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An Roinn Oideachais agus Eolaíochta**

**Department of Education and Science**

**Subject Inspection of Mathematics**

**REPORT **

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**St Joseph’s Secondary School**

**Rush, County Dublin**

**Roll number: 60343T**

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**Date of inspection: 2 December 2008**

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Subject provision and whole school support

Summary of main findings and recommendations

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

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This report has been written following a subject inspection in St Joseph’s Secondary School, Rush. 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 was given an opportunity to comment in writing on the findings and recommendations of the report, and the response of the board will be found in the appendix of this report.

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St Joseph’s Secondary School caters for 293 boys and 187 girls. Timetable provision for Mathematics is good. Five class periods of Mathematics per week are allocated to first, second and third year class groups. Transition year (TY) students receive three mathematics lessons per week. Leaving Certificate Applied students receive four class periods of Mathematics per week for year one and year two of their course. In the case of the established Leaving Certificate, fifth year class groups are timetabled for five periods of Mathematics per week and six mathematics lessons are allocated to sixth year students. Mathematics lessons are well spread across the week and day and this is good practice.

In all year groups except second year mathematics lessons are concurrently timetabled. This arrangement is intended to facilitate the provision of learning support to those who need it and also, to provide students with flexibility in changing levels. This is very good practice. In second year two class groups, one group studying Mathematics at higher level and the other taking ordinary level Mathematics are timetabled concurrently, thus providing flexibility in level choice for students in these class groups. Since flexibility of movement between levels is important in Mathematics, it is recommended that concurrent timetabling be extended to all second year class groups

Students are assigned to mixed-ability classes in first year. In second and third year students are assigned to higher and ordinary level classes on the basis of achievement in formal end-of-year examinations. Teacher observation and student preference also play a role in decisions regarding levels. Change of level can only take place in consultation with students, parents and class teachers. There is one mixed ability TY class group. In fifth and sixth year students are assigned to higher and ordinary level class groups on the basis of performance in the Junior Certificate examination and of personal choice. Students are then divided into ordinary and higher level groups and are assigned to mixed ability classes within the level groups. This approach to assigning students to levels is good.

The mathematics department comprises eleven teachers. It is mathematics department policy that classes retain the same teacher from year to year for the duration of a cycle and this is good. Higher level Mathematics at both junior and senior cycle is rotated among all members of the teaching team. This very good practice will contribute to the retention of the high level of expertise that currently exists within the mathematics department and will greatly assist the department in meeting the challenges of the forthcoming revisions to the mathematics syllabuses.

Teachers make use of a wide range of teaching resources for teaching and learning in Mathematics. These are kept in a central location and are shared among mathematics teachers. They include Irish Mathematics Teachers’ Association resources, overhead calculators, geometry sets, probability kits, geostrips, pie-chart templates, ‘fun folders’ and a range of puzzles. Key words for Mathematics have been produced to enable mathematics teachers to support students with literacy difficulties. There is a diverse range of books, videos and compact disks of mathematical interest that are suitable for all age groups and abilities. These books are used to provide mathematics teachers with ideas for making mathematics lessons more relevant and enjoyable for students and for encouraging students to take an interest in Mathematics outside of the classroom. Mathematics teachers use everyday objects such as boxes and containers of different shapes and sizes in the teaching of volume and area. It was evident from the range of objects acquired that mathematics teachers are constantly aware of the mathematics in the world around us and are keen to avail of every opportunity to bring everyday mathematical ideas into the classroom. The acquisition of a transparent box containing nine spherical Christmas decorations provides a very good example of this. Mathematics teachers have established a folder of useful handouts and are in the process of making these resources accessible through a shared electronic folder. It is clear from the extensive range of mathematics resources built up over time by the mathematics department that Mathematics enjoys a lively and vibrant position within the school.

The mathematics department has good access to information and communications technology (ICT). The school computer room is available through a booking system and is mainly used for teaching and learning in LCA Mathematics. There is an interactive whiteboard in one science laboratory and mathematics teachers who are timetabled in this room have access to it. There is a mobile data projector and laptop both of which are regularly used for teaching and learning in Mathematics. The department has recently acquired a fixed data projector; this will be situated in a mathematics room which will be timetabled on a rotational basis to provide all mathematics teachers with some access to this useful piece of ICT equipment. Teachers use a wide range of mathematics-related computer software and frequently incorporate material from a variety of suitable websites into their lessons. The mathematics department is well provided for in terms of ICT resources and these are routinely used to making mathematics lessons interesting for students.

Students in need of learning support are identified through communication with feeder primary schools, pre-entry assessment, diagnostic testing, psychological assessment and ongoing teacher observation. Support is provided through the creation of foundation level classes, small group withdrawal or individual withdrawal where necessary. The school has some experience with the provision of in-class learning support in mathematics classes and it is good that extension of this model of delivery is being considered. Re-assessment takes the form of end-of-topic tests and teacher observation. It is good that students are returned to their mainstream class group when significant improvement in Mathematics is achieved. Overall, there is a very high level of learning support in Mathematics provided to students who are identified as needing it.

Students
of Mathematics participate in a wide variety of co-curricular mathematics
related activities. Each year the mathematics department celebrates *Maths Week
*and* World Maths Day. *These celebrations include the involvement of
first and second year students in the Dublin City University (DCU) *Maths
Magic Show*, participation in the *PRISM* mathematics challenge and the
organisation of a puzzle station for first year students run by fifth year
students. At Christmas time the mathematics department organises a Christmas
quiz and a giant *Snakes and Ladders *game. It was reported during the
inspection visit that these are significant events in the life of the school and
are enjoyed by students and teachers alike. Participation in extra-curricular
mathematics activities is very good practice as it allows students to
experience Mathematics for pleasure, raises the profile of Mathematics within
the school and makes Mathematics accessible to all.

Formal planning time is allocated three times per year as part of the whole-school planning process. Records are maintained of all planning meetings and minutes are kept. Teachers frequently engage in planning for Mathematics during the year through regular lunchtime meetings. Much informal discussion takes place among members of the mathematics teaching team. The position of department co-ordinator is currently held by an experienced member of the teaching team and this position rotates yearly among all mathematics teachers. This good practice will contribute to the retention of expertise within the mathematics department. There is a high level of collaboration and co-operation among mathematics teachers and they clearly work very well together as a team. Newly appointed teachers enjoy a very high level of support from more experienced colleagues. This takes the form of a formal induction programme for newly appointed teachers. The school is involved in the University College Dublin (UCD) mentoring programme for newly qualified teachers and recent appointees are strongly encouraged by school management to attend in-service courses. All of this is very good practice.

It was evident from the review of the planning documentation that significant progress has been made in planning for Mathematics. The plan includes mathematics department policy on student access to levels, provision for students who experience difficulty with Mathematics, provision for students for whom English is an additional language, homework and assessment procedures, resources available and extra-curricular activities planned. The plan also contains department policy on motivating students towards an appreciation of Mathematics. It was clear from the review of the minutes of planning meetings that ongoing planning for classroom activity takes place. This takes the form of discussions around the incorporation of active methodologies in lessons. The results of this excellent practice were evident in all of the lessons observed. The minutes of planning meetings also show that the mathematics department reviews decisions and practice on an ongoing basis.

The mathematics plan contains schemes of work for each year group. These consist of lists of topics to be covered within agreed timeframes. It was clear from the range of methodologies observed, from the diversity of the resources accumulated over time and from the minutes of planning meetings that the plan does not accurately reflect the wide variety of teaching strategies used in practice. It is recommended that the mathematics plan be further developed over time so that it fully reflects the day-to-day work of mathematics teachers. Through ongoing revision and review, the plan should become a living document that reflects and informs classroom activity, puts the students at the centre of planning and provides the mathematics department with an additional forum for sharing ideas and expertise.

TY is a recent addition to the programmes offered by the school. The TY plan reflects the underlying principles of a good TY programme. The programme consists of topics that are well chosen for a mixed-ability group. Each of these is taught using active and interactive methodologies. Students engage in project work, pair work, and group work. One project on Simpson’s rule involved students finding the area of each country that was represented by a nationality in the class group. A second project involved students designing a garden to scale. The resulting projects are proudly displayed on the classroom walls. It is clear that opportunities are provided for students to experience Mathematics on an enjoyable level. The study of Fibonacci sequences, a project on famous mathematicians or a module of Applied Mathematics are suggested as further options for this very good TY programme.

It is recommended that the mathematics department undertakes an analysis of the certificate examinations results obtained by students each year. The school’s performance should then be compared with the national norms and these analyses should inform future planning for Mathematics.

High quality teaching and learning were evident in all of the lessons observed. Teacher instructions and explanations were very clear. A good example of this was observed in a lesson on the fundamental principle of counting where the students were engaged in activities that served to explain the underlying concept with clarity. In this lesson the students were divided into groups, some completed an exercise with playing cards that was designed to help them to explore the number of ways in which the cards could be arranged; the teacher directed the students to discover a system of arranging the cards that would illustrate the core mathematical concept. Another group was expected to list all the possible arrangements of four students on four chairs. These activities were well consolidated by subsequent written exercises and teacher examples. Reference was made to the preceding activities throughout the teacher explanations. The empty chairs were used to demonstrate the concept as students were called to the front of the class to illustrate the point. The comprehensive treatment of the lesson content and the clarity of the explanations together with the variety of activity made this an excellent lesson.

The pace of the lessons observed was lively yet appropriate to the ability level of the students. A good mix of teacher instruction and student exercise was used to keep lessons interesting and students engaged. Teachers were careful to relate new material to prior learning. In the higher level Leaving Certificate lesson on complex numbers observed the teacher was very careful to revise any prerequisite material before introducing any new content. This practice is very worthwhile. Teachers made good use of questioning to engage students and to assess learning. In some cases teachers used probing questions to ascertain individual student perspectives. This very good practice allowed teachers to direct explanations in order to address areas of difficulty for students. In all cases teachers used higher-order questions requiring reflection and consideration to help students to explore difficult concepts and ideas.

Active methodologies were used in most of the lessons observed. In many cases students were given the opportunity of working in pairs or groups. This was very successful and facilitated the creation of vibrant and lively learning environments where students could engage fully with their course material. Teachers were careful when choosing pairs, there was a conscious effort made to optimise the learning opportunities for both students. In one lesson, three students were called to the board to correct homework while the teacher provided individual assistance to any student who had experienced difficulty. While the three students were at the board the rest of the class was divided into three groups; each to check the work of the student nearest to them. The remainder of the class engaged in the task completely and demonstrated great respect for their fellow students. This approach worked very well. In another case the class group was divided into two groups and each was expected to work on an exercise on Venn diagrams. Once completed, the groups exchanged Venn diagrams and analysed each others’ work. These are examples of methodologies and teaching strategies that were observed, during the evaluation, to work well.

Teachers are careful to allow students to explore mathematical concepts for themselves. This was apparent in a lesson on co-ordinate geometry observed. The main objective of this lesson was to encourage the students to understand the idea of slope and in particular its relationship with parallel and perpendicular lines. The lesson opened with a computer game on the idea of slope that involved students calculating the slope of a line, without the formula, directly from a graph. Throughout this game the students enthusiastically demonstrated their ability to perform this task. Following this the teacher expected the students to deduce the formula for the slope of a line. This was achieved by the majority of the students in the class without help from their teacher. Once the formula had been deduced the students then worked on an exercise which expected them to calculate the slopes of two different lines and also to graph the lines. The students were then asked for their observations. Most of the students could identify the relationship between the slopes of parallel lines and although they found the relationship between the slopes of perpendicular lines more difficult to describe, they would have identified this relationship in time with more examples. This investigative methodology was ideal for the achievement of the objectives of this excellent lesson and a thorough understanding of the concepts was demonstrated by most of the students.

Teachers integrate ICT into teaching and learning in Mathematics wherever possible. The interactive whiteboard was observed to be used effectively in a geometry lesson and the software used served to highlight the concepts of the lesson very well. The interactive whiteboard was prepared in advance of the lesson with all of the planned teacher examples. This strategy contributed to the pace of the lesson and to student participation and engagement. The LCA lesson observed provided an example of very good practice in terms of the seamless integration of ICT into teaching and learning. In this lesson students were engaged in holiday planning and budgeting. There was a computer available for student use in the classroom, with internet access. This enabled individual students to research holiday destinations on the internet as part of lesson activities. The students in this class group worked in pairs while their teacher provided assistance where required. High quality learning took place during the discussions that arose from a variety of lesson activities and at the conclusion of the lesson all of the students had a clear appreciation of the value of budgeting when planning a holiday.

The wide variety of methodologies and teaching strategies employed by teachers and the diverse range of teaching resources used for active learning are evidence of the generous sharing of ideas, experience and expertise that characterises the mathematics department in St Joseph’s Secondary School. The teachers of Mathematics share an enthusiasm for the subject; the transfer of this enthusiasm to their students was clearly demonstrated in the evaluation. The rapport between students and their teachers is very good. Teachers are very encouraging, affirming and supportive of student effort. Class management was very good in all cases and standards of student behaviour were high. In interactions with the inspector the majority of students demonstrated an interest in Mathematics.

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All students are formally assessed at Christmas. Summer examinations are held for first, second, TY and fifth years. Third and sixth year students sit ‘mock’ examinations in February. Common examination papers are set for formal assessments. It was evident from the review of common examination papers that the standard and the graduated nature of questions provides every student with the chance of passing while simultaneously providing sufficient challenge for the more able student. This is representative of best practice and contributes to the high quality of information derived from the results of these examinations. Reports are sent home on foot of all formal examinations and parent-teacher meetings take place annually.

Learning is assessed through oral questioning in class, teacher observation, and end-of-topic tests. In some cases teachers are using comments when correcting student work, to provide students with valuable feedback and encouragement. This practice is worthwhile and the extension of its use is encouraged.

It was evident from the review of student copybooks that the standard of student work is high in the majority of cases and that it is well monitored by teachers. In keeping with good practice homework is set regularly and is usually corrected as part of the following lesson. There is a homework policy for Mathematics.

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The following are the main strengths identified in the evaluation:

· Timetable provision for Mathematics is good.

· Teachers make use of a wide range of teaching resources for teaching and learning in Mathematics.

· The mathematics department is well provided for in terms of ICT resources and these are routinely used to make mathematics lessons interesting for students.

· There is a very high level of support provided to students who need extra help with Mathematics.

· Students of Mathematics participate in a wide variety of co-curricular mathematics related activities.

· Good progress is being made on planning for Mathematics.

· The TY plan reflects the underlying principles of a good TY programme.

· High quality teaching and learning were evident in all of the lessons observed.

· In all cases teachers used higher-order questions requiring reflection and consideration to help students to explore difficult concepts and ideas.

· Teachers use a wide variety of methodologies and teaching strategies in their lessons.

· There is very good assessment practice in the setting of tests.

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

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· To allow for flexibility in changing levels all second year class groups should be concurrently timetabled.

· The mathematics plan should be further developed over time so that it fully reflects the day-to-day work of mathematics teachers.

· The mathematics department should undertake an analysis of the certificate examinations results each year, compare the school’s performance to the national norms and use these analyses to inform future planning 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 June 2009*

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**Appendix**

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**Submitted by the Board of Management**

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**Area 1: Observations on the content of the inspection report**

The BOM of St Joseph’s Secondary School is heartened by the findings of this Inspection. The BOM congratulates the teachers for their commitment and professionalism as outlined in this report. The BOM is particularly impressed by the high level of team work which is described in the report. Furthermore, the Maths department has asked the BOM to acknowledge in its response the positive, helpful work of the inspector.

**Area 2: Follow-up actions planned or undertaken since the completion
of the inspection activity to implement the findings and recommendations of
the inspection**

It is hoped that staffing allocations will permit concurrent timetabling of all groups in future. The principal will make every effort to achieve this within resources available to her. The mathematics department will undertake an analysis of results each year. The results will also be available to the BOM for the purpose of comparison with national norms.

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