An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Gaelcholáiste Mhuire (AG)
An Mhainistir Thuaigh, Corcaigh
Roll number: 62531H
Date of inspection: 20/21 October 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Gaelcholáiste Mhuire. 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 mathematics team is large, with seven teachers, the majority of whom are subject specialists, involved in the teaching of the subject in the current year. First-year students are taught in two mixed-ability groups. This is good practice as it allows students time to complete the transition from primary school and to adjust to the pace and content of mathematics lessons at post primary level. In the context of the school it has allowed for the gradual introduction of Irish mathematical terminology and allowed students to adjust to Irish language instruction in the subject. Both groups have been taught by the same teacher for a number of years.
In most year groups two mathematics classes are created. In the current year there is a third group in fifth year and in second year. Second year classes generally follow the higher level syllabus. In the current year a third smaller class group has been created. Students wishing to follow the ordinary level syllabus are catered for during three of their five mathematics lessons. Such ongoing review of student needs and adjustment of provision is good practice.
In second, third, fifth and sixth years, mathematics classes are timetabled concurrently. This allows for the creation of level-specific classes and students can follow the highest appropriate level for as long as possible while still retaining the option of changing level. For students wishing to change level parental consultation with their class teacher is required before the change is permitted.
Teachers are assigned to classes and levels by school management following an annual consultation process. It is 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. Currently Leaving Certificate higher level is the responsibility of one senior member of the teaching team while at junior cycle levels are rotated among a wider group of teachers. To take advantage of the experience built up over the years and to retain the high degree of teacher expertise at higher Leaving Certificate level, it is recommended that rotation of levels within senior cycle be gradually introduced.
The time allocated to Mathematics at both junior cycle and senior cycle is appropriate to syllabus requirements. Junior cycle classes have five periods, generally of forty-five minutes duration, each week. In one instance a class has a different mathematics teacher for one of their lessons each week. It is suggested that this practice be avoided, if possible, in future years as this does not facilitate continuity of approach.
TY classes have four periods of mathematics each week. Senior cycle classes have five periods each week and, in the current year one of the fifth year ordinary level classes has an extra class period.
The main resources used in the teaching of Mathematics are the textbook and whiteboard. Teachers have access to overhead projectors and the school has recently installed an Interactive Whiteboard in one of the classrooms. Some teachers availed of training in its use. Apart from TY classes there is little evidence of the use of information and communication technology (ICT) in the teaching of Mathematics.
Teachers are facilitated to attend inservice and it was reported that some mathematics teachers have availed of inservice offered by the Mathematics Support Service (MSS). Furthermore, it was reported that some teachers are members of their subject association.
Students from the school have participated in mathematics related classes and activities, organised by UCC, in the past. It is suggested that the opportunities offered by currently available competitions such as the Team Maths Competition, the Irish Junior Mathematics Competition for first-year students, Problem Solving for Irish Second Level Mathematicians (PRISM) competitions and Maths Week activities should be explored. Such national mathematics competitions and activities have the potential to engage and encourage students and raise the profile of the subject.
The school’s management currently undertake an analysis of the school’s performance in the Certificate Examinations in Mathematics in relation to achievement and uptake levels and compare them with national norms. This is good practice as such analysis can be helpful in informing future planning and provision for the subject.
A mathematics department structure has existed in the school for the last three years. It is co-ordinated on a voluntary basis by a member of the team. The role of co-ordinator has rotated among members of the team on an annual basis. This system is encouraged as it will allow each member of the team to gain a deeper understanding of the issues involved in the workings of their subject department.
Formal planning and review meetings are scheduled for subject departments during the school year. Records are kept of such meetings and show evidence of ongoing collaboration and review among Mathematics teachers. The current schedule of meetings lists four half hour meetings to take place before the end of the year. Records of previous meetings show that among the items discussed by the team were the organisation of common assessments, division of students within the year groups, schemes of work for classes and a review of examination results.
Individual teachers have created plans for the classes they currently teach but subject department planning is in the early stages of development. Some documents relevant to the teaching of Mathematics are kept in a subject file. These include the Leaving Certificate and Junior Certificate syllabuses. The NCCA publication Junior Certificate Mathematics-Guidelines for Teachers should be added to the documentation in the subject file. This contains useful advice in the appendices regarding resources and planning, along with other areas of good practice in the teaching of Mathematics. It may be found in the Junior Certificate subjects section of the NCCA website at www.ncca.ie. The current plan also contains aims and objectives of mathematics teaching in the school along with some organisational details and an analysis of student results in the certificate exams. It is recommended that the subject plan should continue to be developed. The immediate focus of the subject planning process should be on the development of current yearly plans with the aid of ICT. These plans should be common plans which are syllabus-based, with clear learning goals and possibly time linked. This will provide a clear focus for teaching and assessment activities. The work already done by teachers can form part of this process but care must be taken to ensure that all mathematics teachers have an input to all sections of the plan.
The Transition Year plan for the school has been reviewed and updated for the current year. This is good practice as it allows the TY mathematics teacher to devise a programme that takes into account the needs and abilities of the students who choose to follow the TY programme. There is a good balance between topics that consolidate the prior learning of students, some elements from the Leaving Certificate programme and other topics, including suggestions from the MSS inservice on TY.
All teachers made individual planning notes and materials available for inspection during the visit; these typically included an annual scheme of work and in some cases student handouts, worksheets, acetates, and test/examination questions and solutions. There were some very good examples of extensive teacher notes and of more detailed schemes of work.
Irish is the language of instruction in mathematics lessons. Many of the students do not come from an Irish-language-primary-school background. The importance of the transition to instruction and learning through Irish is recognised within the school. During first year students are steadily introduced to terminology and teaching through Irish.
In lessons observed, teachers’ preparation for teaching was evident and their presentation of work was generally clear. Students, though passive, were engaged and attentive to their work. Classroom management was good and students were kept on task. There was a sense of mutual respect between teachers and students, creating a positive atmosphere conducive to learning.
In almost all classes visited, lessons were well structured and purposeful and there was evidence of good short-term planning. Clear objectives were set for lessons and the lessons progressed at an appropriate pace with good use being made of time. Where this was not the case, the review of an assessment and the correction of homework resulted in valuable teaching time being eroded and student not being challenged during the lesson. All lessons should contain an appropriate balance between review, instruction and student activity.
Textbook and examination papers were the main resources used during lessons observed. Teachers use the textbook as a source of examples and in some lessons good use was made of handouts. In some lessons very good use was made of the overhead projector (OHP) to illustrate a variety of examples. The whiteboard was used effectively to record key words, important formulae and to model a template of presentation of work for students.
The predominant methodology used in lessons was traditional whole-class teaching. Lessons generally began with the correction of homework by the teacher at the board. This was followed by the teacher demonstrating to the class and then the students working alone on tasks while the teacher assists individuals. Students would have benefited from a variety of methodologies in lessons. For example the use of strategies such as pair work, investigation, consolidation activities, practical work, discussion, group work and quiz activities would have enhanced learning. It is therefore recommended that teachers review methodologies used in lessons and add greater variety to their approaches.
In general, teachers asked lower-order or recall type questions. Less frequently, teachers built on students’ knowledge by encouraging them to explain and justify their thinking and methods. This practice encourages students to be more active in their own learning and places greater emphasis on problem analysis. It is therefore recommended that a varied range of questioning strategies be used to ensure that a combination of lower and higher-order questions is employed in classes.
Examples of good practice in mathematics teaching observed in Gaelcholáiste Mhuire included the use of clear methods in arriving at solutions, an emphasis on clear presentation of work, the appropriate use of mathematical language by teachers and students, ongoing review of terminology and concepts, the use of ICT and attention to individual students.
Teachers had good knowledge of their students’ abilities and there was evidence that teachers set high standards and students strove to achieve them. Students demonstrated a clear understanding of concepts engaged with during the lessons in interactions with the inspector. They were able to answer questions posed to them in a confident manner and justified solutions to questions posed to them. They made relevant connections between topics and used mathematical terminology appropriately. Learning was also evident as students capably applied procedures, taught in class, to similar type problems set during lessons.
Classrooms visited did not have displays of students’ work or of mathematical posters which would have enhanced the visual learning environment. The display of such posters and students’ project work can be effectively used to remind students of key mathematical concepts, formulae or terminology. It is suggested that more use be made of students own work, through projects or examples of high quality work to motivate students.
Students generally have a hardcover copybook for Mathematics. Class work, class notes and homework are all retained in this. This is good practice as the copybook then becomes a valuable resource for student as it contains a template for procedures to be followed while doing homework and a source of examples during revision. An examination of a sample of mathematics copybooks and notebooks during the inspection showed work that was appropriate, relevant and generally well presented. There was evidence of monitoring of students’ work by teachers and students were encouraged to review and correct their own work. The emphasis placed on the clear presentation of work by teachers during lessons was reflected in the work done by students.
Homework has an important role in the learning process and was assigned in lessons observed. The homework was appropriate in terms of the quantity and relevance to the work done during the lesson. Students’ copies and journals revealed that regular homework is assigned which is good practice.
Assessment of student progress is carried out on an ongoing basis through questioning in class, homework and written examinations following the completion of a topic. The two first year classes are commonly assessed and common assessment within levels also occurs in other year groups.
Parents receive a report on student progress twice each year following assessments. All non-exam classes are continually assessed during the first term through a series of topic tests and have formal assessments at the end of the school year. Examination classes are also assessed on an ongoing basis during the first term and then sit the “mock” exams during the second term. Teachers keep a record of the achievement of their students in these assessments. A report is issued to all parents at the end of the first term and a further report is issued following the ‘mock’ exams or following the summer exams as appropriate.
A parent-teacher meeting is held for each year group during the school year. Individual meetings between teachers and parents are arranged as appropriate during the year.
The following are the main strengths identified in the evaluation:
· There was evidence of monitoring of students’ work by teachers and students were encouraged to review and correct their own work.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
Published, November 2009