An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Navan, County Meath
Roll number: 72010I
Date of inspection: 5 April 2006
Date of issue of report: 29 June 2006
This Subject Inspection report
This report has been written following a subject inspection in Beaufort College, Navan. 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 one day 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 principal and 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 the opportunity to comment on the findings and recommendations of the report; the board chose to accept the report without response.
The strong commitment to Mathematics by the management of Beaufort College is evident from the time and resources allocated to the subject. Currently, all classes have between four and six periods per week, averaging out for junior cycle classes at five periods, for senior cycle Leaving Certificate classes at five-and-a-half periods and for Leaving Certificate Applied classes at four periods (of Mathematical Applications) per week. This allocation of time is highly appropriate and meets the subject requirements. The organisation of class time sees classes occurring on each of the five days of the week for classes with five or more lesson periods and on four days of the week for those with four periods. This structure recognises the fact that Mathematics is hierarchical in nature, with new concepts building upon previous knowledge, and the fact that students require time to assimilate new ideas. The positioning of lessons is also well balanced, with each class group having a mixture of morning and afternoon periods throughout the week.
The commitment of teaching resources to Mathematics is highly commendable, with additional class groupings established in four out of the five year groups in the school; in the case of two year groups, an additional two class groupings have been established for Mathematics, allowing the formation of small or level-appropriate classes for students. Average class sizes range from ten at fifth year to twenty at first year, providing the opportunity for significant levels of attention for individual students.
First-year students are assigned to their Mathematics classes on the basis of incoming assessment results, with classes formed to accommodate students studying the subject at all three levels. The ‘streaming’ of students, while not appropriate in all situations, is, in this instance, good practice given the exceptionally wide range of abilities exhibited by students attending the school. Any possible disadvantages are offset by the fact that Mathematics classes throughout the school are concurrently timetabled within each year group. Therefore, the facility exists for students to change level, as appropriate. While students, in line with good practice, are encouraged to study Mathematics at the highest level possible for as long as possible, it is recommended that teachers, through regular monitoring, including the strategic use of common tests, maximise the potential of this facility and ensure that students are appropriately placed at all times.
The resourcing strategy for Mathematics outlined above is the main support provided for students identified as having particular difficulty with Mathematics. However, students identified as having special educational needs can avail of a programme of withdrawal from class for individual or small-group tuition, which may be in Mathematics, if appropriate to their needs. Additional supports are offered to students of higher ability through the NUI Maynooth Access Programme, which sees a number of students attend supplementary classes outside of school time. Extra tuition is also offered, on a voluntary basis, by some members of the Mathematics team. This commitment to the Mathematics education of all students is acknowledged and applauded.
Resources for the Mathematics department, as for other subject departments, are allocated on request to school management. Those currently used within the school to support the teaching and learning of Mathematics include specially developed worksheets for the computer and a range of learning support materials. Teachers of all year groups and levels are encouraged to identify other relevant resources and to acquire them for classroom use.
The allocation of teachers to Mathematics classes is the responsibility of senior management. Currently one member of the Mathematics team takes Leaving Certificate higher level. It is practice within the school for teachers to remain with the same classes through junior cycle and senior cycle, thus maintaining high levels of continuity.
Teachers are facilitated in accessing in-service courses; seminars provided by the Junior Certificate Mathematics Support Service (JCMSS) were attended by all relevant teachers and the Regional Development Officer for the Support Service visited the school. Teachers are encouraged to maintain contact with developments in Mathematics education through the JCMSS and to access relevant training whenever possible.
Currently, the work of the Mathematics department is not co-ordinated, and planning and preparation have taken place largely on an individual basis. In order to take full advantage of the strengths of the Mathematics team, it is recommended that a position of co-ordinator of Mathematics be introduced, thus helping to ensure the structured management of the collaborative planning process, including the addressing of challenges in the teaching of the subject. Consideration should be given to the establishment of the position on a rotating basis, thus allowing each member of the Mathematics team to gain a deeper understanding of the issues involved in the workings of their subject department.
It has not been usual practice for the Mathematics teachers to meet as a group; meetings to discuss particular issues such as special educational needs and preparations for inspection have, however, taken place. It is recommended that the Mathematics teachers identify and avail of opportunities for meeting. Furthermore, it is important in the interests of continuity and progress that records of discussions and outcomes/decisions of such meetings be maintained.
The Mathematics teachers drew up documentation in preparation for the inspection visit. The work involved in this task is acknowledged and the product is a good starting point for future departmental collaboration. An element of departmental planning includes agreeing programmes of work for all year groups and levels. These should be more than simply lists of topics, and should include the identification of key skills within topics, and methodologies and resources that can appropriately assist students in acquiring these key skills.
The teachers made individual planning notes and resources available for inspection during the visit; these included more detailed programmes of work, student worksheets, class tests and a variety of background materials.
The content of lessons observed was appropriate to syllabus and level, and teachers were well prepared for their teaching. Teachers’ presentation of work was clear and lessons were purposeful. Students were attentive to their work and showed an interest in achieving in Mathematics. In lessons where teachers had high expectations for students, students responded with high levels of engagement with the topic and higher quality responses to questions posed. A positive working relationship between students and teachers was evident in all classes visited and classroom management was appropriate and effective.
Teaching was mainly traditional in style; typically teachers presented work at the board and 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 to be gained from involving students more actively in their learning. Relevant resources and active methodologies can be accessed from many sources including the JCMSS, the publication Junior Certificate Mathematics Guidelines for Teachers and the Scoilnet website. Certain courses available through the Second Level Support Service, while not specifically for Mathematics teachers, also provide the opportunity for the exploration of a range of teaching methodologies.
Examples of good practice in Mathematics teaching included the use of clear explanations, the appropriate use of mathematical formulae, reference to mathematics in “real life” and the encouragement of student input into problem solving.
Teachers took advantage of small numbers in class to monitor the work of individual students and keep students on task and there were commendable levels of attention to individual students in all classes observed. In addition, teachers used questioning as a means of involving students in the lesson. There was varied and acceptable practice with regard to the addressing of questions to individual students and/or whole class groups, but there were some cases where directing questions at named students would have been more appropriate as a means of checking students’ understanding. In line with good practice, student effort was, in all cases, affirmed by teachers.
Student progress is formally and regularly assessed in class tests and term examinations and teachers maintain records of results obtained by students. 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 at Beaufort College revealed work that was appropriate, relevant and generally well presented. However, although there was clear and commendable evidence of teacher monitoring, students were not always marking their work. It is recommended that, in continuing to monitor students’ copybooks, not only would the completion and presentation of work be checked, but also that it has been marked right or wrong and that relevant corrections have been noted.
An analysis of students’ performance in the State examinations over the last four years indicates that a significant number may not be taking Mathematics at the appropriate level. Co-ordinated and systematic monitoring of student progress should be prioritised, and advice regarding the level at which the subject should be studied should be formalised, to both parents and students, as soon as a concern develops. Discussion and review of uptake rates and results should form a regular and natural part of the planning activities of the Mathematics department.
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.