An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
Cross and Passion College
Kilcullen, Co. Kildare
Roll number: 61690W
Date of inspection: 13 January 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Cross and Passion 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; the board chose to accept the report without response.
Timetabling provision for Mathematics in junior cycle is good. Mathematics classes are initially mixed ability in first year. Students are assigned to levels at the end of January in first year following a range of assessment procedures and consultation with parents and teachers. Mathematics classes are banded for the remainder of junior cycle and are timetabled concurrently within the bands. This is very good practice as it allows students to follow the highest level possible for as long as possible, it enables students to change level should the need arise, and facilitates collaborative curricular planning, particularly in the area of assessment.
Timetabling provision for Mathematics in senior cycle is very good. Transition year (TY) is compulsory and students are provided with three classes of Mathematics per week. Mathematics classes are banded in TY and students are assigned to levels on the basis of their performance in the Junior Certificate mathematics examination or following the completion of a competency test in Mathematics. There are five classes of Mathematics per week in fifth and sixth year while those students taking higher-level Mathematics in sixth year are provided with an additional period of Mathematics per week. Students in fifth and sixth year following the Leaving Certificate Applied (LCA) programme are provided with three classes of Mathematical Applications per week.
Procedures for identifying and supporting students in need of learning support or with special education needs (SEN) are very good. All incoming students sit a range of standardised tests including the Drumcondra Verbal and Numerical Reasoning Test. The schoolís guidance counsellor and the learning support co-ordinator administer the tests and following an analysis of the outcomes they visit the feeder primary schools to meet with the sixth-class and learning-support teachers. The purpose of these meetings is to discuss the performance of the students in the assessment test. The opportunity is also taken to complete a standard form, designed to create a comprehensive profile of each incoming student. In addition, students who have already had their learning or other needs formally assessed by the National Educational Psychological Service (NEPS) in primary school are identified. Parents and students are then invited to attend the schoolís information evening where the learning support team avail of the opportunity to speak to parents and to collect completed psychological assessments.
At the first staff meeting of the year the learning-support team provide feedback to the entire staff regarding the profile of the different first-year class groups. They also attend the different subject department meetings to provide subject-specific advice and to advise on the most appropriate means of meeting the learning needs of specified students. Learning support is primarily provided through team teaching and in-class co-operative support. However, resource teachers are also assigned to small groups of students with exemptions from Irish in junior cycle and to designated LCA and TY students in senior cycle.
Profiles of students with SEN or in receipt of learning support are developed and learning targets for individuals and groups are set. Student progress is measured by observation of student performance in class and by their performance in differentiated class and formal tests. The performance of students is discussed at the meetings of the learning-support team and targets are reset, based on the degree to which the students attained the desired learning objectives.† Referral forms are available for teachers to record any concerns they may have about individual students. Upon receipt of a referral form, a screening process is set in train: standardised tests are administered, the studentís parents are contacted and, if it is deemed necessary, an assessment is arranged through NEPS. A decision is then taken on the most appropriate model of support to be provided.
Students with exceptional abilities in Mathematics are also identified as part of the enrolment procedure. They are encouraged and facilitated to participate in the programmes operating under the aegis of the Centre for Talented Youth of Ireland (CTYI) in Dublin City University.
The mathematics department is comprised of twelve teachers. The qualifications profile of the department is very good and they work as a very effective team in planning and delivering the mathematics curriculum. Teachers are assigned to classes and levels by rotation and, at present, there are three members of the team who teach higher-level mathematics to Leaving Certificate. Furthermore, it is policy that teachers retain the same class group from second to third year and from fifth to sixth year. This is very good practice as it ensures continuity of approach and facilitates long-term planning.
The mathematics department is very well resourced and the schoolís information and communication technologies (ICT) facilities are particularly good. The school has two computer rooms and has embarked on a process of distributing data projectors into general classrooms. All of the classrooms are connected to the schoolís network via a wireless connection and the teachers, supported by the schoolís board of management, have purchased laptops for use in preparing and delivering lessons and to facilitate collaborative planning. Resources for classroom use have been purchased over the years and are stored centrally. In order to enhance the very good work already underway in identifying and managing resources, it is recommended that an audit of the resources currently available to the mathematics team be undertaken and that the resulting inventory be included in the subject development plan for Mathematics. In addition to the physical resources available to the team, the audit should also include ICT resources including software lists and useful websites. The arrangements for accessing the resources should also be included in the subject development plan for Mathematics.
School development planning is well established in the school and subject development planning forms an integral part of the mathematics departmentís activities. A co-ordinator has been appointed and regular meetings are held. Responsibility for co-ordinating the department rotates between the members of the department and the role of the co-ordinator is clearly outlined in the departmentís planning documentation. This is very good practice as it provides a framework within which planning takes place and enables each member of the department to adopt a leadership role in developing the department. In order to build on the good practice in subject development planning in Mathematics and to inform future planning, it is recommended that the mathematics teachers meet with the senior management team annually to review the performance of students in the state examinations with reference to the statistics supplied by the State Examinations Commission.
A very comprehensive subject-development plan for Mathematics is in place and is updated regularly. Two planning meetings are held each term, the minutes of which are available in the subject development plan. The plan outlines the provision for Mathematics, including access to levels, the grouping of students, the timetabling of classes and details about staffing for the subject. The plan also contains the mission statement for the department, a statement of aims and objectives, lists of resources and the schedule for curriculum delivery. It was particularly noteworthy to see that the plan contained suggested teaching methods and included common and agreed procedures for carrying out standard mathematical operations. To ensure that the plan remains current, it is recommended that the next review of the plan should reflect the recent changes in the delivery of learning support in Mathematics and in the arrangement of mathematics classes in first year.
The existing very good practices in planning could be further enhanced by detailing how different areas of the syllabus could be integrated during lesson delivery and how the resources listed in the plan could be incorporated to enhance teaching and learning. For example, a lesson investigating congruence in geometry might make use of models to illustrate the underlying principles and to provide opportunities for active learning. Dynamic geometry software could also be deployed to prompt further discussions and to illustrate possible solutions.
Separate plans for TY and LCA are in place. Both plans are very comprehensive and while the LCA plan is appropriate to the aims and objectives of the programme, the TY plan needs to be reviewed. The review should focus on selecting content and delivery modes to develop the studentsí confidence in, and appreciation of, Mathematics, and should address identified areas for remediation and skills development.
Individual teacher planning is very good. Comprehensive schemes of work and lesson plans were available for all of the lessons obseved. Planning for the inclusion of resources in lesson delivery, in some instances, was also very good.
Management is proactive in facilitating attendance at continuing professional development (CPD) courses and in enabling the provision of whole-school training. Recently, a course on School Curriculum Development, with a specific focus on Mathematics was provided to the entire staff. Details of the CPD courses attended by mathematics teachers are contained in the subject development plan. The majority of the department are members of the Irish Mathematics Teachersí Association (IMTA) and management covers the cost of membership.
The lessons observed during the inspection were very well planned. The material covered was appropriate to the requirements of the syllabus and was in keeping with the subject development plan. The lessons were purposeful and well managed. The sequencing of material was very good and clear links were drawn to the studentsí earlier learning and to their everyday experiences.† Very good practice in relation to the correct use of mathematical language and the appropriate use of symbols was also in evidence.
The teachers were knowledgeable and taught with enthusiasm and, while the textbook was the primary teaching resource, a number of other very effective teaching methods were also observed. These were seen to best effect in one lesson where active learning supported by appropriate resources and excellent teacher interventions enabled students to investigate introductory statistics. Arranged in small groups and with one student nominated to record the outcomes of each experiment, the students investigated and discussed the mean, mode and median. A worksheet produced by the teacher reinforced the lessonís objectives and encouraged the students to probe the wider relevance of their work.† As a result, the students clearly understood the material being covered in class and could apply it in a number of different situations.
The use of a graduated worksheet was also seen to good effect in supporting a lesson where students were investigating exchange rates and conversions from one currency to another. The students engaged in a series of calculations presented in the context of a foreign holiday and worked through increasingly more challenging material as the lesson progressed. The structure of the lesson enabled the teacher to support individuals as the need arose and also to address the entire group to suggest possible approaches to solving the more difficult problems. In order to build on the existing good work in lesson planning and delivery and to exploit the expertise present in the department, it is recommended that a range of teaching methods, to reduce the reliance on the textbook, to increase levels of differentiation and to enhance the opportunities for student-centred learning, be identified and implemented.
Classroom management was very good. The teachers skilfully kept the lessons on track and dealt with any issues that arose in a positive and creative fashion. As a result, difficulties encountered by individual students provided learning opportunities for the entire group and served to inform how the teacher presented subsequent material. In-class support in the form of team teaching was also observed during the inspection and in all cases it was appropriate and supported the lessonsí objectives, without negatively impacting on the studentsí independence.
Positive student behaviour was evident in all of the classes visited during the inspection. The atmosphere in the classrooms was warm, and the rapport between teachers and students contributed to an open and enjoyable learning environment. There was very good use of teacher-directed questioning. This was particularly true in cases where students were invited to speculate, to suggest possible approaches to problem solving, and to explain their reasoning. Teacher questioning also served to include as many students as possible in problem solving. This was seen to very good effect where the individuals were asked to provide one line in the proof of a theorem before passing on responsibility for the next line to another student. This approach ensured that all the students had to focus on the work in hand and that the responsibility for completing the task was shared between the members of the class.
The quality of student learning taking place was, in almost all cases, very good. The students responded readily to teacher questioning and were well able to carry out any tasks assigned by the teachers. The quality of learning could have been further enhanced if the context in which the material being discussed was established. This would mean that, in addition to being able to carry out the requisite calculations, the students would be able to explain their answers and apply their knowledge. The quality of the studentsí homework copies was very good and the performance of the students in class tests and in the state examinations offered further evidence of the high quality of student learning.
Ongoing assessment occurs through teacher questioning in class, through the assignment and correction of homework, and through in-class tests. Homework is regularly assigned and corrected. In some instances the homework copies contained positive teacher comments and suggestions as to how the studentsí work might be improved. All members of the department should adopt this very good practice, which provides constructive feedback to students and offers avenues for enhanced attainment.
In-class tests take place upon the completion of each topic and records of student attainment are assiduously recorded in the teachersí diaries. Teacher practice in relation to checking and recording student attendance is also very good.
First-year students sit a common assessment in Mathematics just prior to the first-year parent-teacher meeting, which is held at the end of January. The assessment is corrected using a common and agreed marking scheme and the results are collated centrally. The results, which are used to inform student decisions regarding choice of levels, are discussed with the parents at the parent-teacher meeting. The studentsí performance in Mathematics from their arrival in the school is continuously tracked by means of class tests. The results form the basis of the progress report that issues to parents at Christmas and further informs student decisions in relation to the level they will follow once the classes are rearranged following the parent-teacher meeting.
Formal tests are provided for non-examination classes at Christmas and just prior to the summer holidays. Common papers are provided within levels as appropriate. Examination students sit formal assessments at Christmas and sit mock examinations at Easter. Students at the same level take common papers in the mock examinations. The students in third and sixth year are provided with a comprehensive revision schedule, which runs in tandem with their ongoing class work.† The teachers assign questions, which are similar in style and content to those the students will meet in the state examinations. The completed assignments are corrected regularly and ongoing feedback is provided to the students. This is very good practice.
Students in receipt of reasonable accommodation in the state examinations receive appropriate support in class and formal tests.
Reports are issued to parents after each formal assessment and ongoing communication occurs through the use of the student diary, parent-teacher meetings and other less formal means. Progress reports, summarising the ongoing performance of students in the examination classes, are also sent to parents at intervals during the year. Each class group has one parent-teacher meeting per year.
The school promotes positive attitudes to Mathematics by encouraging students to take part in a range of extra-curricular activities pertaining to Mathematics. Junior cycle students participate in Problem Solving for Irish Second Level Mathematicians (PRISM) competitions, organised nationally as part of Maths Week Ireland, while senior cycle mathematics students participate in Team Maths. In addition, the school celebrates attainment and endeavour at its annual awards ceremony.
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 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