An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
St Stephen’s Green, Dublin 2
Roll number: 60820E
Date of inspection: 29 September 2006
Date of issue of report: 22 February 2007
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Loreto College, St. Stephen’s Green. 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, 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.
The Mathematics department in Loreto College has a dedicated and enthusiastic team of teachers. Seven teachers teach Mathematics in the school and, in general, are deployed in line with their qualifications and subject specialism. At senior cycle, it is the policy of the school that teachers whose main specialism is Mathematics take higher-level classes with ordinary-level classes rotated among the remaining teachers within the department. In general, teachers retain the same class grouping from second year onwards throughout both cycles. Management is commended for its policy of recruiting teachers whose main specialism is Mathematics, thus helping to ensure that the high standard of Mathematics teaching within the department is maintained.
On entry to the school students are assigned to one of four mixed-ability classes. Management is commended for the deployment of extra teachers to Mathematics at both junior and senior cycles. For example, in second year, five classes are formed for Mathematics. This has the effect of ensuring that classes remain small and progress at a pace appropriate to students’ abilities. In general, four higher-level classes are arranged at junior cycle and one ordinary-level class. At senior cycle, generally two higher-level classes and three ordinary-level classes are formed. If necessary, foundation level is also provided.
Classes are concurrently timetabled for Mathematics from second year, which is commendable practice as it facilitates movement between levels and allows students to follow a programme of study suitable to students’ needs and abilities. Time allocated to Mathematics is, in general, good particularly at senior cycle, with six periods per week for both fifth and sixth-year classes. However, an issue highlighted was the time allocated to second year classes; at four class periods a week. Management is committed to reviewing this and to increasing the time allocated to Mathematics to five classes per week for second-years. Classes are well distributed throughout the week.
A formal induction programme facilitated by the principal and deputy principal provides support for newly appointed teachers. Members of the Mathematics department ensure that newly appointed teachers are informed, from a subject point of view, about practices and procedures of the department. Higher diploma students are partnered with a ‘master’ teacher and are supported throughout their diploma year.
Teachers’ continual professional development is encouraged by management through the payment of the annual subscription for membership of the Irish Mathematics Teachers’ Association (IMTA) and in facilitating teachers to attend relevant inservice in the subject area. An annual budget is allocated to the Mathematics department. Resources purchased include whiteboard materials, graphing calculators, laptops and projectors. Furthermore, within the school library, there are many mathematical books which students can access for their studies and for reference. Software, such as Graphmatica used in classes, is also available for use in the resource centre for students. Additionally, the Mathematics department has a central location for the storage of shared learning resources, which is easily accessible to all in the staffroom. Such facilities are highly commended in the support of teachers and students in the teaching and learning of Mathematics.
Provision is made for students in need of learning support. In addition to small class groupings, students may, if necessary, receive support at a time other than during Mathematics class time.
Teachers are highly commended for the support and encouragement provided to students in their participation in extra-curricular and co-curricular activities associated with Mathematics. Within the school, students compete in some teacher-run Mathematics puzzles. Many students participate in externally organised competitions, such as table quizzes and multiple choice quizzes organised by the IMTA and the BT Young Scientist and Technology competition. Some students have been invited to compete in the Irish Mathematical Olympiad. Additionally, a number of students have participated in Scholastic Aptitude Tests (SAT) organised by the Centre for Talented Youth, Ireland (CTYI). Participation in such Mathematics competitions and events allows students to experience Mathematics in different contexts, while developing their skills and understanding in different learning environments.
Whole school planning is ongoing with many policies, such as the homework policy and assessment policy in place.
Formal subject planning meetings are facilitated by school management approximately three times per year. Each year a coordinator of Mathematics is nominated. Minutes of meetings are retained and many practical issues are addressed at these meetings, for example, issues such as the allocation of teachers to classes and Mathematics resources. Additionally, many other informal meetings take place during the year.
Individual schemes of work were made available during the course of the inspection. These varied in terms of presentation and content but included an outline of the projected topics to be covered on a monthly and termly basis. Some teachers had included in these schemes the topic, learning objectives, resources, duration of and evaluation of the lesson, while other teachers had a daily outline for each individual lesson. These practices are commendable as they provide clear guidance for the delivery of the curriculum.
Mathematics teachers have collaborated to develop one common long-term plan for the Mathematics department. This comprehensive plan includes the aims and objectives of the subject, an outline of the programme and levels taught by teachers, class organisation, Information and Communication Technology (ICT) facilities, range and variety of resources and curriculum content. This plan ensures that all teachers are aware of the curriculum content for each year grouping and, furthermore, facilitates common assessments to take place at the end of the school year. There are however some areas within the plan that should be reviewed and updated. For example, with particular reference to the curriculum content section, it is recommended that an agreed template for the presentation be used and the learning objectives for each programme be included. It is further recommended that a greater range of effective methodologies be discussed and details of the integration of such be included within the plan.
The Transition Year programme includes Mathematics from the Leaving Certificate syllabus, project work and the integration of ICT into Mathematics. In its current format, the written Transition Year programme does not truly reflect all aspects of the Mathematics programme currently offered to students. For example, the variety of methodologies observed provided students with an opportunity to experience Mathematics in different situations. It is therefore recommended that a review of the Transition Year plan for Mathematics be undertaken to fully record all aspects of the programme offered.
Planning for lessons observed was very good as was seen from the prior preparation of materials such as handouts. In addition teachers had developed individual handouts and other supplementary materials and these were accessed and used during lessons visited.
All lessons were presented in a confident and coherent manner due to effective planning by teachers. Lessons were appropriately paced and time was well used and efficiently managed. Topics such as algebra, fractions and coordinate geometry featured in lessons. By explicitly outlining the aims and objectives for the lesson, students were fully aware of and engaged with the lesson from the outset.
Mathematics terminology, appropriate to the relevant topics and student ability, was used throughout lessons. Frequently teachers skilfully made links between sections within the syllabus and various topics. This practice is very good as it allows students to develop a secure understanding of mathematical concepts.
Textbooks were the predominant resource used in lessons. Teachers did, however, frequently draw on differentiated worksheets to supplement their work. Additionally, effective use was made of the overhead projector and data projector during lessons. Both were used to highlight key points, give a variety of different types of examples or to demonstrate accuracy when plotting graphs.
Teaching in all cases was of high standard and was generally traditional in style. This method is a combination of the teacher demonstrating to the entire class while students work individually. In general there was a good balance between teacher directed learning and student work. Although not observed, there was evidence to suggest that students were exposed to other methodologies. For example, samples of student research, and evidence of project work were made available. Such work demonstrated students’ understanding of statistics and their ability to use cross-curricular links with ICT in the presentation of their work. To ensure that all students’ learning styles are addressed, a variety of methodologies should be included in all lessons. Some examples of such methodologies are outlined in Junior Certificate Mathematics Guidelines for Teachers.
Teachers skilfully used a variety of questioning techniques throughout all lessons observed. In general, recall type questions were used to establish students’ understanding of the topic. Additionally, the use of such questioning allowed teachers to check students’ mental arithmetic, which is good practice.
Questioning strategies allowed teachers to offer a question to the entire class followed by an individual being asked for an answer, thus maintaining the focus of all students on the topic. The use of higher-order questioning by Mathematics teachers allowed students’ to build on their prior knowledge, and to provide reasons for their thinking. This develops students’ confidence in Mathematics and is to be commended.
Lessons were conducted in a warm friendly atmosphere of mutual respect. Teachers addressed students by their first name and were sensitive and discreet when providing assistance while circulating and correcting students’ work. Teachers had a keen and positive interest in their subject and their approach to Mathematics resulted in students’ developing a very good attitude to the subject also.
Most classrooms were teacher-based and many displayed a good variety of mathematical posters. These included 3-dimensional shapes, theorems, formulas and notices advertising mathematical events and competitions.
There was evidence to suggest that teachers set high expectations for their students and that students achieve well. Students eagerly participated in lessons and were highly motivated. Students’ outcomes in terms of knowledge and skills are very good. For example, students were confident and capable of answering questions put to them during the course of the visit and used appropriate terminology. Teachers are commended for encouraging students to study Mathematics at the highest level appropriate to their needs and abilities. Analysis of the State examination results indicates that the participation of students particularly at higher level Mathematics is very good in both junior and senior cycles.
Ongoing assessment is maintained through class questioning and end of topic tests. Formal assessment takes place three times per year for non-examination students, at Christmas, Easter and summer. Examination year groupings sit ‘mock’ exams during the second term. Transition Year students’ final assessment is a presentation of their work in portfolio format. Students’ portfolios, which include their Mathematics project, are presented to an interview team.
Communication between the school and home is maintained in a number of ways including the issuing of school reports on three occasions during the year, letters from the principal, and newsletters. Parent-teacher meetings are also convened for all year groupings and when necessary via telephone. Students are encouraged to use the school diary to record their homework. The effectiveness of the journals varies from class to class, with some regularly recording work and others using the journal sporadically. Consideration should be given to reviewing the effectiveness and purpose of the journal.
Management provides teachers with teacher journals. Within such journals teachers record student absences, incomplete homework, assessment records and the recording of homework assigned to students.
Homework is assigned regularly and is appropriate in terms of the quantity and relevance to the syllabus. Through observation of student copies, homework is generally well organised and presented. Students are encouraged to correct their own work; this is good practice as it gives students an opportunity to take their share of responsibility for progress in their own learning. In most copies there was evidence of written feedback. Some teachers provided such feedback orally during the lesson or on class tests. It is important that the monitoring of copies be consistent throughout the department. In some cases more positive and formative feedback should be written into students’ copies to provide the necessary guidance for further improvement.
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:
Post-evaluation meetings were held with the teachers of Mathematics, deputy principal and principal, at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.