An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
REPORT
Saint Bricin’s College
Belturbet, County Cavan
Roll number: 70350W
Date of inspection: 22 October 2008
Subject provision and whole school support
Summary of main findings and recommendations
Report on the Quality of Learning and Teaching in Mathematics
Subject inspection report
This report has been written following a subject inspection in St Bricin’s College. 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 one day 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. The board of management was given an opportunity to comment in writing on the findings and recommendations of the report; a response was not received from the board.
Subject provision and whole school support
In St Bricin’s College which caters for 166 students, the timetabling of Mathematics is undergoing changes and there is a clear intention on the part of school management to provide the structure for an effective learning environment. The current time allocation at junior cycle is less than ideal with only twelve periods per week between first, second and third years. It is recommended that this be increased to align more closely with subject guidelines. In addition, half the junior-cycle class groups have contact with the subject on only three days of the week, likely leading to difficulties in maintaining continuity and momentum. While not underestimating the intricacies of the timetabling process, every effort should be made by school management to schedule Mathematics for at least four days per week. This would better facilitate daily progress in a subject in which new learning builds to a great extent on previously developed skills and prior learning.
This year, for the first time, Mathematics is concurrently timetabled for third years and for fifth years, that is, the classes undertaking the certificate examinations in June. From next year, this structure should be extended, if at all possible, to second-year and fourth-year classes as a further move in easing access to the different levels of the subject. It is acknowledged, however, that, in schools of the size of St Bricin’s, having a mix of levels in mathematics classes is often necessary.
The process of assignment of students to classes has also undergone change this year. First-year students have been placed in classes on a mixed-ability basis, commendably allowing students time to settle into the college and display their mathematical aptitudes. In future, with the recommended ‘setting’ in second year, a broad separation into levels could be made, followed by a more definitive division in third year. Students as yet unsure of their own abilities could opt to follow the higher-level course at the beginning of second year, in the secure knowledge they could change level at any time during their junior certificate studies.
Mathematics teachers are allocated their classes and levels by school management, keeping in mind the desire for continuity within programmes and each teacher’s experience and expertise. Currently higher-level classes are taught by one long-serving teacher. In order to build capacity in the school, at least one other teacher, who could start at second year and work up to Leaving Certificate, should be introduced to teaching higher level. In this way, all possible advantage could be taken of the experience currently available and collegial sharing and support would be facilitated.
Students in need of numeracy supports are identified through the school’s incoming assessment process, through information received from parents and through the observations of teachers of first-year mathematics classes. A referral form developed in the school allows teachers record their concerns and notes actions taken by the educational support department. The needs of identified students are addressed through supports offered, on a withdrawal basis, from a subject in which they have an exemption or in which there is no certificate examination. It is suggested that other methods of support provision, such as team teaching, be explored in the future.
All students attend regular mathematics class and supplementary supports, available from one of the educational support teachers, take place in small groups. There is informal linking between the mathematics teacher and the support teacher, with the content of the support class closely reflecting that of the regular class. Progress in numeracy is currently assessed using class and term tests administered to all students, but additional testing for students in receipt of numeracy support is under consideration.
Materials available in the school to enhance the teaching and learning of Mathematics include numeracy games, demonstration geometry sets, set rings, mathematics software and miniature white boards. These are stored in the mathematics room, to which all teachers have access.
At St Bricin’s College, a mathematics website has been developed, in conjunction with maths-quarter.com, through which students can access syllabus topics and participate in an on-line forum. To ensure the benefits of this initiative are maximised, a considerable investment has been made in laptop computers for the use of fifth-year higher-level students and in a laptop and data projector for use in the mathematics room. The department’s information and communications technology (ICT) plan also identifies other possible areas for the development of digital teaching and learning strategies.
Teachers are facilitated in engaging in continuing professional development (CPD), and have attended in-service courses offered by the Mathematics Support Service and the Irish Mathematics Teachers’ Association (IMTA). One of the teaching team holds membership of the IMTA and keeps in touch with issues and changes occurring in mathematics education. Students of the school have participated in training for the Irish Mathematical Olympiad.
Planning and Preparation
The mathematics department is co-ordinated by one of the team of three teachers currently teaching the subject. The role of co-ordinator, as indicated in documentation, is to co-ordinate department meetings, redraft the department plan, provide support in the use of ICT for the teaching and learning of Mathematics, and to mentor teachers new to the department. Formal meetings are facilitated around staff meeting times and, reportedly, take place once per term. The minutes of one formal meeting, from early October, were made available for inspection. The sharing of experience and expertise indicated in these minutes is commendable and should be continued. In particular, the proposed sitting-in on each other’s lessons by team members could prove to be a valuable learning experience and is to be encouraged.
Work is underway on developing a department plan and currently it includes syllabus aims and objectives, a long-term plan for the development of Mathematics within the school, a note on the involvement of department members in CPD activities and a plan for the continued development of ICT to support the teaching and learning of Mathematics. With the extensive investment made by the college in ICT, the challenge for teachers now is to plan to ensure its capacity is exploited to the full and will contribute in a positive way to students’ learning.
An overview of work for the school year consisting of chapter numbers or textbook to be completed by term or half-year was present in the department plan. More detailed work programmes for all classes were prepared up to Christmas for second years to fifth years and up to the middle of the autumn term for first years. It is recommended that full-year detailed work programmes for all year groups and all levels be completed and included in the department plan. The programmes should include suggested strategies and activities for students, similar to that already documented in the first-year plan, so as to enhance the learning experience for students.
Planning for differentiation in classroom teaching is particularly important in situations where classes contain groups of students studying the subject at different levels. Such planning should address issues such as the order in which to cover topics, the choice of textbook(s) and appropriate assessment strategies.
All members of the team made personal planning and preparation materials available for inspection. These included a plan for enhancing numeracy skills, individual lesson plans, student-friendly worksheets, students’ notes, prepared acetates and teaching notes. Some materials were particularly commendable and reflect individual teacher’s levels of preparation.
With an analysis carried out of the 2008 Leaving Certificate results there is some awareness in the mathematics department of the school’s standing in terms of achievement and up-take in the certificate examinations. The team is encouraged to continue such an analysis in future years and extend it to include Junior Certificate data. Only then will the information be able to contribute fully to department planning and review activities.
Teaching and Learning
In each of the four lessons observed, teachers had prepared for their teaching, with a student-friendly activity, prepared examples, digital presentations and worksheets each contributing to the enhancement of the learning experience for students. Presentations, whether on projector screen or white board were clear, and methods were, in the main, logical and unambiguous.
There was good and appropriate use of mathematical terminology and notation by teachers and some instances where this was also the case for students. Generally, however, teachers need to encourage greater student involvement in lessons and support their use of the correct mathematics terms in their contributions. Simple ways of achieving this are asking students to accurately explain their workings to questions, to suggest next steps in solutions presented on the board or to identify the nature of errors made in written work.
Commendably, there were classes in which the good practice of explicitly sharing the lesson objective with students was observed. In these same classes, before the end of the lesson, teachers also conducted a review of material covered. While there was one excellent example of class work being linked to prior learning and to students’ everyday experiences, generally teachers need to take time to identify appropriate links with current work and to avail of every opportunity to exploit these links in class.
The majority of lessons were structured around the teacher presenting work at the board or screen followed by the assigning of exercises for student practice. While recognising the usefulness of this ‘traditional’ approach to mathematics teaching, it is recommended that teachers explore ways in which to include alternative student activities into class work. One such activity might be the promotion of pair-work among students to discuss approaches to problem-solving. Also, in one lesson observed, a brainstorming activity generated refreshing enthusiasm and references made by students to a project previously completed were clear evidence of the positive effect of such activities on the learning experience.
Other elements of good practice in mathematics teaching observed at St Bricin’s College included the writing of the lesson objective on the board, a focus on numeracy as a regular lesson-opener, the maintaining of a diary of work covered and homework given for each lesson, and the preparation of digital demonstrations.
In all lessons observed, students were attentive and engaged in the work at hand. Teachers were affirming of students’ efforts and the classroom atmosphere was supportive. The learning environment in the mathematics room was enhanced by the display of posters and by photographs of first-year students engaged in project work.
Assessment
Progress in Mathematics is assessed partially through the assigning and marking of class work and homework. A review of a random sample of students’ copy books indicated such work to be relevant to programme and syllabus. However, in many cases, standards of presentation and the general quality of work was less than it is reasonable to expect. In these cases, much closer monitoring is required, and generally all students should be reminded of the importance of presenting work in a structured and orderly fashion so as to increase the likelihood they will achieve their potential in the subject.
In addition, class tests and end-of-term examinations are used as both formative and summative assessments, providing feedback to students on areas for improvement and achievements to date. Given that the school has moved to teaching first-year classes as mixed-ability groupings, it is recommended that common tests be used with first-year classes throughout the year and at the ends of terms. This practice will support students and their parents in making decisions regarding the level at which to study Mathematics from second year onwards.
This year, for the first time, the school has changed to issuing reports to parents both at the end of Christmas term and summer term and at the middle of the first term and second term. This initiative is indicative of the commitment of the school to working in partnership with the home to improve students’ application and attainment at all subjects, including Mathematics. School-home links are further strengthened at parent-teacher meetings that take place once in the school year for each year group.
Summary of main findings and recommendations
The following are the main strengths identified in the evaluation:
· There is a clear intention on the part of the school management to provide the structure for an effective learning environment for students.
· First-year students are placed in mixed-ability classes allowing them time to settle into school life and to display their mathematical aptitudes.
· The school has developed a mathematics website to enhance the learning of the subject for students, particularly at Leaving Certificate higher level. Considerable investment has been made in computer hardware
to maximise this initiative.
· The sharing of experience and expertise indicated in minutes of a mathematics team meeting is commendable and should be continued.
· Elements of good practice in mathematics teaching observed at the school included the writing of the lesson objective on the board, a focus on numeracy as a regular lesson-opener, the maintaining of a diary of
work covered and homework given for each lesson, and the preparation of digital demonstrations.
· In all lessons observed, students were attentive and engaged in the work at hand. Teachers were affirming of students’ efforts and the classroom atmosphere was supportive. The learning environment in the
mathematics room was enhanced by the display of posters and by photographs of first-year students engaged in project work.
· The school is committed to working in partnership with the home to improve students’ application and attainment, as evidenced by the increase in the number of written reports issued to parents.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· The time allocation to Mathematics and the scheduling of lesson periods should be reviewed. Concurrent timetabling should be extended, if at all possible, to second-year and fourth-year classes as a further
move in easing access to the different levels of the subject.
· Capacity needs to be built within the mathematics team by introducing another teacher to teaching the subject at higher level.
· Full-year detailed work programmes for all year groups and levels should be completed and included in the department plan. The programmes should include suggested strategies and/or activities for students.
Planning for differentiation in classroom teaching should be given attention, particularly given that classes contain groups of students studying the subject at different levels.
· Teachers should take time to identify appropriate links between current work, prior learning and students’ everyday lives, and to avail of every opportunity to exploit these links in class.
· Students’ copy books need much closer monitoring and all students should be reminded of the importance of presenting work in a structured and orderly fashion.
· First-year classes should sit common assessments both throughout the year and at the ends of terms so as to support decisions regarding the level at which to study the subject.
A post-evaluation meeting was held with the teachers of Mathematics, the deputy principal and the principal at the conclusion of the evaluation, when the draft findings and recommendations of the evaluation were presented and discussed.
Published April 2009