An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Douglas Community School
Roll number: 91396R
Date of inspection: 19/20 January 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Douglas Community School. It presents the findings of an evaluation of the quality of teaching and learning in Mathematics and Applied Mathematics and makes recommendations for the further development of the teaching of these subjects 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.
Douglas Community School is an all-boys school. First-year and second-year classes have four mathematics lessons per week and most third-year classes have five lessons. This is less than optimal provision. It was reported during the inspection that the possibility of increasing the provision for Mathematics at junior cycle was under review. This is positive and if possible, given timetabling and allocation considerations, the number of lessons in second year should increase to five. Transition Year (TY) classes have four mathematics lessons per week and this is good provision. Fifth-year and sixth-year classes have five mathematics lessons per week and this is adequate provision. The spread of mathematics lessons across the school day and the school week is good. Classes generally retain their mathematics teacher from second to third year and between fifth and sixth year. This is positive, allowing for the development of consistent teaching approaches with class groups.
Teachers are assigned to classes by management and there is generally rotation of levels within junior cycle. Currently three teachers are involved in teaching to higher level at TY and senior cycle. To retain the teacher expertise of teaching at higher level Leaving Certificate and to take advantage of the experience built up over the years within the team, it is recommended that further rotation of teachers to levels within senior cycle be gradually introduced.
Students wishing to study Applied Mathematics are accommodated within and outside of timetabled hours. Within the timetable, students are provided with two periods per week in both fifth and sixth year. A further three lessons common to both years are provided after school. While this provision is not ideal it is positive that the school is providing an innovative structure through which interested students can access the subject. All involved in this provision are commended.
The mathematics team is currently comprised of twelve teachers. This is large in relation to the size of the current student cohort. On a very practical level, for the facilitation of meetings, the development of collaborative work practices and for planning and review activities, a smaller team would be more appropriate. Therefore, it is recommended that the number of teachers in the mathematics team be reduced. This can be achieved over time through the development of a core team of mathematics teachers, each of whom is allocated significant contact time with the subject.
On entry to the school, first-year students are generally assigned to class groups, each containing a mixture of ability levels. One smaller class group is created to cater for the pace of students who find the subject challenging. For Mathematics, the majority of classes from second year onwards are re-formed to allow for the creation of higher and ordinary level groups. It is evidence of school management’s commitment to providing the most appropriate mathematics education for students that these classes, apart from one small class in second year and two classes in third year, are concurrently timetabled within year groups, from second year onwards. This formation of level-specific groups allows movement between levels, throughout students’ courses of study. Movement between levels is also facilitated by teachers’ ongoing monitoring of, and feedback on, students’ performance. This structure also facilitates a situation where students are encouraged to follow the highest level possible for as long as possible. In some instances, teachers make themselves available to provide extra tuition for higher level students after school. All involved in this provision are commended.
There is no budget for the mathematics department but requests for resources are favourably considered. Each teacher has access to necessary models and geometry equipment. Information and communication technology (ICT) facilities have been provided. Each mathematics classroom has been equipped with a data projector and laptop computer as an aid to teaching and learning. One classroom has an interactive whiteboard installed and plans are in place to increase this provision. Teachers have produced some ICT resources for use with their classes. This is positive. An innovative system is in place in the department where such resources are shared via email. Further resources could be accessed at the Mathematics Support Service (MSS) website www.slss.ie/maths and the Project Maths Development Team website www.projectmaths.ie.
The school is supportive of teachers’ continuing professional development (CPD). Some members of the team have availed of courses organised by the MSS and the Irish Mathematics Teachers Association (IMTA) in recent years. Those involved are commended. Mathematics teachers are encouraged to avail of the opportunities which membership of their subject association can afford them and which is currently funded by the school. Management is to be praised for its support of teachers’ professional development.
Students have the opportunity to participate in a range of co-curricular activities pertaining to Mathematics. In previous years, students have participated in the Problem Solving for Irish Second Level Mathematicians (PRISM) competitions, organised nationally as part of Maths Week Ireland. In the current year it is planned that students will again participate in the Irish Mathematics Teachers Association (IMTA) organised Irish Junior Mathematics Competition during first year and the Team Maths competition for Leaving Certificate students. Such activities help to raise the profile of the subject among students and provide an opportunity to experience Mathematics outside of the classroom. All involved in their organisation are praised.
Students who find the subject particularly challenging are identified through pre-entry assessments, contact with local primary schools and support personnel and teacher observation and assessment during first year. As stated previously, a small class group is created in first year and is continued in second and third year. Assistance for students in these classes is through in-class support. This is good. This support is provided through the timetabling of other members of the mathematics team for some lessons along with the timetabled teacher. This is positive. Similar support is also available for TY and fifth-year classes where necessary and possible. It is suggested that, in the coming year, the team might consider the possibility of having two teachers timetabled fully with one class group to assess if this model of team-teaching would enhance the current good practice in catering for the cohort of students with special educational needs.
Management and the mathematics department have monitored recent student performance in the certificate examinations. A detailed analysis of results indicates that uptake rates at higher level are in line with national trends. The team has also identified low grades achieved at ordinary level as an area to be addressed. Such ongoing review will positively contribute to planning activities within the department.
Planning and Preparation
There is a subject convenor for Mathematics. The current convenor was appointed at the beginning of the current school year. However, there is presently no agreed structure for the appointment to, or term of, the position. It is recommended that the duties of convenor be agreed by the department and written into the subject plan. It is further recommended that the role of convenor would rotate between the members of the team, perhaps on an annual basis. This good practice will enable all team members to experience developments in mathematics teaching and learning and to become aware of the issues that arise in organising a subject department.
There are up to six formal, scheduled meeting of the mathematics department during the course of the school year. Informal meetings are also held throughout the rest of the school year. The potential for full formal meetings of the mathematics department is somewhat hampered by the large number of teachers involved in the teaching of the subject and their involvement in other subject areas. The good practice of keeping electronic records of formal meetings and subject plan has been adopted.
It is suggested that agendas of team meetings be expanded to include a time for sharing feedback from CPD courses attended and input from teachers who may have information on the correction of state examinations. It is also suggested that time be set aside at meetings for teachers to discuss teaching approaches and methodologies used. This is particularly relevant as it is reported that a group of the mathematics teachers are beginning to implement aspects of Assessment for Learning (AfL) in their teaching.
Good progress has been made in the development of the mathematics department plan. The current plan contains a mission statement for the department and aims and objectives for mathematics education in the school. It also includes organisational details, cross-curricular planning, resource lists and long-term plans for each year group and level in the form of topics to be taught per term, details of homework, assessment and reporting procedures. It is recommended that, over time, the topics listed in the plan be written in the form of learning outcomes to be achieved by the students. This could be accomplished by documenting this aspect of the AfL initiative mentioned previously.
There is a TY mathematics plan. The current plan consists of a list of topics to be covered during the year. The current list is confined to material currently on the Leaving Certificate syllabus. Circular M1/00, The Transition Year Programme, states that: “A Transition Year programme is not part of the Leaving Certificate programme, and should not be seen as an opportunity for spending three years rather than two studying Leaving Certificate material.” It is therefore recommended that aspects of the Transition Year programme for Mathematics be reviewed to ensure compliance with the circular. In planning such a programme for TY, it is important to ensure that there is a balance between topics that consolidate the prior learning of students, some work that introduces elements of the Leaving Certificate programme and other non-curriculum material. Ideally it should also reflect the underlying idea of ‘doing maths differently’. It is recommended that the plan be reviewed to reflect the possible use of innovative teaching methodologies, project work, assessment by portfolio and the introduction of non-curriculum material.
There is a comprehensive Applied Mathematics plan. The plan has aims and objectives for Applied Mathematics education in the school, organisational details, cross-curricular planning, teaching methodologies and curriculum content, by term, for the separate and joint lessons.
All mathematics teachers made individually prepared planning and preparation materials available for review during the inspection visit. Included in these were the department plan broken down into detailed weekly and monthly work plans, prepared worksheets and transparencies, homework records, students’ attendance and assessments records and mathematics support-service material. These levels of preparation are acknowledged and commended.
Lessons observed were purposeful and content was appropriate to syllabus and level. The presentation of work observed was clear and preparation for teaching was evident in almost all cases. In line with good practice, many teachers explicitly shared the learning objective of the lesson with students, increasing students’ motivation and involvement. It is suggested that this approach should be extended to all lessons. Teachers are further encouraged to conclude lessons with a plenary session that involves a student review of progress and learning during the lesson.
Lessons generally began with the correction of homework at the board. Following this, teaching was predominantly conducted through the presentation of work, in the form of examples, at the board followed by the setting of exercises for individual student practice. Within this traditional style, teaching was effective. This emphasis on procedures to follow, the ‘how’ of Mathematics, would benefit from the inclusion of more open discussion on the ‘why’ of Mathematics. Students, although passive, were generally attentive and engaged in the work at hand. Teachers were attentive to the needs of individual students and appropriately devoted class time to working with students who were experiencing difficulty. There was mutual respect evident between teachers and students and classroom management was good. Teachers set appropriate high standards of expectation for their students and, in the classes where this was observed, students responded to these expectations. This is positive.
To complement this teacher-directed, whole-class teaching style it is recommended that a wider range of teaching methodologies be explored and developed, to engage students more fully in their own learning. The incorporation of strategies in lessons to take advantage of students’ different preferred learning styles and the involvement of students more directly in their own learning can increase students’ motivation and understanding. Some possibilities might be the inclusion of more open questioning strategies, the use of student-generated questions, pair work, group work, investigation, practical work, discussion, consolidation activities, quiz activities and creative use of ICT. Encouraging students to explain how their answers, including incorrect answers, were reached can be used to extend their understanding and enhance learning. The courses and website of the Mathematics Support Service (MSS), the learning and teaching plans available on the Project Maths Support Service website and the publication Junior Certificate Mathematics Guidelines for Teachers, along with the experience of the members of the mathematics team, could also contribute to this goal.
Many examples of good teaching practice were observed during the lessons, including dealing efficiently with the correction of homework, engaging students through linking topic content to their own interests and experiences, affirming students’ contributions, making appropriate use of mathematics terminology, expecting appropriate terminology from students and monitoring of students’ work.
Students’ knowledge and understanding were generally good. In interactions with the inspector, most students ably and confidently answered questions put to them during the course of the visit, made relevant connections between topics and used mathematical language appropriately. Learning was also evident as students applied procedures, taught in class, to similar-type problems from the textbook or examination papers.
The school’s homework policy has been adapted to form an agreed subject-department homework policy which is implemented by the team. Appropriate homework was assigned in lessons, thus providing students with an opportunity to practise and consolidate mathematical concepts engaged with during the lesson. Students’ copies and journals revealed that regular homework is assigned, which is good practice and in line with the mathematics department policy. An examination of a sample of mathematics copybooks and notebooks revealed work that was appropriate, relevant and reasonably well presented. There was evidence that teachers are monitoring students’ copies.
In many instances, the monitoring by students of their own work in copybooks was not very evident. One of the purposes of the work of students and the efforts of teachers in the area of homework is to create a resource for students, capable of being used for independent learning and revision. Examples done by the teacher as a template of good practice and reproduced in the students’ copies should be clearly labelled as such. It is important that students have the correct version of each problem available in their copybooks, thereby creating a source of reference for themselves and helping them to develop as independent learners. It is, therefore, recommended that the team agree a policy on their expectations of students in relation to written work and that greater emphasis be placed on students having appropriate structures and the correct version of each solution in their copies.
The school maintains good communication with parents. Four school reports are issued for each student during the year. Assessment is carried out on an ongoing basis through monitoring of class work, questioning in class and a written examination at midterm, Christmas, Easter and summer. Certificate examination classes sit their ‘mock’ exams during the second term. In addition, a parent-teacher meeting for each year group is held annually. The student diary is also used as a means of communication between the school and home and vice-versa.
The team engages in some good practices in the area of co-ordination associated with the testing of students. Almost all first-year students complete the same end-of-term and end-of-year tests. Some term tests within levels in other year groups are also common. Common examinations enable comparisons to be made across the whole year group or level. They can also serve a useful purpose in informing students’ choice, or in providing advice to students in relation to levels.
The following are the main strengths identified in the evaluation:
· Teaching was effective.
· Teachers set appropriate high standards of expectation for their students.
· Students’ knowledge and understanding were generally good.
· Appropriate homework was assigned in lessons.
· The school maintains good communication with parents.
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.
Published, November 2009