An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Ballyshannon, Co. Donegal
Roll number: 91506V
Date of inspection: 28 September 2006
Date of issue of report: 21 June 2007
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Coláiste Cholmcille, 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 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 Coláiste Cholmcille, Mathematics is concurrently scheduled throughout third, fifth and sixth year, and within two bands in second year. Such an arrangement is in line with good practice and, given the many and varied demands on the timetable, shows the commitment of the school to providing the appropriate structure within which the subject can flourish. It comes under the remit of school management to assign teachers to class or year groups; from second year on, however, assigned teachers agree who will teach at each level. Leaving Certificate higher level is currently shared between two teachers. It is policy to maintain continuity for students by keeping the same teacher with a class group from second to third year, and from fifth to sixth year.
The allocation of teaching time to Mathematics at senior cycle is good with Leaving Certificate classes having twelve periods per week over two years, Leaving Certificate Applied classes having nine periods over the same time frame, and Transition Year classes having three periods each week during their year of study. At junior cycle, thirteen periods over three years is slightly less than expected; an additional period in either first or second year would ease pressure on course coverage.
The commitment of teacher resources to Mathematics is commended, with additional class groupings established in two year groups in the school, allowing the formation of smaller classes with the potential for greater attention to individual students. The representations made by the Mathematics teaching team in this respect and the responsiveness of school management to such requests are acknowledged.
In the school, first year Mathematics classes are taught in mixed ability settings, commendably allowing new students settle in and demonstrate their mathematical potential prior to decisions being made regarding level of study of the subject. At the end of the year, classes at higher and ordinary levels are formed, following common assessments and teacher advice. Formation of classes at different levels for Leaving Certificate studies is predominantly based on student choice. It is in line with good practice that students are encouraged to study Mathematics at the highest level possible for as long as possible. However, an analysis of students’ performance over the last four years indicates that a significant number, of their own choice, may be taking the subject at an inappropriate level. It is recommended that the subject department, in conjunction with the school’s Guidance department, continue to address this issue, perhaps through the dissemination to students and their parents of information regarding the status of foundation level Mathematics with regard to career choices and further study. In particular, the acceptance of the level for matriculation purposes should be understood.
It is policy within the Mathematics department to maintain numbers in classes following the ordinary level syllabuses as low as possible, so as to allow the best possible attention for students experiencing difficulty in the subject. In addition, students identified as finding Mathematics particularly challenging are offered supplementary tuition in small groups. Such tuition is usually available on a weekly basis and, when possible, provided by a member of the Mathematics team.
Additional tuition for students studying the subject at higher level has been offered for many years, on a voluntary basis and outside of regular timetabled hours. There was also evidence of teachers of students struggling with the challenge of ordinary level making additional time available to them. Such commitment is recognised and applauded.
Information regarding opportunities for teachers’ continuous professional development is communicated to members of the Mathematics team and there is a link between the team and the Irish Mathematics Teachers’ Association (IMTA). Teachers are encouraged to continue to attend courses available, either specifically in Mathematics or in relevant general areas, where possible and appropriate. Information regarding courses attended could be recorded for immediate and/or future dissemination among the members of the Mathematics team.
In recent years, the school has undertaken two projects aimed at promoting learning in Mathematics; “maths for fun” is activity-based and aimed at selected first year students, showing them that Mathematics can be enjoyable; “maths for first year parents” is a refresher course for parents who want to be able to understand and assist their children in their first year of second-level school. The benefits to be gained from such initiatives should not be underestimated and the school, and in particular the Mathematics teachers involved, are commended on their foresight and vision in this regard. Other co-curricular mathematics activities promoted within the school include student participation in the Irish Mathematics Olympiad and the Mathematics quiz for first year students organised by the IMTA.
The Mathematics department is co-ordinated on a voluntary basis by two teachers sharing the workload. It is intended that the position will rotate among members of the team, but discussions have not as yet taken place regarding an agreed term of office. Meetings of the department take place both formally and informally; formal meetings occur usually in conjunction with whole school planning activities when time is made available to teachers; informal meetings take place, as necessary, outside of timetabled hours. Commendably, minutes that are kept of meetings show clear evidence of collaborative planning and review among the Mathematics teaching team. Minutes also show that an analysis of Certificate examination results for recent years has been carried out and both the Mathematics team and school management are aware of the school’s standing.
The Mathematics team have made significant progress in planning. The commitment and effort involved in producing the department plan, in keeping with School Development Planning Initiative guidelines, are acknowledged and are a solid basis for continued departmental collaboration.
The planning document includes aims and objectives for mathematics education within the school, homework and assessment procedures, agreed programmes of work for year groups, programmes and levels, and a description of subject provision for students with special educational needs. Suggested ways in which to progress the department’s planning activities are as follows: firstly, individual education plans (IEPs) included in the department plan currently benefit from informal discussions between the specialist teacher and the Mathematics department. It would now be appropriate to formalise and acknowledge such input in the plans themselves. Secondly, when teachers review the first-year programmes of work, a need for an increase in pace may be indicated; skills in basic arithmetic are refreshed with students on entry to Coláiste Cholmcille and topics including fractions, decimals, divisors, multiples and percentages are covered in the primary school syllabus. Finally, and in the medium term, consideration should be given to expressing programmes of work in terms of learning outcomes – what students will be able to do on completion of a body of work – instead of as lists of content.
A number of teachers made individual planning and preparation materials available during the inspection. These included attendance and assessment records, copies of class tests, and teacher notes, some of which were commendably extensive.
The Mathematics department has a range of resources to support the teaching and learning of the subject, including demonstration geometry sets, laminated posters, overhead projectors, dominoes and Tangrams. While the department itself does not manage a budget, such resources are obtained, on a needs basis, through requests made to school management.
In lessons observed, teachers’ presentation of work was generally clear and preparation for teaching was evident. Students were attentive to their work and there were occasions when enthusiasm for and interest in the subject were apparent. Classroom management was effective and appropriate and students were kept on task. There was a sense of mutual respect between teachers and students, creating an atmosphere that was conducive to learning.
Generally lessons began with the correction of homework. Textbooks and worksheets were the main resources used during lessons, although there was one commendable example of a real-life prop being used to illustrate a new concept. Some classrooms visited had displays of mathematical posters, enhancing the learning environment and reminding students of key mathematical concepts or formulae.
The predominant methodology used in lessons observed was traditional—teacher presentation of work at the board followed by the setting of work for individual student practice. While teachers reported the use of other methodologies in lessons not observed it is, nonetheless, recommended that an expanded range of teaching methodologies be used, along with supporting materials, in recognition of students’ different preferred learning styles.
The pace of lessons observed was generally appropriate. Where this was not the case, the objective or learning intention was unclear. It is recommended that all lessons have a clearly defined objective, one that appropriately challenges students of all abilities, and that the objective is explicitly communicated to the learners. Optimal practice would then see each lesson end with a review of the achievement, or otherwise, of the stated objective.
Teacher-student interaction typically took the form of brief answers to questions posed to individual students or to the class group on finding the next steps in a solution. While there was varied and acceptable practice with regard to the addressing of questions to individual students and/or whole class groups, there were some cases where directing questions at named students would have been more appropriate as a means of checking students’ levels of understanding of particular concepts. There were also some good examples of teachers encouraging students to justify their methods, and, in one instance, of the posing of open questions to challenge students to probe new material being presented.
Examples of good practice in Mathematics teaching observed in Coláiste Cholmcille included the use of clear methods in arriving at solutions, the appropriate use of mathematical language by both teachers and students, ongoing review of terminology and concepts, and high levels of attention to individual students.
Teachers’ main methods of assessing students’ progress are through regular chapter/topic tests and term examinations. Some classes of the same levels receive common tests and it is acknowledged that teachers are continuing to develop policies and practices in this regard.
Grades on written reports issued to parents/guardians at the end of the first term are formulated from the average of grades achieved in class tests from September. This practice is applauded as it justifiably rewards students who work consistently hard throughout the term.
Progress in work covered in class and in study can be seen in student copybooks; an examination of a sample of Mathematics copybooks and notebooks at Coláiste Cholmcille revealed work that was appropriate, relevant and generally well presented. There was evidence of close monitoring of student copybooks, with, in some instances grades being given for effort. This is in line with the principles of ‘assessment for learning’ and is commended.
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 and deputy principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.