An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
De La Salle College
Dundalk, County Louth
Roll number: 63891T
Date of inspection: 7 March 2006
Date of issue of report: 22 June 2006
This Subject Inspection report
This report has been written following a subject inspection in De La Salle College, Dundalk. 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. The board of management of the school 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 to this report.
The time allocated to Mathematics in De La Salle College, Dundalk is in line with subject requirements; five periods per week, predominantly of thirty-five minutes duration, are allocated at junior cycle and six periods of the same duration are allocated at senior cycle (excluding the Transition Year (TY) programme). However, the organisation of class time, leading to some class groups having contact with Mathematics on only four days of the week, is less than ideal. The learning of Mathematics is hierarchical in nature, with new concepts building upon previous knowledge, and students require time to assimilate new ideas, as well as adequate opportunity to practice and apply new learning under the guidance of teachers. Therefore, it is recommended that the scheduling of Mathematics lessons for each class group on each of the five days of the school week be prioritised.
Mathematics classes from second year onwards are concurrently timetabled within each year group, showing commitment to, and understanding of the requirements of the subject. This arrangement is to facilitate students in studying Mathematics at the most appropriate level and to facilitate their movement between classes of different levels. However, the school’s philosophy with regard to meeting the needs of all students sees teachers of all subjects assigned in such a way as to allow base classes of, on average, twenty to twenty-six students. In these circumstances the number of Mathematics class groupings in any year group is the same as the number of base classes in the year group with occasional consequent difficulties in accommodating students at three levels.
Students are encouraged to study Mathematics at the highest level possible for as long as possible. First-year Mathematics classes are banded, with individual classes being mixed-ability within the band, as appropriate. In second year, students choose between higher and ordinary levels, following teachers’ advice based on test results and observation. A commendable additional support to first-year students in making the correct decision is the fact that summer term examinations have common papers. It is notable that decisions regarding level of study remain in the hands of students and their parents and, even when teachers’ advice is not taken, students are accommodated in their choice.
The allocation of teachers to Mathematics classes falls within the remit of senior management. In consultation with relevant teachers, levels are rotated within junior cycle year groups and Leaving Certificate higher level is shared between two teachers. It is policy and practice within the school for teachers to remain with the same classes from first to third year and from fifth to sixth year, thus maintaining high levels of continuity.
Additional supports targeting students identified as having particular difficulty with Mathematics are available mainly through withdrawal from class for small-group tuition with a resource teacher, but also, in the current year, by the provision of additional timetabled lesson periods for one junior-cycle class group. It is commendable that specialist resource tuition in Mathematics is provided and that there is close liaison with mainstream Mathematics teachers. For students studying higher level, there can be informal additional lessons from individual teachers outside of timetabled hours, mainly for the purposes of making up for class time lost.
Resources for the Mathematics department, as for other subject departments, are allocated on request to school management. The range of resources currently available within the school to support the teaching and learning of Mathematics include demonstration geometry sets, volume sets, overhead projector, and demonstration calculator. These are stored in the Mathematics room or in the resource/learning support room, as appropriate, and are accessible to all Mathematics teachers. Internet access is also available.
The Mathematics room is situated in the senior area of the school and is scheduled predominantly for senior students. The physical environment within the room is supportive of teaching and learning in the subject, with posters and information, including that relating to careers in Mathematics. The teachers are encouraged to discuss and agree a plan of access to this room for all Mathematics classes, thus supporting junior as well as senior students in their studies.
Co-curricular Mathematics activities are available to students within the school; some of those with particular talent have participated in the Irish Mathematics Olympiad. The school is encouraged to continue such activities, possibly extending them to include quizzes run by the Irish Mathematics Teachers Association and/or the entering of Mathematics-based projects in the Young Scientist and Technology Exhibition.
Mathematics department activities are co-ordinated by a senior teacher and formal planning and review meetings are scheduled around staff meeting and school planning days. Records are kept of such meetings and they show clear evidence of ongoing collaboration and review among Mathematics teachers. Informal discussions between small groups of teachers also take place on a regular basis.
The Mathematics team have made commendable progress in planning; the department plan includes overall aims and requirements for Mathematics education within the school, outline programmes of work for each year group and level, reference to a variety of methodologies, and a description of provision for students with special educational needs, which is in line with good practice and is commended. To build on this solid foundation, a review of programmes of work should see them expanded to include not only lists of topics, but also key skills and key terms for students to know and understand. Resources, including software packages, to assist students in acquiring such key skills should then be identified and obtained by the Mathematics department. In addition, with regard to the overall department plan, consideration should be given to agreeing and formalising policies on, for example, student assessment, the assignment, monitoring and correction of homework, and the role of the calculator as a teaching and learning tool.
Care should be taken not to overlook the syllabus as the most important resource document for curriculum planning. The publications Junior Certificate Mathematics Guidelines for Teachers and Calculators: Guidelines for Post Primary Schools could also make a significant contribution to this area.
Almost all teachers made individual planning notes and materials available for inspection during the visit; these typically included student handouts, worksheets, acetates, and test/examination questions and solutions. There were some very good examples of extensive teacher notes and of the adaptation of the department work programme to specific class groups.
Teaching observed was traditional in style. Teachers presented work at the board and, typically, followed this with the setting of work for individual student practice. To expand on this traditional teaching style, it is recommended that a wider range of teaching methodologies be explored and developed, keeping in mind students’ different preferred learning styles and the benefits from actively involving students in their learning.
The content of lessons observed was in all cases appropriate to class and level and was in line with syllabus requirements. Teachers’ presentation of work was clear and lessons were purposeful. However, in order to ensure the goal of the lesson is, at all times, clear to students, it is suggested that teachers consider explicitly stating the lesson objective. Such a statement can increase student motivation and provide a sense of accomplishment on achieving the day’s goal.
Students were generally attentive in lessons and classroom management was, in almost all cases, appropriate and effective. There was often a good rapport between teachers and students and, commendably, an affirmation of student effort. In lessons where teachers showed high expectations for their students, the students responded appropriately.
Examples of good practice in Mathematics teaching included the encouragement of explanations by students, the recapping on previously covered work, the highlighting of cross-curricular links, and the acknowledgement of alternative methods in reaching a solution. There were also some good examples of the use of mathematical language by both teachers and students. Teachers are encouraged to refer, at every possible opportunity, to the use of Mathematics skills in ‘everyday life’ as a normal part of Mathematics class.
Student progress is formally assessed in class tests and term examinations and teachers maintain records of results obtained by students. The good practice of assessing students after each chapter or topic covered is normal practice for almost all Mathematics teachers in De La Salle College; it is recommended that this practice extend to all teachers as a matter of course. Common papers are prepared for first-year summer term examinations and are also used with other appropriate groups in an informal arrangement between co-operating colleagues. Parents/guardians are kept informed of their child’s progress in a range of appropriate ways, including twice yearly written reports.
Student copybooks provide ongoing insights into daily achievements in work covered in class and in private study; an examination of Mathematics copybooks revealed work that was appropriate, relevant and generally well presented. In many cases, there was clear evidence of teacher monitoring.
An analysis of uptake rates in the State examinations for the last four years indicates good participation at higher and ordinary levels. Mathematics teachers displayed an awareness of levels achieved in the State examinations and the school’s standing in this regard.
The following are the main strengths and areas for development 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 principal and with the teachers of Mathematics at the conclusion of the evaluation at which the draft findings and recommendations of the evaluation were presented and discussed.
Submitted by the Board of Management
Area 1: Observations on the content of the inspection report
The Board of Management recognises the positive tone of the report and the recognition of many commendable practices by the Maths Department. It is school policy that Mathematics lessons are scheduled for each school day and every effort is made to implement this policy within the increasingly complex timetabling demands. This was emphasised by the Principal at the post-evaluation meetings. The Report does not recognise the school’s commitment to this policy and its implementation.
Area 2: Follow-up actions planned or undertaken since the completion of the inspection activity to implement the findings and recommendations of the inspection