An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Athboy Community School
Athboy, County Meath
Roll number: 91517D
Date of inspection: 5 November 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Athboy 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 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.
Athboy Community School caters for 262 boys and 258 girls. Timetable provision for Mathematics is very good. In the junior cycle five class periods of Mathematics are allocated per week to first, second and third year groups. Transition year (TY) students are timetabled for three periods of Mathematics per week. Leaving Certificate Applied (LCA) students receive three mathematics lessons per week for year one and year two of their programme. In the case of the Established Leaving Certificate, fifth and sixth year students have six mathematics lessons per week. This level of provision is in line with syllabus guidelines. Post Leaving Certificate (PLC) courses are available in the school and PLC students receive two double periods of Business Calculations per week. Mathematics lessons are evenly spread across the week and day which is good practice. In second and third years there is a higher level class, a block comprising a higher level class and an ordinary level class that are concurrently timetabled and a block consisting of an ordinary level class and a foundation level class that are concurrently timetabled. All mathematics lessons in fifth and sixth years are concurrently timetabled. This is good practice as it allows flexibility when students need to change levels.
Students are assigned to mixed-ability class groups in first year. For second year, students are assigned to higher and ordinary level class groups on the basis of performance in continuous assessments that take place throughout first year and end-of-year class tests. Where possible, change of level is facilitated throughout second and third year. There is one TY class group and it is of mixed ability. For the senior cycle, while Junior Certificate results act as a guide to level choice, consideration is also given to student preference and teacher observation. On this basis, students are assigned to higher, ordinary and foundation level classes. Change of level takes place following consultation with teachers, students, parents and the school principal. Written parental permission is also required. All of this is good practice.
The mathematics department comprises ten teachers. School management decides on teacher allocation to classes and levels in close consultation with the teachers themselves. It is mathematics department policy that teachers retain classes from year-to-year through to the conclusion of a cycle. This continuity is good practice. Junior cycle higher level mathematics is rotated among all members of the mathematics teaching team. Leaving Certificate higher level Mathematics is rotated between two mathematics teachers. It is recommended that more teachers should become involved in teaching higher level Leaving Certificate Mathematics; a larger team at this level would assist the mathematics department in meeting the challenges of the forthcoming revisions to the mathematics syllabuses.
Teachers have access to a range of resources that are used for teaching and learning in Mathematics. These include overhead projectors, geometry equipment, probability kits, meter sticks, and 3D solids. In addition to these resources, molecular models, chemical jigsaws and a wide range of mathematical games and puzzles are used challenge students of TY Mathematics. A variety of books and compact disks of mathematical interest have been collected over time and these are used to make TY mathematics lessons more interesting and relevant. It is good that members of the mathematics teaching team have compiled a shared bank of useful handouts and worksheets. Mathematics teachers have access to the school’s computer room and there are a number of mobile data projectors and laptop computers available to them. Information and communications technology (ICT) is used in teaching and learning in Mathematics by a minority of teachers. It is recommended that teachers of Mathematics explore ways in which ICT could be further incorporated into mathematics lessons. In some cases teachers have created PowerPoint presentations for use in mathematics lessons, the continuation and extension of this work is encouraged and it is suggested that the resulting presentations be shared among members of the mathematics teaching team. Teacher continuing professional development is fully facilitated and teachers are encouraged by management to attend in-service courses. Newly appointed teachers benefit from the induction and mentoring programme organised by the school.
Students who are in need of learning support are identified through pre-entry assessment, psychological assessment, communication with feeder primary schools and ongoing teacher observation. Support in Mathematics is provided through one-to-one withdrawal, small group withdrawal, and the creation of smaller class groups. Commendably, in-class support is also provided through team teaching. Progress is monitored through ongoing standardised testing, in-class testing and teacher observation. Students receive assistance for the duration of their need and return to their mainstream class group when sufficient progress has been made. This is all very good practice. A very high level of support is provided to students who experience difficulty with Mathematics and support that best suits the needs of the students is provided from a wide range of options.
Formal planning meetings are held once per term. Records are maintained of these planning meetings and minutes are kept. Mathematics teacher regularly meet on an informal basis to discuss any day-to-day issues that arise. There is currently no co-ordinator for the mathematics department although there is clearly close co-operation and collaboration among members of the mathematics teaching team. It is recommended that a mathematics co-ordinator be appointed to oversee the planning process for Mathematics. In time, this position should rotate among members of the mathematics department.
It was evident from the review of planning documentation that significant progress has been made on planning for Mathematics. The plan includes department policy on student access to levels, provision for students who need extra support with Mathematics, planning for interculturalism, homework and assessment. It was evident from the review of the minutes of mathematics department meetings that discussions around assessment for learning (AfL) have taken place and it is clear that these have informed the mathematics department assessment policy. This is very good practice. It is recommended that the mathematics teaching team engages in further planning for classroom activity to include discussion around particularly successful lessons, active methodologies, group and pair work and ICT in teaching and learning.
The plan also contains schemes of work. These are in terms of topics to be covered within agreed timeframes and are in some cases very detailed. It is good practice that, where possible, the schemes for higher and ordinary levels in each year group are co-ordinated so that any student who changes level mid-year will have covered the same material as the group he or she is joining. It was evident from the range of teaching resources available and the observation of classroom practice that the mathematics plan does not accurately reflect the day-to-day work of mathematics teachers. It is recommended that the mathematics department plan be developed over time so that it reflects classroom practice more closely. Through ongoing revision and review the plan should become a living document that puts the students at the centre of planning and informs classroom activity.
The plan for TY Mathematics reflects the principles of a good TY programme. A good balance is achieved between Leaving Certificate course content and material that is not on the Leaving Certificate course. Every opportunity is provided for students to experience Mathematics on an interactive and enjoyable level through the use of mathematical puzzles and games. The plan has a very cross-curricular focus with the Mathematics of Physics, Chemistry, Biology, Engineering, Geography and Electronics playing a large part of student experience in TY. An engineering project to produce a structure, using straws, which will support the weight of a marble, provides a very good example of this. The students complete this project following the viewing of a documentary about bridge building and there is a competition to construct the highest straw tower. The TY plan includes the incorporation of ICT in teaching and learning in Mathematics through the use of PowerPoint presentations on graphs. On completion, each section of the TY programme is evaluated by students. The results of this evaluation are used to make improvements to the TY mathematics programme. Each year the TY plan is reviewed and revised to suit the incoming cohort of students. All of this is in keeping with recommended planning practice.
Each year the results of the certificate examinations are analysed and compared to the national norms. This is good practice. It is recommended that this analysis be used by the mathematics department to inform future planning for Mathematics.
Seven lessons were observed in the evaluation. In all cases, lessons were purposeful and appropriate to the syllabus. Teacher explanations and instructions were clear and lessons were well structured. Teachers were careful to relate new lesson content to the work of previous lessons. This good practice helps students to situate new ideas and to appreciate the interconnections between mathematical concepts. In the case of the higher-level Leaving Certificate lesson on limits observed, the teacher was careful to outline the relevance of limits as a prerequisite for future work on graphs. The abstract nature of the concept was easier to accept by the students once they had a graphical explanation with which to associate it and once its future uses had been explained. This approach made the explanation very clear and resulted in effective learning. At the beginning of some of the lessons observed, teachers shared the learning intentions with the students. Best practice in this regard occurs where the lesson objectives are written on the board at the beginning of class and the achievement of these objectives is checked at the end of the lesson. It is recommended that the learning intentions of each lesson be shared in this way.
The predominant methodology used was teacher example followed by student exercise. Teachers made good use of questioning both global and directed to assess learning and to engage students. Chorus answering was discouraged and students were allowed ample time to answer teacher questions. This is good practice. In some cases higher-order questions, requiring reflection and consideration were used effectively to encourage students to explore difficult ideas for themselves. This type of questioning is very beneficial as it promotes critical thinking and problem-solving skills that are essential for success at all levels. Teachers should be particularly conscious of using higher-order questioning strategies where students are expected to apply learning in unfamiliar situations. Problems in area and volume that involve recasting provide a good example of this. It is important that students gain plenty of experience of working through the conceptual aspects of these types of problems for themselves. It is appropriate in these situations to focus on general problem solving strategies rather than providing students with a conceptual breakdown of the problem and expecting them to then apply the formulae. It is therefore recommended that the use of higher-order questioning strategies be adopted by all teachers and used at every opportunity.
In all cases the pace of lessons was lively yet appropriate to the ability level of the students. In most cases the learning activity was frequently changed to keep lessons interesting and students involved. Where this occurred, the value of class time was optimised by students remaining engaged throughout the lessons. It is recommended that a variety of learning experiences be provided in all lessons. Teachers were careful to use real life explanations where possible. This was of particular note in the TY lesson where Simpson’s rule was explained using the idea of removing topsoil from a field in strips. This visual image was referred to throughout the lesson and enhanced student understanding of the concept. This is an example of very good practice. In this lesson some students reported having difficulty in accepting the formula for Simpson’s rule, it is suggested that this be explored through investigation. Finding the area of a circle, for example, using the traditional formula and then using Simpson’s rule to estimate the same area would provide a valuable exercise that would easily achieve this. This investigation would have the additional benefit of opening up discussion around estimation.
The lesson content of the LCA lesson observed was well chosen. In this lesson, students were studying the Mathematics involved in planning a holiday. Commendably, the teacher had provided a range of holiday brochures for this task. Throughout this lesson the teacher engaged students through discussion and questioning and in keeping with good practice related the lesson content to students’ own personal experiences. However, the main learning activity in this case was teacher led and the students tended towards disengagement as the lesson progressed. It is recommended that for LCA class groups a wider variety of learning experiences be incorporated into each lesson. Active methodologies that involve project, group or pair work would be ideal for achieving the learning objectives of the LCA mathematics programme.
In-class provision of learning support was observed to be very successful. Two classes were visited where a second teacher had been provided to assist students who experience difficulty with Mathematics. In the case of the first year lesson observed, the main teacher used a variety of strategies to differentiate learning in order to best meet the needs of all of the students in the class group. The teacher used a number of techniques to make explanations appeal to students with differing learning styles. Each new idea was presented using an oral explanation, a written description, and a student activity. In order to make the lesson more accessible to students for whom English is an additional language, the teacher was careful to use physical gestures wherever possible in explanations. In the study of currencies, the handout used included currencies from each country represented by a nationality in the class group. Another handout used a shopping receipt in an exercise on rounding. Designing handouts like this enables students to gain an appreciation of Mathematics in everyday life and makes mathematics lessons more interesting and relevant. Questions were chosen and directed carefully according to student ability and each student was given an opportunity to participate in answering. The learning support teacher discreetly provided additional support to specific students who needed extra help. This lesson was representative of excellent practice because the needs of the students were met with great sensitivity and patience shown by both the mainstream teacher and the learning support teacher and the learning was differentiated to accurately meet individual student needs. This was achieved with lively enthusiasm and in an atmosphere of fun.
Classes were well managed and a high level of student behaviour was observed in all cases. The relationships between students and their teachers is characterised by good humour and warmth. Teachers are encouraging and affirming and students respond with engagement and respect. In all, the evident good rapport that exists between students and their teachers has contributed to the development of supportive learning environments where students can study Mathematics with confidence.
Second and fifth year groups are formally assessed at Christmas and in May. First year students sit class tests at these times. ‘Mock’ examinations are held for third and sixth year groups in February. All year groups are continually assessed throughout the year and performance in these assessments forms part of the result, along with end-of term assessments, that is posted home to parents. In the case of TY students, continuous assessments are relied upon exclusively to provide reports to parents. Parent-teacher meetings take place annually. Learning is routinely assessed through oral questioning in class and students sit class tests at the end of each topic studied.
It is evident from the review of student copybooks that the standard of presentation of student work is high and that students are making progress in Mathematics. It is mathematics department policy to routinely monitor student work and to encourage students to adopt a well-organised, logical approach to the layout of their work. This close attention was reflected in the standard of presentation of student work. In keeping with good practice, homework is set regularly and the mathematics department have agreed the amount of homework that is considered appropriate for each year group and each level. Most teachers engage in assessment for learning (AfL) practices by using comment-based marking in the correction of homework and tests. This is worthwhile as it provides students with critical feedback and can be a source of positive reinforcement and encouragement.
The following are the main strengths identified in the evaluation:
· Timetable provision for Mathematics is very good and current timetabling of Mathematics provides a high degree of flexibility when students need to change levels.
· The mathematics department has access to a range of resources including ICT for teaching and learning in Mathematics.
· A very high level of support is provided to students who experience difficulty with Mathematics and support that best suits the needs of the students is provided from a wide range of options.
· All the lessons observed were purposeful and appropriate to the syllabus, teacher explanations and instructions were clear and lessons were well structured.
· Teachers make good use of questioning, both global and directed, to assess learning and engage students.
· In all classes visited, the pace of lessons was lively yet appropriate to the ability level of the students.
· The relationships between students and their teachers are characterised by good humour and respect. Teachers are encouraging and affirming and students respond with engagement.
· It is evident from the review of student copybooks that the standard of presentation of student work is high and that students are making progress in Mathematics.
· Teachers engage in assessment for learning (AfL) practices by using comment-based marking in the correction of homework and tests.
· The plan for TY Mathematics reflects the underlying principles of the TY programme very well.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· In order to maintain high levels of expertise within the mathematics department, more teachers should become involved in teaching higher level Leaving Certificate Mathematics.
· It is recommended that teachers of Mathematics explore ways in which information and communications technology (ICT) could be further incorporated into mathematics lessons.
· A co-ordinator of the mathematics department should be appointed to oversee the planning process for Mathematics.
· The mathematics teaching team should engage in planning for classroom activity; this should include discussion around particularly successful lessons, active methodologies, group and pair work and ICT in
teaching and learning.
· The use higher-order questioning strategies to help students to explore mathematical concepts and ideas should be adopted by all teachers.
· All mathematics lessons should include a variety of learning experiences for students.
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 March 2009
Submitted by the Board of Management
Area 1: Observations on the content of the inspection report
The Board of Management of Athboy Community School welcomes the findings of the recent Subject Inspection in Mathematics. The Board is happy to see that the ongoing good work of the Mathematics teachers has been acknowledged and that the Inspectorate is happy with the arrangements made for the teaching of Mathematics in the school.
.Area 2: Follow-up actions planned or undertaken since the completion of the inspection activity to implement the findings and recommendations of the inspection
School management will encourage more teachers to become involved in the teaching of Mathematics at higher level Leaving Cert.
A co-ordinator for the Mathematics department will be appointed to supplement the co-ordinators for each year.
The Mathematics teaching team will continue to be encouraged to engage in collaborative planning and sharing of good practice with a view to increasing learning by pupils.