An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
St. Johnís College
Le Fanu Road, Ballyfermot, Dublin 10
Roll number: 60510M
Date of inspection: 15 September 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in St. Johnís 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 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 board of management of the school was given an opportunity to comment on the findings and recommendations of the report; a response was not received from the board.
Timetabling provision for Mathematics in St. Johnís College is good. Each first-year class group has four periods of Mathematics per week, while the remaining class groups in both junior cycle and senior cycle have five periods. Students taking Leaving Certificate Applied (LCA) have five periods of Mathematical Applications per week. Each class period is forty minutes long. The scheduling of the mathematics classes throughout the week is also good. Each class group has at most one period of Mathematics per day and these are well distributed through mornings and afternoons.
Mathematics classes are banded in first year. The two upper bands are mixed ability and the remaining two bands participate in the Junior Certificate Schools Programme (JCSP) and follow the ordinary level course. Some of these students may opt for foundation level in due course. Classes are streamed in second and third year. There are four mathematics class groups in each of the two years. The top stream in each case takes higher-level Mathematics. The two middle streams take ordinary level and the remaining stream participates in JCSP and takes foundation level. The mathematics classes are not timetabled concurrently in junior cycle, and this means that if a student wishes to change levels he must also change his class group. It is recommended that this element of the timetabling of Mathematics be kept under review and that, where possible, concurrent timetabling of Mathematics be provided in each year of junior cycle.
Mathematics classes are streamed in fifth and sixth year with the top stream, in each case, taking higher level. The remaining streams all initially follow the ordinary level course. However, a significant number of students opt for foundation level as they progress through the Leaving Certificate programme. Classes are timetabled concurrently in each year. This is very good practice as it enables students to follow the highest level for as long as possible. It also facilitates movement between levels when the need arises, and it encourages greater collaboration in curriculum delivery and assessment.
St. Johnís College maintains very close links with its feeder-primary schools through its participation in the Schoolsí Completion Programme (SCP), through the activities of its home-school-community liaison co-ordinator and the collegeís learning-support co-ordinator. These links are a key component in the collegeís enrolment procedures, as the needs and experiences of prospective students are established prior to enrolment. The school holds an open night every October and invites the parents of prospective students to attend. At this meeting, parents are informed about the collegeís policies and practices and the range of programmes available to students. Application forms and the arrangements regarding the assessment of incoming students are distributed. An induction day for incoming students is held shortly after the open night. The incoming students are invited to participate in a range of curricular and extra-curricular activities and to become familiar with the layout of the college. Upon enrolment, the students are assessed using a standardised test which targets verbal reasoning together with curricular tests in English, Irish and Mathematics. The results of these tests are used to assign incoming students to class groups in first year. Currently, the mathematics test used as part of the entrance assessment is set and corrected by teachers in the mathematics department. It is recommended that the sixth-class teachers in the feeder primary schools be invited to engage in this process, as this would provide an opportunity for teachers to dialogue regarding the strengths, weaknesses and interests of the incoming students and would create a forum where relevant information about students could be shared.
The procedures for identifying and supporting students with special educational needs (SEN) are very good. Students with SEN are identified prior to enrolment. The collegeís learning support coordinator visits the feeder primary schools to meet with the class teachers and also maintains regular contact with the SCP coordinator and the home-school-community liaison co-ordinator. The learning-support team also meets with the parents at the open night. 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 NEPS.
Upon enrolment in the school, those identified with SEN are retested in Mathematics and English. The support model for each student is then designed and agreed following consultation with staff, management and parents. Learning support in Mathematics is provided through the withdrawal of students in small groups from subjects other than Mathematics and through in-class support. Parents are informed in writing of the arrangements being proposed and parental consent is required if students are being withdrawn from class for additional support in Mathematics. The material covered during withdrawal is linked very closely with the content taught during the regular mathematics classes and is agreed during meetings between the resource teachers and class teachers. The progress of students in receipt of additional resource teaching is communicated to parents through personal notes, telephone calls and through the JCSP communication mechanisms. The performance of students in learning support is discussed regularly at team meetings and procedures for returning students to mainstream classes are then put in place, where appropriate.
The mathematics department is very well resourced. Computers and data projectors were available in almost all of the rooms visited during the inspection, and a comprehensive range of resources to support teaching and learning in mathematics is provided. There is no formal budget for Mathematics at present, but it is reported that the school intends to provide budgets to each of the subject departments in the coming school year.
The mathematics teachers and students are also engaged in a range of activities to promote numeracy and an appreciation of Mathematics. The mathematics teachers are participating in the JCSP numeracy programme this year, and the students have engaged in project work involving surveying, analysing and compiling data. This cross curricular and multidisciplinary approach in teaching and learning Mathematics is very good practice.
School development planning is well established in St. Johnís College and a comprehensive subject development plan for Mathematics is in place. The plan addresses the existing provision for Mathematics in the college, the arrangements for studentsí access to levels and programmes, agreed classroom-management strategies, homework and assessment procedures, resources lists, procedures for supporting students with SEN and a wide range of teaching methods to be adopted in delivering the mathematics curriculum. The subject development plan also details the topics to be covered by each year and level. While this is very useful, it could be further enhanced by specifying the delivery schedules for the different topics. This would particularly facilitate individual planning and the coordination of common assessments.
The mathematics department is ably co-ordinated by one of the teachers. Regular meetings are held and minutes of these meetings are available in the subject development plan. It would be preferable if the responsibility for co-ordinating the department was rotated by agreement between the members of the department. This would act as a vehicle for professional development and provide opportunities for each team member to adopt a leadership role in developing the department and to becoming aware of new developments and trends in teaching and learning Mathematics.
The very good work being done by the mathematics department in the area of planning could be further enhanced by referring to the statistics available from the State Examinations Commission to inform future planning. It is recommended that the mathematics department meet with the principal each year to analyse these statistics in order to compare the uptake of the different levels and studentsí performance in the certificate examinations with the national norms. It is further recommended that any issues arising be subsequently addressed as part of the planning process.
Individual teacher planning for Mathematics is very good. All of the teachers made their planning materials available to the inspector during the inspection and in almost all cases it was comprehensive and relevant and reflected the particular needs of the students in the different classes. There was extensive use of information and communication technologies (ICT) in preparing lesson plans and worksheets, and in recording the performance of students in class and in formal tests. Planning for the use of resources in teaching and learning was particularly good and this was reflected in the seamless fashion in which the resources were subsequently integrated into the lessons observed during the inspection.
Collaboration with colleagues in relation to individual planning can be very beneficial. This is particularly true in relation to the teaching of core mathematical operations and in identifying common problems encountered by students during lessons, doing homework and completing class tests. It is recommended that a list of core mathematical operations be identified and that common practice be agreed and implemented in the teaching of them. The list of operations and the agreed common practice should be included in the subject development plan for Mathematics.
Procedures for supporting newly appointed teachers are good. Newly appointed teachers meet with the principal or the deputy principal for an afternoon prior to the beginning of the school year. This meeting addresses classroom-management techniques, the schoolís ethos and how the various procedures should be followed in relation to discipline, including that of promoting positive behaviour. They are also made aware of relevant policies. A post holder has responsibility for supporting and meeting with newly appointed teachers, particularly in the first term. They are then paired with an established teacher, preferably in their own subject area, who acts as a mentor for the remainder of the year.
The lessons observed during the inspection were well planned. In all cases, the teachers had prepared curricular materials in advance of the lessons. These were used to reduce the amount of teacher-led activities and to create a learning environment that was student centred, busy and challenging. The content of the lessons was appropriate and in some cases quite challenging for students. There was good continuity with the material that had been covered in earlier lessons. Greater emphasis should be placed however, on contextualising the material being covered and exploring its relationship with different areas of the mathematics course.
A particularly good example of lesson planning and delivery was observed where students used a commercially produced set of resources. These allowed them to establish their strengths and weaknesses in working with numbers and provided them with a range of exercises which became more difficult as they progressed. It was really impressive to see the students organise themselves at the start of the lesson, identify what they were going to do during the lesson and seek help when the need arose. The teacher input was limited to answering studentsí questions and offering one-to-one assistance when required.
A range of teaching methods was observed during the inspection. These included team-teaching, worksheets for students, ICT integration and the use of the overhead projector. In one lesson, PowerPoint was used to prepare and present an area of the algebra syllabus in junior cycle. The teacher worked through different procedures using the animation features of the software, the slides were given to the students in the form of worksheets which were then stored in their mathematics folders. This mode of lesson delivery facilitated good teacher movement and student engagement and also provided each student with an extensive resource, which included solved problems, structured procedures for dealing with various mathematical operations and revision materials.
Positive behaviour was evident in all of the classes visited. The lessons were conducted in an atmosphere of mutual respect, with good humour and empathy for all studentsí needs. Student engagement was very good and they contributed positively by asking relevant questions and proposing alternative approaches to problem solving. In some cases teachers made good use of questioning to elicit factual responses to specific questions. There was however, an over reliance on global questioning and very little emphasis was placed on encouraging students to hypothesise and engage in higher-order thinking.
Practices relating to the assigning and correcting of homework in Mathematics are good. Homework is assigned during each lesson and is corrected at the beginning of the subsequent lesson. The homework copies examined during the inspection were well maintained, and in some cases, the very good practice of teachers providing constructive comments was in evidence This good practice could be further enhanced by revising the existing homework policy for Mathematics to include the roles and responsibilities of all stakeholders, including students and parents. It is further suggested that the practice of students amending their own work be included as a key assessment vehicle in the revised homework policy.
Formal common assessments are held at Christmas, and just prior to the summer holidays. Common papers are set and corrected using common marking schemes. The results are collated centrally and are used to inform studentsí decisions regarding choices of levels. This is very good practice as it enables the performance of individuals to be gauged against the norm. In addition, class tests are set at the end of each topic. The results of these tests are stored in the teachersí diaries and were made available to the inspector during the inspection.† State examination students sit formal assessments at Christmas and have mock examinations early in the second term. Students taking the same level have common papers in the mock examinations
Reports issue to parents after each formal assessment and, when necessary, formal letters are sent informing parents of any concerns relating to performance or behaviour that may have arisen during the course of the year. In addition, each class group has one parent-teacher meeting per year and private meetings between teachers and parents can be organised at any time.
The following are the main strengths identified in the evaluation:
∑ A good standard of teaching and learning was observed during the inspection.
∑ Timetabling provision for Mathematics is good.
∑ The procedures for identifying and supporting students with special education needs are very good.
∑ Teachers and students are engaged in a range of activities to promote numeracy and an appreciation of Mathematics.
∑ Subject development planning is well advanced and a comprehensive subject development plan for Mathematics is in place.
∑ The mathematics department is ably coordinated.
∑ Individual teacher planning in Mathematics is very good.
∑ Procedures for supporting newly appointed teachers are in place and are working effectively.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
∑ It is recommended that the timetabling of Mathematics in junior cycle be kept under review and that, where possible, concurrent timetabling of Mathematics be provided in each year of junior cycle.
∑ It is recommended that the sixth-class teachers in the feeder primary schools be invited to participate in the entrance assessment process in Mathematics.
∑ It is recommended that the mathematics teachers meet with the principal each year to analyse the statistics made available by the State Examinations Commission in order to compare the uptake of the different levels and the studentsí performance in the certificate examinations with the national norms and that any issues arising be subsequently addressed as part of the planning process.
∑ It is recommended that a list of core mathematical operations be identified and common practice be agreed and implemented in teaching them. The list of operations and the agreed common practice should also be included in the subject development plan for Mathematics.
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 January 2009