An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Loreto Secondary School
Clonmel, County Tipperary
Roll number: 65330M
Date of inspection: 19 March 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Loreto Secondary School. 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 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.
In the current year the mathematics teaching team comprises nine teachers. Management allocates teachers to year groups and, following consultation, to individual classes. Teachers generally continue with classes from second year to third year and from fifth year to sixth year. This is good practice. Levels are rotated between some members of the teaching team. The full rotation of teachers in the junior cycle is commended. In order to extend the expertise necessary for teaching higher-level Leaving Certificate Mathematics, it is recommended that more teachers become involved at this level. This will enable the school to meet the changing needs of the curriculum in the coming years.
Mathematics classes in each year group, apart from first year and Transition Year (TY), are timetabled concurrently and this is good practice. Concurrent timetabling allows students to follow the highest level possible for as long as possible and facilitates change of level where necessary. In second year, third year and sixth year, an additional class group is created to cater for students who find Mathematics particularly challenging and this is commended. Students in need of learning support are identified through pre-entry and post-entry assessments, contact with local primary schools, parents and teacher monitoring during first year. Support is provided along traditional lines, that is, through the provision of individual and small-group tuition during withdrawal from subjects other than Mathematics. Learning support can continue throughout the school life of the students if necessary. Mathematics learning support is sometimes provided by members of the mathematics department. There are very close informal links between the mathematics teachers and the members of the learning support team. They consult each other on a regular basis to ensure that uniformity of content and approach is observed. This high level of collaboration is commended.
Time allocated to Mathematics is good. All junior-cycle and fifth-year classes are timetabled for five periods each week. TY is optional within the school and a majority of students choose to avail of the programme. Three class periods are allocated to TY Mathematics. Sixth-year classes have six lesson periods. Lessons commendably are distributed evenly throughout the school day and the school week.
Students are assigned to classes on a mixed-ability basis in first year and in TY. At the beginning of second year, students are assigned to two higher-level streamed classes on the basis of their first-year performance, and to two ordinary-level classes on a mixed-ability basis. It is recommended that the class formation system for Mathematics be reviewed annually to ensure that it continues to meet the needs of the students. Mixed ability within levels takes account of varying rates of student development and can exploit the correlation between levels of teacher expectation and levels of student achievement and should be seriously considered at higher level as well as ordinary level.
There is a variety of teaching resources available. Teachers have access to a computer room and the school has recently purchased a number of data projectors to support teaching. The school funds the purchase of mathematical teaching aids on request. Whiteboard drawing instruments, number lines, playing cards, books and worksheets are stored in the staffroom and are available to the team.
The school is committed to the continuing professional development of its teaching team. It was apparent that teachers have taken advantage of this by organising in-school development sessions and taking part in courses organised by the Mathematics Support Service (MSS). This is positive.
The mathematics department encourages participation in the Team Maths competition organised nationally by the Irish Mathematics Teachers’ Association (IMTA) and World Maths Day activities. Students also attended a lecture in the University of Limerick as part of Maths Week. This is very good practice as it raises the profile of the subject within the school and enables students to enjoy and appreciate Mathematics outside of the classroom setting.
The mathematics team undertakes some analysis of the school’s performance in the Certificate Examinations in Mathematics in relation to achievement and uptake levels and comparing them with national norms. An analysis of results over recent years indicates strengths in both these areas. Such analysis is useful in informing future planning and provision for the subject.
The mathematics department is currently co-ordinated on a voluntary basis by a senior member of the team. To allow each member of the team to gain a deeper understanding of the issues involved in the workings of their subject department and to share the workload, it is recommended that the role of co-ordinator should rotate among members of the team, perhaps on an annual basis.
Formal planning and review meetings are scheduled around staff meeting and school planning days and occur about three times a year. Records are kept of such meetings and they show evidence of collaboration and review among the mathematics team. Recent discussions have included the school’s special educational needs policy and the integration of the new ICT equipment into the teaching of Mathematics. Informal discussions between small groups of teachers also take place on a regular basis.
The mathematics team has made commendable progress in planning. The department plan includes overall aims and objectives for mathematics education within the school, organisational details of classes and teachers, reference to methodologies and resources and cross-curricular planning, which is in line with good practice. The plan also includes procedures for homework, assessment, record keeping and reporting.
The long-term plan contains a list of topics to be covered by each year group and level annually. It is recommended that the mathematics department continue this good work and further develop the long-term plan for Mathematics. Ideally the yearly plan should be divided into sections by term, or half year, to allow greater co-ordination within levels. This revised plan should include an outline of sections of the syllabus at junior and senior cycle and the key skills for students to acquire under each of these sections. The school’s mathematics plan should contain details of the teachers who have attended CPD courses in Mathematics and the topics covered.
Mathematics planning for TY is good. TY classes are formed on a mixed-ability basis and do not have a prescribed textbook. Within the plan, there is a good balance between topics that consolidate the prior learning of students, some work that introduces elements of the Leaving Certificate programme in an innovative way and other topics such as women mathematicians, sudoku and puzzles. A folder of resources has been prepared containing a range of materials and topics of interest. This is positive.
Teachers made individual planning and preparation materials available during the inspection. Included in these materials were schemes of work, examples of student worksheets and handouts, transparencies prepared for the overhead projector, extensive teacher notes, and large banks of test papers, common examination questions and solutions. A folder containing a selection of these resources is available to members of the team. This level of preparation for teaching is commended.
Teaching observed was generally of a high standard. In the classes visited, lessons were well structured and purposeful, and preparation for teaching was evident. Instruction began with a clear outline of the lesson content. This is positive. However this practice could be enhanced if 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 methodology 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. Good use was made of time and the lessons progressed at a challenging pace appropriate to student’s abilities. It was evident that teachers had high expectations of the students and the students responded accordingly. Topics such as geometry, graphs, vectors and area featured in the lessons observed. A variety of methodologies was used to engage students and stimulate their interest. There were some good examples of the use of worksheets, pair work and relating learning to the experience of the students being effectively used in lessons.
A range of resources was used in lessons. These included the textbook, whiteboard and overhead projector. In a number of instances information and communication technology (ICT) was used to reinforce concepts learned and enhanced the learning process.
Teaching observed was generally conducted through the presentation of work at the board followed by the setting of exercises for individual practice while the teacher provided assistance to students as required. Within this structure, the teaching was effective. This teaching style can lead to students being generally passive and seeing their role as reproducing the method of solution in similar type problems from the textbook. It is recommended that the team continue to broaden the range of teaching methodologies and include strategies that involve students more and make them less passive participants in their own learning. These could include pair work, group work, investigation, consolidation activities, the use of concrete materials, discussion, and quiz activities, more use of ICT and student project work. The incorporation of these methodologies into lessons can increase motivation and engage students more actively in their own learning. The teaching and learning plans available on the Project Maths Development Teams’ website www.projectmaths.ie should not be overlooked in this regard.
Teachers made use of questioning, both global and directed, during the lessons observed. 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 suggested that it be incorporated into lessons more frequently. Classroom management was effective and discipline was sensitively maintained. Teachers were generally affirming of the efforts of their students leading to positive interactions within the classroom. Teachers set appropriate high standards of expectation for their students and students responded to these expectations. There was a sense of mutual respect between teachers and students, creating an atmosphere that was conducive to learning.
In some classrooms, displays of students’ work or of mathematical posters were used to enhance the visual-learning environment. The display of such posters and students’ project work can be effectively used to motivate students and remind them of key mathematical concepts or formulae. It is suggested that more use be made of students’ own work, through projects or examples of high quality work, to engage students further.
In interactions with the inspector, the students were able to show understanding of the concepts taught and displayed clear, solid mathematical knowledge. They were also able to use appropriate mathematical language. They provided answers, justified solutions to questions posed to them and made relevant connections between topics. Learning was also evident as students were able to apply procedures, learned in class, to similar type problems from the textbook.
The school’s homework policy is implemented by the mathematics team. Lessons generally began with the correction of homework and appropriate homework was assigned in all lessons visited, providing students with an opportunity to consolidate and practise mathematical concepts engaged with during the lesson. An examination of students’ copies and journals revealed that homework is regularly assigned, which is good practice and in line with the mathematics department policy. An examination of a sample of mathematics copybooks and notebooks revealed work that was appropriate, relevant and well presented. There was evidence that teachers are monitoring students’ copies. In some instances the good practice of using positive comments to encourage students’ efforts was noted.
Students’ progress is monitored on a regular basis through questioning in class, review of homework and written assessments following the completion of a topic. All first-year classes are assessed commonly at the end of the school year and common assessment within levels also occurs in other year groups. This is good practice.
Non-examination classes have formal examinations at Christmas and summer. All classes are continually assessed during the first term and sit a formal assessment at the end of the school year or, in the case of examination classes, sit their ‘mock’ examinations during the second term. Teachers retain records of students’ achievements in assessments. Progress is formally reported to parents twice each year. In addition the student journal is used for informal communication and as a means of informing parents of progress. Each year group has a parent-teacher meeting annually. This level of communication with parents is commended.
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, November 2009