An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Deansrath Community College
Clondalkin, Dublin 22
Roll number: 70040H
Date of inspection: 22 October 2008
Report on the Quality of Learning and Teaching in mathematics
This report has been written following a subject inspection in Deansrath Community 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 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
Timetabling provision for Mathematics in junior cycle is very good. Mainstream mathematics classes are provided with five forty-minute periods per week, classes are mixed ability until Christmas in first year and following common assessments classes are then streamed. Streaming remains in place for the remainder of junior cycle. Mathematics classes are timetabled concurrently to enable movement between and within levels. The top stream follows higher level while the remainder take ordinary level with a small number opting for foundation level. The distribution of classes throughout the week is good and the balance of provision in Mathematics between morning and evening is also very satisfactory.
Students are selected to participate in the Junior Certificate Schools Programme (JCSP) upon entry to the school in first year. Two small mathematics classes are formed from this cohort and the students follow a common programme designed to consolidate their knowledge of basic Mathematics and to equip them to cope with the Mathematics they will encounter in everyday life. It was evident from the lesson observed during the inspection that the programme is being implemented effectively and that the students are expected to adhere to good practice in carrying out basic mathematical operations. There is one JCSP mathematics class group in second and third year with an additional period per week being provided for the third years.
The JCSP classes typically follow foundation level Mathematics but it is evident that, should the need arise, students in JCSP classes are facilitated to follow ordinary level.
Provision for Mathematics in senior cycle is also good. Leaving Certificate mathematics classes are streamed. The top stream follow higher level, the majority of the remaining students choose ordinary level, while a number opt for foundation level following consultation with the class teacher and the guidance counsellor. Mathematics classes are timetabled concurrently within each year group to facilitate students wishing to change level. In addition, students in the Leaving Certificate Applied (LCA) programme have four periods of Mathematical Applications per week.
The school’s enrolment procedures are very good and are supported by the close links that have been established with the feeder primary schools through the Schools Completion Programme (SCP). The principal and the school’s public relations officer visit each feeder school to speak with the fifth and sixth class groups. Invitations to the school’s open day, which is held in November, are issued during the visits and enrolment takes place the following week. Once the incoming cohort has been identified, the schools home-school-community liaison (HSCL) co-ordinator and the year head for incoming first years visit the primary schools. The purpose of these visits is to establish the strengths, interests and weaknesses of each of the incoming students and to ascertain if there are any issues with respect to behaviour or attendance. Entrance assessments, which include standardised tests in Mathematics and English, are then held in late November. Following analysis of the results of the assessments tests the students and their parents hold private meeting with the year head to discuss the most suitable placement for the student and to outline the school’s policies and procedures.
Students in need of learning support or with special education needs (SEN) are also identified as part of the school’s enrolment procedures. The schools learning support co-ordinator visits the primary schools following the entrance assessments to meet with the class teachers and also liaises with the SCP coordinator, the group’s year head and the home-school-community liaison co-ordinator. Incoming students who have had their learning or other needs formally assessed by National Educational Psychological Service (NEPS) while in primary school are identified and applications for extra resources are then submitted by the school to the Department of Education and Science for consideration. If it is deemed necessary, additional assessments for some students are also arranged through the psychology service of Co. Dublin Vocational Education Committee (VEC).
Learning support in Mathematics is provided by withdrawal in small groups from subjects other than Mathematics. Withdrawal takes place following consultation with parents and the class teacher. Close links are maintained between the learning-support and class teachers to ensure that the material being covered during withdrawal, while addressing underlying weaknesses, is in line with the work being done in mainstream classes.
Mathematics teachers are assigned to classes and levels by rotation in both senior and junior cycle. This is very good practice as it ensures that all members of the team gain experience of teaching the different levels, encounter a range of learning styles and have an opportunity to deploy an assortment of teaching methods. In addition, it is school policy that teachers retain the same class group from second to third year and from fifth to sixth, thus ensuring continuity of approach. A number of Postgraduate Diploma in Education (PGDE) teachers are engaged in teaching Mathematics in the school and while this is most commendable it is suggested that PGDE teachers should not be assigned to mathematics classes in senior cycle.
The mathematics department is well resourced. The available resources are detailed in the subject development plan for Mathematics and are stored centrally in the school’s resource room. Mathematics classes also have access to one of the school’s three computer rooms and to an interactive whiteboard. A data projector is available exclusively to the mathematics teachers. Such resources provide the opportunity for active teaching and learning to take place and to create a visually stimulating learning environment, which reduces the reliance on the textbook as the primary teaching resource. It is recommended therefore, that explicit reference be made in the subject development plan to the appropriate integration of Information and Communication Technologies (ICT) in the teaching and learning of Mathematics. Active teaching methods, which will allow for the utilisation of the existing resources, should be identified and developed and a strategy for their implementation in mathematics lessons should be documented. Assistance in carrying out this work is available from the second level support service www.slss.ie.
Subject development planning in Mathematics is well advanced. The mathematics department is ably coordinated, and responsibility for coordinating the department rotates between the team members. This is very good practice. The mathematics department holds regular planning meetings, the minutes of which are available in the subject development plan for Mathematics.
A comprehensive subject development plan is in place. The plan addresses the existing provision for Mathematics in the school, the arrangements for students’ access to levels and programmes, schemes of work for each year and level, homework and assessment procedures, resources lists, procedures for supporting students with special educational needs and record keeping and reporting procedures. While admirable progress has been made in planning, it is recommended that the subject development plan for mathematics be further developed to specify the strategies to be employed in teaching mixed-ability classes in first year and to meet the unique needs of its student cohort thereafter. Planning should focus on how Mathematics can be made more accessible to students whose command of English is poor and on reducing reliance on the more traditional teaching methods in mainstream classes. It is further recommended that the team members agree standard procedures for carrying out core mathematical operations and also include these in the plan.
Concerns relating to students’ attainment and academic standards were raised in the subject development plan and are identified as key challenges to be addressed in long-term planning in Mathematics. Examination of uptake rates and student performance in the state examinations suggests that there are grounds for concern. It is recommended that the mathematics team undertake an analysis of statistics available from the State Examinations Commission annually and that the outcomes serve to establish appropriate benchmarks and inform ongoing planning.
Individual teacher planning was, in most cases, very good. Additional materials in the form of differentiated worksheets were prepared by many of the teachers and were seen to best effect when they facilitated differentiation and collaborative learning, rather than simply serving as a substitute for the textbook. Planning for the inclusion of resources in teaching and learning was good and in one case it was of the very highest quality. In this case, the interactive whiteboard facilitated a lesson that was enjoyable, visually stimulating and inclusive of all of the students in the class.
Management supports attendance at continuing professional development (CPD) courses and a comprehensive range of courses has been attended by members of the mathematics team in recent years. Whole-school training in numeracy across the curriculum was delivered by the JCSP support service this year, while the second-level support service has also provided training for the entire staff on active teaching methodologies. Newly appointed teachers are provided with an induction programme which includes a workshop provided by Co. Dublin VEC.
Many of the lessons observed during the inspection were well planned, they proceeded at a satisfactory pace and were delivered with enthusiasm and care. The material covered during the inspection was appropriate. The teaching style in the mainstream classes was mainly traditional with teacher exposition followed by students working individually on material assigned by the teacher. In such cases, the textbook was the primary teaching resource and there was an over reliance on verbal communication with the students. While the teachers worked diligently, the effectiveness of the lessons would have been greatly enhanced by integrating visual aids such as ICT or the overhead projector. The use of such resources would have rendered the lesson content more accessible to the students many of whom are newcomers and have limited English.
There were two particularly good examples of ICT integration in evidence. In both cases the interactive whiteboard was utilised to deliver the lesson content in a very structured fashion and enabled the teacher to support individual students when the need arose. One of these lessons also involved the use of games to enhance engagement and to support the lesson’s objectives. The lessons were successful in meeting the needs of the students, in facilitating teacher movement and in broadening the range of learning opportunities for the students.
Positive student behaviour was evident during the inspection. Discipline was appropriately maintained and the lessons were conducted in an atmosphere of mutual respect. This was particularly manifest in one class where senior cycle students were engaged in investigating proportional representation and worked in partnership with a group of pupils from a local primary school. The senior students adopted the role of facilitator, encouraging the primary-school pupils to carry out calculations and discussing the outcomes with them. It was a very enlightening and enlivening experience. It provided a range of learning outcomes including the use of formulae and an appreciation of the relevance of Mathematics in everyday life. The lesson also served to develop the self-confidence of all of the participating students.
Differentiation, facilitated by good teacher circulation and the use of excellent worksheets was observed in a number of instances. In one such case the students worked independently following individual education plans and interacted with the teacher when the need arose. There was admirable insistence on correct procedures for adding and subtracting integers and any difficulties encountered by individual students offered opportunities for shared learning. The students were engaged with the lesson throughout and there was ample evidence that the lessons objectives were realised. It is recommended that the differentiated approach to teaching Mathematics observed in this instance be adopted in mainstream Junior Certificate and Leaving Certificate classes and that strategies to facilitate more direct interaction between the teacher and student be identified and implemented.
Homework and assessment procedures are outlined in the subject development plan for Mathematics. Homework is assigned regularly and, in most cases, corrected, annotated and amended. There was evidence of formative assessment and of students amending their own work in some of the homework copies. These very good practices should be adopted as standard procedures in the department and included in the homework policy for Mathematics. It is suggested that the existing homework policy be amended to include the roles and responsibilities of students and parents and to recognise that one of the intended outcomes when setting homework is to provide opportunities for shared learning among the students when the homework is being corrected in class by the teacher.
Ongoing assessment occurs through the use of teacher questioning in class, homework assignments and class tests which are held at the end of each topic. The class tests are set by most of the mathematics’ teachers and records of student attainment in the class tests are kept in the teachers’ diaries. It is recommended that end-of-topic tests be set and corrected by all members of the mathematics team and that the subject development plan be amended to reflect this change in practice.
First-years students sit a formal common examination in Mathematics at Christmas. This examination is set and corrected by a teacher from the department who is not involved in teaching Mathematics in first year. The results of this examination are collated and are used to inform student choice when the classes are banded upon their return to school in January. This is very good practice as it enables students to compare their performance against the rest of the cohort and it facilitates collaborative planning in designing the first-year mathematics programme A second formal examination takes place just prior to the summer holidays and common questions are set within levels where appropriate. The remaining non-examination classes sit formal examinations at Christmas and summer and the good practice of modelling the style and layout of the certificate examinations is adopted.
Students in third and sixth year are provided with formal examinations at Christmas and sit the mock examinations early in the second term. Students in receipt of reasonable accommodation in the state examinations are facilitated appropriately in the mock and in-house examinations. The mathematics’ teachers share responsibility for correcting the mock examination papers. They also meet to discuss the results and to identify any issues that need to be highlighted when giving feedback to the students. This is very good practice.
Reports issue to parents following the formal and mock examinations and ongoing communication with parents occurs through the student diary, telephone contact and through the use of formal letters. In addition, each class group has one parent-teacher meeting per year and less formal, meetings can be arranged, if required. Examination classes also have one tutor-parent teacher meeting in the first term. This is very good practice as it provides an additional opportunity to inform parents of any issues that have arisen and to identify strengths and areas for development.
The school facilitates student participation in a range of co-curricular and extracurricular activities, including the Hamilton Prize and the Trinity Access Programme. In addition students from the school attend workshops provided by Tallaght Institute of Technology, the purpose of which is to engage the students in active learning in Mathematics through the use of programming, robotics and other ICT-rich methodologies. The school also supports the attendance of its students at revision courses in Mathematics provided by the National College of Ireland.
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, with the principal and deputy principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published, November 2009