An Roinn Oideachais agus Eolaíochta

Department of Education and Science



Subject Inspection of Mathematics




Presentation College

Terenure, Dublin 6W

Roll number: 76092K



Date of inspection: 5 May 2006

Date of issue of report: 15 December 2006




Report on the Quality of Learning and Teaching in Mathematics

Subject Provision and Whole School Support

Planning and Preparation

Teaching and Learning

Assessment and Achievement

Summary of Main Findings and Recommendations

Report on the Quality of Learning and Teaching in Mathematics



This Subject Inspection report


This report has been written following a subject inspection in Presentation College, Terenure, 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 college. The evaluation was conducted over one day 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.


Subject Provision and Whole School Support



There are five teachers of Mathematics in the college. In junior cycle, teachers decide among themselves who will teach the different levels and in general levels are rotated. However, in recent years, the teaching of the Transition Year (TY) programme and of Leaving Certificate Mathematics at senior cycle is not rotated among the Mathematics teachers. This should be reviewed as it is not good practice that a school would not be able to utilise all teachers to deliver a particular level or programme. It is therefore recommended that all teachers avail of the opportunity to teach Mathematics in all programmes and at all levels in order to develop expertise within the Mathematics team.


The college has a policy of arranging classes into mixed-ability groupings in junior cycle. However, banding takes place in third year for both Mathematics and Gaeilge. Junior cycle students choose their level at the beginning of third year. In the current year there are four groupings of Mathematics and this has resulted in two bands each comprising two Mathematics classes. Some concern was expressed by teachers at the practice of having mixed-ability groupings in second year. However, on occasion teachers decide to teach both the ordinary and higher level syllabus within a second year class grouping. It is therefore recommended that consideration be given to the banding of Mathematics from second year to ensure that all students follow a level appropriate to their needs and ability.


TY students are arranged into mixed-ability class groupings and are not timetabled concurrently. At senior cycle generally one higher-level class grouping is arranged with the remaining students arranged in mixed-ability ordinary-level class groupings. These classes are concurrently timetabled. Generally the teaching of foundation level takes place within an ordinary-level class grouping. However, recently sixth year foundation-level students are withdrawn and have two of their foundation-level Mathematics classes independently of ordinary-level classes. Management is commended for providing this extra support. Time allocated to Mathematics is good at both junior and senior cycle. Management is commended for its allocation of six class periods per week to sixth-year class groupings.


There is no specific annual budget assigned for Mathematics. However, the college has purchased overhead projector calculators and three-dimensional shapes, and teachers have access to overhead projectors. Some teachers expressed concern about difficulties in accessing photocopying paper and acetates for class.  To ensure that Mathematics teachers have access to necessary resources, it is recommended that they collaborate to identify and prioritise appropriate teaching and learning resources and that these resources should be retained in a central location.


Some teachers indicated that they had attended the revised Junior Certificate inservice course for Mathematics. Management is to be commended for facilitating a follow-up visit from a member of the Junior Certificate Support Service in Mathematics. In more recent times the practice has developed whereby the principal nominates a representative of the Mathematics department to attend inservice. This nominee then returns and distributes all materials from the inservice to the remaining members of the department. It is recommended that the nominee chosen to represent the department be rotated among the teachers thus ensuring that all Mathematics teachers are given the opportunity to attend inservice.

Planning and Preparation


Work on school development planning is ongoing in the college. The regional coordinator from the School Development Planning Initiative (SDPI) is currently collaborating with staff on the development of subject planning in the college.


A coordinator of Mathematics is selected each September.  The college has developed a list of duties assigned to the position of subject coordinator. For example some of the responsibilities of coordinator include the distribution of documentation and information to all teachers in the department and liaising with the principal regarding changes in the choice of textbook. Management provides time for formal meeting at the beginning of the school year. Further informal meetings take place on a needs basis.  The college has timetabled formal meeting time into the annual calendar. However, it was reported that this meeting time is not being used.


Minutes from formal Mathematics meetings are recorded. However the content of these minutes is limited. Future records should include more information. Consideration should also be given to circulating minutes of meetings to all member of the Mathematics department.


The Mathematics department has developed an agreed long-term plan for the subject. This plan includes the chapters of the textbook to be covered for each year grouping, assessment procedures for each year grouping, resources available for the teaching of the subject and teaching strategies. Work on the development of the plan is to be commended. To further enhance the plan it is recommended that it should be based on the syllabus rather than the textbook. It should also include the learning outcomes and key skills that each year group should achieve. Furthermore a wider range of methodologies should be included such as the incorporation of the use of Information Communication Technology in the teaching and learning of the subject. There is some sharing of common assessments by Mathematics teachers which is good practice. In the context of further planning, it recommended that the Mathematics department extend the use of common assessment procedures for year groupings, where applicable.


The college’s Transition Year Mathematics programme is based on the Leaving Certificate syllabus. Circular M1/00 The Transition Year Programme outlines that the TY programme should not be seen as an opportunity to begin Leaving Certificate material. Instead Mathematics in TY should give students the opportunity to learn the subject in different contexts in order to improve understanding. It is therefore recommended that the Transition Year programme be reviewed to ensure compliance with the circular.  To this end a useful support is available at where teachers can access resources, newsletters, information on teaching and learning strategies, interdisciplinary links and curriculum ideas pertaining to TY Mathematics.


All Mathematics teachers have developed good short-term plans of work and have developed resources individually. Such planning is highly commended as it guides the teachers’ day-to-day work in the classroom while promoting continuity and steady progression in the students’ learning.


Teaching and Learning


Lessons were presented in a confident and coherent manner. Clear aims were established at the beginning with each class group. In general, time was used effectively. However, on occasion, the lesson could have progressed more quickly as students were already familiar with the topic. Topics such as calculus, binomial theorem and graphs featured in lessons observed while other classes worked on revision materials and examination papers.


In all lessons, teachers used Mathematics terminology appropriate to the relevant topics and students’ ability. Best practice was evident where teachers created links between various topics or sections of the syllabus. This had the effect of consolidating students’ understanding of the topic and is a practice that should be extended to all lessons.


The methodology used in all lessons was traditional whole-class teaching. This was a combination of the teacher demonstrating to the entire class group and students working individually on assigned work. Some students did become passive due to a significant amount of material being communicated by the teachers. While this methodology does have its merits, it does not suit all students. It is therefore recommended that a variety of methodologies be used in all lessons as suggested in the long-term plan for the department. Consideration should be given to including investigation and consolidation activities, practical work, discussion, group work and quiz activities such as those outlined in the Junior Certificate Guidelines for Mathematics Teachers.


Questioning techniques varied from lesson to lesson. In general, teachers used global questions to establish a topic or identify students understanding of the topic and continued with individual questioning of students.  However, interaction between teacher and students generally took the form of brief answers by the students to closed questions by the teacher. In these situations questions were generally recall in nature. For example, questions focused mostly on finding steps to the solution to a problem.   Less frequently, teachers used higher-order questions to elicit students’ understanding of the topic. For example, students were encouraged to develop their answers through a series of probing open-ended questions. It is recommended that a varied range of questioning strategies be employed which helps to consolidate learning and maintain student engagement with the topic.


In most lessons the textbook was used appropriately as a source of reference and supplementary graded worksheets helped to support the learning activities.  Such preparation ensured the smooth transition in the learning experience. Calculators were used appropriately in lessons observed. Effective use was made of the overhead projector during lessons with the preparation of material for use done in advance of the lesson.   Such prior preparation of materials is to be commended as it allowed teachers to circulate and provided individual attention to students who had difficulties with the topic.


In general, classes were conducted in an atmosphere of mutual respect where teachers gave varied and appropriate encouragement to all students.  Teachers were always affirming of all students. When necessary attention was given to students it was done discreetly and sensitively.


Most teachers are classroom based and generally classrooms had mathematical material on display. This is good practice as it is conducive to a good learning environment.


Assessment and Achievement


The assessment of students takes many forms, for example, class questioning, homework, end-of-topic examinations and continuous assessment. Non-examination students sit formal house examinations in February and in the summer. Examination students sit ‘mock’ exams in February.


The college maintains good communication with parents. It issues three school reports to parents of students in non-examination classes and two to parents of students in examination classes. Parent-teacher meetings are held for each class grouping. In addition, student journals are used by students to record homework and by parents to record reasons for student absences. Parents were not required to sign the journal on a weekly basis.


Teachers retain good records of student attendance. During the course of the inspection, it was noted that a significant proportion of students were absent. Furthermore, from observation of teachers’ records, it was evident that absenteeism is an ongoing problem. This makes the teaching and learning of Mathematics difficult as the continuity of the learning experience for some students is disrupted. It is therefore recommended that a whole-school approach be adopted to address the issue of attendance.


The homework assigned was appropriate in terms of quantity and relevance to the topics engaged within the lessons. There was evidence to suggest that teachers are monitoring Mathematics homework copies. There were some good examples of practice where teachers provided formative assessment to students. However, it is recommended that this practice be extended to all copies and class groups. Additionally, it is recommended that students be encouraged to take a more active role in the correction of their homework.


Student outcomes, in terms of knowledge and skills, varied from class to class. Many students were confident in justifying and explaining their answers. In general, the uptake of higher level in both Junior and Leaving Certificate Mathematics is good. Teachers are to be commended for keeping the number of students taking foundation-level to a minimum.


The college arranges award ceremonies for students at Christmas and again at the end of the school year. During these award ceremonies students are acknowledged for their sporting and academic achievements. This is commendable practice. In recent years students have participated in the Team Maths table quiz arranged by the Irish Mathematics Teachers Association. This is commendable practice as it provides students with opportunities to engage with the subject while experiencing Mathematics in a different learning environment.




Summary of Main Findings and Recommendations


The following are the main strengths and areas for development identified in the evaluation:

§        Teachers have developed good individual short-term plans for Mathematics.

§        Teachers of Mathematics have developed a long-term plan for the department.

§        There were some good examples where teachers used higher-order questioning.

§        There is good communication between the college and parents.

§        Teachers retain good records of students’ attendance and assessment.


As a means of building on these strengths and to address areas for development, the following key recommendations are made:

§        Teachers should avail of the opportunity to teach Mathematics in all programmes and at all levels in order to develop expertise within the Mathematics team.

§        Consideration should be given to the banding of Mathematics from second year to ensure that all students follow a level appropriate to their needs and ability.

§        The Mathematics department should collaborate to further advance their long-term planning for the provision of Mathematics in the college.

§        The Transition Year Mathematics programme should be reviewed to ensure compliance with Circular M1/00.

§        A greater variety of methodologies and questioning strategies should be used in lessons.

§        The college should engage in a whole-school approach to address the issue of attendance.


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.