An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Roll number: 63190M
Date of inspection: 24 March 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Coláiste Mhuire. 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 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.
Timetabling provision for Mathematics is very good. First year classes are provided with four periods of Mathematics per week and there are five periods of Mathematics per week in second and third year. Mathematics classes are mixed ability in first year and are banded in second and third year. The bands are formed at the end of first year following a series of common assessments and consultation with the class and learning-support teachers. The provision of mixed-ability classes in first year allows students to settle into the school and begin their second-level education in a familiar and supportive environment. However, in order to provide additional time to tackle the junior cycle syllabuses, consideration should be given to formation of the bands at Christmas in first year following ongoing common assessments during the first term.
Upon completion of junior cycle, students may opt to enter transition year (TY) or go directly into fifth year. Two mixed-ability classes are formed in TY and they are each provided with four periods of Mathematics per week. Mathematics classes are banded for the remainder of senior cycle. There are seven periods of Mathematics per week in fifth year and six periods per week in sixth year. All class periods are forty minutes long. Apart from first year, mathematics classes are timetabled concurrently within each year group. This is very good practice as it allows students to continue with the highest level possible for as long as possible and facilitates long-term collaborative planning.
The systems in place to identify and support students with special education needs or in need of learning support are student-centred and effective. A written report outlining the strengths, interests and needs of each individual incoming student is provided to the school upon enrolment. The principal also liaises with the parents of incoming students in order to become familiar with the profile of each student and to access any completed psychological assessments. Applications for extra resources are then submitted by the school to the Department of Education and Science for consideration.
All incoming students sit a range of standardised tests including the Drumcondra Reasoning Test (DRT1998). The tests are administered by the school’s guidance counsellor and an analysis of the results is provided to the learning-support team. If it is deemed necessary, additional assessments for some students are also arranged through the National Educational Psychological Service (NEPS).
Learning support in Mathematics is provided through the withdrawal of students in small groups from subjects from which they have been granted an exemption. In exceptional circumstances one-to-one withdrawal is also provided. The learning-support team liaise closely with the class teachers to ensure that the material being covered during withdrawal, while addressing underlying weaknesses, is in line with the work being done in mainstream classes. The learning-support team also provide the class teachers with strategies to support students with special educational needs in mainstream classes. These strategies are included in the subject development plan for Mathematics.
Students with exceptional abilities in Mathematics are very well catered for. Strategies to support such students are detailed in the subject development plan for Mathematics and a range of initiatives designed to challenge and motivate them are in place.
The mathematics department is comprised of eight teachers. The members of the department work as an effective team and their efforts ensure that Mathematics has a positive profile within the school. The established members of the department provide good leadership and have contributed greatly to the development of the department. The teachers are assigned to levels by rotation and the qualifications profile of the team members is very good. 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.
Management has been proactive in investing in the school’s information and communication technologies (ICT) facilities. Mathematics classes have access to the school’s computer room, and a number of classrooms have been equipped with interactive whiteboards. ICT integration in lesson preparation and delivery was evident during the inspection. Other resources to assist in active teaching and learning of Mathematics are also available to the department. In order to facilitate resource procurement and development, it is recommended that an audit of all resources available to the department be conducted and that the resulting inventory be included in the subject development plan for Mathematics. It is further recommended that a member of the department be chosen to identify suitable ICT resources, to suggest strategies for their integration into teaching and learning and to source appropriate training.
Subject development planning is well established in the school. Formal planning meetings are facilitated as part of staff meetings and it was evident that regular informal planning also takes place. The department is very ably co-ordinated and a comprehensive subject development plan, which is reviewed in August each year, is in place. Management have adopted the very good practice of analysing student performance in the certificate examinations with reference to the statistics supplied by the State Examinations Commission. This process should form an integral part of department planning and should be carried out annually by the department itself.
A comprehensive subject development plan for Mathematics is in place. The plan includes a statement of aims and objectives and details the arrangements for student access, timetabling provision and strategies for supporting students with special educational needs. The plan also includes detailed yearly plans for each year and level. In addition, all of the mathematics teachers prepare thorough schemes of work for each of their class groups. In order to build on the existing good practice in planning, it is recommended that schemes of work be framed in terms of key learning outcomes which will inform differentiation and facilitate the use of agreed procedures for carrying out core mathematical operations.
A short TY mathematics plan is in place. The programme as outlined in the plan is in keeping with the aims and objectives of TY. However, it is recommended that the plan be reviewed to include detailed schemes of work, intended learning outcomes and the teaching methods to be employed in delivering the programme. Furthermore, the content outlined in the existing plan should be altered to increase the number of topics which lend themselves to the integration of ICT and active teaching and learning methods.
Planning for the inclusion of resources in teaching and learning is very good. ICT, the overhead projector and differentiated worksheets were successfully integrated into the lessons observed during the inspection. The various resources served to support the lessons’ objectives, to enhance student engagement and to create a challenging and stimulating learning environment.
Individual teacher planning is very good. The mathematics teachers made their planning documentation available during the inspection and in all cases it was found to be comprehensive and relevant. It was evident that student performance in homework and in class tests informs lesson planning and delivery. The ability and willingness of the teachers to amend lesson content and delivery styles in response to student need is a very impressive feature of the department’s short-term planning.
Management actively supports attendance at continuing professional development (CPD) courses and a number of whole-school professional development events have been provided in the recent past.
The lessons observed during the inspection were well planned. The material covered was appropriate to the curriculum and to the needs and abilities of the students. The teachers were very knowledgeable and there was very good adherence to the use of correct methods in carrying out mathematical operations. The students were provided with effective strategies to enable them to engage in problem solving in a logical and systematic fashion. The lessons proceeded at a suitable pace, were well structured and useful links were made with the material covered in previous lessons.
A variety of teaching methods was observed during the inspection. Very good practice was evident where ICT was used to revise the construction and interpretation of pie charts. The interactive whiteboard was used to demonstrate the correct procedure when measuring the angles in each segment of the pie chart and how the segments should be constructed. The use of ICT allowed the teacher to illustrate correct procedure clearly and to reiterate it frequently and efficiently. Furthermore, the teacher was free to move around the room assisting individuals and assessing their work without affecting the flow of the lesson.
Group work was used to very good effect in the revision of area and volume and Simpson’s rule. In this instance, the students were grouped into teams of four and were seated in clusters around the room. A series of graduated worksheets were distributed and the teams worked together to solve the problems as quickly as possible. The use of textbooks was not allowed and, as a result, discussion and speculation formed a central part of the problem solving process. Once a given worksheet was completed it was passed on to a neighbouring group for correction. Each team could then gauge their performance compared to their peers. The teacher, through good circulation, ensured that each team member contributed to the work of the team. The students were engaged throughout the lesson and contributed to a productive and enjoyable learning experience.
A lesson on sequences and series was greatly enhanced by the use of the overhead projector. The acetates produced by the teacher supported the lesson’s objectives, were visually simulating and presented the subject matter in an accurate and systematic fashion. The use of the overhead projector meant that the teacher was free to interact with individual students, to provide ongoing feedback and to continually monitor their work. Homemade posters were also used to reinforce the lesson’s key learning outcomes and to provide a fresh focus for the lesson as it drew to its conclusion. The use of these resources, coupled with adherence to good practice in carrying out calculations and solving problems, ensured that the lesson was productive, focused and enjoyable.
Classroom management was very good. The teachers had very high expectations of the students’ behaviour and engagement. These expectations were realised. In addition, the students were eager to learn. They asked very good questions and made constructive contributions and suggestions. Very effective use was made of teacher questioning. Questions were used to elicit factual responses, to monitor student learning and to encourage students to explore the deeper meaning of the material in hand. The lessons proceeded in an atmosphere of mutual respect, the teachers were affirming of the students’ efforts and the students responded in a very positive fashion.
The quality of student learning was very good. They responded readily and knowledgeably when questioned by the teacher. In their interactions with the inspector, the students were confident and displayed a good knowledge of Mathematics. The performance of students in class and formal tests and in the state examinations offers further evidence of the high quality of student learning.
Ongoing assessment occurs through teacher questioning in class, the correction of homework and the provision of class tests. Practices regarding the assignment and correction of homework are very good. Homework is regularly assigned and corrected. The student copies are well maintained and in some instances they contained positive teacher comments and suggestions. In one case the very good practice of students amending their own work was also evident. The practice of teachers providing written feedback and of students amending their work should be adopted as standard in the department. In-class tests take place upon the completion of each topic and details of student attainment are assiduously recorded in the teachers’ diaries. Teacher practice in relation to checking and recording student attendance is also very good
When planning lessons due cognisance is taken of student performance in homework assignments and in class tests. In many instances, the lesson content was modified to reflect the difficulties encountered by students or in response to student questions. This is very good practice as it supports the needs of individual students in a timely and relevant manner.
Formal tests are provided for non-examination classes at Christmas and just prior to the summer holidays. Examination students sit formal assessments at Christmas and sit mock examinations at Easter. 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. 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 with great distinction in Team Maths. In addition, the Br. Philip Award for Excellence in Mathematics is presented annually to the student identified as having contributed most to Mathematics in the school during the year.
The following are the main strengths identified in the evaluation:
· Timetabling provision for Mathematics is very good
· The systems in place to identify and support students with special educational needs or in need of learning support are student-centred and effective.
· The members of the department work as an effective team.
· The mathematics department is well resourced and has access to the school’s ICT facilities.
· Subject development planning is well established, a co-ordinator is in place and a subject development plan has been developed.
· Individual teacher planning and planning for the inclusion of resources are very good.
· The quality of teaching and learning is very good.
· Practices in relation to ongoing and formal assessment are very good.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· It is recommended that an audit of all resources available to the department be conducted and that the resulting inventory be included in the subject
development plan for Mathematics. It is further recommended that a member of the department be chosen to identify suitable ICT resources, to
suggest strategies for their integration into teaching and learning and to source appropriate training.
· It is recommended that schemes of work be framed in terms of key learning outcomes which will inform differentiation and facilitate the use of agreed
procedures for carrying out core mathematical operations.
· It is recommended that the TY mathematics plan be reviewed to include detailed schemes of work, intended learning outcomes and the teaching
methods to be employed delivering the programme. Furthermore, the content outlined in the existing plan should be altered to increase the number of
topics which lend themselves to the integration of ICT and active teaching and learning methods.
Post-evaluation meetings were held with the teachers of Mathematics at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published, November 2009