An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Ratoath, County Meath
Roll number: 76088T
Date of inspection: 18 November 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Ratoath College, Co. Meath. 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. 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.
Ratoath College is a recently established school with an enrolment of 269 boys and 197 girls in the current year. Timetable provision for Mathematics is very good. First, second and third year groups are allocated five periods of Mathematics per week. Transition Year (TY) students receive three mathematics lessons per week. Six mathematics lessons are provided for fifth year students. There is currently no sixth year class group in the school but next year’s sixth years will be timetabled for six mathematics lessons per week. In keeping with good practice, Mathematics lessons are evenly distributed across the day and week.
The mathematics teaching team comprises seven teachers and allocation to classes and levels is decided by management in close consultation with the teachers themselves. It is mathematics department policy that students retain the same teacher from year to year for the duration of a cycle, which is good practice. Currently the majority of mathematics teachers’ timetables include responsibility for teaching higher level mathematics class groups. It is good that there are plans to rotate higher level Mathematics in the senior cycle among as many mathematics teachers as possible. This will help to maintain high levels of expertise within the mathematics department and will support the mathematics team in meeting the challenges of the forthcoming changes to the mathematics syllabuses.
Considerable thought and effort has been put into devising a method of dividing classes to ensure that the needs of all of the students are met to the greatest extent possible. Students are assigned to mixed ability classes in first year. For second and third year, students are divided into higher and ordinary level classes. Classes in these year groups are concurrently timetabled, a good arrangement as it provides flexibility in changing levels. There is currently one TY class and it is of mixed ability. There are two class groups in fifth year, one higher level group and one ordinary level group. Fifth year mathematics lessons are timetabled concurrently. Students are encouraged to study the highest level possible for as long as possible and change of level is facilitated by concurrent timetabling. Levels are decided on the basis of performance in school examinations, teacher observation and the certificate examinations. Student preference plays a significant part in level choice and change of level can only take place in consultation with students, parents and mathematics teachers. There is evidence that this is working very well.
Students in need of learning support are identified through pre-entry assessment, communication with feeder primary schools, ongoing teacher observation, psychological reports, diagnostic testing, and interviews with students and their parents. Support is provided through team-teaching where two teachers share responsibility for teaching the class and in-class support; in practice, this results in one teacher teaching the class group and the other providing focused support for students who experience difficulty with Mathematics. In a small number of cases students are withdrawn from the mainstream group for mathematics lessons. This is all very good practice. It is recommended, however, that where learning support is provided exclusively within the mainstream class that focused, targeted, withdrawal be also considered as a complementary form of learning support provision. This could consist of one or two class periods of withdrawal provided to students prior to the beginning of each new area of learning. This preparation would also provide students with opportunities to practise the necessary basic skills that would allow them to get a head start on the study of new material. In the case of students for whom English is an additional language, these lessons could enable key words and key explanations to be covered in advance of starting a new topic.
Teachers make full use of a wide range of teaching resources for teaching and learning in Mathematics. Each teacher has a trundle wheel, geometric solids, playing cards, dice, bingo games, and grouping circles. In addition there are shared resources that are kept in the mathematics room and are shared among members of the mathematics department. These include geometry equipment, balancing scales with weighted fractions, probability kits, overhead calculators, and algebra tiles. Mathematics teachers have compiled a bank of shared handouts and worksheets to supplement the text book and to support lesson activities. There are also a number of mathematics reference books that are kept in the mathematics section of the school library. These resources are used in active lessons to allow students to explore difficult mathematical concepts in a concrete way. This is very good practice. Teacher continuing professional development (CPD) is fully facilitated and teachers are encouraged to attend in-service courses. The school is one of the initial group engaging in Project Maths and all mathematics teachers have had access to the related in-service courses. There is an induction and mentoring programme in place to support teachers new to the school. It is clear from the extensive range of mathematics resources built up over time by the mathematics department that Mathematics is well supported and enjoys a lively and vibrant position in the school.
Information and communications technology (ICT) is very well provided for. Every classroom is fitted with a ceiling-mounted data projector and personal computer (PC) with broadband internet access. There are also a number of interactive whiteboards and four school computer rooms that are used for teaching and learning in Mathematics. There is a very high level of computer expertise within the mathematics department since all teachers have availed of training in this area. The acquisition of further ICT skills has been identified by some of the mathematics teaching team as an area for development and commendably, mathematics teachers who have the required expertise will provide this training. Teachers optimise the value of these ICT resources by incorporating ICT into teaching and learning in Mathematics at every opportunity. It was evident throughout the inspection visit that teachers make considerable effort to create PowerPoint presentations, to research relevant lesson content on the internet, and to source interactive lesson material. These are all well chosen, designed to capture the imagination of the students, make lessons fun, and enhance the clarity of mathematical explanations. Teachers have created an electronic folder where effective ICT lessons can be stored and shared. It was evident from the outstanding quality of the ICT material produced by members of the mathematics department that each teacher is fully committed to ensuring the highest standard of ICT usage in teaching and learning in Mathematics.
Students of Mathematics participate in a range of co-curricular mathematics related activities. Events are organised each year to celebrate Maths Week and World Maths Day. This year’s celebrations included a school mathematics inter-class quiz, the creation of mathematics posters, and the completion of mathematics puzzles. Students also participate in the Team Maths competition. It is good that there are plans to increase the variety of extra-curricular mathematics activities over time. The mathematics department runs a lunchtime weekly Math Magician club for students. In observing this it was evident that the students derive great pleasure from performing mathematics related magic tricks for each other. It is clear from the enthusiastic participation of both students and teachers in the various activities organised by the mathematics department that students are given every chance to experience Mathematics for pleasure.
Three formal planning meetings are scheduled per term for the development of the mathematics plan. Frequent formal meetings of the mathematics department are held outside of allocated planning time and the main business of these meetings is the sharing of classroom practice. These provide the forum for teachers to demonstrate successful lessons, ICT skills, active methodologies and useful teaching strategies. In addition mathematics teachers informally discuss any day-to-day issues that arise, this regularly occurs through email; these emails are saved and provide a comprehensive record of mathematics department activity. Records of all formal meetings are maintained and minutes are kept within the department’s planning documentation. There is a co-ordinator for the mathematics department; this position will rotate among all members of the mathematics teaching team. The extent to which mathematics teachers share experience and expertise has contributed to high standards of classroom practice across all mathematics teachers. This consistency of good practice is also a by-product of team teaching. The openness to and genuine welcoming of contributions from each member of the mathematics teaching team has contributed to the development of a very high degree of creativity in lesson planning and design. The result of this collaboration is evident in the wide variety and the high quality of teaching strategies and methodologies used in the classroom and from the very high levels of student interest and enthusiasm for the subject demonstrated through the course of the evaluation.
The plan for mathematics opens with the mathematics department ‘guiding vision’. The main focus of this is to foster an appreciation for Mathematics and to meet the needs of all students. The aims and objectives of the plan have been developed from this vision. The plan includes mathematics department policy on student allocation to levels, timetabling of Mathematics, planning for students who need support with Mathematics, homework and assessment. Teaching methodologies are also included in the planning documentation. In addition there is a list of resources available and in-service courses attended. The plan closes with a needs analysis for the mathematics department. Expertise existing within the subject department, that might address some of the needs, is identified. It is clear from the records maintained that this plan is subject to regular revision and review. The plan for Mathematics is a living document that informs and reflects classroom activity and puts the student at the centre of planning. This is excellent planning practice.
The overall mathematics plan contains schemes of work for each year group which consist of topics to be covered within agreed timeframes. These schemes in turn have been developed into individual teacher plans. They are divided into weekly and daily plans that are flexible and are subject to ongoing review. These plans are exemplary; they are set out in terms of lesson objectives, learning outcomes, resources required and a notes column for review comments resulting from teacher observation. A section for teaching methodology and differentiation strategies is also included. Teacher individual plans are detailed and comprehensive and are of a very high quality. It is clear that considerable thought and effort went into their creation. This has contributed to focused and well organised lessons where teachers are fully prepared and students can participate in a wide range of learning activities.
The TY plan observes the spirit of the underpinning principles of a good TY programme. Every opportunity is provided for students to gain an appreciation for the subject. Students are encouraged to participate in mathematical activities that illustrate the relevance of mathematics in our everyday lives and promote Mathematics as a subject to be studied for pleasure. An impressive range of ICT resources in the form of Power Point presentations has been developed to support teaching and learning of TY Mathematics. The TY plan strikes a good balance between Leaving Certificate course content and material that is not on the Leaving Certificate course. The programme is well designed to be taught in a mixed ability setting, its aim is to be accessible to all students while providing challenge for the better able student. Students engage in project, group and pair work in their study of all elements of the TY programme. Wherever possible, puzzles and games are used to promote an interest in the subject and to help students to develop their problem-solving skills. The TY plan facilitates student engagement with Mathematics on an interactive and enjoyable level and encourages the development of positive attitudes to the subject. It is suggested that a module of Applied Mathematics be considered to complement this very good TY plan.
High quality teaching and learning were evident in all of the lessons observed. At the beginning of each class visited the learning intentions of lesson were explicitly written on a Power Point slide. This practice ensured that lessons had a clear focus and were well structured. Understanding was checked on completion of each objective. In junior cycle lessons, this was done using ‘traffic lights’. Each student has a set of ‘traffic light’ cards, one green, one orange and one red each representing a different level of comprehension. At various points throughout each lesson the teacher requested that students to hold up the card that best described their level of understanding. This provided teachers with a very accurate assessment of student needs. Teachers acted on this information by providing extra clarity for students who were experiencing difficulty. It is suggested that this mechanism be used to provide extra challenge, in the form of more difficult exercises, for students who have achieved full understanding.
Teacher instructions and explanations were very clear and thorough. Teachers involved students fully in lessons through very good use of questioning. In all cases open questions were used to help students to work through difficult concepts and ideas. Students were encouraged to explore ideas in a variety of different ways. This was of particular note in a higher-level fifth year class. In this case the teacher was careful to take more than one approach to solve a problem in logarithms. Some of these approaches were the result of student contribution. This practice ensured that students were encouraged to examine the underlying concepts thoroughly. The students were expected, in this lesson, to anticipate the outcome of each problem so that their workings would be directed towards the solution from the outset. This very good practice expects students to take an organised logical approach to problem solving.
The pace of the lessons was lively yet appropriate to the ability level of the students in all cases. Great variety in learning activity was integrated into each lesson observed; this kept lessons interesting and students on task. A fifth year ordinary-level lesson, on functions and graphs, provided a good example of this. This lesson opened with a teacher example in Power Point. Students were involved through questioning at every stage of this example. The Power Point slides were prepared with graph paper; this supported the lesson very well and enabled the teacher to anticipate problems that students might encounter on completion of individual exercises. The students were then expected to work in pairs, on related exercises, to graph straight lines. Following this they were encouraged to discuss their observations and to offer predictions. This was particularly valuable where students were asked to examine lines with negative and positive slopes and to give their observations. Students were allowed ample time to form opinions and these were discussed comprehensively. This is an example of very good practice mainly because the mix of tasks in this lesson contributed to very high levels of student participation and engagement.
Teachers integrate active methodologies into lessons where appropriate. In a volume and area lesson observed the students worked on finding the dimensions of a range of 3-D solids. The teacher also provided the students with card and scissors, the students were expected to create a number of cones and to measure the dimensions of these. The surface areas and volumes of the 3-D solids and the cones were then calculated using the formulae. The students worked in small groups and freely moved around the classroom where necessary. Throughout this lesson the teacher provided individual assistance to any students who needed support with the task. It was explained that in preceding lessons the students were encouraged, through discussion, to explore different ways to find the curved surface area of cylinders that they had made themselves. A handout was used at the conclusion of this active lesson; this was designed to consolidate the mathematical concepts explored through the lesson activities. This is an example of very good practice because the lesson content was comprehensively explored, the mathematical concepts were consolidated following the activities, and many learning styles were targeted through the use of such variety in learning activity.
Students were encouraged to explore mathematical concepts for themselves. The lesson on co-ordinate geometry observed provides a good example of this. This lesson was introduced with a brief history of Descartes. A Power Point presentation was prepared with a picture of Descartes’ ceiling complete with a number of flies. The students were asked to find a way of describing the positions of the flies. The students were enthusiastic and offered a number of suggestions, many of which were correct. The teacher applauded them for discovering co-ordinate geometry for themselves. Another good example of this discovery-type methodology was observed in an algebra lesson. The main objective of this lesson was to enable student to gain an understanding of gathering like terms in an algebraic expression. The teacher provided a large number of different coloured blocks and a number of students were called to the front of the class to demonstrate how they would organise the blocks into categories. This simple but very effective technique allowed students to visualise the concept with great clarity by working through the idea in a concrete way for themselves. These are examples of very good practice.
Three lessons involving team-teaching were observed during the evaluation. In all cases both teachers successfully shared responsibility for teaching the lesson. This arrangement facilitated the use of active methodologies and enabled students who required extra support with Mathematics to receive that support with their peers. The lessons were all well prepared, well organised and each team of teachers worked very well together.
ICT was observed to be used very effectively in all lessons. Power Point presentations were very well designed to capture student interest. In all cases these were colourful and attractive and served to add clarity to examples and explanations. In the TY lesson observed the interactive whiteboard was used to engage and involve students. In this case the students, who worked in groups, were given many opportunities to come to the board and complete the activities organised for the lesson. It was evident from observation of this and many other lessons that teachers put considerable effort into sourcing suitable lesson material on the internet. This has resulted in lesson content that has enormous appeal to students. At the conclusion of another lesson the teacher used a game template, taken from the internet, to revise and recap the lesson. This game involved students answering routine mathematical questions that their teacher had filled into the template. This activity proved most enjoyable for the students and the teacher alike because the questions were presented in such an attractive format. These are representative of the many effective uses of ICT observed during the evaluation.
The relationship between students and their teachers were observed to be very good. Teachers are warm, caring, encouraging and affirming. This together with the wide variety of methodologies and teaching strategies used have facilitated the creation of secure, vibrant, and dynamic learning environments where students can engage with Mathematics with confidence. On the walls of each of the classrooms visited student projects were proudly displayed and teachers have created stimulating mathematical environments. Class management was very good in all cases and standards of student behaviour were high.
First, second and fifth year students are formally assessed at Christmas and in May. Examination class groups are formally assessed in October and ‘mock’ examinations are held in February. Reports are sent home on foot of these formal assessments. Progress reports are also sent home in student journals in October and February. Common examination papers are set within levels, this is good practice. It is clear from the review of examination papers that graduated questions are set. This is intended to enable each student to experience some degree of success in examinations and to ensure that the quality of the information from test results is high. It is mathematics department policy to use assessment for learning (AfL) approaches in the correction and setting of tests. This good practice provides positive feedback and advice for students. Parent-teacher meetings are held annually.
Learning is routinely assessed through oral questioning in class and the use of ‘traffic lights’. Class tests are set at the end of each topic or chapter studied. Homework is set regularly and usually corrected as part of the following lesson. It is school policy to provide positive feedback in the form of notes in student journals and postcards are frequently used to report success in Mathematics to parents. Students can receive ‘student achievement certificates’ for achievement in Mathematics. In junior cycle classes, teachers use ‘stamps’ to provide feedback and encouragement to students. All of this is representative of very good assessment practice.
Teachers routinely engage in self assessment. In some classrooms there is a suggestion box where students can submit suggestions for the improvement or enhancement of lessons, this practice is strongly encouraged by teachers. Teachers evaluate each other’s practice on an ongoing basis; this is facilitated by team teaching. A standard evaluation sheet has been produced by the mathematics department to formalise this process. The results of the certificate examinations are analysed each year and compared to national norms. Uptake rates are carefully monitored. This analysis is used as a means of evaluating the school’s performance. The very high level of teacher and student evaluation that is engaged in by the mathematics department is evidence of a commitment to developing a department that embraces change and strives for excellence.
The following are the main strengths identified in the evaluation:
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
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 May 2009
Submitted by the Board of Management
Area 1: Observations on the content of the inspection report
The Board of Management of Ratoath College are delighted with a truly outstanding report, which outlines the high standard of teaching and learning that is currently taking place within the school.
The Board wishes to thank all members of the Maths Subject Team who have worked diligently over the past four years to build the Maths Department. The report itself commends the teachers for the high quality of teaching which captures students imaginations and makes lessons fun and interesting, for the outstanding quality of the ICT material produced and for their effective strategies in assessing the pupils.
Ratoath College prides itself on its progressive and modern approach to teaching and learning. This approach was given due recognition in this report.
Area 2: Follow-up actions planned or undertaken since the completion of the inspection activity to implement the findings and recommendations of the inspection
The recommendation of the inspector was implemented immediately.