An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
Brigidine Secondary School
Mountrath, County Laois
Roll number: 63410A
Date of inspection: 1 October 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Brigidine 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 studentsí work, and had discussions with the teachers. The inspector reviewed school planning documentation and teachersí 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; a response was not received from the board.
Timetabling provision for Mathematics is in line with national norms. There are four periods of Mathematics per week in First and Second Year and five periods per week thereafter. Class periods are forty minutes long. Mathematics classes are timetabled concurrently in each year. This is very good practice, as it enables the movement of students between levels and facilitates collaborative planning in curriculum delivery and student assessment. The distribution of mathematics classes throughout the week is also good, but it is undesirable that third-year students are provided with two periods of Mathematics on Mondays. It is recommended that this element of timetabling be kept under review to ensure that when five periods are provided each week there should be no more than one class period per day.
Mathematics classes are mixed ability in first year and are streamed thereafter. A common mathematics programme is followed in first year. The initial emphasis of the programme is on consolidating and developing the studentsí mathematical knowledge and skills, and more exacting material and techniques are introduced in the latter part of the year. This is very good practice. It ensures that any weaknesses in learning can be identified and addressed, and the students receive a good grounding in the core mathematics methods. Students in first year sit common mathematics assessments. The results of these tests are collated and are used to assign them to appropriate levels in second year.
Prospective students are informed about the school during visits made by the principal to the main feeder schools. These visits take place each November and are followed by an open day for pupils. This event is designed to allow prospective students and their parents to become familiar with the schoolís facilities and the curricular and extra curricular activities. Following the open day, an information evening is provided for parents who are intending to enrol students in the school. Application forms, arrangements for admission to the school and a range of policies are distributed at this stage.
The procedures for supporting students who need learning support are good. Class teachers in the feeder-primary schools are contacted by telephone and the profiles of incoming students are discussed. †Incoming students who have had their learning or other needs already formally assessed by the National Educational Psychological Service (NEPS) in primary school are identified, and applications for extra resources are then submitted by the school to the Department of Education and Science for consideration. If it is deemed necessary, additional assessments for some students are also arranged through NEPS.
All incoming students are assessed in verbal and numerical reasoning using the AH3 test and reading ages are measured by using the Young Cloze test. Once the students have settled into first year, their mathematical ability is again assessed using the wide range achievement test (WRAT 4). Additional assessments are organised by the school with parental consent if this is deemed necessary. It is recommended that the school refer to Circular 0008/2007 www.education.gov.ie to ensure that the standardised tests currently being used are included in the list of approved tests contained therein.
Learning support and resource teaching in Mathematics is provided through the withdrawal of students from subjects other than Mathematics, following consultations with parents. There are a large number of teachers involved in providing learning support and good procedures are in place to ensure that common and agreed practices are followed. Comprehensive student profiles are completed. These profiles are developed in consultation with the student, the class teacher and the learning-support teacher, and detail the studentsí strengths, weaknesses, and interests. Each profile is stored in the studentís learning support folder. Only members of the mathematics department deliver learning support in Mathematics, and the content to be covered is agreed following discussion with the class teacher. An outline of the content of each learning support lesson is contained in each studentís folder.
The performance of students in receipt of learning support is tracked and recorded using the schoolís standard procedures. Parents are informed through comments included on report sheets that are sent with the results from the schoolís formal examinations. Issues arising during the year are relayed to parents immediately by telephone. The learning support co-ordinator maintains a separate, secure, administrative folder for each student who is in receipt of learning support. There are two learning support resource rooms, each of which is equipped with information and communication technologies (ICT) facilities. Students who are in receipt of learning support also have access to one of the schoolís two computer rooms.
Students with exceptional abilities in Mathematics are also identified as part of the enrolment procedure. They are encouraged and facilitated to participate in the programmes operating under the aegis of the Centre for Talented Youth of Ireland (CYTI) in Dublin City University.
Teachers are assigned to teach all the levels in junior cycle by rotation, but just one of the teachers currently takes higher level at senior cycle. It is suggested that, as an integral part of ongoing department planning additional teachers be encouraged to take higher-level Mathematics to Leaving Certificate, and that the practice used in assigning teachers to levels in junior cycle be replicated in senior cycle.
The school has good ICT facilities, but otherwise the resources for teaching Mathematics are limited. It is recommended that the mathematics department undertake an audit of existing skills and resources, and that advice from the second level support service www.slss.ie †be sought about how to begin addressing any shortcomings identified in the audit.†
School development planning is well advanced in the school and subject planning in Mathematics is very good. A co-ordinator has been appointed and regular meetings take place. The schedule of meetings together with the minutes of the meetings is included in the subject development plan. The members of the mathematics department meet every August to review and amend the subject-development plan. The department also analyses the performance of students in the state examinations with reference to the statistics supplied by the State Examinations Commission. This informed and enlightened approach to subject planning is very good practice.
The subject-department plan for Mathematics is comprehensive and includes the mission statement for the department, a statement of aims and objectives, key learning outcomes, notes on classroom organisation including seating plans and lesson structure, lists of agreed text books, the schedule for curriculum delivery, planning for students with special needs and cross-curricular links. The schedule for curriculum delivery is very detailed and gives the content to be covered in the programme for each year group, month by month.
In order to build on existing good practice in planning, it is recommended that strategies to integrate different areas of the syllabus routinely in the teaching and learning of Mathematics be identified and outlined in the subject-development plan. It is also suggested that the existing good practice regarding the use of agreed procedures in carrying out core mathematical operations in lessons be detailed in the plan.
Almost all of the teachers made their personal planning materials available during the inspection. These were found to be comprehensive and relevant. In addition, the teachersí diaries were used to record attendance, homework completions and performance in class tests.† The very good practice of developing and recording student profiles was also evident in a number of cases
Management is proactive in supporting attendance at continuing professional development (CPD) courses and a comprehensive list of the courses attended by the teachers is included in the subject development plan for Mathematics. The majority of the teachers are members of the Irish Mathematics Teachersí Association (IMTA)
Newly appointed teachers participate in an induction programme which is provided by the principal. †This includes an introduction to the schoolís policies and ethos and an outline of the procedures to be followed in relation to homework and assessment, classroom management and the implementation of the code of discipline.
The lessons observed during the inspection were well planned. The amount of time however, spent correcting homework should be uniform and in line with the guidelines in the subject- development plan. Links were drawn to material covered in earlier lessons and the material covered was relevant and included: calculus, coordinate geometry of the line, rearranging formulae, statistics, linear programming and quadratic equations.† The lessons proceeded at a suitable pace, were well-structured and the various elements of the lesson were knitted together skilfully.
Expositions by teachers followed by an activity for students were the primary teaching methods in evidence during the inspection. While the teachers were knowledgeable and taught with enthusiasm a more student-centred approach would be welcomed. The integration of information and communication technologies (ICT) was evident in one lesson where students used spreadsheets to produce pie charts, trend graphs and bar charts. The material produced was very impressive and served as a shared learning resource for the class.
Teachersí use of questioning was very good. Questioning was primarily used to elicit factual responses from named individuals, but the very good practice of using open-ended questions and engaging the students in higher-order thinking was also in evidence. This was particularly striking in one instance where the students were asked to imagine the shape of a cubic function, to explain their reasoning and to predict the number of roots the associated cubic equation should have. This exploration served as an ideal introduction to the topic in hand and grounded the material firmly in the studentsí previous learning.
In addition, teacher questioning also served to involve as many students as possible in problem solving. This was particularly effective where individuals were invited to provide one line in the solution to a problem before passing on responsibility for the next line to another student. In this way, a solution to the problem was arrived at by students operating in relays. It guaranteed that all members of the class group had to co-operate with one another and concentrate fully on the material in hand.
The lessons proceeded in an atmosphere of mutual respect where the highest standards of behaviour and engagement were expected and realised. Positive attitudes towards Mathematics were in evidence and the quality of student learning as demonstrated by studentsí responses to questions, the quality of the studentsí written work and their ability to carry out common mathematical operations were very impressive. Analysis of the uptake rates and student attainment in the state examinations provided further evidence of the high quality of learning.
Great care was taken to meet the needs of individual students in all of the lessons visited during the inspection. During student activities, the teachers moved around the classrooms assisting students as the need arose, and occasionally invited students to go to the marker board to illustrate their solutions. In this way, difficulties encountered by individuals and any innovative ideas that emerged were used to enrich the learning experience of all members of the class and to deepen their understanding of the matter in hand. This approach to differentiation could be further enhanced through the use of graduated worksheets, the content of which could be tailored to the needs of the students in question.
Practice relating to assigning and correcting homework in Mathematics is in line with the schoolís homework policy. Homework is assigned at the end of each lesson and is corrected at the beginning of following class. In most cases, care was taken to ensure that the correction of homework acted as a shared learning experience. Students were asked to identify any problems they had encountered and, occasionally, to demonstrate their approach to problem solving to the class group by exposition at the board. The homework copies examined during the inspection were well maintained, contained positive teacher comments and in one case, the good practice of students amending their own work was also in evidence. Practice in relation to the correction of homework would be greatly enhanced by standardising the process by which students amend their own work and by specifying, in the schoolís homework policy, the roles and responsibilities of all stakeholders.
Ongoing assessment occurs through teacher questioning and through class tests which are set upon completion of each topic. The results of the class tests and any issues arising regarding compliance or difficulties with homework are stored in the teachersí diaries. Formal examinations are held in late November and again prior to the summer holidays. Common papers, corrected in accordance with an agreed marking scheme are provided in first year and common papers are set within levels for the remaining years. Mock examinations are held just prior to the midterm break in the second term and students taking the same level sit common papers. Written reports issue to parents following formal and mock examinations.
Ongoing communication with parents occurs through the use of the student diary and telephone contact, and formal letters are also issued if the need arises. In addition, each class group has one parent teacher meeting per year and less formal meetings can be arranged if required.
Positive attitudes towards Mathematics are promoted by facilitating studentsí participation in the annual regional table quiz organised by the Irish Mathematics Teachersí Association and by the provision of a range of in-school activities to celebrate Maths Week. An awards evening is also held each year to recognise attainment and endeavour.
The following are the main strengths identified in the evaluation:
∑ The quality of teaching and learning in Mathematics in the school is good.
∑ The students demonstrated a very positive attitude towards Mathematics.
∑ Timetabling provision for Mathematics is in line with national norms.
∑ The procedures for supporting students in need of learning support are very good.
∑ The school has good ICT facilities.
∑ School development planning is well established and subject planning in Mathematics is very good.
∑ The mathematics department is ably co-ordinated and a comprehensive subject development plan for Mathematics is in place.
∑ Teachersí individual planning and preparation for class is good.
∑ Management is proactive in supporting the continuing professional development of the teaching staff.
∑ A homework and assessment policy is in place and is being implemented.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
∑ It is recommended that the scheduling of classes be kept under review to ensure that when five periods are provided each week there should be no more than one class period per day.
∑ It is recommended that the school refer to Circular 0008/2007 www.education.gov.ie to ensure that the standardised tests currently being used by the school are included in the list of approved tests contained therein.
∑ It is recommended that the mathematics department undertake an audit of existing skills and resources and that advice from the second level support service (www.slss.ie) is sought to address any shortcomings identified as a result of the audit.
∑ It is recommended that strategies to integrate different areas of the syllabus routinely in the teaching and learning of Mathematics be identified and outlined in the subject-development plan.
Post-evaluation meetings were held with the teachers of Mathematics, with the principal and deputy principal, at the conclusion of the evaluation when the draft findings and
Published January 2009