An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
St Finian’s Community College
Roll number: 70120F
Date of inspection: 30 April 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in St Finian’s Community College as part of a whole-school evaluation. It presents the findings of an evaluation of the quality of teaching and learning in Mathematics and makes recommendations for the further development of the teaching of this subject in the school. The evaluation was conducted over two days during which the inspector visited classrooms and observed teaching and learning. The inspector interacted with students and teachers, examined students’ work, and had discussions with the teachers. The inspector reviewed school planning documentation and teachers’ written preparation. Following the evaluation visit, the inspector provided oral feedback on the outcomes of the evaluation to the principal, deputy principal and subject teachers.
In the junior cycle, four mathematics lessons per week are allocated to first, second, and third year groups. In the case of the Leaving Certificate (Established), fifth and sixth year groups are timetabled for five class periods of Mathematics per week. Optimal provision for Mathematics is a lesson per day. It is therefore recommended that the timetable provision for Mathematics be increased by one lesson per week for two of the three junior cycle years. This increase in provision would be of particular benefit to students studying the higher level Junior Certificate course. The Junior Certificate School Programme (JCSP) is offered by the school and students taking part in this programme receive six periods of Mathematics per week in first and second years and five periods of Mathematics per week in third year. There are four Mathematics lessons provided for Leaving Certificate Applied (LCA) year one and year two students. This is good provision. It keeping with good practice, Mathematics lessons are evenly distributed across the week.
First year students are allocated to one of two bands for all subjects or to a separate JCSP class. One band comprises two classes each of which contains students who are considered to be in the same range of general ability and who are expected to take higher-level subjects. The other band comprises three classes, each with students of a similar range of general ability who take predominantly ordinary level subjects. In Mathematics, students in the JCSP class tend to take foundation level. Students are assigned to base classes on the basis of pre-entry assessment and consultation with feeder primary schools. In second year, for Mathematics, the students from the two first year higher level groups are divided into one higher level class group and another class where both higher and ordinary levels are taught. Since mathematics lessons for first year groups are timetabled at different times, and the same occurs for second years, movement between levels requires a complete change of base class group. In third year, two of the five mathematics classes are concurrently timetabled, one is higher level and the other is ordinary level. This is good as it facilitates the changing of levels, when necessary, for the students who are in these classes. Mathematics classes in fifth and sixth year are concurrently timetabled, an arrangement which allows for flexibility in level choice for students. Since such flexibility is very important for students of Mathematics, it is recommended that the timetabling arrangements for Junior Certificate classes be reviewed and that every effort be made to introduce concurrent time-tabling of Mathematics for all groups taking ordinary and higher level as soon as is possible.
The mathematics department comprises fifteen teachers. School management decides on teacher allocation to levels in close consultation with the teachers. It is department policy that classes retain the same teacher from year to year. This is good practice. Levels are rotated between most members of the teaching team. This is very good practice as it will enable the school to maintain a high level of expertise in teaching higher level syllabuses and to meet the changing needs of the mathematics syllabus in the coming years.
Teachers make use of a wide variety of teaching resources. These are kept in a central location and are shared by the members of the teaching team. They include geometry equipment, sets of mathematics tables and books, calculators, geometrical shapes and handouts. ICT facilities can be accessed through the computer room and members of the mathematics department avail of these mainly for LCA lessons. Teacher continuing professional development (CPD) is facilitated by school management. Teachers are encouraged to attend in-service courses. Although there is no set budget for the mathematics department, requests for resources are favourably considered. Overall, the mathematics department is well supported within the school.
The JCSP is an option that is taken by students who, in general, benefit from a high level of extra support in school. Students in need of learning support are identified through discussions with feeder primary schools, results of pre-entry assessments, and ongoing teacher observation. Once identified students are then assessed to establish their individual level of need. To monitor progress, assessments are carried out again at the end of each year. Students are profiled so that their individual needs can be accurately met and it was reported that parents make a valuable contribution to this process. Support is provided by individual withdrawal from subjects other than Mathematics and the creation of smaller class groups, usually of JCSP students. Commendably, support is also provided through team teaching, where students experiencing difficulties can receive help with Mathematics during mathematics lessons from the learning support teacher. The school has created a well equipped resource room where students have regular access to a wide range of puzzles, games, and computer software all designed to support learning in Mathematics. Good communication exists between members of the learning support team and the mathematics department; this generally takes place on an informal daily basis. A very high level of support is provided, by the members of the mathematics teaching team and the learning support team, to students who find Mathematics challenging. This support is provided with great care and sensitivity and is warmly commended.
Formal planning time is allocated on school development planning days and staff council days. Regular subject department planning meetings are organised as required. Day-to-day planning takes place on an informal basis. The position of mathematics department co-ordinator rotates between members of the teaching team. Records are maintained of all formal meetings and minutes are kept. There is a strong spirit of team work between members of the mathematics department and they work together within a culture of co-operation and collaboration. It is evident that teachers routinely share ideas and discuss teaching methodologies. This is commended as it can be particularly beneficial to new teachers or teachers new to areas of the curriculum, for example LCA. The collaboration around classroom activity that currently takes place is commended and it is recommended that it be continued and built upon over time.
It was evident from the inspector’s review of planning documentation that school development planning has progressed to dealing with specific subject areas. The plan for Mathematics opens with the department’s aims and objectives. These are clearly central to school mathematics policy and there is evidence that progress is being made on the achievement of these objectives. The plan contains details of the mathematics department’s policy on: allocation to levels, learning support, assessment, homework, and the needs of students for whom English is an additional language. Lists of effective teaching methodologies, resources available and in-service courses attended are also included in the planning document. It is clear that good progress is being made on planning.
The plan contains schemes of work for each year group. These consist of lists of topics to be covered within the year. It is recommended that consideration be given to co-ordinating the schemes for higher and ordinary levels in each year group so that the same topics are studied by students of both levels at the same time. This would ensure that students who need to change class group have covered the same course material as the students of the group they are joining. Approximate timeframes for the covering of each topic should also be included in the planning document. This would help to ensure that adequate time is allocated to each part of the syllabus.
A high quality of teaching and learning was evident in the lessons observed. Lessons had a clear focus and were well structured in all cases. The learning objectives of each lesson were shared with the students at the beginning of all the lessons observed. Best practice in this regard occurs where the teacher writes the aims of the lesson on the board at the beginning of the lesson and then checks at the end to see if they have been achieved. It is recommended that teachers share the learning objectives in this way because it increases student motivation and leads to a sense of accomplishment on achieving the day’s goal. Continuity with previous lessons was maintained by the use of questioning to check learning and understanding thus linking lesson content with previous knowledge. All of this is good practice.
In all cases, the pace of the lessons observed was lively yet appropriate to the ability level of the students. A good mix of teacher example and student exercise was used to break up lessons and keep them interesting. Teachers, in most lessons observed, took advantage of higher-order questioning to encourage students to think for themselves and engage independently with their course material. This is commended since it helps students to develop the critical thinking and problem-solving skills that are essential for successful learning in Mathematics. The continued use of higher-order questioning is therefore encouraged and it is recommended that it be incorporated into all lessons by all teachers at every opportunity. Teachers, in all cases, achieved a good balance between teacher input and student activity. This facilitated the high levels of student participation and engagement evident in the lessons observed. Teachers have commendably created stimulating learning environments where students experience success at Mathematics and can develop an appreciation for the subject.
In some of the lessons observed handouts were used to supplement the text book. In all cases these were well chosen and were supportive to learning. For example, in one lesson observed the handout chosen guided the students in an experiment to test the veracity of Simpson’s rule. The students were expected to find the area of a circle using the traditional formula, then using Simpson’s rule and to compare the answers. The instructions on the handout were very clear and easy to follow; this allowed the students to explore the concepts of the lesson independently with individual help from their teacher, where necessary. This handout was very supportive of learning as it facilitated students in gaining a deeper understanding of the uses and usefulness of Simpson’s rule. Teacher explanations were clear in all cases and student questions were welcomed and answered with patience. Good presentation was modelled by teachers, and they were careful to include all the steps in worked examples. It was evident that this attention to detail is reflected in student work. These high standards are therefore commended.
In one lesson observed the students were expected to work through a trigonometric proof. Wisely, the teacher carefully warned against the memorising of such theorems. This provides an example of good practice in the teaching and learning of theorems. Through the geometry section of the Junior Certificate course it is possible for students to explore the nature of absolute mathematical proof. This section of the course also provides students with a valuable introduction to the rigours of logical argument. It is therefore very important that students be allowed plenty of time to work through geometry theorems in the junior cycle and to gain as full an understanding of their mathematical significance as possible. There was some evidence that inadequate time was allocated to allow a comprehensive study of a small number of theorems and it is recommended that more time be allocated to the study of geometry in future planning.
It was evident from the review of student project work that active methodologies are employed by some teachers. One class group visited had completed projects on geometry and the resulting work was proudly displayed on the classroom wall. Another class group had used data from outside the classroom to form bar charts and the finished projects were also displayed on the classroom wall. Engaging in project work provides students with opportunities to enjoy Mathematics and to experience pride in their work. Some students also have regular access to ICT in teaching and learning in Mathematics, through the use of appropriate mathematics software. This was particularly evident in the JCSP classes visited as the use of active methodologies is central to the ethos of the JCSP. Since the employment of active methodologies is beneficial across all ability ranges, it is recommended that, where appropriate, active methodologies are more widely incorporated into mainstream class groups.
The evident good rapport that exists between teachers and students allows for the development of supportive learning environments where students can engage with Mathematics with confidence. Students respond positively to the very encouraging and affirming manner of their teachers. High expectations are set for students and they respond accordingly, consequently students are able to demonstrate an enthusiasm for and an interest in Mathematics.
It is evident from the review of student copybooks that the standard of student work is high and that students are making very good progress in Mathematics. Teachers routinely monitor student work and encourage students to maintain good presentation. This is good practice. Homework is set regularly and corrected promptly in all cases. Some teachers are taking advantage of this valuable opportunity to use comment-based marking. This is commended as it provides students with critical feedback, allows for self-correction and can be a source of positive reinforcement. It is therefore recommended that the use of comment-based marking be extended to all classes. Information on assessment for learning practices is available on the NCCA website (www.ncca.ie).
Formal examinations take place for all students at Christmas. First, second and fifth year groups have an additional assessment at Easter and sit formal examinations in May. Third and sixth year groups also sit ‘mock’ examinations. It is commended that students who will receive reasonable accommodations in their certificate examinations will also receive them for their ‘mock’ examinations. This is very good practice as it ensures that student experience in the certificate examinations is accurately reflected in the ‘mock’ examinations. Reports are sent home on foot of all formal assessments and parent teacher meetings take place annually.
Prizes are awarded for achievement and improvement in Mathematics. Students are encouraged to take part in the PRISM Maths Challenge. In past years students have been involved in training for the International Mathematical Olympiad. Participation in Mathematics related extra-curricular activity is very good practice as it raises the profile of Mathematics within the school and enables students to experience Mathematics for pleasure.
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:
timeframes should be included for the covering of each topic.
Post-evaluation meetings were held with the teachers of Mathematics and with the principal, and deputy principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published January 2009