An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Meán Scoil Mhuire
Convent Road, Longford
Roll number: 63760E
Date of inspection: 6 May 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Meán Scoil Mhuire, Convent Road, Longford. 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 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.
Excellent provision is made for teaching and learning of Mathematics in the school. In senior cycle, there are six periods per week comprising four single periods and one double period. Applied Mathematics is offered in senior cycle outside of the normal subject options. In junior cycle there are four periods per week for Mathematics in first year and five periods per week thereafter. The distribution of mathematics classes throughout the week is very good. Classes are well distributed between morning and afternoon periods. The provision for Mathematics in Transition Year (TY) is three periods per week
Classes in first year are mixed ability. Students follow a common programme, take common class tests and sit three formal common assessments throughout the year. The results of the formal tests are stored centrally and are used to inform decisions regarding the most appropriate levels students should follow for the junior certificate examinations. Mathematics classes are timetabled concurrently in second and third year. One higher-level class is formed at the beginning of second year, the remaining classes are banded; two of these follow the higher-level syllabus, two take ordinary level and three small learning-support classes are also provided. Students in the learning-support classes follow the ordinary-level course for as long as possible but some then take foundation level in the Junior Certificate examination. The arrangement for Mathematics in third year mirrors provision in second year
Students are encouraged to aspire to take the highest level possible and the movement of students between levels is readily facilitated. Students sit common tests and common questions within class tests throughout second and third year. This is good practice as it enables teachers to profile each student and to gauge their performance within their peer group. Furthermore it enables students to choose the level that is most appropriate to their needs and abilities.
TY is optional and, following the receipt of applications, students are selected using established and agreed criteria. The TY mathematics classes are mixed ability. One higher-level and one fast-paced ordinary-level class are formed at the beginning of fifth year, the remaining ordinary-levels classes are mixed ability. Students who are taking foundation level are catered for in small group settings.
Applied Mathematics is currently provided in senior cycle as an optional subject but will be included in the formal timetable next year. Currently two periods per week are provided for this option. The commitment to providing Applied Mathematics is commended.
Prospective students are initially informed about the school during visits to the feeder primary schools by the school principal. These visits, which occur in January or February, are followed by an open day when the students visit the school with their parents for an orientation session. Application forms are available at this open day. Each student who enrols then attends for interview, together with his or her parent. Parents are invited to attend a post-enrolment meeting where information regarding school policies and procedures is disseminated and parents’ questions and concerns are answered. The school’s guidance counsellor visits all the feeder primary schools to meet with the sixth-class teachers and also meets individually with the parents of incoming first years. These very comprehensive induction measures, which serve to identify the needs of the incoming students and inform parents and students of the school’s practices and procedures, are highly commended.
Students in need of extra support in Mathematics are identified during of the school’s induction process and through a variety of testing procedures. Incoming students sit standardised tests in March and again in September following enrolment. In addition, the school has devised specific tests to identify the level of mathematical skills possessed by the students. The first-year mathematics programme is designed to address the shortcomings and to build on the strengths identified by the various tests. The classes in first year are mixed ability and in-class support in the form of team teaching is provided for those identified with special educational needs (SEN) or in need of learning support.
The mathematics teachers have attended a wide range of continuing professional development (CPD) courses. Details of the various courses attended by staff are included in the mathematics department subject development plan. This is good practice as it provides colleagues with an avenue to any resources that may have been disseminated, and to new developments in the subject. Management supports attendance at CPD courses and, just prior to the inspection, had arranged for whole-school training in differentiation in the mixed-ability setting. This enlightened approach in response to the evolving learning environment in the school is highly commended.
A range of resources for teaching and learning Mathematics has recently been purchased and the teachers of Mathematics have access to a laptop and data projector. Integration of information and communication technologies (ICT) and other resources in teaching and learning Mathematics was evident during the inspection and it is intended to enhance the ICT provision in the mathematics department as part of the school’s development plan.
Teachers are assigned to classes and levels on a rotating basis and by agreement with management. However, teaching the higher level Mathematics to classes in senior cycle typically alternates between two colleagues. It is suggested that, as an integral part of the school’s CPD programme, additional teachers be identified and assigned to higher-level Mathematics in the coming years. It is policy and practice within the school for teachers to remain with the same class groups from second to third year and from fifth to sixth year, where possible, thus maintaining high levels of continuity.
Subject development planning in Mathematics is excellent. An experienced member of staff currently co-ordinates the work of the mathematics department and responsibility for coordinating the department rotates every five years. There are two formal planning meetings each year and minutes of these meetings are included in the subject-development plan. The development plan for mathematics is very comprehensive and is subject to regular review.
The schedule for content delivery in the subject-development plan for Mathematics details the topics to be covered by each year group and for each level in every year of their respective courses. It is recommended that the delivery schedule be revised to specify the topics to be covered by each year and level each month. This would further support the excellent work being done in delivering common assessments and common revision programmes and would be an invaluable resource for newly appointed and substitute teachers
Informal planning was very evident during the inspection. It was clear that teachers within year groups collaborate in relation to the progress of their students, the approach to be adopted in preparing common assessments and in preparing common revision programmes. There is an informal agreement among the members of the mathematics department regarding the most appropriate methodologies and approaches to be used in teaching various aspects of the course. The use of common methodologies is very good practice particularly in light of the movement of students between levels and it is recommended that this practice be formalised and that the agreed approaches and methodologies be included in the subject development plan.
Planning for teaching and learning Mathematics in TY is also at an advanced stage. The school’s TY mathematics programme provides opportunities for students to consolidate previous learning and to develop new skills; it also gives the students an appreciation of the importance of mathematics in everyday life. The TY mathematics plan outlines clearly how these objectives are to be achieved and includes a range of very innovative approaches to engaging the students in their own learning.
All of the teachers of Mathematics made their personal planning documentation available and in all cases plans were found to be relevant, comprehensive. The teachers’ diaries contained details of students’ attendance, the results of assessments, homework assignments and completions. In addition, some teachers had prepared a diverse range of classroom resources as an aid to teaching and learning. These resources will be made available to all members of the mathematics department on the school’s local area network (LAN) in the coming months. This approach to sharing resources is highly commended.
Planning for students experiencing difficulties in Mathematics or in receipt of learning support is very good. Comprehensive student profiles and individual education plans (IEPs) are in place for all of those students who are in receipt of resource hours.
The uptake of higher-level mathematics in junior cycle is very good. However, a significant number of students who are successful at higher level in the Junior Certificate mathematics examination do not choose the higher level in senior cycle. It is reported that a whole-school initiative that will have the support of management and will involve the mathematics team and the school’s guidance counsellor is planned for the coming year. This initiative is designed to encourage a greater uptake by students of higher-level mathematics in senior cycle. This is highly commended
Teacher planning and preparation for all of the lessons observed during the inspection was very good. The lessons were clear and well presented. The teachers taught with enthusiasm and the students engaged with the subject matter enthusiastically. The textbook was the primary resource but additional material in the form of differentiated worksheets, ICT resources were also in evidence. These additional resources enhanced the teaching and learning experience and enabled students to participate in a fashion most appropriate to their needs and abilities. The teaching style was mainly traditional but the teachers were skilful and the quality of the lessons observed during the inspection was very good.
The classes proceeded in an atmosphere of mutual respect. The teachers’ interactions were warm and caring and they were mindful of the strengths and weaknesses of the students. In one lesson students were tackling very challenging material, which involved algebraic fractions leading to quadratic equations. There was a range of abilities in the class group, but the strategy employed by the teacher, which drew on the students’ existing knowledge and skills and incorporated them into robust procedures made the material accessible to all of the students. Each student in the class was involved at some stage in developing the procedures and contributed to a very positive, inclusive and enjoyable learning experience.
In another lesson, ICT and active methodologies were used to support the teaching and learning of Simpson’s Rule and to engage the students in self-directed learning. A PowerPoint presentation was used to introduce Simpson’s Rule and to share the lesson’s learning objectives. The class group then went outside and marked out an irregular shape on the surface of a paved area of the schoolyard. They worked in teams to segment the area and to take the relevant measurements, which would enable them to use Simpson’s Rule to estimate the area of the irregular shape. They also estimated the area by approximating the number of square paving tiles contained within the shape. The class group returned to the classroom to complete their final calculations and to compare the two estimates. As a follow-up activity, the students were challenged to suggest refinements to their procedures that might improve the accuracy of their results. This very impressive lesson was ably facilitated by the teacher and was a compelling example of how a range of methodologies could be incorporated into the teaching and learning of Mathematics.
Good practice was also evident in another class where students had prepared their own learning aids in the form of number lines and hundred squares. These were taped to the students’ desks and were referred to when dealing with addition and subtraction of integers. This innovative practice reduced the reliance on calculators for rudimentary calculations and helped to develop the students’ confidence with the subject matter.
Classroom management and student discipline was excellent. The atmosphere in the classrooms was warm and the rapport between teachers and students and among the students themselves contributed to an inclusive and friendly learning environment. Very good practice was observed in the use of differentiated worksheets in teaching percentages in a mixed-ability class. The teacher first presented very appropriate strategies for working with percentages and was then free to circulate and deal with individual students as they worked through the worksheet. A very positive learning environment ensued where each student was actively engaged with the lesson and had an opportunity to contribute to the lesson’s learning outcomes.
Student learning was very evident. They responded readily and knowledgeably when questioned by the teacher. Teacher questioning was the primary means of ongoing formative assessment and was used extensively in the lessons observed during the inspection. It is suggested that a greater degree of differentiated questioning be used to challenge the more able students and to encourage students to speculate, hypothesise and defend their reasoning.
A number of learning-support classes were visited during the inspection and in all cases the quality of the work observed was very impressive. The material being covered was appropriate, the learning environment was challenging and student centred.
The homework copies were, in all cases, very good. They were well laid out, corrected regularly and contained corrections, comments and annotations. In their interactions with the inspector, the students were confident and displayed a good knowledge of Mathematics.
Practices relating to assigning and correcting homework in Mathematics are very good. Homework is assigned during each lesson and is corrected by the students themselves under the direction of the teacher. Teachers’ comments and students’ corrections were evident in the samples examined by the inspector. It is recommended that the practice of students amending their own work be adopted uniformly across the mathematics department and that it be included as a key assessment vehicle in the subject-development plan
Formal common assessments for first-year students are held at Christmas, Easter and just prior to the summer holidays. These assessments are corrected using a common marking scheme and the results are collated centrally and are used to inform student decisions regarding choice of levels at the end of first year. Common assessments are set in second and third year within the bands as the needs and opportunities arise. Students taking state examinations sit formal assessments at Christmas and do mock examinations at Easter. Students at the same level take common papers in the mock examinations.
Reports are issued to parents after each formal assessment and ongoing communication occurs through the use of the student diary, parent-teacher meetings and other, less formal, means. Each class group has one parent-teacher meeting per year.
Students’ achievements are recognised by the school’s awards ceremony, which is held each May. The ceremony recognises excellence and endeavour in academic pursuits, sports and a range of school-related activities. Students’ achievements in Mathematics are included for recognition at the awards’ ceremony.
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 the principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published October 2008