An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Glenageary, County Dublin
Roll number: 60090Q
Date of inspection: 26 November 2008
REPORT ON THE QUALITY OF LEARNING AND TEACHING IN MATHEMATICS
This report has been written following a subject inspection in Rathdown School conducted as part of a whole school evaluation. 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.
Rathdown School operates a combination of thirty-five and forty-minute class periods. Time allocated to Mathematics in Rathdown School is very good; for example, five Mathematics lesson periods weekly are allocated to each junior cycle year group. Transition Year (TY) Mathematics is allocated four lesson periods each week. Five lesson periods are allocated to fifth-year Mathematics groups and six lesson periods a week are allocated to sixth-year Mathematics.
Concurrent timetabling of Mathematics takes place from first year onwards which is good practice as it provides the opportunity for students to follow a level most appropriate to their abilities. However, it is resulting in students not having daily contact with Mathematics. For example, even though sixth-year students have six classes per week of Mathematics, there is no Mathematics timetabled on one day of the week. While acknowledging the complexities of facilitating concurrent timetabling and the attempts made to have daily contact with Mathematics, consideration should be given to exploring alternative ways in which daily contact with the subject can be achieved.
This year the Mathematics department comprises seven teachers of Mathematics and a Post Graduate Diploma in Education (PGDE) student of Mathematics. Teachers are given opportunities to rotate the teaching of levels particularly at junior cycle. In senior cycle the practice is that two teachers share in the rotation of the teaching of higher level, but this does not rule out opportunities for other members of the department from being included in the rotation. This is good practice and allows for the creation of a wide skills base among the teachers within the department. The general practice is that teachers remain with a class grouping throughout a cycle and sometimes from first year through to sixth year.
The current first-year students are assigned to one of three mixed-ability classes. Commendably, management has deployed an extra teacher to Mathematics which has allowed for the creation of four first-year Mathematics groups. During the second half of the first school term, first-year students sit a common Mathematics assessment and students who find Mathematics challenging are identified and a small class grouping is arranged to ensure that the needs of all students are catered for. In second and third year, one extra teacher has been deployed to Mathematics and this has resulted in the creation of three higher-level and two ordinary-level Mathematics classes in each year.
TY is compulsory in the school. Management deploys an extra teacher to TY Mathematics and this facilitates the creation of four class groupings. Two class groupings are arranged for students who have taken higher level in their Junior Certificate Maths examination with a similar arrangement for students who have taken ordinary level in the Junior Certificate examination. The concurrent timetabling of Mathematics for TY students facilitates a modular approach to the teaching of the subject. Extra teachers are deployed in both fifth and sixth year, which results in four mathematics classes formed in these year groups. In fifth year, two higher-level mathematics classes are formed but, by sixth year, one class group of higher-level usually remains, with three ordinary-level classes formed. In both Junior and Leaving Certificates, foundation level is offered but its uptake is minimal.
Rathdown School has a wealth of resources available for the teaching and learning of Mathematics. These include three-dimensional mathematical equipment, interactive whiteboards, data projectors and textbooks, all of which can be accessed by teachers. The school library has an array of mathematical texts that can be accessed by students or teachers as aids or references. In addition the school’s information and communication technology (ICT) system hosts mathematical material, which has been developed and uploaded onto the school’s intranet by members of the mathematics department and is used in the teaching of the subject. The intranet is also used by students to submit project work online to teachers. The mathematics department is currently exploring ways in which teacher-developed resources can be accessed by students on the intranet. Mathematics teachers are commended for their commitment to regularly updating their skills and resources to enhance the teaching of the subject in the school.
The Mathematics department receives an annual budget from management and this is used to pay teachers’ annual subscription to the Irish Mathematics Teachers Association (IMTA), entry fees to mathematics competitions for students and the purchasing of maths textbooks for the school library. Management is commended for facilitating teachers to attend relevant in-service courses. Such support by management is commended.
Students in Rathdown School are given many opportunities to participate in co-curricular mathematics competitions. For example, students participate in the ‘Problem Solving for Irish Second Level Mathematicians’ (Prism) competition and the IMTA-organised first and sixth-year competitions, with considerable success. Students’ achievements are acknowledged at school assemblies. In addition, teachers give extra support to their students in Mathematics after school. Teachers are commended for their support of students and for their promotion and encouragement of Mathematics. To further promote and highlight activities in Mathematics within the school, consideration should be given to using a notice board to display details of mathematics events, competitions and to acknowledge students’ achievements.
As is the practice in many of the school’s subject departments, the most senior member of the subject takes responsibility for the co-ordination of the subject and retains the position from year to year. The head of department’s responsibilities include convening subject meetings, leading the mathematics team and disseminating relevant information relating to Mathematics; all of which are undertaken in an efficient and effective manner. Consideration should be given to the rotation of this position to allow for the responsibility to be shared among members of the department.
Management facilitates planning time at regular intervals during the year. In addition, the mathematics department has many informal meetings. Minutes of the department meetings, which include organisational procedures and decisions about specific issues, are recorded. This is good practice.
A long-term plan for Mathematics has been developed and includes the organisational details for the provision of Mathematics in the school, the curriculum content for each year grouping, an outline of homework procedures, teacher in-career development and assessment of students. However, there are some aspects of the plan that require further development. For example, it is recommended that the content for each year group be rearranged into the desired learning outcomes that students should achieve and timeframes associated with each learning outcome. As already mentioned, members of the department have developed a wealth of resources located on the school’s intranet. However, there is no reference to these within the mathematics plan. It is therefore recommended that an audit of mathematics resources be undertaken and a listing be included with the mathematics plan. The department reported that regular and ongoing review of the subject plan is undertaken with adjustments made where necessary, which is commendable.
The TY plan presented includes consolidation of Junior Certificate material, some Leaving Certificate topics and studying of Mathematics through research and discovery methodologies. The available TY plan does not entirely reflect the current practice, particularly for higher-level students within the department and consequently should be updated to include topics that have been omitted.
Individual planning documents made available during the evaluation were comprehensive. Over the years, a considerable wealth of knowledge has been developed among members of the mathematics department and teachers are commended for their collaboration and sharing of materials, particularly those that have been developed individually for the teaching of Mathematics.
The mathematics department undertakes an analysis of students’ achievements in the State Examinations. A review of past examination results demonstrated that students’ participation in higher level in both Junior and Leaving Certificate is high, with many achieving very well at this level. Furthermore, as already noted, foundation level is rarely taken.
In all lessons observed, there was a positive atmosphere of mutual respect between teacher and students and between student and student. Students’ inputs were welcomed and, in many instances, individual attention was given in a sensitive and discreet manner. This provided a positive learning environment.
Calculus, arithmetic, surface area and statistics were among topics observed in lessons. All lessons were presented in a confident and coherent manner. Teachers displayed very good subject knowledge and were enthusiastic about Mathematics. Learning objectives were clearly established at the beginning of the lesson and the content of the lessons was appropriate to the students’ abilities and allowed for continuity where appropriate.
Teaching observed was of a high standard with a variety of methodologies used. In some lessons, effective use was made of traditional whole class teaching. This involved a combination of the teacher demonstrating a technique to the class and students then working alone on tasks while the teacher circulates to provide individual attention. The use of concrete materials to teach surface area was very effective. For example, students were given appropriate material to cut and rearrange three-dimensional shapes into two-dimensions, which allowed them to identify and calculate the surface areas. In another lesson, students were given materials and were required to manipulate them into three-dimensional shapes. When sufficient competencies in this skill had been gained, they were then required to design and construct their own nets. This is highly commended as it provides students with opportunities to explore the structures of shapes and to become fully engaged in their own learning. The method of giving students an opportunity to present their analysis and findings of real life statistical topics was very effective. It allowed students to take responsibility for their learning and provided the opportunity to question students about their interpretation of topics being studied. Teachers were aware of the importance of students experiencing a range of methodologies during the learning of Mathematics in recognition of their preferred learning styles.
Resources were used effectively. The use of a laptop and data projector aided the teaching of key mathematical topics and allowed for the illustration of accuracy when completing a question on graphs. Effective use of ICT equipment allowed for correction of student work and afforded teachers the opportunity to circulate to check students’ attempts at questions and provide immediate feedback. Other resources used in lessons included samples of statistical material retrieved from newspapers, the whiteboard and prepared worksheets. Resources used provided necessary support at key stages during lessons. Teachers are commended for the prior preparation of such materials in advance.
Communication within the lessons was very good. There was good use of recall type questions to establish students’ understanding of a topic or to provide the next step in a solution to a question. In many instances, the use of higher-order questions was commendable as it provided students with opportunities to address misconceptions or incorrect answers while allowing teachers to challenge students to offer a rationale for their answers. However, care should be taken to maintain the focus of student-centred learning by allowing students to give their solution to a question before the teacher proceeds with the solution.
In all lessons observed, it was evident that high standards are being set by teachers, and that students strive to achieve these standards. Additionally, very good use was made by both teacher and students of mathematical terminology. Interactions between students and the inspector were very positive. Frequently, students demonstrated clear understanding of the work they were doing and were capable of making connections between various sections of the syllabus, all of which is very good practice.
Learning in all lessons was purposeful. Students frequently initiated questions which demonstrated their engagement with the lesson indicating that they had reflected on the material being studied. This is commended. Classroom and time management were appropriate. Students were cooperative and attentive which allowed for focused learning in all lessons. Through observation of students’ work, there was evidence that good progress is being made by students.
Assessment forms part of the ongoing teaching and learning of Mathematics in Rathdown School. For example, frequent questioning during lessons allowed teachers to assess students’ understanding of the topic and their readiness to move forward. Students also have end-of-topic assessments as well as their formal Christmas and summer examinations. Common assessments are utilised in Mathematics, which is good practice.
Homework, which was regularly assigned, was suitably challenging. The homework policy for Mathematics was implemented by all teachers. This is laudable.
Students’ work in many instances was presented in a logical and neat manner. There was evidence of monitoring of this work by teachers with some constructive comments given on areas to improve. Such practice should be used in marking all students’ work.
Communication with home is maintained using a variety of mechanisms. Parent-teacher meetings are convened for each year group. Two school reports are issued following formal school examinations. In addition, progress reports are issued for students of fifth and sixth-year classes. ‘Mock’ examinations are arranged for third and sixth-year students.
The following are the main strengths identified in the evaluation:
· There is very good whole school support for Mathematics in Rathdown School in the provision of time and the additional deployment of teachers to the subject.
· The Mathematics department is well organised.
· There is a wealth of resources that have been developed by the Mathematics department.
· Planning for Mathematics is ongoing and regularly reviewed.
· Teaching is of a high standard with a good range of methodologies and questioning strategies used in lessons observed.
· Assessment of students is ongoing and the department operates common assessments.
· Teachers set high expectations and are commended for their promotion of and enthusiasm for the subject.
· Students are given many opportunities to participate in co-curricular activities in Mathematics.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· The long-term plan for Mathematics should be reviewed to include learning outcomes.
· The TY plan should be updated to acknowledge the omitted work that is currently studied by students.
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 October 2009