An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Castledermot, County Kildare
Roll number: 70670R
Date of inspection: 13 May 2008
REPORT ON THE QUALITY OF LEARNING AND TEACHING IN MATHEMATICS
This report has been written following a subject inspection in Coláiste Lorcain, Castledermot, Co. Kildare. 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.
Each school day in Coláiste Lorcáin is organised into nine class periods. Five of these are of forty minutes duration and the remainder are thirty-five minutes. Timetabling provision for Mathematics in the school is in line with national norms. In senior cycle, there are five periods per week and four periods per week are provided in junior cycle. The distribution of mathematics classes throughout the week is good, and they are well timetabled between mornings and afternoons. It is recommended that the mathematics provision be kept under review, and that the school development planning team discuss the feasibility of providing one mathematics period per day in junior cycle.
Mathematics classes are mixed ability in first year. Students follow a common programme, take common tests in class and sit formal common assessments during the year. Learning support is provided by withdrawing students from classes other than Mathematics, and the learning-support programme is designed to reinforce the material being covered in the mainstream classes.
Classes are set for Mathematics in second year. There is one higher-level mathematics class and two ordinary-level classes. One small learning-support group is also formed and the students in this group follow ordinary level for as long as possible. There are two higher-level mathematics classes in third year and two mixed ability ordinary-level classes. A small learning-support class is also formed in third year. Mathematics classes are streamed in senior cycle and a small class group is formed in both fifth and sixth year to support those students who have been identified as requiring learning support. It is policy that all mathematics classes in each year group are timetabled concurrently to enable students to study at the highest level possible, for as long as possible.
Transition Year (TY) is optional and is offered to all students upon completion of junior cycle. Mathematics classes in TY are mixed ability and three periods per week are provided.
Prospective students are initially informed about the school during visits by the school principal to feeder primary schools. These visits take place in October and are followed by an open night for prospective parents and students in late November. The open night offers them the opportunity to sample the school’s various activities and to learn about the school’s policies and procedures. The deadline for parents enrolling their children in first year is typically within one month of the open night. Incoming students are then invited to sit standardised tests in verbal and mathematical reasoning in February. Students are assigned to mixed ability classes in Mathematics upon entry to the school.
Students in need of extra support in Mathematics are identified during the school’s induction process. The learning-support team attend the open night and meet with individual parents to discuss students’ educational needs, and become aware of any learning support or resource requirements. The results of the standardised tests are analysed by the learning-support team and students are selected for further testing in order to identify their particular needs. This further testing takes place in September and the learning support and resource cohorts are identified at this stage.
Details of the continuing professional development courses (CPD) attended by members of the mathematics department are included in the department’s subject-development plan. The list of courses that have been attended is impressive. The plan gives details of the material covered, and the resources made available, during these courses. This is very good practice as it provides department members, and particularly newly-appointed teachers, with a valuable teaching resource.
The mathematics department is very well resourced and the teachers of mathematics have access to a range of information and communication technologies (ICT) including laptops, data projectors and interactive whiteboards. There was evidence of ICT integration, particularly in the preparation of classroom materials, viewed during the inspection. In addition, the learning-support team utilises a range of resources in teaching and learning. It is recommended that the mathematics team contact the Second Level Support Service (www.slss.ie) to identify an additional range of resources that would facilitate the inclusion of active methodologies in mainstream classes.
Newly-appointed teachers are provided with an induction programme which is managed by a post holder and supported by a staff handbook. The induction programme is currently under review as part of ongoing school-development planning.
Teachers are assigned to classes and levels on a rotating basis, and by agreement with management. However, the higher level Mathematics in senior cycle typically alternates between two teachers. It is suggested that, as an integral part of the school’s CPD programme, additional teachers be identified and assigned to higher-level Mathematics in the coming years. It is policy and practice within the school for teachers to remain with the same class groups from second to third year, and from fifth to sixth year, where possible, thus maintaining high levels of continuity.
Subject development planning in Mathematics is at an advanced stage. The mathematics department is jointly coordinated, formal planning meeting are held once each term, meetings are minuted and the minutes are included in the subject-department plan. It is clear that there are frequent informal planning meetings, where issues such as common assessments, special needs and learning support are discussed.
A very comprehensive subject-development plan for mathematics is in place. It is reviewed regularly and addresses all of the issues pertinent to the successful delivery of the mathematics curriculum. The schedule for content delivery in the subject-development plan is precise and specifies the topics to be covered by each year group and level each month. This very good practice streamlines curriculum delivery and facilitates continuity when students change level.
The mathematics plan for TY is integrated into the main subject-development plan. It is also very comprehensive and it details the objectives of the TY mathematics programme and the means by which the objectives will be met. The TY mathematics programme seeks to develop students’ confidence in, and appreciation of, Mathematics, and addresses identified areas for remediation and skills development. The material included in the TY mathematics programme is very appropriate and can be delivered using a range of methodologies. The methodologies to be adopted are outlined in the plan and include a range of very innovative approaches to engaging the students in their own learning. It is recommended that these innovative approaches be incorporated across the mathematics department and into the teaching and learning of Mathematics outside of the TY mathematics programme.
Individual teacher planning is excellent. All of the teachers made their personal planning materials available and in all cases these were relevant, comprehensive and appropriate. A lesson plan, written to an agreed template, was available for each lesson observed during the inspection. The teachers recorded in their diaries students’ attendance, homework completions and performance in class tests. The very good practice of student profiling was also evident in many of the teachers’ diaries.
It was evident during the inspection that practice in relation to teaching core mathematical operations such as factorising the quadratic and solving linear equations varied. While all the methods observed were correct, it is recommended that a list of core-mathematical operations be identified and common practice be agreed and implemented in the teaching of them. The list of operations and the agreed common practice should also be included in the subject- development plan.
Teacher planning and preparation for all of the lessons observed during the inspection was very good. Additional teaching and learning resources had been prepared by all of the teachers in advance of all of the lessons, and this meant that there was no over reliance on the textbook as the primary teaching aid. The material covered was appropriate and the lessons proceeded at a suitable pace.
The atmosphere in the classes was very warm, the teachers were affirming of the students and the students responded positively. The walls of the classrooms were adorned with students’ work, relevant posters and useful tips and tricks. This contributed to an environment where positive attitudes towards Mathematics were fostered and developed.
Positive student behaviour was evident in all of the classes visited and the teachers were skilful in facilitating student involvement and in managing the delivery of the lessons. A key feature of the lessons was the level of differentiation achieved by the teachers. In one class where students were learning about statistics, a differentiated worksheet was prepared in advance of the lesson and it was distributed, once the introduction to the lesson was complete. The teacher then moved around the room assisting individuals and occasionally used the marker board to deal with any issues that arose during the lesson. In this way, difficulties encountered by individuals and any innovative ideas that emerged were used to enrich the learning experience of all members of the class and deepen their understanding of the matter in hand. The material covered in the worksheet became gradually more testing and some of the later problems were designed to challenge the most able students. This is very good practice, as it provided all members of the class with an opportunity to engage with the material being covered at a level appropriate to their abilities.
In another lesson, a theme from a game show was adopted to introduce the concept of probability and risk aversion. The teacher explained the concept behind the game show and encouraged the students to speculate as to the strategies contestants should adopt, in order to be successful. The students then explored how the expected outcomes from the various activities, which occur during the game show, might be calculated. An individual was then chosen to play the game, and the remainder adopted the role of members of the television audience. At each critical point during the game, the audience calculated the expected outcome and offered advice to the contestant. The lesson was fun; the approach adopted was innovative and well planned and resulted in a very positive learning experience.
Student learning was very evident. A homework policy is in place and the mathematics teachers adhere to it rigorously. The homework copies were, in all cases, very good. They were well laid out, corrected regularly and contained corrections, comments and annotations. Regular class tests are given and each student maintains a separate copy for these. In some cases, the parents were required to sign the tests. This is very good practice and is highly commended. The students responded readily and confidently to teachers’ questioning and during their interactions with the inspector.
Practices relating to ongoing assessment are very good. Homework is regularly assigned and corrected. The homework copies contain teacher comments and in some cases the students amended their own work. Class tests are given at the end of each topic, and formative assessments, through the use of teacher questioning, was evident during the inspection.
Formal assessments for non-examination junior cycle classes are held at Christmas and just prior to the summer holidays. Common formal assessments with common marking schemes are provided for first-year students and common examinations within levels are arranged for the remaining non-examination classes. Third-year students sit mock examinations early in the second term, and students taking the same level sit common papers. The class teachers correct the papers. Results are issued to parents after each formal assessment.
Students in senior cycle have monthly assessments and results are issued to parents. In addition, fifth-year students sit formal examinations at Christmas and again just prior to the summer holidays. Sixth-year students sit mock examination early in the second term with students at the same level taking common papers. The papers are corrected externally. Results are issued to parents after each formal assessment
Ongoing communication occurs through the use of the student diary, parent-teacher meetings and other, less formal, means. Each class group has one parent-teacher meeting per year.
Students’ achievements are recognised by the school’s awards ceremony, which is held each May. The ceremony recognises excellence and endeavour in academic pursuits, sports and a range of school-related activities. The school facilitates the participation of students in the Prism competition.
The following are the main strengths identified in the evaluation:
· The time allocated to Mathematics at both junior cycle and senior cycle is in line with national norms.
· The procedures adopted to support those with special education needs and in need of learning support are very good.
· Management is proactive in facilitating attendance at relevant CPD courses.
· The mathematics department is very well resourced and the ICT facilities in the school are very good.
· Planning for Mathematics is excellent. The mathematics department is ably co-ordinated, and it was evident that the mathematics team collaborates very effectively.
· Homework, assessment and reporting procedures are in place and are implemented very effectively.
· The TY mathematics programme is very comprehensive and a range of innovative practices in teaching and learning in TY were evident during the inspection.
· Teaching and learning to a very high standard was observed during the inspection.
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 mathematics provision be kept under review and that the school-development planning team discuss the feasibility of providing
one mathematics period per day in junior cycle.
· It is recommended that the innovative approaches evident in TY mathematics classes be incorporated across the mathematics department
and into the teaching and learning of Mathematics outside of the TY mathematics programme.
· It is recommended that the mathematics team contact the Second Level Support Service (www.slss.ie) to identify an additional range of resources
to facilitate the inclusion of active methodologies in mainstream classes.
· It is recommended that a list of core mathematical operations be identified and that a common practice be agreed and implemented to
teach them. The list of operations, and the agreed common practice should also be included in the subject-development plan.
Post-evaluation meetings were held with the teachers of Mathematics and the principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published October 2009