An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Avondale Community College
Avondale, County Wicklow
Roll number: 70810H
Date of inspection: 21 November 2008
REPORT ON THE QUALITY OF LEARNING AND TEACHING IN MATHEMATICS
This report has been written following a subject inspection in Avondale 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 and subject teachers. The board of management of the school was given an opportunity to comment on the findings and recommendations of the report; the board chose to accept the report without response.
Time allocated to Mathematics in Avondale Community College is very good. In junior cycle, five classes per week are allocated to first, second and third year groups. Transition Year (TY) students are timetabled for three classes per week. Fifth and sixth year students each have six class periods per week. School management facilitates concurrent timetabling of Mathematics for all year groupings, except TY. This is commendable as it creates opportunities for students to choose a level most appropriate to their abilities.
First year students are assigned to mixed-ability class groups for about two weeks. They then sit a Mathematics examination and classes are banded for Mathematics. Ongoing monitoring of students is undertaken and movement, when necessary, between bands is permitted. In general, one higher and two ordinary level class groupings are arranged in junior cycle with foundation level offered on a needs basis. An optional TY was introduced in 1997 and this year two mixed ability classes have been formed. In senior cycle, banding takes place for Mathematics. The practice in general is to have one higher-level class and two ordinary class groupings. Ongoing monitoring of students by teachers identified a need to create a small class grouping for some students who find Mathematics challenging. This provision was introduced last year for some fifth-year students and continues this year into sixth year. This additional allocation is commendable and its facilitation by management is acknowledged.
Students are encouraged to remain with the highest level possible for as long as possible. In the event that a student wishes to change level, communication with home is made and consent is sought. However, it was reported that there is on occasion reluctance on the part of students to take a level more appropriate to their ability. Teachers and management should explore ways in which students are encouraged to aim towards their full potential and in the selection of the most appropriate Mathematics level particularly at Leaving Certificate.
Six teachers are deployed to teach Mathematics in Avondale Community College. Teachers are deployed in line with their specialism. Commendably, teachers have the opportunity to teach levels at junior cycle on a rotational basis, with two member of the department rotating the teaching of higher level at senior cycle. This practice allows for the development of expertise within the Mathematics department. Additionally, the facility to remain with a class grouping within a cycle is further evidence of good practice.
Decisions regarding resources are taken collectively at department meetings with requests for resources progressed by the co-ordinator to the principal. Teachers are generally classroom based and many have access to a wide range of materials, including data projectors and overhead projectors. Additionally, each teacher receives a list of Mathematics-specific resources which are retained centrally and accessed for use in the teaching of Mathematics.
Teacher continual professional development (CPD) and training is supported by management. Teachers have received in-house CPD and have also been facilitated to attend subject-specific training. In line with best practice upon their return teachers share resources received during their in-service among colleagues in the Mathematics department. The school has recently received in-service training in the area of Assessment for Learning (AfL), following which each subject department has chosen three strategies to adopt. There was evidence that all teachers of Mathematics are following the chosen strategies during lessons observed. Newly appointed teachers are supported through the school’s mentoring programme and by attendance at Co. Wicklow Vocational Education Committee in-service for newly appointed teachers. Management’s support of newly appointed teachers and of continuing professional development is acknowledged.
Through careful planning the learning support department and the Mathematics department have planned to ensure that best practice is observed in the provision of numeracy support in Mathematics. The provision of support in Mathematics takes many forms and includes the creation of a Leaving Certificate class group in which support is offered, individual withdrawal and team teaching. Ongoing review and consultation among both departments takes place to optimise the available resources and to ensure that the most appropriate support is given that will best suit the individual needs of students. There is evidence from the documents provided that the mainstream teacher and the Mathematics numeracy support teacher work closely in the provision and continuity of support offered to students. Teachers are commended for the implementation of best practice in the provision of support in Mathematics and for their commitment to ongoing review. In addition to supporting students with special educational needs, the school is currently looking at opportunities to develop programmes for gifted students, and this is commendable.
Many students are given opportunities to participate in co-curricular activities in Mathematics. For example, some students have been chosen to participate in the Irish Mathematics Olympiad while others participate in the Centre for Talented Youth in Dublin City University. Additionally, teachers reported providing extra Mathematics lessons to students particularly at higher level. Support by teachers for their students is commended. Involvement in the Irish Mathematics Teachers Association is commendable and reflects the interest of teachers in their subject.
The Mathematics department presented as a cohesive and well organised team of teachers. A co-ordinator is appointed every two years on a rotational basis. This is good practice as it ensures that members of the department are given the opportunity to share in the responsibility of co-ordination and operation of a department. Duties assigned to the position of coordinator include convening department meetings, liaising with senior management and recording decisions taken.
Formal subject department meetings are facilitated with many informal meetings taking place on a monthly basis. Minutes of meetings are recorded on a school report template that includes the action to be taken, the person responsible and the time frame, and on which matters for the next meeting can be noted. This document facilitates focused discussion and action planning. Minutes of meetings retained indicate that issues discussed include the Mathematics plan, class organisation, decisions taken and identification of necessary action, personnel assigned to the activity and stated timeframe. Through this process the department has identified concerns and is adopting a variety of strategies to address areas of concern. For example, the department has identified a need to increase numeracy skills among a cohort of second-year students and has developed an action plan which will be implemented and reviewed over the coming term. This is very good practice and teachers are commended for their work in this regard.
There is clear evidence that members of the Mathematics department have collaborated and documented a long-term plan for the department that includes the organisiation details of the department along with the yearly scheme of work for each year group. To further enhance the department’s plan it is recommended that reference to relevant syllabus content and learning outcomes for each year group be identified and included.
In line with the philosophy of the TY programme, the school’s TY Mathematics programme provides students with an opportunity to consolidate junior cycle material, to encounter new material and to study current affairs through Mathematics. For example, the use of the “You do the Maths” document sourced from the Department of Foreign Affairs allows students to discuss and engage with numeracy, data management and statistics. The TY Mathematics programme provides students with opportunities to continue to develop competencies in Mathematics while also engaging with Mathematics in different contexts and this is commendable.
Individual planning documentation presented by all teachers was comprehensive. Teachers use the long-term Mathematics plan and have developed individual programmes of work which are divided into term programmes of work. Care is taken to ensure that, in so far as is possible, topics are studied concurrently within year groupings. In addition preparation for lessons was very good and all necessary worksheets and resources were prepared and to hand in advance of lessons.
In all lessons the chosen content was appropriate, in line with syllabus requirements and suitable to the students’ abilities. To reinforce the Mathematics department’s AfL strategies, lessons frequently opened with the stating or writing down of the learning objectives for the lesson. In addition the practice of marking off each objective upon its completion was noteworthy as it demonstrated to students that progress within the lesson has been made and the objective achieved.
Topics observed included statistics, area and volume and arithmetic. All lessons were presented in a confident manner. The lessons were appropriately paced with time used effectively. The use in many lessons of real life situations served to enhance the learning experience for students and is very good practice. Examples of this approach included the use of snooker via data projector, to teach algebra, and reference to text messaging to teach the terminology of a variable in algebra.
The use of mathematical terminology by teachers in all lessons was exemplary. Frequently teachers asked students to give an example of their understanding of terminology, and this is commendable practice. In addition, students’ use of appropriate mathematical terminology reflected exposure to mathematical terms on a regular basis.
The predominant method used was teacher demonstration, involving an exemplar followed by a selection of questions for students to practise. This method allowed teachers the opportunity to circulate to give individual attention to students who had difficulty with the assigned exercises. Paired work featured to a lesser extent in lessons observed. Even though these methods were effectively used it is important that the learning styles of all students be addressed through the continual introduction of other methodologies that will complement those in the current repertoire. A range of methodologies can be sourced in the Junior Certificate Mathematics Guidelines for Teachers.
Questioning strategies varied within lessons. There was a good balance between teacher input and student work in all lessons. At the beginning of lessons questions were used to establish the next step in a solution or to recall a concept from a previous lesson or prior learning. Effective, although used infrequently, were higher-order questions which had the effect of engaging students by extending their understanding or providing them with opportunities to justify their answers. Where appropriate, increased use of higher-order questions is to be encouraged.
All lessons were conducted in a positive atmosphere of mutual respect and were reflective of the philosophy of the school. Students were co-operative and this allowed for good progress to be made in all lessons observed. Teachers set high expectations for students commensurate with their abilities. Students responded positively to clear class rules and teacher instructions. Inputs from students were affirmed and, when necessary, students were encouraged to check if their answer was correct before proceeding with their work, and this is good practice. Commendably students responded positively to these expectations and were engaged and focused on the work at hand.
In all lessons observed learning was purposeful and there were many instances where students demonstrated very good knowledge and understanding of the topic. Additionally, there were many instances where students were given opportunities to work and become independent learners and enjoyed the challenge. There was evidence in lessons of students taking an active role in their own learning. For example, many students took time to reflect on newly acquired skills and questioned their teachers to ensure that they had correctly understood new concepts.
During teacher discussion and interaction with the inspector, students demonstrated good levels of comprehension of topics being studied and responded appropriately to questions posed to them.
Resources used in lessons included the overhead projector, worksheets and data projector. All were used effectively and at key stages to engage students with the lesson. The sourcing of resources from the Revenue Commissioners to teach tax credits and tax-related issues is commendable as it ensures that students’ work is set in context. Commendably, many classrooms displayed both student-produced and commercially acquired mathematical posters, further supporting AfL strategies. Such displays served to enhance the learning environment for students and to act as a teaching aid for the subject.
Homework was assigned in all lessons observed. The content of the material chosen was suitably challenging for students to practise newly acquired concepts. Students were instructed to record homework in their students’ diaries; however, there was evidence that they do not always do so. It is recommended that this matter should be address on a school-wide basis.
The assessment of students takes many forms. Ongoing regular assessment takes place at the end of a topic. Formal assessment takes place at Christmas and summer for non-examination years with Christmas and mock examinations for examination years. Many teachers collaborate to develop some common assessments for in-house examinations. The department is currently planning to extend this practice for Christmas and summer examinations and this is commendable.
Through observation of teachers’ documentation, there is evidence that teachers retain good records of students’ attendance and achievement. Communication between the school and home is maintained on a regular basis. The school issues school reports following formal examinations. Parent-teacher meetings are convened for all year groups, and newsletters, the school website and students’ diaries are all used to provide information to parents. In addition, subject teachers can issue a progress report for an individual student when they deem it necessary to inform a parent of a student’s performance. Furthermore, the recent introduction of postcards home to celebrate students’ achievements in Mathematics is commendable.
In line with the AfL strategies, the Mathematics teachers provide written feedback to students who achieve less than forty per cent in Mathematics examinations. Furthermore, there is evidence that many teachers are providing written feedback in students’ copies regarding suggested areas of improvements, and this is commendable practice.
At regular intervals throughout sixth year, students meet with the principal and guidance teacher. These meetings provide an opportunity to develop a timetable for study and set targets to assist students as they prepare for the examinations. Such supports for students are further examples of mechanisms to ensure that students are well supported in Avondale Community College.
The following are the main strengths identified in the evaluation:
· There is very good support by management for Mathematics in Avondale Community College, through the timetabling provision, facilitation to attend in-service and provision of resources.
· The Mathematics department works as a cohesive team, collaborating to develop and implement strategies that address the needs of students.
· The Mathematics department has developed a collaborative plan for Mathematics in Avondale Community College.
· Students are given opportunities to participate in co-curricular Mathematics activities.
· Mathematics students receive positive affirmation from their teachers and were confident and able to use appropriate terminology during questions posed to them during the evaluation.
· There is evidence of close collaboration between the learning support and the Mathematics departments in the organisiation and provision of numeracy support to students.
· Students presented as being positive about their work and were engaged in lessons observed.
· There were many examples of good practice in the teaching and learning of Mathematics.
· There were examples of very good use of a range of resources used in lessons.
· Students are regularly assessed in Mathematics and there are good mechanisms for informing parents about students’ progress.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· The development of a range of teaching methodologies and questioning strategies to be used in all lessons is encouraged.
· Some modification to update the long-term plan for Mathematics is necessary to reference the relevant syllabuses.
Post-evaluation meetings were held with the teachers of Mathematics and with the principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published June 2009