An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics and Applied Mathematics
Saint Benildus College,
Stillorgan, County Dublin
Roll number: 60261R
Date of inspection: 29 November 2007
Report on the Quality of Learning and Teaching in Mathematics and Applied mathematics
This report has been written following a subject inspection in St Benildus College, Stillorgan, conducted as part of a whole school evaluation. It presents the findings of an evaluation of the quality of teaching and learning in Mathematics and Applied Mathematics and makes recommendations for the further development of the teaching of these subjects 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 stated goal of Mathematics teaching in Saint Benildus College is to provide the concepts and skills necessary for all students to cope with life’s challenges and to promote good practice and appreciation of Mathematics by all students. The structure of the timetable and the provision for the subject support this goal. All third-year, fifth-year and sixth-year classes are timetabled concurrently within their year group. Second year mathematics classes are arranged in two bands of three classes each and are concurrent within the bands. Transition Year (TY) classes are arranged in two concurrent bands of two classes each. This structure facilitates access to appropriate levels and movement between levels for all students. First-year classes are taught in mixed-ability groups. From first year on classes are streamed, although at senior cycle the higher level classes are formed on a mixed-ability basis. Lessons are either of forty or forty-five minutes
duration. Mathematics lessons for all classes are spread evenly throughout the school day and the school week.
The subject provision is good. All junior cycle classes have five periods of Mathematics each week. The TY classes have three periods each week. The provision for Leaving Certificate is five periods per week in fifth year and has increased to six periods in sixth year in recent years following requests from the mathematics department. School management is commended for this allocation and for its ongoing support for mathematics provision. In the current year, following an early review of student needs, an extra class group has been created in fifth year to allow a third smaller higher-level group to be formed. In sixth year, ordinary-level students, identified as finding the subject challenging, have been timetabled for two extra lessons during lunch time. Students wishing to study Applied Mathematics are accommodated within the timetable and have five periods each week in fifth and sixth year.
Students are encouraged to follow the highest level possible for as long as possible. It is school policy that pupils who wish to change level are required to have a parental consent form signed before being allowed to change.
Prior to entry to the school, prospective students sit an assessment in Mathematics and their performance is recorded. Student progress is then carefully monitored in first year. Students identified as having particular difficulties in the subject are then assessed again through the use of a diagnostic test. This is good practice. Those students assessed as needing support are assisted through withdrawal for small group tuition, from classes other than mathematics classes. There is close informal contact between the learning-support teacher and the mathematics teacher. Student progress is monitored and parents are informed. In second year, where the classes are streamed within bands, team teaching is used to provide support to students in one class group. Also, in second year and other year groups, efforts are made to have ordinary-level classes as small as possible. These are commendable measures to meet the needs of all students of Mathematics.
It is normal practice within the school for teachers to remain with the same class groups from second to third year and from fifth to sixth year, where possible, thus maintaining high levels of continuity. Teachers are assigned to classes by school management following a consultation process. There is some rotation of mathematics teachers between levels and cycles. This is positive. However, rotation has been somewhat limited up to this point, and it is recommended that senior management, together with the mathematics department, should examine the possibilities of a more fully rotational system. This is important, given the need to maintain a wide skills base in the teaching of all levels and cycles. Considerable experience and expertise have been built up by members of the mathematics department in the teaching of the junior cycle and in particular the senior cycle higher-level courses over a long number of years. This should be viewed as a strong foundation and resource upon which the induction of colleagues can be built.
School management facilitates and encourages attendance at continuous professional development (CPD) courses and postgraduate courses, and a number of teachers have availed of courses presented by the Mathematics Support Service (MSS) in recent years. The board of management provide a grant to any member of staff undertaking a postgraduate course. This is commendable.
While there is no specific budget for Mathematics, teachers have access to resources such as overhead projectors (OHP), laptops and data projectors. Reasonable requests for purchase of resources are granted. As teachers are not classroom based the good practice of having some laptops and data projectors connected and on movable stands has been adopted.
Currently the team for Mathematics comprises ten teachers. Two of these currently teach Mathematics to one class group only. It is suggested that, if possible, in future timetabling that these teachers be assigned more than one class group for Mathematics.
School management has provided training in the use of information and communication technology (ICT) and this training has been availed of by all staff. Classrooms have a broadband internet connection point. Currently ICT is sometimes used in the preparation of materials for use in mathematics classes but not as a teaching aid except in the case of the TY classes. The Mathematics department is encouraged to continue to develop the use of ICT in support of the teaching of Mathematics.
There is no subject convenor for Mathematics. Two senior teachers cooperate in the running of the department. It is suggested that the structure of the running of the department should be reviewed with a view to having the position of coordinator rotated, either singly or in twos, among the members of the team. This structure would allow each member of the team to gain a deeper understanding of the issues involved in the workings of their subject department. There is a formal meeting of the department at the start of the academic year, where programmes of work, in the form of chapters from the textbook, for each year group and level are agreed. It would be important for the mathematics teachers to also include references to syllabus content and intended learning outcomes, when drawing up their programmes of work. Minutes are kept of these meetings and this good practice should continue. It is reported that the mathematics teachers meet informally on a regular basis to coordinate common work covered, to plan common examinations and to facilitate the smooth running of the department on an ongoing basis. All involved are commended.
There is a subject plan for Mathematics. The plan includes a mission statement, overall aims and requirements for mathematics education within the school, reference to a variety of methodologies and resources, and a description of planning for students with special educational needs, organisational details and a list of textbooks to be used by each year group and level. This is in line with good practice and is commended. It is suggested that the further division of the current half-yearly plans into monthly or bi-monthly segments might prove useful as a further aid to common planning.
Almost all teachers made individual planning notes and materials available for inspection during the visit. These typically included solutions to textbook problems, student handouts, worksheets, acetates, records of homework given and test and State examination questions and solutions. There were some very good examples of extensive teacher notes and of the adaptation of the department work programme into a more detailed weekly plan including topics to be taught to specific class groups.
Teaching was predominantly conducted through the presentation of work at the board followed by the setting of exercises for individual student practice. Within this traditional style, teaching was effective, lesson content was appropriate and in line with syllabus requirements and agreed programmes of work. The presentation of work to students was clear and suited to the task, and teachers were well prepared for their teaching. Students were generally attentive and engaged in the work at hand. Teachers were attentive to the needs of individual students and devoted class time to working with students who were experiencing difficulty. There was mutual respect evident between teachers and students and classroom management was good.
To complement this teacher directed, whole class teaching style, it is recommended that a wider range of teaching methodologies be explored and developed, to engage students more fully in their own learning. The incorporation of such strategies in lessons takes advantage of students’ different preferred learning styles and incorporates the widely accepted benefits for students of being actively involved in their own learning. Having students as active participants in their own learning can increase student motivation and understanding. The courses and website of the Mathematics Support Service (MSS) and the publication Junior Certificate Mathematics Guidelines for Teachers along with the experience of the members of the mathematics team could all contribute to this goal.
Teachers are commended for setting appropriate high standards of expectation for their students. In the classes observed, students responded to these expectations. In first-year classes observed, the teachers’ board work was used as a model and template of good practice to encourage high standards of presentation in students’ work. In one instance, a notes copy was used by students to record notes and specific examples of work recorded on the board. In another instance, students took down the examples into their copybooks in a different colour. The high standard of presentation of students own work evident in their copybooks reflected the standard set and expected by the teachers concerned.
In one TY lesson observed, a PowerPoint show was used to engage student interest and direct their learning. Students’ learning was achieved through work in pairs on a related worksheet, where answers had to be agreed within each pair. The learning was facilitated by questioning of the pairs and by drawing the group together for whole class teaching at appropriate times during the lesson. Differentiation was achieved by having some more difficult questions prepared, as groups completed the original assignment.
Many other examples of good teaching practice were observed during lesson visits including engaging students through the use of concrete materials, affirming students’ contributions, making appropriate use of mathematics terminology, expecting appropriate terminology from students, and monitoring of students’ work. There was a commendable example of students being encouraged to explain how their answers, including incorrect answers, were reached to extend their understanding and enhance learning.
Students’ outcomes in terms of knowledge and understanding were generally good. Most students ably and confidently answered questions put to them during the course of the visit, were able to make relevant connections between topics and used mathematical terminology appropriately. Learning was also evident as students purposefully applied procedures, taught in class, to similar type problems from the textbook or worksheet.
Student progress is assessed through oral questioning, the assignment and correction of class work, homework, regular class topic tests and term examinations. First-year students receive two, common, formal assessments during the year. These assessments and results from topic tests are used to set students in second-year classes. Other common assessments occur within levels where appropriate in other year groups.
Staff members are well supported through the provision of teachers’ diaries. In almost all cases, teachers retain records of their students’ attendance and use the diaries to record student assessments and in some cases assigned homework is also noted.
Parents receive a report on student progress twice each year following assessments. Non examination classes have formal assessments at Christmas and summer. Examination classes are assessed on an ongoing basis during the first term and a report is issued in early November. A further report is issued following the ‘mock’ exams. A parent-teacher meeting is held for each year group during the school year. The student diary is also an effective means of communication between the school and home and vice versa. In some cases, parents are asked to sign corrected class tests as a further means of communicating student progress.
Homework has an important role in the learning process and was assigned in all lessons observed. Students’ copies revealed that regular homework is assigned which is good practice and in line with the mathematics department policy. An examination of a sample of mathematics copybooks and notebooks revealed work that was appropriate, relevant and generally well presented. There was evidence that teachers are monitoring students’ copies. Good practice was evident where teachers encourage students to correct and amend their work as this encourages students to develop as independent learners.
In some instances, in particular when board work was used to correct homework students whose work was correct were not challenged during that part of the lesson and valuable teaching time was eroded. It is recommended that the current range of strategies employed to correct homework be reviewed to ensure that the optimal balance between the value to students of having work corrected and the best use of teaching time is achieved. Some possible strategies to review homework include board work, prepared transparencies for the OHP, the use of PowerPoint, handouts with completed answers to questions, using comment based monitoring to direct students’ attention to errors and possible solutions and peer correction of work.
The mathematics department has monitored student performance in the Certificate Examinations and this information is used to inform planning. St Benildus College is justifiably proud of the uptake rates of its students at higher level in the State examinations and the results of all its mathematics students in the State examinations.
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 October 2008