An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
St. Augustineís College,
Dungarvan, County Waterford
Roll number: 64890W
Date of inspection: 25 and 26 February 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in St. Augustineís College carried out as part of a whole school evaluation. 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 studentsí work, and had discussions with the teachers. The inspector reviewed school planning documentation and teachersí written preparation. Following the evaluation visit, the inspector provided oral feedback on the outcomes of the evaluation to the principal and subject teachers.
The schoolís timetable provides forty-five periods per week, some of thirty-five minutes duration and some of forty minutes. The timetabling provision for Mathematics is very good. All junior cycle classes have five periods each week and in senior cycle this increases to six. The Transition Year (TY) classes have three periods of Mathematics each week. In addition to this, classes are spread evenly throughout the school day and the school week. Mathematics classes in third, fifth and sixth years are timetabled concurrently to allow separate classes for higher-level and ordinary-level students. In the interests of maintaining high levels of continuity, the good practice of teachers remaining with the same class groups from first year to second year and from fifth year to sixth year, where possible, is followed.
A small number of students who wish to study Applied Mathematics as an extra Leaving-Certificate subject are catered for outside of formal timetabled hours. Lunchtime classes are available for fifth-year and sixth-year students and the teacher involved is highly commended.
Students are assigned to mixed-ability classes in first year and generally remain as a group until the end of second year. At the beginning of third year classes are reformed to allow students to follow the higher or ordinary level syllabus. This is good practice as it encourages students to follow the highest level possible for as long as possible. In these third year classes the practice is to have mixed ability within levels.
TY is optional for students within the school; however a majority of students opt to take the programme. The mathematics classes are arranged on a mixed ability basis. At the beginning of fifth year students opt for higher or ordinary level. The higher level classes are formed on a mixed-ability basis. Within ordinary-level classes students follow a common course for about one month and are commonly assessed at the end of this. Following this assessment the teachers decide whether to continue with the mixed-ability groups or to stream the classes on the basis of their performance. Thus, while the current fifth year group of ordinary level pupils are in mixed ability classes, this is not always the case. While entering the caveat that mixed-ability teaching within levels takes account of varying rates of student development and exploits the correlation between levels of teacher expectation and levels of student achievement, the teachers are nevertheless commended for a flexible approach and openness to varying their provision based on the perceived best fit for studentsí approach.
Incoming first-year students are assessed prior to entry to the school in a number of areas including Mathematics. Students who find the subject particularly challenging are identified through this pre-entry assessment and teacher monitoring and assessment during first year. These students are generally supported through a system of withdrawal from classes, other than mathematics class, for small group tuition for as long as required. The learning support teacher is a member of the mathematics team and close informal contact is maintained between him and the classroom teachers. It is reported that other means of support have been used including, in one instance, team teaching. The school also provides an extra allocation of hours, beyond those allocated by the Department of Education and Science, to ensure that a high level of support is provided to students. This extra allocation and the flexibility of approach as to how it is used are commended.†
Information and communication technology (ICT) is currently used mainly in the production of materials to enhance the teaching of Mathematics and to a lesser extent in classroom teaching. All classrooms are now networked and have broadband internet access. The mathematics team have recently been given a data projector and a laptop computer is on order. Classes also have access to an ICT room where some mathematics software has been installed. It is suggested that, in order to support the teaching and learning of the subject, strategies to integrate ICT more directly into lessons should be discussed and included within future reviews of the teamís plan.
Management is commended for supporting the continuous professional development (CPD) of teachers by facilitating opportunities to attend in-service in Mathematics during school time. Some teachers have attended, and plan to attend, a range of in-service courses organised by the Mathematics Support Service in a number of topics.
The mathematics department structure, established in the school in recent years, is co-ordinated on a voluntary basis by a senior member of the team. To allow each member of the team to gain a deeper understanding of the issues involved in the workings of their subject department and to share the workload, it is recommended that the role of co-ordinator should rotate among members of the team, perhaps on an annual basis.
Formal planning and review meetings are scheduled around staff meeting and school planning days and occur about three times a year. As all subject meetings occur simultaneously and most members of the mathematics team also teach another subject, having all members of the team present at meetings can be a challenge. It is suggested that two rounds of meetings, in series, be held during these days. The subjects in each round should be chosen so as to minimise the number of teachers whose two subjects occur in the same round. Records are kept of such meetings and they show clear evidence of ongoing collaboration and review among mathematics teachers. Informal discussions between small groups of teachers also take place on a regular basis.
The mathematics team have made commendable progress in planning. They have used diagnostic templates and have collaborated and developed a comprehensive long-term plan for Mathematics along School Development Planning Initiative (SDPI) guidelines. The department plan includes overall aims and objectives for mathematics education within the school, organisational details of classes and teachers, outline programmes of work for each year group and level, reference to a variety of methodologies, and a description of provision for students with special educational needs, which is in line with good practice and is commended. The plan also includes procedures for homework, assessment, record keeping and reporting. It contains a list of CPD courses attended by teachers in recent years and a note on the availability of ICT facilities in the school.
The TY plan for the school is differentiated according to the teacher who has each group. In one instance there is a good balance between topics that consolidate the prior learning of students, some work that introduces elements of the Leaving Certificate programme in an innovative way and other topics such as specific irrational numbers and practical use of the compound interest formula. The other programme contains much material more closely associated with the current Leaving Certificate programme. There is a need for more cohesion in terms the TY programme than is currently in evidence. As classes are of mixed ability, having classes following significantly different programmes seems unnecessary and will make further collaborative planning more difficult. It is therefore recommended that the mathematics department review the TY plan to ensure that there is a clear distinction between Leaving Certificate material and the TY mathematics programme.
All teachers made individual planning and preparation materials available during the inspection. Included in these materials were schemes of work, examples of student worksheets and handouts, transparencies prepared for the overhead projector, extensive teacher notes, and large banks of test papers, examination questions and solutions. This level of preparation for teaching is commended.
Lessons generally began with the correction of homework at the board by the teacher. The purpose of the lesson was then shared with the students. This is good practice as it stimulates interest in the lesson and captures studentsí attention. Teaching was then predominantly conducted through the presentation of work at the board followed by the setting of similar problems from the textbook for individual students to practice what they had observed. This allowed time for the teacher to provide individual attention to students who might be experiencing difficulty. Within this traditional style, teaching was effective, lesson content was appropriate and in line with agreed programmes of work and syllabus requirements.
Work set during lessons was clear but challenging and students responded well to their teacherís expectations. Teachers were well prepared for their teaching and students were attentive and engaged in the work at hand. Teachers were aware of and attentive to the needs of individual students and devoted class time to working with students who were experiencing difficulty. There was mutual respect evident between teachers and students and good student behaviour facilitated an effective but relaxed classroom management style conducive to learning. Studentsí progress and effort were affirmed in an atmosphere that created confidence and encouraged studentsí use of appropriate mathematical language.
To complement this general, 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. Some examples could include investigation, pair work, consolidation activities, practical work, discussion, group work, quiz activities and greater use of ICT. The inclusion of such strategies into the purposeful lessons observed should harness the widely accepted benefits for students of being actively involved in their own learning and take advantage of studentsí different preferred learning styles. The courses and website of the Mathematics Support Service (MSS) and the publication Junior Certificate Mathematics Guidelines for Teachers along with the sharing of the experiences of the members of the mathematics team could all contribute to this inclusion.
Interactions between teachers and students typically took the form of brief answers to questions posed to individual students or to the class group by the teacher on finding the next steps in a solution. There were also some good examples of teachers encouraging students to justify their methods and in some instances, of the posing of more challenging questions to encourage students to probe new material being presented and to create links to previous learning. The use by all teachers of some probing questions in mathematics lessons should appropriately challenge students and assist them in developing their skills in the area of problem analysis, mathematical thinking and mathematical communication. There were also examples of students asking questions, reflecting their engagement with learning in the lessons.
Most teachers have been allocated their own base classrooms. A wide range of commercial posters and student-generated work had been used to enhance these rooms. This is commended as it has created a visually stimulating mathematical environment.
In interactions with the inspector, the students were able to demonstrate understanding of the concepts they had learned and how to apply them to problems. They could make connections to previous learning and displayed clear mathematical knowledge.
Formative assessment of students is carried out on an ongoing basis by questioning in class, through correction and monitoring of homework and student work during class and through monitoring of students during lessons. The mathematics department has, for the past two years, adopted a policy of continuous assessment to provide summative assessment of all non-State examination students. Studentsí progress is monitored throughout the year by means of a series of tests administered at the end of a topic and results are recorded in the Teacherís Diary. These are then combined with an overall end-of-year examination to provide the students final result. Third-year and sixth-year students are also continuously assessed and also sit pre-State examinations during the second term.
The school maintains good communication with parents. Parent-teacher meetings are held for each year group. Two school reports are issued for each student during the year. Additionally, the student diary can be used as an effective means of communication between the school and home and vice-versa.
Apart from the previously mentioned fifth-year students who are commonly assessed after one topic is taught in fifth year, other assessments are generally set and monitored by individual teachers for their own classes. It is recommended that the mathematics team move towards more common assessments or assessments having a common core of questions with agreed marking schemes. Common examinations enable comparisons to be made across the student cohort. It can also serve a useful purpose in informing studentsí choice, or in providing advice to students, in relation to levels. It should be possible to achieve this within the current assessment structure in the school.
An analysis of studentsí performance in the State examinations over the last four years indicates that uptake rates at higher and ordinary levels are good at both Junior and Leaving Certificate level. It is recommended that discussion and review of uptake rates, as well as results, are used as a regular and natural part of the planning activities of the mathematics department.
At the time of the visit the mathematics department was planning the schoolís involvement in World Maths Day. Activities had also been arranged for Maths Week in October including participation in the Prism mathematics competitions. The school has previously been involved in the Team Maths competition and has taken part in Irish Junior Mathematics Competitions. This very good practice is commended as it allows students to have an interest in Mathematics outside of the classroom, raises the profile of the subject within the school, gives students the opportunity to enjoy Mathematics and see it applied to problem solving in a new and stimulating way. All those involved in these activities are commended.
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, October 2008