An Roinn Oideachais agus EolaŪochta

Department of Education and Science

 

Subject Inspection of Mathematics

REPORT

 

Saint Aidanís Community School

Brookfield, Tallaght, Dublin 24

Roll number: 91338D

 

Date of inspection: 11 November 2008

 

 

 

 

Subject inspection report

Subject provision and whole school support

Planning and preparation

Teaching and learning

Assessment

Summary of main findings and recommendations

 

 

Report on the Quality of Learning and Teaching in Mathematics

 

Subject inspection report

 

This report has been written following a subject inspection in St. Aidanís Community 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 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.

 

 

Subject provision and whole school support

 

Procedures for facilitating the transfer of students to St Aidanís from its feeder primary schools and for ascertaining their mathematical abilities are very good. Ongoing contact with the schools is maintained through the operation of the School Completion Programme, the home-school-community liaison scheme (HSCL) and through the close working relationships that exist between the schoolsí principals. Students intending to attend St Aidanís school are invited to attend the schoolís open day, which is held in March each year. During the open day the prospective students are made familiar with the layout of the school, are provided with an opportunity to meet the staff and students, and are given the opportunity to participate in a range of curricular and extra-curricular activities. Once the incoming cohort has been identified arrangements regarding their assessment and induction are set in train.

 

The schoolís special education needs (SEN) co-ordinator, guidance counsellor and home-school-community liaison officer all play pivotal roles in the transfer programme and in ensuring that comprehensive student profiles are in place prior to the studentsí arrival in the school. The guidance counsellor takes primary responsibility in relation to running the entrance assessments, while the SEN coordinator liaises with class and resource teachers in the primary schools to establish the strengths, interests, aptitudes and additional education needs of the incoming students. Any issues regarding attendance or behaviour and any particular aptitudes in the social, sporting and recreational areas, are established by the HSCL coordinator.

 

Initial assessment tests are held following the schoolís open day. The assessments comprise standardised numerical and verbal reasoning tests together with written tests in Mathematics, English and Irish. The written tests are prepared and corrected in collaboration with the primary school class teachers. The performance and most appropriate placement of each incoming student is discussed in the aftermath of the assessment, and initial work is then done on the composition of the first year class groupings. A second assessment is held in June. In this instance, the student sit tests in Irish, English and Mathematics and due cognizance is taken of the results when the first year class groups are finalised.

 

Classes are banded in junior cycle and the timetabling provision for mathematics is good. The top band is provided with four classes of Mathematics per week, while the two middle bands and the lower band have five. The top band follow higher-level Mathematics while the middle bands follow ordinary level, with a number opting for foundation level in the Junior Certificate examinations. The lower band participates in the Junior Certificate School Programme and follows foundation level Mathematics.  The middle band classes are timetabled concurrently for Mathematics and this enables the formation of a class group following ordinary level solely in third year and facilitates movement between levels as the year progresses. While every effort is made to ensure that students are correctly placed, it is recommended that consideration be given to timetabling all of the mathematics classes concurrently and to providing five classes of Mathematics per week for all class groups, irrespective of the level.

 

Timetabling provision in senior cycle is very good. There are five classes of Mathematics per week in fifth and sixth year, while students participating in the Leaving Certificate Applied Programme (LCA) are provided with three classes of Mathematical Applications per week. All class periods are forty minutes long.

 

Procedures for identifying and supporting students with SEN, or in need of learning support, are comprehensive, student centred and inclusive. Very close links are maintained with the special educational needs co-ordinators in the feeder primary schools. Students who have had their learning or other needs formally assessed by National Educational Psychological Service (NEPS), while 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. Learning support in Mathematics is provided through collaborative in-class support, with some students being withdrawn in small groups from subjects other than Mathematics.

 

The class teacher refers students, who are to be withdrawn for additional support in Mathematics, to the SEN co-ordinator. The mathematics specialist in the learning support team, in collaboration with the class teacher and the student, designs a student-specific time-bound programme to address the identified areas of weakness. The programme incorporates well-defined learning outcomes, assessment schedules, and procedures for evaluating the effectiveness of the programme.  Regular feedback on individual studentís progress is provided to the class teacher, to the student, and to the SEN co-ordinator. The student is returned to the mainstream class upon successful completion of the programme.

 

The in-class support model being implemented in Mathematics is excellent. The lessons observed during the inspection were well organised: all students had their own individual learning outcomes for the lessons and they worked in the main as independent learners, using a range of resources to achieve their goals. The teachers supported the students in an appropriate fashion but the emphasis remained firmly on enabling learning, on allowing the students to develop problem-solving skills, and to master key mathematical procedures. Information and communications technology (ICT) was used innovatively to support the lessonsí objectives and to track the studentsí progress.

 

Exceptionally able students are also identified as part of the schoolís enrolment procedures and additional support in the form of extra classes, designed to accelerate their progress, are put in place. Furthermore, such students are given additional support in accessing third-level education through the schoolís participation in the Accessing College Education (ACE) programme.

 

The mathematics department is comprised of ten teachers and they are assigned to classes and levels by rotation, following consultation with the principal. Furthermore, it is policy that teachers retain the same class group from second to third year and from fifth to sixth year. This is very good practice as it ensures continuity of approach and facilitates long-term planning.

 

The school is a participant in the Connect project in partnership with South Dublin County Council, the Department of Education and Science, and the National Centre for Technology in Education (NCTE). The project is now in its fourth year and the students have been actively involved in the project for three years. As a result of the project, each teacher has been provided with a tablet laptop and, when the cycle of provision is complete, every student will also have access to a laptop for use in school and at home. In addition, a wireless network, with access to a customised virtual learning environment (VLE) and the Internet, is also in place. An ICT specialist, whose function is to provide technical back up and to assist in developing the VLE, has been appointed to the project. The population of the VLE with curricular material is already underway and teachers from each department have been appointed to identify suitable materials and software that will bring added value to the project.

 

The advent of such extensive ICT resources provides the mathematics department with a great opportunity, but also with considerable challenges. The department have enthusiastically embraced the project; all of the team members have received appropriate training; ICT integration was evident in some lessons observed during the inspection; and the VLE is already populated with appropriate website addresses and mathematical games. Two of the team members have been chosen to identify suitable resources and to recommend strategies for their integration into teaching and learning. This is very good practice as it guarantees that the purchase of software and the development of resources takes place in a planned manner and that materials that are produced will be relevant, useful and appropriate to the needs of the school.

 

Planning and preparation

 

School development planning is well established and subject development planning in Mathematics is under way. A co-ordinator has been appointed and regular meetings, facilitated as part of every second staff meeting, are held. Responsibility for co-ordinating the department rotates between the members of the department. Individuals have also been identified to manage the departmentís response to the challenges provided by the Connect project and the rapid development of the schoolís ICT Infrastructure.

 

A nascent subject development plan for Mathematics is in place. The plan details the existing timetabling provision for Mathematics, class lists, and meticulous schemes of work which include content, delivery schedules, and the resources to be employed in their delivery. The plan also contains a very comprehensive section in relation to learning support and SEN. In order to build upon the existing good work, and in response to the changing learning environment in the school it is recommended that the subject development plan be reviewed to include overarching aims and objectives, minutes of the departmental meetings, common and agreed approaches to teaching core mathematical operations and procedures, and strategies for integrating ICT into teaching and learning.

 

The subject development plan for Mathematics makes reference to LCA and includes templates for the studentsí tasks and key assignments. It would be preferable if a more complete picture of the programme being offered was available and it is recommended that a separate plan for Mathematics in LCA be developed. This plan should include schemes of work and delivery schedules, appropriate teaching methods and learning strategies, resource lists, and learning outcomes.

 

The mathematics department and management analyse the performance of the students in Mathematics in the state examinations with reference to the statistics supplied by the State Examinations Commission. As a result, the uptake of ordinary-level Mathematics in both the Junior and Leaving Certificate has been identified as a primary target for improvement. This informed and enlightened approach to subject planning is very good practice.

 

Individual teacher planning for Mathematics is good and in some cases it is of the very highest quality. The planning materials made available to the inspector during the inspection were comprehensive and relevant, and reflected the particular needs of the students in the different classes. Planning for the inclusion of resources in lessons was also good and there was extensive use of information and communication technologies (ICT) in preparing lesson plans and worksheets, and in recording the performance of students in class and in formal tests. In some instances, teachers made use of an excellent planning template, which outlined the lesson content, teaching methods, and learning outcomes. It is suggested that this template should be put into the subject development plan for Mathematics to assist in lesson planning across the department.  In order to further enhance collaboration in developing lesson plans, it is recommended that a list of the difficulties regularly encountered by students during lessons, when doing homework and in completing class tests, be identified and that the most successful strategies in overcoming them be agreed and included in the subject development plan for Mathematics.

 

The continuing professional development (CPD) of the teachers is a priority for management, particularly in light of the schoolís involvement in the Connect project, and a comprehensive range of courses has been provided for the members of the mathematics team in recent years. Training in the use of ICT and in the development of the VLE is ongoing, while whole-school training in classroom management has also been provided in recent times.

 

Newly appointed teachers meet with the principal and deputy principal upon joining the staff and are made familiar with the schoolís policies and procedures. Ongoing follow-up meetings take place during their first year. A mentor is also provided to support their induction into the school and to make them familiar with the ways of the school.

 

Teaching and learning

 

Many of the lessons observed during the inspection were well planned, they proceeded at a satisfactory pace and were delivered with enthusiasm and care. In some instances great care was taken to share the lessonís objectives with the students at the outset of the lesson. This is very good practice. The material covered in lessons observed during the inspection was appropriate and included: statistics, timetabling, algebra, coordinate geometry of the line, matrices and linear algebra and number. A range of teaching styles was in evidence. These included the very effective use of ICT and various student-centred activities. However, there was an over-emphasis on the use of traditional methods in mainstream mathematics classes. In such cases the lessons were teacher-led, there was little individual or group student activity, the textbook was the primary teaching resource and there was an over reliance on verbal communication with the students. While the teachers worked diligently, the effectiveness of the lessons would have been greatly enhanced by reducing the reliance on teacher exposition, increasing the emphasis on student-centred learning, and in negotiating the lesson structure and learning objectives at the outset.

 

There were two particularly good examples of ICT integration in evidence. In one case the students, working to individual plans, balanced their activities between written work and the use of their laptops. Their engagement with the material was excellent and their determination to reach the agreed goals outlined in their plans was exemplary. Collaborative in-class support, in the form of team teaching, supported the lessons goals and facilitated a high degree of differentiation, where the needs of individual students were catered for as an integral part of the lesson. In the second case, ICT was used to support the lessons objectives by enabling the teacher to illustrate correct procedures for carrying out algebraic operations, to reinforce good practice, and to address common errors as the need arose. The use of ICT facilitated ready access to exemplars of good practice, enabled effective teacher movement, and supported differentiation.

 

Excellent lesson planning was also evident in two separate classes where statistics was being studied. In one instance, the students engaged in an impromptu survey and the results were used to create a frequency distribution table, and to generate discussion on the mode and mean of such distributions. In the second case, the Internet was used to research and interpret bar charts, to engage the students in creating frequency distribution tables and in finding the mean and mode. The lessons provide very good examples of how the challenges presented by the Connect project can be met, how ICT can be integrated into teaching and learning Mathematics, and how it can provide an environment that is engaging, stimulating, and challenging.

 

Positive behaviour was evident in most of the classes visited. The lessons were conducted in an atmosphere of mutual respect, with good humour, and empathy for the needs of the students. The teachers were very affirming of the studentsí efforts and had high expectations of their behaviour and attainment. Student engagement was, in almost all cases, very good and they contributed positively by asking relevant questions and proposing alternative approaches to problem solving. In some cases, teachers made good use of questioning to elicit factual responses to specific questions. There was, however, an over reliance on global questioning and not enough emphasis was placed on encouraging students to hypothesise and engage in higher-order thinking.

 

Various examples of very good student learning were evident during the inspection. This was particularly true where students were engaged in agreeing the lesson objectives and where their written work was supported by appropriate teacher assessment strategies. Best practice was in evidence where studentsí work was corrected regularly, contained teacher comments and corrections, and corresponding student amendments.

 

Assessment

 

Assessment procedures are very good. Non-examination class groups sit class tests at the end of each topic and common papers are provided where appropriate. More formal in-class tests also take place prior to the mid-term break in November and these, together with the results of the class tests, inform the reports that issue to parents prior to the mid-term break. Formal examinations also take place at Christmas and again prior to the summer holidays. Results also issue to parents after each of these events.

 

Students in examination classes have scheduled tests each month. Reports, recording the performance of each student, are given to the relevant year head. The year head meets with each student, each month, to discuss progress and to agree targets for the following month. In addition, formal examinations take place at Christmas and the students sit mock examinations early in the second term. The class teachers correct the mock examinations and they meet to discuss common errors, strengths, and areas for improvement, prior to delivering feedback to the students.

 

Practice in relation to homework assignment and correction is varied. Best practice was evident where the homework was regularly assigned and corrected and where the correction of homework served to provide classes with shared learning experiences. Furthermore, homework frequently helped underpin the lessons learning objectives and gave students opportunities for independent and collaborative learning. The schoolís homework policy is currently under review and management is engaged in consultation with the different stakeholders regarding the most appropriate model to be adopted. This proactive and inclusive approach to policy development is very good practice

 

Ongoing communication with parents occurs through the student diary, telephone contact, and through the use of formal letters. Each non-examination class group has one parent-teacher meeting per year, while the examination classes are provided with two. In addition, the year heads are particularly proactive in organising meetings with parents to discuss studentsí progress, to inform parents of any issues that have arisen, and to identify strengths and areas for development. This timely, positive and student-centred approach to engaging with parents is highly commended.

 

Summary of main findings and recommendations

 

The following are the main strengths identified in the evaluation:

 

         A good standard of teaching and learning was observed during the inspection.

         Procedures for facilitating the transfer of students to St Aidanís from its feeder primary schools, and for ascertaining their mathematical abilities, are very good.

         Timetabling provision for Mathematics in junior cycle is good and timetabling provision in senior cycle is very good.

         The procedures for identifying and supporting students with special education needs are very good.

         Exceptionally able students are identified as part of the schoolís enrolment procedures.

         The in-class support model being implemented in Mathematics is excellent.

         The school has extensive ICT facilities and the mathematics department has engaged positively with the new technologies.

         School development planning is well established and subject development planning in Mathematics is under way.

         Individual teacher planning in Mathematics is good.

         The continuing professional development of the teachers is a priority for the school management.

         Procedures for supporting newly appointed teachers are in place and are working effectively.

         Assessment procedures are very good.

         Arrangements for communicating with parents are comprehensive, timely and student-centred.

 

 

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

 

  • It is recommended that consideration be given to timetabling mathematics classes within each year group concurrently and to providing five classes of Mathematics per week for all class groups in junior cycle, irrespective of the level.
  • It is recommended that the subject development plan for Mathematics be reviewed to include overarching aims and objectives, minutes of the departmental meetings, common and agreed approaches to teaching core mathematical operations and procedures and strategies for integrating ICT into teaching and learning.
  • It is recommended that a separate plan for Mathematics in LCA be developed and that this should include schemes of work and delivery schedules, appropriate teaching methods and learning strategies, resource lists, and learning outcomes.
  • It is recommended that a list of the problems regularly encountered by students during lessons, when doing homework, and in completing class tests be identified and  that the most successful strategies in overcoming them be agreed and included in the subject development plan for Mathematics.

 

 

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.

 

 

 

 

Published, October 2009