An Roinn Oideachais agus Scileanna
Department of Education and Skills
Subject Inspection of Mathematics
Christian Brothers Secondary School
Thurles, Co Tipperary
Roll number: 65450W
Date of inspection: 01 December 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in CBS, Thurles. 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 the 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.
Teachers are assigned to mathematics classes by management. In line with good practice there is rotation of levels within junior cycle. Currently two teachers are involved in teaching to higher level at senior cycle. In light of the current upward trend in enrolment and the expected increase in Leaving Certificate higher-level mathematics uptake as a result of the syllabus changes in Project Maths, it is recommended that further rotation of teachers to the higher level within senior cycle be gradually introduced. The practice, which has been introduced in the current year, of each teacher of the mathematics programme in Transition Year (TY) teaching a module to each group of students will begin to build capacity at this level. All involved in this initiative are praised.
Commendably, following a review, the time allocation to Mathematics is being increased. Lessons in the school are of thirty minutes or thirty-five minutes duration. In the current year both first-year and third-year classes have five periods of Mathematics each week while senior cycle classes have six periods. The TY grouping receives three periods of mathematics tuition each week. The allocation to second year has been increased to six periods in the current year and it is planned that the third year allocation will also increase to six in the coming year.
The spread of mathematics lessons across the school day is good. It is noteworthy that the mathematics lessons within each year group are timetabled concurrently. This is an encouragement to students to follow the highest level possible for as long as possible. Students who wish to change level are allowed to do so following a consultation process involving the school principal, the guidance councillor, the class teacher and parents. Transfers can then take place at specified times during the school year. Classes generally retain their mathematics teacher from second year to third year and from fifth year to sixth year. This is positive as it allows for the development of consistent teaching approaches with class groups.
There is no specific budget for the mathematics department but requests for the purchase of resources are favourably considered. Each teacher has access to a range of resources including whiteboard drawing equipment. A high level of information and communication technology (ICT) facilities has been provided. Each mathematics classroom has been equipped with a data projector and desktop computer as an aid to teaching and learning. Teachers have produced some ICT resources and accessed others for use with their classes. An innovative system is in place in the department whereby such resources are made available in an electronic folder on the school server and can be accessed in each classroom.
The school is supportive of teachers’ continuing professional development (CPD). Members of the team have availed of the Project Maths in-service in the current year. Members of the mathematics team have also visited another school in the region to learn about the teaching and learning in the subject. Those involved are commended. Mathematics teachers are encouraged to avail of the opportunities which membership of the Irish Mathematics Teachers Association (IMTA), can afford them and which is currently funded by the school.
Students have the opportunity to participate in 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 IMTA-organised 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 post-entry assessments, contact with local primary schools and support personnel, and teacher observation and assessment during first year. Commendably, senior management has prioritised the early identification of these students and also early intervention to support them. A small class group is created before Christmas in first year and is continued in second and third year. Assistance for students in these classes is provided through the small number in the group working at a pace appropriate to their abilities. Students are also supported through withdrawal for one-to-one and small-group tuition during times outside of their mathematics lessons. This is good. This support is provided by members of the mathematics team and there is informal communication between these teachers and the classroom teacher. It is suggested that, in the coming year, the team might consider the possibility of having two teachers timetabled fully with a class group to assess if this model of team-teaching would enhance the current good practice. Commendably, there is also a “maths support group” in first year and sixth year. This consists of groups of students who receive support in Mathematics at lunch time once per week. An interactive whiteboard is available to enhance this support.
At the beginning of second year, students are set into mathematics classes in order of ability on the basis of the results from their previous summer examinations. To exploit the correlation between levels of teacher expectation and levels of student achievement, and to take account of varying rates of student development, it is recommended that class formation for Mathematics be reviewed. It is recommended that students be divided into higher and ordinary level groups and that achieving mixed ability within these levels would be the main motivation in class formation. This would allow for the highest possible expectation for the greatest number of students.
Management and the mathematics department have monitored recent student performance in the certificate examinations. This detailed analysis of results has led to the objectives within the school of increasing the uptake rates at higher level and the elimination of low grades at ordinary level. Such ongoing review will positively contribute to future planning and teaching activities in Mathematics within the school.
There is a subject co-ordinator for Mathematics. The role of co-ordinator rotates between the members of the team on a biannual basis. This is good practice and 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 three 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 good practice of keeping electronic records of formal meetings and subject plan has been adopted.
It is suggested that agendas of future team meetings be expanded to include a time for discussion of feedback from the Project Maths in-service courses attended and input from teachers who may have information on the correction of state examinations. This would allow time for teachers to discuss teaching approaches and methodologies to be used in implementing the changed curriculum.
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, planning for students with additional educational needs, resource lists and teaching methodologies as well as details of homework, assessment and reporting procedures. The long-term plan for each year group and level is in the form of chapter headings from the textbook to be taught per half-year. It is recommended that, for the coming year, the planning initiated here should be developed to include the ‘common introductory course’ proposed as part of the Project Maths curriculum initiative. This should be integrated into the first-year section of the plan along with the other topics to be taught to first-year students. It is further recommended that the use of learning objectives within topics should, over time, be extended to all sections of the long-term plan.
It is good practice that a TY mathematics plan has been developed. The plan contains a list of topics to be covered during the year. The current list consists, in the main, of material currently on the Leaving Certificate syllabus. In planning 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. It is recommended that this plan be reviewed. Ideally the plan should reflect the possible use of innovative teaching methodologies, project work, assessment by portfolio and the introduction of non-curriculum material.
There was evidence of the sharing of teaching resources among the team. Teacher resources that were available for inspection in the folder included revision sheets and common tests. The shared folder on the school server contains resources that are available for use, and can be added to, by all members of the team. This is positive and can lead, over time, to a range of appropriate and topic-specific ICT resources being in place for the teaching of Mathematics.
The quality of teaching observed was good. Lessons were well planned and structured and content was appropriate to syllabus and level. Preparation for teaching was evident and the presentation of work was clear. In line with good practice, most teachers explicitly shared the learning objective of the lesson with students, increasing students’ motivation and involvement. Best practice in this regard would see the topic of the lesson expressed as a learning target to be achieved by the students. Teachers are further encouraged to conclude lessons with a plenary session that involves a student review of their progress and learning during the lesson. It is suggested that this approach should be extended to all lessons.
A feature of many of the lessons visited was the integration of ICT at appropriate times during the lesson. This is highly praised. On occasion this was accompanied by handouts or summaries of the ICT content.
Further examples of good teaching practice observed during the lessons included dealing efficiently with the correction of homework, affirming students’ contributions and efforts, engaging students through linking the lesson content to their own interests and experiences, and using, and expecting from students, the appropriate mathematics terminology. There are also instances where teachers are providing extra tuition to students outside of their timetabled hours and this is commended.
Lessons generally began with the efficient correction of homework at the board. Following this, although a range of methodologies was used, there was an over-reliance on teacher exposition and example followed by the setting of exercises for individual student practice. This emphasis on teacher explanations on procedures to follow, the ‘how’ of Mathematics, would benefit from the inclusion of more open discussion on the ‘why’ of Mathematics leading to students seeing their role as active participants in their own leaning. Students, although generally passive, were attentive and engaged in the work at hand. Teachers were attentive to the needs of individual students and appropriately allocated 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 appropriately high standards of expectation for their students and students responded to these expectations.
In the current year there are three TY class groups. It is planned that the groups will rotate between the three teachers over the course of the year. This is a positive innovation that will increase the teachers’ experience of teaching different material to groups and the students will also have an opportunity to experience different pedagogical styles over the course of the year.
Students demonstrated knowledge and understanding of topics engaged with during lessons. In interactions with the inspector, students confidently and competently answered questions put to them during the course of the visit, made relevant connections between topics, used mathematical language appropriately and applied their learning to problems posed in unfamiliar contexts. Learning was also apparent as students applied procedures, taught in class, to similar-type problems from the textbook or examination papers.
In some instances teachers have made efforts to enhance the physical working environment with a range of teacher-generated posters and samples of students’ work’ as a reminder of key concepts and to create a mathematically stimulating visual setting. This is commended and should be extended to all rooms where Mathematics is taught.
The school’s homework policy has been agreed for first-year and second-year students and is in the process of being developed for the other year groups. Appropriate homework was assigned in all lessons visited, thus providing students with an opportunity to practise and consolidate mathematical procedures learned during the lesson. In line with good practice, students’ copies and journals revealed that regular homework is assigned. 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.
The school maintains good communication with parents. Each month, parents of third-year, fifth-year and sixth-year students receive a report in which their son is given a score in each subject on his level of effort and commitment during the previous month. Ongoing assessment is carried out through the monitoring of class work, homework and questioning in class. Students also sit formal examinations at Christmas and summer, or in the case of certificate examination classes, ‘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 good practices in the area of co-ordination of the testing of students. Commendably all first-year students complete the same end-of-term and end-of-year tests. This good practice is also applied within levels in other year groups. This enables comparisons to be made across the whole year group or level and also serves a useful purpose in informing students’ choice in relation to levels.
The following are the main strengths identified in the evaluation:
· Teachers set appropriate high standards of expectation for their students.
· 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 at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published May 2010