opportunity to address issues of concern or misconceptions.
The general methodology used by teachers in lessons observed was traditional whole-class teaching. This includes the teacher demonstrating a technique and students completing a range of exercises to practise the technique. Even though this teaching method was executed to a high standard it is not always the most suitable to ensure that the learning styles of all students are catered for. A range of methods should therefore be used when teaching Mathematics and appropriate methods chosen when planning a lesson. Reference to the methodologies outlined in the Junior Certificate Guidelines for Teachers would be helpful in this regard. More innovative practice was observed to be highly effective. For example, in lessons where the learning was grounded in real-life situations, it was evident that students enjoyed the practical nature of the topic and that the use of authentic resources added to their enjoyment of the learning experience.
Teachers used questions to establish students understanding of the topic and to recall facts from previous lessons. The use of higher-order questioning was particularly good as it allowed the teacher to challenge students’ understanding and required them to justify and provide a rationale for their suggested answer. For example, during the completion of an exercise on taxation students were encouraged to draw inferences from their calculations. This was commendable practice and should become a feature in more lessons where appropriate. However, if higher-order questioning is to be used to the full, sufficient time must be given to students to reflect on the questions being asked before the teacher intervenes and provides an answer.
Many classrooms visited were teacher based. In such classes student work was displayed and included student-developed revision posters for Applied Mathematics which highlighted relevant formulae. Teachers have sourced commercially produced Mathematics theme posters and have also enlarged relevant pages from Mathematical log tables for use as posters and learning aids. The inclusion of students’ work in addition to commercially produced posters is highly commendable and adds to an appropriate learning environment.
Resources used during the lessons included textbooks, examination papers and prepared worksheets. The preparation of support material such as articles from the national newspapers and teacher-developed learning aids that simulated real-life situations for the teaching of taxation in TY was very effective. However, the data projector was only used to project questions from examination papers although all classrooms visited had access to ICT. It is recommended that planning for the full use of available ICT resources be undertaken.
Interactions between students and the inspector were good. Students used relevant and appropriate mathematical terminology. It was clear from students’ questions to their teachers that they were engaged with the work in hand and used such opportunities to check their own understanding. This is commendable as it allows students to become actively involved in their own learning.
Students are assessed on a regular basis by their teachers. Weekly effort grades are award to students based on their performance and attitude to work. In addition three formal assessments take place for students during the year. The Mathematics department uses a combination of an agreed common paper and an individual teacher’s paper for the formal assessment of its students. In this way student achievements are regularly monitored and comparisons can be made within levels. Third-year and sixth-year students sit ‘mock’ examinations in the second term. Following formal assessments school reports are issued to parents that detail students’ achievements in examinations, participation in class, effort grades and written work.
In lessons observed teachers modelled best practice in the presentation of work on the whiteboard. However, work in students’ copies was not always well presented. This issue was discussed during the evaluation and the Mathematics department is currently reviewing its policy regarding presentation of student work. The outcome of this review should make it clear to students that they have a responsibility in this area. Furthermore, it was clear that not all students are sharing in the responsibility of correcting their work and this deficit should also be addressed in the review of policy.
Good practice in relation to the monitoring of students’ work was observed and the inclusion of helpful feedback is commended.
The following are the main strengths identified in the evaluation:
· There is very good whole-school support for Mathematics in St.Columba’s College through timetable provision, facilitation of teachers to attend continual professional development,
the resources allocated to the subject, and the allocation of an additional teacher to the subject in sixth year.
· The Mathematics department is coordinated effectively by the school-appointed head of department. The department has made very good progress with the development of
departmental documents such as a Mathematics teacher handbook and a Transition Year Mathematics resource manual.
· There is very good support for students who find Mathematics challenging or who have mathematical talent.
· Opportunities for students to encounter Mathematics in contexts out of the classroom situation are very good, through participation in Mathematics competitions and other events.
· Examples of excellent and innovative teaching and learning practice were observed.
· Students’ achievements in Mathematics are very good particularly at higher-level.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· The Mathematics department should collaborate to combine existing documents into one succinct long-term planning document that includes the learning outcomes to be
achieved by each year group and level.
· The Mathematics teachers should continually seek to expand the range of methodologies used and select those most appropriate to the learning intention.
· The Mathematics teachers should plan for the full use of the available resources, particularly the ICT equipment, in their teaching and learning practices.
Post-evaluation meetings were held with the head of the Mathematics department and with the principal at the conclusion of the evaluation when the draft findings and recomendations of the evaluation were presented and discussed.
Published February 2010