An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
St Paul’s Secondary School
Monasterevin, County Kildare
Roll number: 61702D
Date of inspection: 5 October 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in St. Paul’s 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 deputy 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.
St. Paul’s Secondary School is just emerging from period of uncertainty and turmoil regarding the management structures in the school. It has been operating without a board of management for almost three years and, until recently, both members of the senior management team were employed in an acting capacity. The acting management team received the support of a manager who was appointed by the school’s trustee. A permanent principal and deputy principal are now in place and a board of management will shortly be appointed. Great credit is due to all concerned that the school has overcome these difficulties and is seeing increasing enrolment and provides a broad and balanced curricular programme.
The mathematics department, thanks to effective leadership and collaboration, is well organised. It comprises five teachers, the majority of whom have an appropriate qualification in Mathematics. Responsibility for teaching higher-level Mathematics in junior cycle is shared between two of the teachers while just one of the teachers takes higher-level in senior cycle. This model is working very well at present. However, as student numbers in the school increase, consideration will need to be given to developing the capacity of the department so that at least one other teacher is in a position to take Mathematics to higher level in senior cycle. Teachers retain the same class group from second into third year and from fifth into sixth year. This facilitates long term planning and continuity of curriculum delivery and is very good practice.
Members of the mathematics department have been proactive in attending continuing professional development courses and are currently engaged in ongoing in-service training to prepare for the roll-out of Project Maths. Management is willing to defray the cost of membership of the Irish Mathematics Teachers’ Association. In light of the considerable changes in curriculum content and delivery espoused by Project Maths, it is suggested that the members of the department should consider joining the association and availing of the various supports it provides.
The mathematics department is well resourced and management is committed to assisting the further development of the department. Classes have access to the school’s computer room and a bank of ten laptops is available to students. The mathematics teachers have access to a laptop and data projector and to other audio visual devices. In order to facilitate the implementation of the active teaching methods advocated by Project Maths, it is recommended that one of the mathematics teachers be selected to audit the existing resources in the school and to ascertain if resources need to be procured. In particular, resources to exploit the schools information and communication technology infrastructure in lesson delivery should be identified. Arrangements for sharing appropriate resources should be put in place and detailed in the subject department plan for Mathematics. Assistance in carrying out this work is available from the Second Level Support Service http://www.slss.ie/.
Timetabling provision for Mathematics is very good. There are four periods of Mathematics per week in first year and five periods per week for the remainder of the junior cycle. Upon completion of junior cycle, students apply to enter transition year (TY) or can go directly into fifth year. There are three periods of Mathematics per week in TY and five periods per week in fifth and sixth year. Class periods are forty minutes long. Mathematics classes are timetabled concurrently in each year. This provides students with easy access to the level most appropriate to their needs and is very good practice. The distribution of mathematics classes throughout the week is very good, as is the balance of provision between morning and afternoon.
The mathematical capabilities of students entering the school are established by means of a mathematics competency test, designed by the mathematics department in the school. Following an analysis of the results, two class groups are created and, if resources permit, a small discrete learning support class group is also formed. The top two groups follow an agreed programme in Mathematics but proceed at different rates. Plans are now in place to introduce a standardised test to determine the mathematical capabilities of incoming students and to track their progress in an ongoing manner through junior cycle. This is to be welcomed. However, the existing mathematics competency test should also be retained as part of the assessment process. The function of the test needs to be rationalised and should focus on identifying the weaknesses and strengths in the mathematical knowledge and skills of the incoming cohort. Mixed-ability classes should be formed and a common programme with common assessments should be delivered for the duration of the first term. The programme should seek to address the issues emerging from the entrance assessments and should focus on the delivery of key skills and on building the mathematical competency of the entire cohort. Upon completion of the common programme, and an analysis of the outcomes of the different assessments, the mathematics classes can then be set.
Procedures for identifying students in need of learning support or with special educational needs are good. As part of the transfer programme, and following the entrance assessments, representatives from the school, including the learning-support co-ordinator, visit the feeder primary schools to meet with the principal and the relevant class or learning-support teacher. The purpose of these meetings is to establish the educational and other needs of the incoming students. Interviews with parents and reports from school’s home-school-community liaison officer provide valuable additional insights. Completed psychological assessments are collated by the school’s guidance counsellor and applications for additional support are submitted to the Department of Education and Science for consideration. Additional psychological assessments are arranged if it is deemed necessary.
Targeted numeracy support in the school is limited. Learning support in Mathematics in second and third year is provided by the formation of small discrete class groups while it is intended to provide support in first-year classes through in-class co-operative teaching once the first year taster programme is complete. This development is very welcome and is indicative of a proactive and developmental approach to the provision of learning support and to maximising the use of the school’s resources.
Subject department planning in Mathematics is very well advanced. The department is very ably co-ordinated. Regular planning meetings of the department are held. The agendas and minutes of these meetings are kept in the subject department plan for Mathematics. The department has begun to use the data provided by the State Examinations Commission to review the performance of the students in the certificate examinations and to determine trends in the uptake of the different levels. This informed approach to subject department planning is very good practice.
A comprehensive subject department plan for Mathematics has been developed. The plan, framed within clearly defined aims and objectives, details the department’s structure and resources, arrangements for student access to levels and arrangements in place to support students with special educational needs. Practices in relation to homework and assessment, including assessment materials and a summary of the analyses mentioned above, are also included in the plan. The plan also details the schemes of work for each year and level in the form of chapter and topic lists, together with a proposed delivery schedule.
In order to further enhance the very good work already underway in planning, it is recommended that the schemes of work be developed to specify key deliverables in the form of learning outcomes in each section. It is further recommended that the members of the department identify and agree the most effective teaching methods to achieve the specified learning outcomes and agree common approaches to teaching core mathematical operations. The agreed learning outcomes and teaching methods should then be included in the subject department plan. This process will capture the existing good practice and help to generate a culture of collaboration in lesson preparation and delivery.
An admirable mathematics programme for TY is in place. The content of the programme is in keeping with the aims and objectives of TY and includes a range of topics designed to give the students an appreciation of the relevance of Mathematics in everyday life, as well as more traditional material. The plan also details the innovative and student-friendly assessment procedures adopted in the programme. Under these procedures, the students are awarded credits for their work on each of two research projects and their performance in two class tests. In order to further develop the TY mathematics programme, it is recommended that the more traditional material on the programme be reviewed. In undertaking the review, cognisance should be given to the intended learning outcomes, which in turn should address the students’ competence in carrying out key mathematical operations. The new content should also provide enhanced opportunities for active teaching and learning.
Individual teacher planning was, in nearly all cases, very good. Teaching resources that supported the lessons’ objectives and were appropriate to the needs of the students were successfully integrated into a number of lessons. In the most successful instances, these resources incorporated the techniques the students would recognise from other areas of the curriculum to enhance their understanding of the material in hand. The preparation and integration of these resources meant that there was very little reliance on the textbook and that a flexible and student-centred approach could be adopted throughout the lessons.
The lessons observed during the inspection were delivered with clarity and enthusiasm. Good links were established with the students’ earlier learning and there was very good emphasis on procedure and on the explicit use of correct method in problem solving. The rationale for adopting particular methods was clearly explained and, in some instances, a number of methods were discussed before the most appropriate one was chosen. This is very good practice.
The lessons had good structure. In a number of cases, the teachers outlined the lessons’ objectives at the outset of the lessons and provided a summary just prior to their conclusion. This very good practice ensured the lessons proceeded at a suitable pace, that the teaching methods adopted were appropriate and the different strands of the lesson were brought together in a cohesive fashion. The practice of establishing the lessons’ objectives at the outset in the form of learning outcomes should be adopted as common practice across the department.
A number of teaching methods were observed during the inspection. These included the integration of visual aids, teacher exposition, the use of graduated worksheets and group and pair work. In one instance, the overhead projector, supported by worksheets, was used very effectively to investigate congruency. These resources enabled the students to discover by experiment if given pairs of triangles were congruent and encouraged and enabled them to explain their reasoning. Before the conclusion of the lesson, the students fixed the worksheets into their mathematics notebooks, thereby utilising them as a valuable revision aid. The lesson was purposeful and provided opportunities for the students to develop their skills and to work independently.
Student behaviour and engagement, in all of the lessons observed, was very good. They responded positively to teacher questioning and supported the work of the teacher by participating enthusiastically in any work assigned to them. Classroom interactions were warm and respectful and very positive attitudes towards Mathematics were in evidence.
The quality of learning was good. The students had a good understanding of the various concepts under discussion and the quality of their verbal responses and of their written work was very satisfactory. Utilising the analysis of uptake and student attainment in the state examinations, management has identified a number of areas for development, particularly the number of students taking foundation level in both junior and senior cycle.
Practices in relation to assessment are very good. A draft homework policy is in place and is being implemented. Homework is assigned at the end of each lesson and corrected at the beginning of the following lesson. The student’s homework copies are very well maintained; they are neat and tidy and are monitored regularly. In some instances, the students amend their own work as homework is being corrected in class. This is very good practice and should be specified as a key assessment activity in the final draft of the school’s homework policy.
Continuous assessment is a central feature of assessment practices in the school. Mathematics students sit regular class-based tests, the results of which are collated and form the basis of the reports that issue to parents at Christmas and prior to the summer holidays. Students in first, second and fifth year sit a formal examination in May each year. Student performance in this examination is also used to inform the summer report. The reports that issue in regard to TY students are informed by the credit system described earlier.
Students in third and sixth year sit mock examinations shortly after Christmas each year. Students in receipt of reasonable accommodation in the state examinations receive appropriate support in the mock examinations.
Practice in relation to recording student attendance and attainment in class and formal tests is very good. Roll call is taken at the beginning of class and is noted in the teacher’s diaries. Reports are issued to parents after each formal assessment and ongoing communication occurs through the use of the student diary. In addition each class group has one parent-teacher meeting per year.
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 deputy principal, at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published, March 2010