An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Mullingar, County Westmeath
Roll number: 63270K
Date of inspection: 23 April 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Coláiste Mhuire, Mullingar, Co. Westmeath. 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 Mhuire is organised into eight class periods. Four of these are of forty minutes duration and the remainder are forty-five minutes. Timetabling for Mathematics in junior cycle is very good. Each class group in junior cycle is timetabled for one period for Mathematics each day totalling five periods per week. The balance of provision in Mathematics between morning and evening is also very satisfactory.
For the first time this year mixed-ability classes have been formed in first year. The school is commended for introducing this change. Classes in second and third year are grouped in bands. This facilitates the movement of students between levels and enables them to strive towards attaining the level which is most commensurate with their abilities. It is intended that this arrangement will remain in place when the present first-year cohort enters second year.
Provision for Mathematics in senior cycle is also good with five periods per week being provided. Classes are streamed and run concurrently. Applied Mathematics is provided for students outside of school hours.
Following an analysis of the mock examinations this year an additional mathematics class was created to support those experiencing difficulties with the ordinary level course. The commitment of management to the provision of this additional support is commended
Students intending to enrol in Coláiste Mhuire are informed about the school during visits by the principal and a post holder to the local primary schools. The school’s brochure and pertinent school policies are distributed during these visits. Prospective students in outlying schools receive this material by post. Invitations to the school’s open morning are then issued. During the open morning prospective students and their parents are introduced to the school, are given an opportunity to visit each subject department, meet with the teachers and students and sample some of the school’s activities. Completed application forms must then be returned by parents within one week of the open morning.
Students with special education needs (SEN) or those requiring learning support are identified as part of the enrolment process. Parents furnish information to the school on the application forms. The learning-support coordinator makes contact with the sixth-class teachers in the local primary schools and with individual parents to access psychological assessments and to discuss any special requirements. All incoming students sit standardised tests prior to entry to the school. These tests target numerical and verbal reasoning. Following a collation of the results, the school’s learning-support team meet to discuss the most appropriate support for those students who have SEN or other learning support needs. When it is deemed necessary, the school arranges assessments for those students who have not already completed psychological assessments but who are deemed to need support for learning.
Upon entry to the school in first year, the students are assigned to mixed-ability classes and are withdrawn in small groups for learning support. Students’ progress is tracked through consultation with the subject teachers and through the use of common-class tests. Referral of students not in receipt of learning support but who may need occasional support occurs through consultation with the class teacher, the learning-support co-ordinator and the students’ parents. Learning-support provision is student centred, timely, and flexible and is highly commended.
Newly appointed teachers receive an induction programme which includes meetings with the principal, the deputy principal and the co-ordinator of the mathematics department. Teachers are assigned to different levels by rotation and in accordance with the preference of each individual teacher. Teachers are facilitated to attend continuing professional development (CPD) courses pertaining to Mathematics. It is recommended that the list of courses attended and a list of any resources presented at the courses be included in the subject department plan. The teachers are members of the Irish Mathematics Teachers’ Association (IMTA).
Management has been proactive in developing the school’s information and communication technologies (ICT) infrastructure. Many classrooms are equipped with a computer and a data projector and there was evidence of ICT integration in some of the lessons observed during the inspection. Furthermore, the subject-department plan details the intention of the mathematics team to integrate more active methodologies in teaching and learning. These innovations, which are serving to broaden the students’ experience of Mathematics, are commended.
There is no formal budget for Mathematics but management responds favourably to requests for new equipment and resources. It is recommended that, in order to facilitate the adoption of more active methodologies, a suitable range of resources should be accessed. The mathematics support service (www.maths.slss.ie) is available to offer support and advice in this regard.
The mathematics department is co-ordinated on a voluntary basis. Responsibility for co-ordinating the department rotates between the team members. This is good practice as it enables each team member to explore new developments in mathematics teaching and learning and to become aware of the issues that arise in organising a subject department. Formal planning meetings take place three times per year. These meetings are recorded and the minutes are kept in the subject department plan.
The subject-department plan for Mathematics is well written and comprehensive. It contains a mission statement for the department and includes organisational details, resource lists and long-term plans for each year group and level, the topics to be taught, the school’s homework and assessment policies and an analysis of the results of the state examinations. Furthermore, the plan contains details about teaching methodologies, learning support materials, links to resources and it identifies areas for future development. This plan is subject to ongoing revision and different editions were in evidence during the inspection. This planning work is very impressive as it indicates the responsive and collaborative nature of the work of the mathematics department.
Common assessments in first year, which include graduated questions, and the creation of an additional class group to support those experiencing difficulties in sixth year indicates an admirable level of collaboration between the members of the mathematics team. In addition, the team has agreed a schedule for the delivery of the mathematics curriculum for each year and level. It is recommended that this schedule be modified to specify the material to be covered month by month with each year group and level.
Individual teacher planning is very good. The teachers’ diaries record students’ attendances, homework completions, and performances in class and formal tests. Teachers are very aware of the strengths and weaknesses of the students in their care and the lessons proceeded in a fashion that reflected this. Student profiles are developed through an analysis of performances in the various tests and this is used to inform their choice of levels, when the occasion arises. Best practice was seen in one case where a separate notice board was used to inform students of upcoming tests and of homework and study practices.
The learning-support team records the progress of each student who is in receipt of learning support. Class teachers are made aware of the students in their classes who are in receipt of support, and are informally consulted and updated on their progress.
The lessons observed during the inspection were well planned. The language used by the teachers was appropriate and every effort was made to contextualise the material being taught through reference to the students’ own experiences. The lessons proceeded at an appropriate pace and the material covered was relevant and challenging. The teachers taught with enthusiasm and were very knowledgeable about Mathematics. A very impressive feature of the lessons was the care taken by teachers to provide problem-solving strategies and to insist on the adoption and illustration of correct methods when solving problems.
In one case, simplifying algebraic expressions was approached in an exemplary fashion. Analogies were drawn between the students’ experiences of adding fractions in primary school and the questions being tackled. Good practice in the use of mathematical language, correct procedures and a strategic approach to problem solving was very evident.
Good practice was also evident where students were provided with strategies to break down complex geometric problems into their component parts and to apply the technique across a range of problems. This resulted in the students being enabled to approach very challenging material with confidence and with a robust problem-solving methodology.
Teaching styles were mainly traditional, comprising teacher expositions followed by whole-class activity. However, the integration of ICT and other active methodologies were also observed. In all cases, student engagement was very good. They were anxious to learn, asked pertinent questions, offered opinions and proposed solutions to problems.
Lessons proceeded in an atmosphere of mutual respect. Students were constantly affirmed and responded with very positive behaviour. The classrooms’ walls were adorned with student work and subject-specific posters. The teachers moved around the classes assisting individuals as the need arose, and students were invited to perform at the marker board to illustrate their solutions and ideas to the wider student body. Differentiation was also observed when students were individually invited to come to the teacher’s desk to work through more challenging material. This commitment to providing such a positive learning environment is commended.
In all classes, good use was made of questioning. It was refreshing to observe that the questions not only elicited factual responses from individuals and from the group but also encouraged students to hypothesize, to speculate and to explain their reasoning. This incorporation of higher-order questioning as an integral part of teaching and learning is commended.
Student learning was very evident. They responded readily to teachers’ questioning and the quality of their homework copies was excellent. Best practice was observed in the use of a separate hardback copy by students to record the material covered in class. A very impressive learning resource resulted, which was immediate, relevant and of the students own making. It is recommended that this practice be adopted across the mathematics department.
During their interaction with the inspector the students displayed confidence in, and a very positive attitude towards, Mathematics. They understood mathematical language and were aware of the existence of different approaches to solving particular problems.
Ongoing formative assessment through the use of teachers’ questioning was very evident during the inspection. Difficulties encountered by the students with assigned exercises provided opportunities for additional learning. Different approaches to the work in hand were discussed and the students’ understanding of, and familiarity with, problem-solving techniques was constantly explored.
Homework and assessment procedures are outlined in the subject plan for Mathematics. Homework was discussed at the beginning of each class; this enabled the students to mark and amend their own work. The students followed good practice in this regard and in one case best practice was observed where students corrected and amended their own work using a second colour to highlight corrections. Students are assessed at the end of each unit by means of in-class tests and records of the results were made available to the inspector.
Non-examination classes have formal assessments three times per year: in November, February and just prior to the summer. Results issue in each case. Students in first year take common examinations, which are corrected using agreed and common marking schemes. There are common tests, or common questions within tests in second year when the opportunity arises. Students in examination classes have formal tests in November and sit mock examinations in February, with students taking the same level receiving common papers.
Analysis of students’ performance in the state examinations occurs during departmental planning and is recorded in the subject department plan. Furthermore, meetings are held to discuss the results of the mock examinations to decide if any interventions are required. This is very good practice as it enables informed planning and relevant response to any issues arising.
Communication with parents occurs through the use of the student journal and formal letters relating to compliance with homework and assignments are issued. Other less formal means are also deployed where necessary. Reports are issued to parents following each formal assessment and one parent-teacher meeting takes place per year. Teachers, students, parents and the wider-school community celebrate student’s achievements by means of an awards ceremony that is held in the final term.
The school provides opportunities for students to participate in extracurricular and co-curricular activities associated with Mathematics. Students have competed in Team Maths competitions and some students also participate in Problem Solving for Irish Second Level Mathematicians (PRISM) competitions, organised nationally as part of Maths Week 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 and the principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published September 2008