An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Coolock, Dublin 5
Roll number: 60550B
Date of inspection: 20 March 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Chanel 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 and subject teachers.
Chanel College has a current enrolment of 425 boys. Timetable provision for Mathematics is good. In the junior cycle first, second and third year groups are allocated five class periods of Mathematics per week. Transition year (TY) students are timetabled for three mathematics lessons per week. Five periods of Mathematics are provided weekly for fifth and sixth years. This level of provision is in line with syllabus guidelines. In keeping with good practice, mathematics lessons are evenly distributed across the week.
In first year students are allocated to mixed-ability class groups. The school offers the Junior Certificate School Programme (JCSP) and students availing of this option are taught Mathematics together as a group. In third year there is a higher level class, an ordinary level band and a foundation level class. TY is optional and there are two TY mixed ability mathematics groups. For fifth and sixth year there is a higher level class, an ordinary level class and a foundation level class. Students are assigned to levels on the basis of performance in Christmas and summer examinations. Student preference and teacher advice also play a role in level selection. Mathematics lessons in third, fifth and sixth years are concurrently timetabled. This allows for flexibility of movement for students who need to change levels. This is all very good practice.
With the exception of second year, the arrangements that are made for students to study Mathematics at a level appropriate to their ability are good. In second year there is a higher level class, a mixed-ability class and an ordinary level band. The mixed-ability class was observed as part of the evaluation and it was clear that it contained higher, ordinary and foundation level students. This arrangement is unsatisfactory for the students of this class group, particularly for those taking the higher level course. Since most second year class groups are timetabled at different times for Mathematics movement between levels is not possible for the majority of second years. It is therefore recommended that all second year mathematics classes be concurrently timetabled so as to enable all higher level students to be taught as one class group.
The mathematics department comprises nine teachers. It is department policy that classes retain the same teacher from year to year for the duration of a cycle. This is good practice. Higher level mathematics in both the junior and senior cycle is currently the responsibility of one experienced member of the mathematics teaching team. It is recommended that the number of teachers teaching higher level Mathematics be increased. As well as guarding against over-dependence on particular members of the teaching staff, this measure would strengthen the department’s capacity to meet the challenges of the forthcoming revisions to the mathematics syllabuses.
Students in need of learning support are identified through communication with feeder primary schools, pre-entry assessment, diagnostic testing and ongoing teacher observation. Support is provided through individual or small group withdrawal from subjects other than Mathematics, and the creation of smaller classes. Commendably, team teaching is also used to enable students who have been identified as needing support to receive that support during mainstream mathematics lessons. JCSP students benefit from the extra support provided as part of their programme. Ongoing assessment takes the form of end-of-topic tests and teacher observation. The communication between mathematics teachers and the learning support department is very good and usually takes place on an ongoing informal basis. A wide range of resources has been provided for the learning support department. These include mathematics-related board games, play currency, magnetic fractions, decimals and percentages, and tangram sets. Learning support teachers frequently use exercises and activities from a range of supportive computer software as additional teaching strategies to complement lessons. Overall a very high level of support is provided for students who have been identified as needing support with Mathematics and the type of support that best suits individual student need is chosen from a range of valuable options.
Information and communications technology (ICT) is well provided for in the school. Two computer rooms and a number of laptop computers and data projectors are available for teaching and learning in Mathematics. Some classrooms have been recently fitted with interactive whiteboards. It is very good that ICT is frequently incorporated into mathematics lessons by the majority of teachers. The continuation of this practice is encouraged and it is suggested that the rooms that are fitted with interactive whiteboards be rotated among all mathematics teachers in order to contribute to the regular use of ICT to complement mathematics lessons. Teachers make use of a variety of resources in teaching and learning in Mathematics. These include geometry equipment, posters, JCSP workbooks, 3-D solids, scales, probability sets and class sets of mathematical equipment. In keeping with best practice the woodwork department of the school has produced teaching aids that can be used for teaching area and volume, geometry, and trigonometry. A bank of useful handouts and worksheets has been created and this is kept in a central location and shared among mathematics teachers. In order to build on these resources it is suggested that teachers collect everyday objects such as boxes, spheres and containers of various shapes and sizes that could be used in the study of Junior Certificate volume and area. Furthermore it is suggested that students be encouraged to produce models that can be used in solving Junior Certificate problems in volume and area and geometry. Teacher continuing professional development (CPD) is facilitated by school management.
The mathematics department is justifiably proud of the school’s achievement in the Irish Junior Mathematics Competition and students attend the annual Mathemagic lectures in Dublin City University (DCU). Junior cycle students recently participated in events organised by a local business entitled ‘Working It Out’, this involved students participating in a variety of activities and using Mathematics to record and analyse their performance. Participation in extracurricular mathematics related activities such as these is a very worthwhile way of encouraging an interest in Mathematics outside of the classroom.
Formal planning time is allocated to Mathematics four times per year as part of the whole-school planning process. Records are maintained and minutes are kept. Frequent informal day-to-day meetings also take place among members of the mathematics department. There is close co-operation among mathematics teachers and the members of the department work well as a team. The co-ordination of the mathematics department is currently the responsibility of an experienced mathematics teacher. It is recommended that this position be rotated among all members of the department over time. This measure would enable the mathematics department to derive the benefits of each teacher’s individual perspective as well as providing an opportunity for each teacher to gain experience of co-ordinating the department.
It was evident from the review of planning documentation that good progress is being made on planning for Mathematics. The plan opens with the aims and objectives of the mathematics department. Details of department policy on assessment, homework and on teaching students who require support with Mathematics are contained within the plan. There are schemes of work for each year group; these are in terms of topics to be covered within given timeframes. The plan also contains a list of effective teaching strategies that could be used to enhance student learning in Mathematics. A list of key words for each chapter of the text books has been compiled to help teachers to support students with literacy difficulties. There is a list of resources including useful websites included in the plan. This comprehensive plan is stored in a common area of the staffroom and is readily available as a source of valuable information and guidance.
It is evident from the review of the minutes of mathematics department meetings that discussion and planning takes place around classroom practice. The planning process for Mathematics regularly uses the ‘diagnostic window’ to help the mathematics teaching team to identify areas for development and areas that are working well. The mathematics department takes a reflective approach to planning and the plan is reviewed and updated regularly. The mathematics plan is a document that informs the work of the department and is in keeping with good planning practice.
It is evident from the observation of lessons that the full range of classroom activity that takes place is not fully reflected in the mathematics plan. It is recommended that the mathematics department develop a shared folder of lesson plans that are set out in terms of learning objectives, teaching methodologies, resources necessary and modes of assessment. This would provide mathematics teachers with a forum for the sharing of expertise and experience that can have such a positive effect on teaching and learning for students.
The TY programme for Mathematics provides opportunities for students to experience Mathematics for pleasure and interest. The thirteen-week module that has been designed is suitable for a mixed-ability setting. Students study topics that are not on the Leaving Certificate course such as prime and perfect numbers, the mathematics of business, Pythagorean triples, Fermat’s last theorem and mathematical puzzles. These topics are chosen to encourage students to appreciate the relevance of Mathematics in their everyday lives and to cultivate a sense of wonder and enjoyment in the subject. To complement this very good TY plan a module of Applied Mathematics is suggested with a particular focus on the Mathematics of road safety, which would include the study of linear motion and collisions.
Each year the school’s performance in the certificate examinations is compared to the national norms. It is recommended that this analysis be used to inform future planning for Mathematics.
High quality teaching and learning was evident in the lessons observed. The predominant methodology used was teacher-led exposition. Students were encouraged through questioning to become fully involved in lessons. In most cases higher order questions were used to help students explore difficult ideas. This was particularly evident in a lesson on sets observed. This lesson opened with the setting of a problem for the students to solve. A logical approach, which encouraged students to think for themselves, was chosen in the initial presentation. Throughout this lesson the students worked in partnership with their teacher and demonstrated genuine interest in the achievement of the learning objective. This was an excellent lesson because the approach taken was conceptual and logical and through collaboration with each other and their teacher the students were facilitated in the development of the problem solving and critical thinking skills that are essential for success in Mathematics.
In most cases lessons had a clear focus and strong structure. In one case however, although a structure had been established, there was a tendency to periodically deviate from it. These occasional distractions resulted in a loss of valuable class time. It is therefore recommended that teachers share the learning objectives explicitly with students at the beginning of each lesson by writing them on the board. This practice would serve to strengthen the structure of lessons and provide direction and guidance for students. This would give students awareness, from the outset, of what to expect from the lesson and enable them to see the lesson progress in a structured way. The achievement of the learning objectives should be checked at the end of the lesson. This good practice contributes to student motivation and encourages students to take personal responsibility for their own learning, leading to a sense of achievement.
Teachers varied the learning activity throughout lessons; this helped to maintain high levels of student interest. In most cases lessons consisted of teacher example followed by student exercise or activity. This was supported by the provision of individual attention where necessary. In one case the students after an initial introduction, were expected to study the example in the text book and then to attempt the following exercises, without prior teacher example. The teacher acted as facilitator by providing support and assistance when students encountered difficulty. While completing the exercises some students spontaneously broke into small groups or pairs and worked together on solving the problems. This methodology worked very well. The students demonstrated the benefits of this approach by taking responsibility for their own learning, by engaging enthusiastically with their classmates, by remaining on task throughout the lesson and by demonstrating the confidence to discuss and challenge ideas. At various times throughout the lesson the teacher, with student contribution, worked through solutions on the board; this was done to consolidate learning and for students to correct their own work. The learning activities of this excellent lesson were complemented by the high level of respect that students demonstrated for each other and their teacher.
In general the pace of lessons was appropriate to the ability level of the students and teachers made efforts to differentiate learning to suit the variety of needs in their class groups. In some cases this was achieved explicitly by setting different class work for different students and in others it was achieved by careful questioning and targeted individual attention. This is good practice. In most cases lesson content contained material that was accessible to all students and challenging enough for the more able student. In one case however the content of the lesson provided insufficient challenge for some of the class group and this together with the lack of lesson pace resulted in students who were reluctant to participate and who disengaged. It is therefore strongly recommended that the good practice of differentiating the learning experience to suit the needs of the students in the particular class group be extended to all lessons.
One team teaching lesson was observed as part of the evaluation. During this lesson the teacher had responsibility for the majority of the teaching activities and the learning support teacher provided individual support to students and played a supportive role in the management of classroom activity. Student care was central to the activities observed in this lesson. The teacher provided very clear instructions and explanations. Examples that related to the work of previous lessons were frequently used to relate the new material presented to prior learning. Students were expected to draw bar charts as part of their study of statistics and the teacher provided rulers and pencils where necessary. A poster was used to illustrate the key ideas and the students completed exercises from a very supportive JCSP workbook. This excellent lesson was very well planned and a very high level of support and encouragement was provided for the students in this class group.
In general classroom management was observed to be very good. The quality of student co-operation tended to be highest in lessons where the content suited the ability levels in the class group and where lessons progressed at a lively pace. Teachers related to their students with patience, warmth and respect. Teachers were affirming and encouraging of student effort and the relationships between students and their teachers were characterised by good humour, sensitivity and a genuine sense of care.
All class groups with the exception of TY are assessed at Christmas. Summer examinations are held in May for first, second and fifth year groups. Students taking the certificate examinations sit ‘mock’ examinations in February. TY students are continuously assessed throughout their module. Common examination papers are set within levels which is good practice. It is evident from the review of examination papers that questions that range in difficulty are set. In the mixed ability, first year summer examination the structure and format have been designed to enable most students to experience some degree of success; this positive approach encourages learning and student confidence. Reports are sent home on foot of all formal examinations and parent-teacher meetings take place annually.
Learning is routinely assessed through oral questioning in class and students sit class tests regularly. Homework is given daily and usually corrected as part of the following day’s lesson. This was successful in most cases observed. In one case, however, because a considerable number of students had not completed homework, the checking of homework at the beginning of class proved to be quite disruptive and time consuming. It is therefore recommended that the procedures around giving, checking and monitoring homework be reviewed. It is suggested, for example that strategies that encourage students to continue with class work while homework is being checked along with ways of ensuring more students complete homework be explored. One approach may be to limit the amount and frequency of homework for some class groups. Homework reports are sent home to parents five times per year.
It was evident from the review of copybooks that most students are engaging well with their course material and are making steady progress. Work is well monitored by teachers and the presentation of students work is of a high standard.
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 at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published December 2009