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An Roinn Oideachais agus Eolaíochta**

**Department of Education and Science**

**Subject Inspection of Mathematics**

**REPORT **

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**Fingal**** Community College**

**Swords, County Dublin**

**Roll number: 70121H**

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**Date of inspection: 9 April 2008**

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Subject provision and whole school support

Summary of main findings and recommendations

**Report on the Quality of Learning and Teaching
in Mathematics**

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This report has been written following a subject inspection in Fingal Community College as part of a whole-school evaluation. 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.

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Timetable provision for Mathematics is generally good. In the junior cycle, five Mathematics lessons per week are allocated to first and third year groups. Second-year groups are timetabled for four class periods per week. This overall level of provision is in line with the Junior Certificate syllabus guidelines. At senior cycle there are four mathematics lessons per week provided for Leaving Certificate Applied (LCA) year one students and three lessons per week for year two students. In the case of the Leaving Certificate (Established) groups five lessons are provided for the fifth year group and six lessons per week are provided for sixth-years. This is good provision. As a means of improving retention of students at Leaving Certificate higher level, it is suggested that an increase in the timetable allocation for the fifth year classes be considered.

Mathematics lessons are evenly distributed across the week, which is good practice. In the junior cycle, however, lessons are predominantly timetabled for the afternoon. It is recommended that, in future timetabling, lessons be more evenly distributed across the day. Concurrent timetabling of Mathematics occurs from first year through to sixth year. This provides students with a high degree of flexibility in changing levels. Concurrent timetabling enables the mathematics department to adopt a very student-centred approach to level choice. This concurrent timetabling of Mathematics is highly commended.

Students are assigned to one of three bands, from the beginning of first year, on the basis of pre-entry assessment. Generally there is a class in each year group which contains students who will study Mathematics at higher level, an ordinary-level band and a foundation-level class. The mathematics department is strongly committed to encouraging students to study the highest level possible for as long as possible. It is department policy that any student wishing to attempt to study higher level Leaving Certificate Mathematics be given the opportunity, including those achieving higher grades in Junior Certificate ordinary level Mathematics. Movement between levels takes place in consultation with students, parents, year-heads, school management and the guidance counsellor where necessary. This very good practice is commended.

The mathematics department comprises twelve teachers. School management decides on teacher allocation to levels and classes in close consultation with the teachers themselves. It is department policy that, where possible, classes retain the same teacher from year to year. This is good practice. Levels, in the junior cycle, are rotated between most members of the mathematics teaching team. In the senior cycle, the higher level Leaving Certificate class group alternates between two members of the mathematics teaching team. It is recommended that rotation at higher level Leaving Certificate be broadened to include some of those currently teaching higher level in the junior cycle. This would enable the school to build up expertise in the teaching of higher level Leaving Certificate mathematics and thus, strengthen its capacity to respond to the changing needs of the mathematics syllabuses in the coming years.

Teachers make use of a wide variety of teaching resources. Three ceiling-mounted data projectors are available for use with teacher laptop computers and the mathematics department has been allocated a personal computer (PC) for the integration of information and communications technology (ICT) in teaching and learning in Mathematics. There are plans to further enhance the ICT equipment available for use in Mathematics. Teachers share access to a wide range of teaching aids, such as, sets of mathematics tables, geometry instruments, metre sticks and other measuring equipment. The metalwork and woodwork departments of the school have generously provided the mathematics department with 3-D models for use in Leaving Certificate trigonometry and a variety of other teaching aids. LCA students are provided with calculators, geometry sets, folders, and ring binders. Teachers have made use of an interesting range of commercial posters to enhance the physical learning environment. Teacher continuing professional development (CPD) is fully facilitated. Teachers are encouraged by management to attend in-service courses. The school funds membership of The Irish Mathematics Teachers’ Association on request. Although there is no set budget for the mathematics department, requests for resources and equipment are favourably considered. The high level of whole-school support for Mathematics is commended.

Students in need of learning support are identified through discussions with feeder primary schools, following pre-entry assessment, and from ongoing teacher observation. Once identified, students are then assessed to determine their individual level of need. To monitor progress, re-assessments are carried out at the end of each year. Students are profiled so that their individual needs can be accurately met and parents are encouraged to make a contribution to this process. Learning support is provided through the creation of smaller class groups and individual withdrawal from subjects other than Mathematics. All members of the learning support team, providing support with numeracy, have qualifications in Mathematics and teach mainstream mathematics classes. It was reported to the inspector that the team teaching of mainstream class groups undertaken in past years had been very successful. It is suggested that team teaching be considered as a possible format for incorporating learning support into mainstream classes. Good communication exists between members of the learning support team and the mathematics department; this generally takes place on a daily informal basis. Since the learning support provided is designed to reflect and complement the work of each student’s mainstream class, it is suggested that a system be created to formalise the communication process with the teachers of Mathematics in order to facilitate weekly planning by the learning support team. A comprehensive, cohesive, committed approach to meeting the individual needs of the students requiring support was evident during the evaluation and it is highly commended.

Formal planning time is allocated three times per year as part of the whole-school planning process. To facilitate teachers who teach more than one subject, the meeting schedule on school planning days is split to ensure attendance of all members of the mathematics teaching team at the planning meeting for Mathematics. This is very good practice. Mathematics teachers also meet regularly on an informal basis. Since the organisation of learning support forms such a large part of the informal meetings that take place on a day-to-day basis, it is recommended that a portion of the mathematics planning time on school planning days be devoted specifically to planning for learning support so as to ensure all mathematics teachers are included. Records are maintained of all formal meetings and minutes are kept. The position of mathematics co-ordinator currently rotates between two senior members of the teaching team, although the entire team takes responsibility for the carrying out of duties. The members of the mathematics department operate within a culture of collaboration and co-operation and this has led to a spirit of team work and collegial support. This is very good.

It was evident from the inspector’s review of planning documentation that school development planning has progressed well in Mathematics. The plan for the subject opens with a mission statement specific to Mathematics, one that was found during the evaluation to follow through well in the school’s practices. The plan contains details of the mathematics department’s approach to students’ choice of levels, learning support, assessment, homework, and to teaching students for whom English is an additional language. Topics that are considered suitable for cross-curricular links are identified within the plan and ways in which these links might be created are also explored. Lists of resources available and in-service courses attended are also included in the department plan. There is evidence that some collaborative planning for classroom activity has begun, mainly in the areas of planning policy around effective teaching methodologies and the use of ICT in teaching and learning. It is recommended that this good work be continued and built upon and that plans for revision and review be incorporated, so that the plan can become a living document that can inform everyday teaching and learning in Mathematics.

In keeping with good practice, all teachers maintain individual class plans. These mainly consist of schemes of work, in topic blocks and broken down into lessons to be covered within set timeframes. The LCA plan, reviewed by the inspector, provides an example of an excellent individual subject plan. It consists of a list of topics to be covered, with the corresponding skills that students would be expected to have acquired by the end of each topic. It also outlines the methodologies to be employed alongside the resources required for each lesson. Most importantly it included a blank space for review comments, to be filled in after each lesson. This level of planning is exemplary.

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The content of all of the lessons observed in Fingal Community College was relevant to the syllabus and in line with the mathematics department plan. In most cases, it was evident that the lessons were well planned and all the necessary resources were utilised. The learning objectives were shared with the students in all of the lessons observed. Best practice in this regard occurred where the teacher wrote the aims of the lesson or the main topics to be covered on the board and then checked at the end to see if these had been achieved. It is commended that every effort was made to link new material with work previously done, thus reinforcing learning and helping to situate new ideas. In some cases teachers endeavoured to relate lesson content to students’ own experience. This is good practice as it helps students to identify with the course material. The pacing of the lessons was challenging yet realistic and appropriate to the ability level of the students. Teachers’ explanations were clear.

Generally teachers made effective use of the resources at their disposal. Teachers’ work on the whiteboard was very clear in all cases. The degree to which teachers modelled good presentation was commendable. Great care was taken to include all the relevant steps in worked examples and attention was routinely paid to detail. Teachers have built up a wide range of resources and some of these can be shared through computer access. The hand-outs used to complement some of the lessons observed were appropriate to the ability level of the students. In some of the lessons observed a student was chosen to correct homework on the whiteboard. This is a very simple but effective way to actively involve students in their own learning. A very high level of respect was shown by the remainder of the class group to the student at the whiteboard. It was clear that teachers are very familiar with the individual needs of their students and that they subtly differentiate learning to target those needs. This is very good practice.

The teaching observed consisted mainly of teacher example followed by student exercise. Within this traditional approach, teaching was effective. Teachers made very good use of questioning, both global and directed, throughout the lessons observed. Best practice was seen where more open and probing questions were used to encourage students to think for themselves. The widespread use of this type of questioning is commended, since it is so beneficial to learning in Mathematics. For example, in a higher level lesson observed the students were expected to attempt an exercise that was challenging and unfamiliar and, with encouragement from their teacher, they succeeded in solving the problem. This very good practice helps students to develop an appreciation of mathematical endeavour and leads to a great sense of personal satisfaction.

In most of the lessons observed the level of student participation and engagement was high. Consequently, students were able to demonstrate learning with enthusiasm. Generally, there was a good variety of learning activity which kept the lessons interesting and the students engaged. Most teachers have created secure learning environments, where students can engage with their course material with confidence. This has been achieved through the good balance between teacher input and student activity observed in some classes. Where it has been established this good balance has facilitated the employment of a range of more active methodologies that make Mathematics enjoyable for students. It was observed that, where there was a lack of lesson structure, students tended to lose interest and become disengaged. It was evident that students experienced difficulty in maintaining focus when lengthy explanations led to an imbalance between teacher input and student activity. It is therefore recommended that the good balance achieved in the majority of lessons observed be extended to all.

The relationships between students and teachers were observed to be mutually respectful, in most cases. This has led to the creation of a working environment where high expectations are set for students and where students respond accordingly. The high standard of student behaviour and the good working atmosphere that exists in most of the classrooms visited have enabled students to contribute to and participate fully in lessons with confidence. Students were actively engaged in their work in most of the lessons observed and this served to eliminate any opportunities for disruptive behaviour. Positive approaches to managing behaviour were most effective in dealing with any discipline issues that arose. This very good practice is commended. It was clear that, where negative discipline methods were employed, students became further disengaged. Although this occurred in a minority of cases it is a cause for concern, since in order for students to reach their full potential, it is essential for them to engage fully with their course material. It is therefore recommended that the positive discipline methods evidenced in most of the lessons observed be used by all teachers in all lessons.

It was reported to the inspector that some teachers regularly use the table quiz format to assess learning. Active methodologies such as these are commended as they can help students engage with Mathematics in a positive way. In interactions with the inspector the students displayed an interest in and an enthusiasm for Mathematics. The students were able to demonstrate solid mathematical knowledge and a clear understanding of the concepts taught, they were also able to use appropriate mathematical language. Teachers have made considerable effort to enhance their physical working environments with a wide range of commercial and student-generated posters. This is commended as it has created a visually stimulating mathematical environment.

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All students, with the exception of sixth-years, are formally assessed in November. Summer examinations are held in May for first, second and fifth year groups. Sixth-years are continuously assessed and ‘mock’ examinations are held for third and sixth year groups. Students who will receive reasonable accommodations for the certificate examinations also receive them for the ‘mock’ examinations where possible. This is very good practice, as it ensures that student experience in the certificate examinations is accurately reflected in the ‘mock’ examinations. Reports are sent home on foot of these formal examinations and parent-teacher meetings take place once a year. Learning in Mathematics is routinely assessed through oral questioning and students sit class tests at the end of each chapter or topic studied. Teachers have ongoing communication with parents through notes in student journals. This close monitoring of student progress is commended.

Homework is set regularly, corrected promptly and monitored carefully in all cases. Some teachers use comment-based marking and this is a valuable support to student learning as it provides students with critical feedback, allows for self-correction and can be a source of positive reinforcement. The use of this type of marking is therefore commended. It was clear from the inspector’s review of student copybooks that the standard of presentation of student work was high.

At the beginning of each school year teachers analyse the certificate examination results and use this analysis to inform planning. The central aim of the mathematics department is to encourage students to study the highest level possible for their ability. A real commitment to the achievement of this aim underpins the work of the teachers. This commendably high level of commitment has contributed to high retention rates from Junior Certificate higher level to Leaving Certificate higher level.

LCA students are continuously assessed through the completion of key assignments. On inspection, the standard of presentation of the key assignments contained in the LCA year two student folders was found to be high. However, some of the key assignments completed in year one of the cycle were not included in the folders. It is important that all key assignments for both years be kept in student folders and it is suggested that these folders remain within the school.

Prizes are awarded for achievement and improvement in Mathematics. Students are encouraged to take part in the BT Young Scientist and Technology Exhibition and receive recognition at prize- giving for their participation. In past years students have been involved in training for the International Mathematical Olympiad. Participation in mathematics-related extra-curricular activity is very good as it raises the profile of Mathematics within the school and enables students to experience Mathematics for pleasure.

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The following are the main strengths identified in the evaluation:

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- A very student-centred approach to level choice and a high degree of flexibility in changing levels is facilitated by concurrent timetabling.
- The central aim of the mathematics department is to encourage students to study Mathematics at the highest level possible for their ability and a real commitment to the achievement of this aim underpins the work of the teachers.
- Teaching and learning in Mathematics benefits from a high level of whole-school support for the subject.
- There is good provision for learning support in Mathematics.
- The members of the mathematics teaching team operate within a culture of collaboration and co-operation and this has led to a spirit of team work and collegial support.
- Good progress is being made on planning in Mathematics.
- Widespread use of open and higher-order questioning in Mathematics was observed.
- In most of the lessons observed the level of student participation and engagement was high.
- In the lessons observed, the students were able to demonstrate solid mathematical knowledge and a clear understanding of the concepts taught, they were also able to use appropriate mathematical language.

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

- The rotation of teachers at Leaving Certificate higher level should be broadened to include more of those currently teaching Junior Certificate higher level.
- It is recommended that the good work begun in planning for Mathematics be continued and built upon and that plans for revision and review be incorporated, so that the plan can become a living document that can inform everyday teaching and learning in Mathematics.
- All teachers should incorporate a variety of learning tasks in their lessons and should ensure that there is a good balance between teacher input and student activity in each lesson.
- Positive approaches to managing behaviour should be used by all teachers in all mathematics lessons.

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 January 2009*

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