An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Christ King Girls’ Secondary School
Half Moon Lane, South Douglas Road, Cork
Roll number: 62692I
Date of inspection: 25 February 2009
Report on the Quality of Learning and Teaching in Mathematic
This report has been written following a subject inspection in Christ King 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 and subject teachers.
The mathematics teaching team is large, with fifteen teachers involved in the teaching of the subject in the current year. The school also has a number of Post Graduate Diploma in Education (PGDE) students teaching some mathematics lessons in the school.
The school offers its students the Junior Certificate and established Leaving Certificate (LC) programme, as well as an optional Transition Year (TY) programme. The majority of students opt to follow the TY programme. Teachers are assigned to year groups and classes following consultation with management. There is generally continuity with classes from first to third year and from fifth to sixth year. There is rotation of levels at junior cycle and more limited rotation at higher LC level. Applied Mathematics is offered as an optional module in TY and students wishing to follow the subject at LC level are accommodated through the provision of lessons within and outside of timetabled hours.
Timetable provision for Mathematics is good in the senior cycle, with four lessons per week for TY classes, five lessons per week for fifth-year ordinary level and six lessons for fifth-year higher level and all sixth-year groups. Optimal provision for junior cycle Mathematics is a lesson per day. In Christ King School each junior cycle grouping has two years with four periods per week and one year with five periods per week, over the three years. In the current year, the second-year students are timetabled for five lessons each week. If possible, within timetabling constraints, the allocation to junior cycle Mathematics should be increased and every effort should be made to ensure that students in their Junior Certificate examination year have five periods of mathematics tuition.
In a small number of instances, due to reported timetable constraints, classes have 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.
First-year classes are arranged on a mixed-ability basis and there is a common assessment for all students at the end of their first year. Classes are timetabled concurrently from second year onwards and this is good practice. Concurrent timetabling allows students to follow the highest level possible for as long as possible and facilitates students who wish to change level. The structure adopted up to the end of third year is mixed ability within levels. Mixed-ability teaching within levels caters for varying rates of student development and acknowledges the connection between levels of teacher expectation and levels of student achievement. In TY, fifth year and sixth year, the school operates a merit-based placement system for allocating students to classes. This arrangement of classes can cause difficulty, for instance, for students who wish to change level. The allocation to class arrangements for students has been adapted by the mathematics department and should be kept under review to ensure that the needs of the students are best served at all times.
The school facilitates the continuing professional development of its teaching team. Teachers have taken part in courses organised by the Mathematics Support Service (MSS), the Irish Mathematics Teachers Association (IMTA) and the Irish Applied Mathematics Teachers Association. This is commended as it will help to facilitate the integration of a variety of teaching methodologies to meet the forthcoming syllabus, pedagogical and assessment changes in Mathematics and the changing needs of the school’s population.
While there is no specific budget for Mathematics, all reasonable requests for purchase of resources are granted. A range of teaching resources, stored centrally in the staff room, is available to members of the team. These include whiteboard drawing equipment, overhead calculators, geometric shapes and algebra tiles. There is also a comprehensive range of worksheets, handouts, notes on various topics, past examination papers and MSS resources. The team has access to a well-equipped computer room with mathematics software packages installed. There was little evidence of the use of information and communication technology (ICT) in the classrooms. It is reported that more use will be made of ICT in the classrooms as resources allow.
The school provides opportunities to participate in extracurricular and co-curricular activities associated with Mathematics. Students have competed in the Team Maths competition and Junior Mathematics competition organised by IMTA. The school also participates in the Problem Solving for Irish Second Level Mathematicians (PRISM) competitions, organised nationally as part of Maths Week Ireland, held in October. Support for students in such activities is commendable.
Students who find Mathematics particularly challenging are identified through a pre-entry assessment, contact with primary schools, discussion with parents and teacher-monitoring during first year. The school responds to the needs of these students by the creation of a small class group in each year in junior cycle. In some instances, students are withdrawn from lessons for one-to-one tuition where appropriate.
An analysis of students’ performance in the state examinations over the last four years reveals significant uptake and achievement rates at higher level at both Junior and Leaving Certificate level. It is noted that discussion and review of uptake rates, as well as results, are conducted within the school. This is good practice and should be used as a regular and natural part of the planning activities of the mathematics department.
The staff of Christ King School received an input on ‘Assessment for Learning’ (AfL) from a member of the School Development Planning Initiative (SDPI) team. A number of members of the mathematics team are implementing aspects of AfL in their mathematics teaching. It is planned to provide feedback to the mathematics department on this initiative. This is positive. When successfully implemented, aspects of AfL can have a significant impact on the teaching of Mathematics.
An experienced member of the mathematics team has acted as subject co-ordinator on a voluntary basis for a number of years. In the current year, the department has appointed another member of the team to the position and has agreed that the role of co-ordinator will rotate within the mathematics department, ideally on an annual basis. This is positive and will ensure the development of a wide leadership-skills base within the department. As an aid to this, the team might agree a set of duties for the co-ordinator and record them in the department plan.
Formal planning and review meetings are scheduled around staff meetings and school planning days, and occur about three times a year. It is reported that ongoing informal contact is also maintained. The good practice of record-keeping at formal meetings is in place and these records show evidence of ongoing collaboration and review within the team. Recent issues discussed by the team include the allocation of class time at third year, the organisation of classes in fifth year and the piloting of AfL in some mathematics classes.
There is a comprehensive written plan for Mathematics. The department plan includes overall aims and objectives for mathematics education within the school along with organisational details, a list of the resources available, co-curricular planning and homework guidelines. The plan also sets down a detailed programme for each year group and level within the school. Each topic has been divided into sub-topics and a timeframe for the completion of each of these is included. This is good practice.
The focus of the TY plan and teaching is on Leaving Certificate material. It comprises, predominantly, a list of leaving certificate topics to be covered during the year. 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, strongly recommended that this plan be extended to incorporate a wider range of mathematical experience. The spirit of the TY programme puts the emphasis on teaching different Mathematics or on Mathematics taught differently. Although some Leaving Certificate material can form part of a TY plan it is suggested that this valuable opportunity be exploited to encourage students to engage with Mathematics on an enjoyable level and to help them gain a greater appreciation for the subject. Students commencing TY in 2010 will study the revised Strand 1 and Strand 2 components of the new Project Maths syllabus. This could provide a valuable opportunity to use the methodologies outlined in the teaching and learning plans prepared by the Project Maths Development Team (PMDT). A number of these are available on the website www.projectmaths.ie. As the six TY mathematics classes are concurrently timetabled, teachers have the opportunity to prepare a short module and, through rotation, deliver it to each class group.
There is also a comprehensive applied mathematics plan structured similarly to the mathematics plan. The TY element of this plan is in keeping with the principles of the programme and utilises elements of the IAMTA-prepared TY module. Students also participate in an online “stock market game” as part of their programme. The commendable aim of introducing Applied Mathematics in TY is to increase the number of students who will take the subject to Leaving Certificate level at both higher and ordinary level.
The fact that the mathematics department documentation has expanded to fill three large folders, comprising a planning folder, a department folder and a resources folder, is evidence of the collaboration and sharing of resources within the department. A range of syllabus documents and guidelines, support-service material, along with materials produced by individual members of the team are available for use by all the team. This is good practice.
The lessons observed in Christ King School were well structured, purposeful and appropriate to the syllabus. In all cases, lesson content was appropriate to syllabus and level and teachers’ explanations were clear. In all cases, the lessons were very well planned. In most lessons observed, the learning intentions were shared with the students. Best practice in this regard occurred when the teacher checked at the end of the lesson to see that these targets had been achieved. This practice is worthwhile because it increases students’ motivation and leads to a sense of accomplishment on achieving the day’s goal. It is commendable that effort was made to revise work previously done and to link it to new material being presented, thus helping to reinforce learning and to develop new ideas. The pacing of the lessons was challenging yet realistic, and the content was matched to the ability levels of the students.
The whiteboard, textbook and, in some instances, worksheets were the main resources used in lessons. While not observed, the use of ICT was reported in the teaching of geometry, Applied Mathematics and in the preparation of materials. It is also reported that there are plans to increase the integration of ICT in teaching and learning over time. This is encouraged.
Teaching predominantly consisted of teacher example followed by student exercise. Within this traditional approach, teaching was effective. Teachers made good use of questioning, both global and directed, throughout the lessons observed. Best practice was seen when more open and probing questions were included and used to encourage students to think for themselves. Since this type of questioning is so beneficial to learning in Mathematics, it is recommended that it be incorporated into lessons more frequently.
The relationships between students and teachers were observed to be mutually respectful. This has led to the creation of a working environment where high expectations are set for students and where students respond accordingly. The very high standard of student behaviour and the good working atmosphere that exists in each classroom enables students to contribute to, and participate in, lessons. In interactions with the inspector, the students were able to demonstrate understanding of the concepts taught and could display clear, solid mathematical knowledge. They were also quite comfortable in the use of appropriate mathematical language.
Within lessons, students were generally passive, working individually and reliant on teacher direction. It is therefore recommended that teachers review current methodologies used in lessons and add greater variety to their teaching approaches and that mechanisms for the provision of such approaches be explored by the mathematics department. More use of strategies such as working on student-generated problems, pair work, group work, investigation, consolidation activities, practical work, discussion, group work, quiz activities and the use of concrete resource materials could be used to enhance learning.
Classrooms are generally student based. In some instances, efforts have been made to enhance the physical working environments through the use of a range of commercial and teacher-generated posters. To further enhance the learning environment for all students, it is recommended that teachers display and use examples of students’ mathematical work and project work.
Learning is routinely assessed through oral questioning and end-of-topic tests as appropriate. The school has a homework policy and homework was assigned in all lessons visited. Students’ journals showed that mathematics homework is assigned on a regular basis. In most cases, students are expected to keep separate copybooks for notes and examples as well as class work and homework. The use of a notes and examples copy provides students with a template for the presentation of their own work and, on inspection, the standard of students’ presentation was found to be high. Copybooks also revealed that homework is corrected promptly and is being monitored in all cases. Records of student achievement are kept by all teachers. In many instances students are expected to write corrections into their copybooks and to indicate when their own answers are correct. This is very good practice as it ensures the creation of the copybook as an excellent study resource.
Students are formally assessed twice a year at Christmas and summer. Common examination papers are set for first-year students and generally within levels for subsequent year groups. Third-year and sixth-year groups also sit mock examinations. Reports are sent home on foot of these formal examinations. Parent-teacher meetings take place once a year for all year groups except TY and the students’ journal is also used as a means of two-way communication between the school and parents.
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:
Published, December 2009