An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Holy Family Secondary School
Newbridge, County Kildare
Roll number: 61682A
Date of inspection: 14 April 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Holy Family Secondary School, Newbridge, Co. Kildare. 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 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.
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 in first year and five periods per week thereafter. The distribution of mathematics classes throughout the week is very good and they are divided well between morning and evening.
The provision in transition year (TY) comprises two periods per week and the students are also provided with a module of applied mathematics as part of the wider science programme. The provision of Applied Mathematics in TY is commended and it is recommended that it be subsumed into the TY mathematics programme, which should then be extended to three periods per week.
Classes in first year are mixed ability. Students follow a common programme and take common class and formal tests throughout the year. Classes are banded in second and third year and run concurrently in both years. A common programme is followed in second year as far as is practicable and decisions relating to the level that students will eventually take is delayed for as long as possible. 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 class is mixed ability. The classes in senior cycle are streamed and students are encouraged to follow the highest possible level for as long as possible
Applied Mathematics is provided in senior cycle as an optional subject. The provision comprises two periods per week. There is one class group in fifth year. This group will continue to the Leaving Certificate and another class is expected to form from the cohort entering senior cycle in the coming year.
Prospective students are informed about the school by means of the school’s information pack, which is distributed by the guidance counsellor during formal visits to the feeder primary schools. An open night is held in late autumn where enrolment takes place, and in the following weeks the school principal meets individually with each incoming student and their parents. Students with special education needs (SEN) or those in need of learning support are identified during the enrolment process. The school’s learning support coordinator attends the open night and initial contact is made there. Fuller, more detailed, discussions are facilitated through private meetings if the need arises. Completed documentation, including psychological assessments, is presented at the meeting with the principal.
Students in need of support in Mathematics are identified through the use of standardised tests, contact with the primary school class teachers, consultation with the Special Education Needs Organiser (SENO) and through direct contact with parents. Upon entry to first year the students are assigned to mixed-ability classes in Mathematics. This is very good practice as it allows them to settle in and engage with the subject in a fashion that is most appropriate to their needs, early experiences and talents. Learning support in Mathematics is provided in a number of ways in the school. Students are withdrawn in small groups from subjects other than Mathematics and the learning support teacher also provides in-class support in selected mathematics classes. Furthermore, both the learning support teacher and the learning-support coordinator give in-class support to those experiencing difficulties in the mathematical areas of subjects such as business and science. Finally, referral forms are available in the staff room to enable teachers to alert the learning support coordinator to students they identify as being in need of an intervention. These arrangements are flexible, child-centred and inclusive and are highly commended.
Management and staff are committed to continuing professional development. 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. The courses attended are numerous and include some taken in the teachers’ own time. Materials presented at these courses were being used in classes visited during the inspection and they were also used to inform the design of the school’s TY curriculum. This enlightened approach to the integration of new ideas and approaches into teaching and learning is very welcome.
Resources for teaching and learning Mathematics are plentiful. These include: geometry sets, cards and dice, clinometers, probability kits, algebra cards, geometry shapes, laptops and data projectors. In addition, mathematics classes have access to the school’s computer rooms.
Integration of information and communication technologies (ICT) in teaching and learning Mathematics was evident during the inspection and the school’s parents’ association is supporting an initiative to enhance the ICT infrastructure even further. It was evident also that the school’s local area network (LAN) is being used to share resources. It is recommended that this innovative practice be extended to include all existing ICT resources and any that are developed in the future.
Newly appointed teachers attend an induction programme which is provided by the Second Level Support Service (SLSS) in the local education centre or in the school as numbers dictate. Teachers are assigned to classes and levels on a rotating basis and by agreement with management. The rotation schedule from 2001 to 2009 is contained in the subject department plan. This is very good practice as it enables forward global and individual planning. 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.
School development planning is very well established and subject planning in Mathematics is very good. An experienced member of the department coordinates planning in Mathematics and one formal planning meeting take place each term. Minutes of these meetings are taken and are included in the subject department plan. The subject department plan is comprehensive. It includes: curriculum content, the schedule for content delivery by year and level, resource lists, CPD programmes attended, the teacher rotation schedule from 2001 to 2009 and details of how Mathematics relates to the other subjects in the school. In addition, the teaching of Mathematics in learning-support classes and to those with special education needs is also addressed.
The schedule for content delivery in the subject plan details the topics to be covered by each year and level in each 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. In one case, the approach to homework and classroom delivery was completely altered following consultation with colleagues in the department, management and parents. This student-centred and flexible approach to curriculum planning and delivery is commended.
Personal planning documentation was made available by all the teachers and in all cases it was found to be excellent. The teachers’ diaries contained details of student attendance, results of assessments, homework assignments and completions. In addition, teachers had prepared a diverse range of classroom resources as an aid to teaching and learning.
Teacher planning and preparation for all of the lessons observed during the inspection was excellent. The lessons were clear, well presented and proceeded at a suitable pace. Materials, prepared in advance, were seamlessly incorporated into the lessons and served to create a student-centred learning environment. The teachers were knowledgeable, caring and enthusiastic. The students engaged with the lessons and contributed positively in all cases.
Many different teaching methodologies were in evidence. Information and communication technologies (ICT) were integrated in most lessons and the students were engaged in paired work, investigations and constructions. The incorporation of these methodologies meant that differentiation in the lessons was very good. Students were enabled to work at an appropriate pace and the teachers were available to assist individuals when the need arose.
In one lesson, ICT was used to support the teaching and learning of functions. Teacher demonstration utilising graphing software was followed by individual student activity supported by excellent intervention by the teacher when needed. The student activity was facilitated by a worksheet, which reinforced the lessons goals, challenged the students and provided them with problem-solving strategies. The lesson was an exemplar of good practice in ICT integration.
Good practice was also evident in another class where students studied probability while working in groups. They experimented by throwing dice and recording the results on a worksheet. The results from all the groups was analysed using ICT. The students were then encouraged to propose a general rule from the results of the analysis. The approach adopted in the lesson was very refreshing. The lesson was student-centred, well managed and the students engaged with the subject matter enthusiastically.
Classroom management was very good. The atmosphere in the classrooms was warm and the rapport between teachers and students and among the students themselves was excellent. The students asked pertinent questions, behaved very respectfully and approached the subject with a sense of fun. The teachers were affirming of the students, supported individuals as the need arose and made very effective use of questioning to support the learning goals. Very good practice was observed in the teaching of counting where, supported by ICT and the use of models, sound mathematical principles were taught and continuous two-way interactions ensured that everyone participated productively in the lesson.
Student learning was very evident. They responded readily and knowledgeably when questioned by the teacher. 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.
Practice relating to assigning and correcting homework in Mathematics is in keeping with the school’s homework policy. Homework is assigned during each lesson and is corrected by the students themselves under the direction of the teacher. Teacher comments and student corrections were evident in the samples examined by the inspector. It was reported that a pilot project investigating the benefits of formative assessment is underway with a number of classes and that it is intended to mainstream the practice once the pilot phase has been evaluated. This good practice, in critically examining the benefits of altering current practice, is commended.
Formal assessments for non-examination classes are held at Christmas and just prior to the summer holidays. Students in first year take common assessments, which are corrected using a common marking scheme. Common assessments are set in second and third year as the needs and opportunities arise. A common resource of class tests and student scores is available on the school’s LAN. This enables the development of student profiles in Mathematics and informs students’ decisions regarding choice of level. Students in the examination classes sit formal tests at Christmas and take mock examinations in the second term. Students at the same level take common papers in the mock examinations.
Reports issue to parents after each formal assessment and ongoing communication occurs through the use of the student diary, tests being sent home for annotation, 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. Achievements in Mathematics are recognised at these awards. In addition, students of Mathematics participate in the Mathematics Olympiad.
The following are the main strengths identified in the evaluation:
· The time allocated to Mathematics at both junior cycle and senior cycle is excellent.
· The arrangement of classes in junior cycle with mixed ability in first year and banding for the remainder of the junior cycle, which enables students to take the highest level possible for as long as possible, is very good.
· The procedures adopted to support those with special education needs and learning support are very good.
· Management is proactive in facilitating attendance at relevant CPD courses.
· School development planning is well advanced and planning in Mathematics is very good. The mathematics department is ably co-ordinated and it was evident that the mathematics team collaborates very effectively.
· Students wishing to study Applied Mathematics are catered for.
· Homework, assessment and reporting procedures are in place and are implemented effectively.
· Teaching methodologies are varied and ICT is an integral part of teaching and learning Mathematics.
· Teaching and learning of a very high standard was observed during the inspection.
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 Applied Mathematics module be integrated into the TY mathematics programme and that the provision be extended to three periods per week.
· It is recommended that the innovative use of ICT to share resources be extended to include all existing resources and to those to be developed in the future.
· It is recommended that the curriculum delivery schedule, as outlined in the subject department plan, be revised to specify the topics to be covered by each year and level each month.
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 September 2008