An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
REPORT
Ballinrobe Community School
Ballinrobe, County Mayo
Roll number: 91462E
Date of inspection: 26 April 2007
Date of issue of report: 6 December 2007
Subject provision and whole school support
Summary of main findings and recommendations
Report On The Quality Of Learning And Teaching In MATHEMATICS
Subject inspection report
This report has been written following a subject inspection in Ballinrobe 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 the teachers.
Subject provision and whole school support
On entry to the school, first-year students are assigned to class groups each containing a mixture of ability levels. For Mathematics, classes from second year onwards are re-formed, creating higher and ordinary-level groupings. It is evidence of school management’s commitment to providing the most appropriate mathematics education for students that all classes are concurrently timetabled, within year groups, from second year onwards. This generally allows the formation of level-specific groupings and movement between levels, throughout students’ courses of study. Movement between levels is also facilitated by teachers’ ongoing monitoring of student performance and collegial cooperation. It is noteworthy that students are encouraged to follow the highest level possible for as long as possible.
Class groupings have, in general, relatively small numbers, with averages ranging from twenty to twenty-five students. This context is acknowledged when noting that no additional teachers are scheduled for Mathematics. This has led, however, to a situation where, in some year groups access to the full range of levels of the subject is hindered. Linked to this issue is the system by which supports for students identified as finding the subject particularly challenging are currently provided (see following paragraph). Consideration should be given to reviewing the structural arrangements for Mathematics so as to ensure the maximum possible access to all levels.
During the month of September, students in first year sit standardised tests as a means of identifying those in need of specific supports or interventions. Such students are also identified through communications with primary schools, parents and, in the case of Mathematics, the first-year mathematics teachers. Support is available in the form of withdrawal from class in a subject other than Mathematics and can range from one to six periods per week depending on need and available resources. Once students have decided on their choice of optional subjects (from second year onwards) there can be difficulties in finding suitable withdrawal periods. Tuition is undertaken by teachers who currently teach or have previously taught mainstream Mathematics, with each individual timetable prepared by the learning support co-ordinator. It can be the case, however, that support for a student might be divided among a number of teachers. Teachers involved receive guidance on suitable strategies and methodologies from the co-ordinator and it is the responsibility of each teacher to monitor the effectiveness of the intervention. In conjunction with the structural review recommended in the previous paragraph, it may be appropriate to realign the current model of support and consider forming additional mathematics class groupings within concurrently timetabled ‘sets’.
Over recent years, changes have been made to the mathematics curriculum at primary level, with implications for teachers and students alike at second level. It is recommended that subject-specific links be created with a selection of teachers of sixth classes in local ‘feeder’ schools. Members of the mathematics team could use the opportunities provided by such links to share information with their primary counterparts on course content, methodologies and approaches. As well as contributing to better mutual understanding among teachers it would be a valuable additional measure in easing the transition for students from primary to post-primary level.
School management allocates teachers to mathematics ‘sets’ and teachers agree levels at which to teach. At junior cycle, levels are rotated, with continuity maintained from second to third year (and fifth to sixth). Leaving Certificate higher level is currently undertaken by one teacher. Teachers are facilitated in attending professional development courses; notification of courses in Mathematics is passed to the subject co-ordinator who informs relevant teachers and seeks agreement on attendance. Three courses have been attended by three teachers during this school year.
It is commendable that students studying at higher level can be offered supplementary classes by teachers, outside of scheduled hours, on a voluntary basis. The dual commitment of teachers and students, who avail of the additional tuition in great numbers, is recognised and applauded.
Planning and preparation
The mathematics department in Ballinrobe Community School has been formally co-ordinated for the past two years, although the role was carried out in an informal manner for a number of years prior to that. It is intended that the position, which does not form part of a post of responsibility, will be rotated among members of the team, allowing each member to gain a deeper understanding of the issues involved in the workings of their subject department.
Formal meetings are scheduled at the beginning and end of the school year. Additional meetings, between dedicated groups of teachers teaching within the same year group, take place outside of scheduled hours. Records of these meetings indicate that, in line with good practice, the team works collaboratively on planning and review activities. At the end of the school year, a report is presented to the principal on the work of and issues discussed by the department throughout the year.
Commendable progress has been made on developing a mathematics department plan. This is in line with School Development Planning Initiative guidelines and includes the school’s mission statement, aims and objectives for Mathematics, details of the way in which the subject is organised and professional development courses attended by team members during the current school year. It is recommended that advantage be taken of the wide range of subject backgrounds of teachers within the department to plan for strong cross-curricular links.
Long-term planning has been addressed through the discussion and agreement of programmes of work for each year group and level in the school. To complement what has already been completed, it is recommended that these programmes of work be expanded in two ways. First, within each topic, key areas or skills for students to master should be identified and documented. Second, explicit links should be made between content areas and relevant active methodologies, furthering the sharing and implementation of sound professional practice among mathematics colleagues. There may also be a need to review the planned time allocation for certain topics, particularly at first year.
A majority of mathematics teachers made personal written planning and preparation materials available for review during the inspection visit. Included in these were records of students’ attendance and assessments, detailed schemes of work including ongoing review, samples of students’ written work, prepared worksheets, programme syllabuses and daily diaries of work completed in class. High levels of preparation are acknowledged and commended.
There is limited planning for the use of information and communication technology (ICT) and restricted access to ICT facilities was reported. However, the mathematics team is encouraged to explore relevant, available software packages and engage with their use through the normal booking system for access to computer rooms in the school.
Teaching and learning
The content of lessons visited was appropriate in all cases and in line with syllabus requirements and agreed programmes of work. Teachers’ presentation of work, using white board and/or overhead projector was generally clear and suited to the task. Teachers were prepared for their teaching and students were attentive and engaged in the work at hand. In keeping with the principles of Assessment for Learning, it is recommended that each lesson would have a structured opening, where the learning intention would be explicitly communicated, and a closing, where the achievement of the intention would be reviewed.
Teaching observed was predominantly conducted through the presentation of work at the board followed by the setting of exercises for individual student practice. To complement this ‘traditional’ approach, it is recommended that a broader range of teaching methodologies and materials be explored and developed. Their incorporation in lessons acknowledges students’ different preferred learning styles and takes advantage of a richer variety of learning opportunities for students. There was, in fact, one particularly laudable lesson where students were actively engaged in an activity prepared by the teacher and the resulting student enthusiasm was refreshing.
Classroom interactions often took the form of brief answers by students to questions posed by the teacher on finding the next steps in the solution to a problem. There were, however, in line with good practice, some cases of teachers using questioning to extend students’ understanding and to encourage the expression of mathematical ideas. This commendable practice can help students to consolidate their learning, maintain engagement with the topic and foster a problem-solving approach. It is recommended, therefore, that all teachers make more use of probing questions, appropriately challenging students and supporting them in developing the skills of mathematical thinking and communication.
There were commendable examples where teachers had appropriately high expectations of students’ capabilities, and in all cases students responded accordingly. Mutual respect between teachers and students and among students was observed.
Examples of good practice observed during lesson visits included teachers affirming students’ efforts, making appropriate use of mathematical terminology, encouraging students to explain how answers were reached, organising students to work in groups and taking specific measures to include all students in the lesson.
Assessment
Student progress is assessed through oral questioning, the assignment and correction of class work, homework and key assignments, class tests and term examinations. There was wide variety in the frequency of class tests, an issue that might be addressed through discussion and agreement on standard practice within the team. Teachers keep records of students’ attendance and achievements in assessments and progress is formally reported to parents/guardians following term and mock examinations, at parent-teacher meetings or in the course of individual appointments.
The good practice has been established of administering common term examinations to first-year classes at Christmas and summer. Such practice supports students in choosing the level at which to study Mathematics for the remainder of the junior cycle. Additional support is then provided through common tests for those classes following the higher level course in the first term of second year.
Analysis of students’ performance in the Certificate examinations focuses on the transition from junior to senior cycles. It is suggested that examination data available in the school and from the website of the State Examinations Commission (www.examinations.ie) be discussed, possibly along lines indicated during the inspection visit, thus maximising its potential for planning and review purposes.
Student copybooks provide ongoing insights into daily achievements in work covered in class and in private study. An examination of a random sample of student copybooks revealed work that was appropriate, relevant and generally monitored by teachers. However, its presentation was sometimes of a poor quality, displaying undisciplined working techniques that can lead to mistakes being made. It is recommended that teachers continue to impress on students the importance of presenting their work in a structured and orderly fashion as a means of assisting them in achieving their real potential in Mathematics.
Summary of main findings and recommendations
The following are the main strengths identified in the evaluation:
- All classes are concurrently timetabled within year groups from second year onwards, generally allowing the formation of level-specific groupings and movement between levels. Movement between levels is also facilitated by teachers’ ongoing monitoring of student performance and collegial cooperation.
- Supports, in the form of withdrawal from classes other than Mathematics, are provided for students who find the subject particularly challenging.
- Students studying the subject at higher level can be offered supplementary classes by teachers, outside of school hours, on a voluntary basis.
- The mathematics department is co-ordinated on a rotating basis. Meetings take place both formally and informally and an annual report is presented to the principal. Records of meetings indicate the team works collaboratively on planning and review activities.
- Commendable progress has been made on developing a department plan and long-term planning has been addressed through the discussion and agreement of programmes of work for each year group and level in the school.
- The content of lessons visited was appropriate in all cases and in line with syllabus requirements and long-term plans. Teachers were prepared and students were attentive and engaged in the work at hand.
- There were some cases of teachers using questioning to extend students’ understanding and to encourage the expression of mathematical ideas. There were also commendable examples where teachers had appropriately high expectations of students’ capabilities, and in all such cases students responded accordingly.
- The good practice has been established of administering common term examinations to first-year classes at Christmas and summer, and for those classes following the higher level course in the first term of second year.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
- Consideration should be given to reviewing the structural arrangements for mathematics, possibly realigning the current model of support intervention, so as to ensure the maximum possible access to all levels for all students.
- It is recommended that subject-specific links be established with ‘feeder’ primary schools as a contribution to easing the transition for students from primary to post-primary level.
- Agreed programmes of work for each year group and level should be expanded by identifying key areas and skills for students to master and by making explicit links between content areas and active methodologies. Both of these additions will further the sharing and implementation of sound professional practice among mathematics teachers in the school.
- Each mathematics lesson should have a structured opening, where the learning intention would be explicitly communicated, and a closing, where the achievement of the intention would be reviewed.
- It is recommended that a broader range of teaching methodologies and materials be explored and developed. In addition, more use should be made by all teachers of probing questions, appropriately challenging students and supporting them in developing the skills of mathematical thinking and communication.
- It is recommended that teachers continue to impress on students the importance of presenting their work in a structured and orderly fashion as a means of assisting them in achieving their real potential in Mathematics.
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.