An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
St. Patrick’s Secondary School
Castleisland, County Kerry
Roll number: 61250R
Date of inspection: 7 October 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Saint Patrick’s Secondary School. 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 one day 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 deputy principal and subject teachers. The board of management was given an opportunity to comment in writing on the findings and recommendations of the report; a response was not received from the board.
Saint Patrick’s Secondary School is a privately owned boys’ school in the town of Castleisland. The current enrolment is eighty-nine students. While the numbers in second and third year are small, there are thirty students in first year and it is hoped, that similar numbers will enrol in the coming years. The school does not currently offer a Transition year (TY) programme.
There is one mathematics class group in each year up to junior certificate level. It is reported that the current class in first year will be divided into two groups in second year. The first-year and second-year classes are taught on a mixed ability basis while in third year the higher and ordinary level courses are taught in the same classroom. Classes in fifth and sixth year are divided into higher and ordinary level groups. Teachers are assigned to classes by management and generally continue with classes from first to third year and from fifth to sixth year.
The provision for Mathematics in the timetable is in line with syllabus requirements. All year groups have five periods of mathematics tuition each week. In the current year, to address reported resource problems and to ensure that all groups retain the five lessons per week, the third-year class and the fifth-year, higher-level class are timetabled together for one period each week. This should be avoided if possible in future timetabling.
The mathematics team currently consists of three members, not all of whom are subject specialists. It is suggested that, while taking due cognizance of resource constraints, management should, over time, endeavour to move to a situation where all teachers of Mathematics are subject specialists.
Students are encouraged to follow the highest possible level for as long as possible. Students who wish to transfer between levels must consult with their teacher and the school guidance counsellor. Following these consultations a signed parental consent form is also required.
Management supports the continuing professional development (CPD) of the mathematics teachers. Teachers have been facilitated to attend courses organised by the Mathematics Support Service in recent years.
There is no formal budget for Mathematics but management responds favourably to requests for equipment purchase and upgrade. A member of the team has constructed an impressive array of hands-on materials and resources to aid in the teaching of Mathematics. These include number-lines, large geometric shapes, peg boards and set circles. These materials are centrally stored and available to all members of the team.
The department has also produced a CD of resources for use by the teachers. The CD contains information and communication technology (ICT) resources produced by the Mathematics Support Service (MSS) and distributed at in-service. The disk also contains relevant syllabuses, teacher guidelines and planning material produced by the team. Each member of the team has a copy of the disk for ongoing use and it is available as a resource for new teachers who may join the department.
The mathematical ability of incoming first-year students is assessed through contact with the local primary schools, consultation with parents and ongoing teacher monitoring and observation during the year. Students identified as finding the subject particularly challenging are supported through extra tuition during withdrawal for small group or one-to-one tuition from classes other than mathematics classes. This support is generally provided by their mathematics teacher thus ensuring a continuity of approach and content for these students.
The school’s management undertakes a review of the performance of their students in the Certificate Examinations in Mathematics in relation to achievement and uptake levels and compares them with national norms. Such analysis is useful in informing future planning and provision for the subject.
The mathematics department structure has been in place in the school for a number of years. Following a recent retirement, it is now co-ordinated on a voluntary basis by an experienced member of the mathematics team. The team have a formal meeting at the beginning of the school year and, as the number of teachers involved is small, informal meetings take place on a regular basis throughout the year as needs arise. The good practice of record keeping of formal meetings is in place and these records show evidence of collaboration and review among mathematics teachers.
Work done on planning to date is good. The comprehensive long-term plan for Mathematics has a section for junior cycle and another for senior cycle. Each section includes a mission statement and general and specific aims and objectives for mathematics education for that cohort within the school. The curriculum content to be covered by each year group and level is presented in the form of topics and further divided into subtopics.
The plan includes a copy of the school’s assessment policy and homework policy. The homework policy has been adapted to a subject specific one for Mathematics. Also included is a sample homework timetable for students in different year groups. The resources mentioned earlier, which are produced in school, are listed along with topics where they might be utilised. The school has produced a learning support policy for Mathematics and this, along with details of the support provided, is included.
The role and use of ICT in the teaching of Mathematics has been identified as the next area in which planning will take place. The recent addition of a new computer room will aid in this endeavour.
Teachers have also engaged in individual planning for the teaching of the subject. All teachers presented individual planning material for review during the inspection. Teachers had modified the long-term plan and broken the work down to topics to be covered each term.
The predominant methodology used in lessons was traditional, whole-class, teacher-directed teaching. This consisted of the teacher demonstrating a procedure to the class, by doing examples on the board, and the students then working alone on similar problems from the textbook while the teacher assisted individuals. Within this structure the teaching was caring and effective.
Students would have benefited from a greater variety of methodologies in lessons. More use of strategies such as working on student-generated problems, pairwork,, investigation, consolidation activities, practical work, discussion, group work, quiz activities and the use of concrete materials would have enhanced learning. Such methods have the effect of encouraging students to become more engaged in the lesson and more active in their own learning. It is therefore recommended that teachers add to the current methodology used in lessons and use greater variety in their teaching approaches.
In the classes visited, lessons were well structured and purposeful and there was evidence that teachers were prepared for their teaching. Lessons progressed at an appropriate pace with good use being made of time. In all cases, clear objectives were set for lessons and communicated to students. This good practice would have been enhanced by a student-centred review of the achievement of these objectives at the end of the lesson.
The main resources used during lessons were board work and textbooks. Teachers used mathematical terminology appropriate to students’ ability and the relevant topics. In order to develop students’ confidence and understanding, clear links were made to previous learning and to other related topics which had been previously taught.
Feedback from students on their level of understanding was regularly sought with extra work being done where this was felt to be necessary. Other classroom interactions typically took the form of brief answers to questions posed to individual students or to the class group on finding the next steps in a solution. There was good practice with regard to variety in the addressing of questions to individual students and whole class groups, as a means of checking students’ levels of understanding of particular concepts. The questioning generally took the form of “next step” or “fill in” type questions. It is therefore recommended that teachers might also engage in the posing of more open questions to challenge students and probe new material being presented.
In interactions with the inspector, students were able to answer questions asked of them in a confident manner using appropriate mathematical terminology and justified solutions to problems posed to them. Students demonstrated a clear understanding of concepts engaged with during the lessons and were able to apply them to similar problems from the textbook.
A positive, caring and affirming working environment was created in all classes visited and classroom management was effective and relaxed. Lessons had good structure, teachers had a clear methodology for procedures which was well demonstrated and students showed an interest in achieving in Mathematics and were attentive to their work. Other examples of good practice in mathematics teaching included encouraging students to think about what they were doing, the use of clear instructions and methods in examples as a template for students, the use of mathematical language and the affirmation of students’ effort and success.
Most class groups are room based but there was very little evidence of mathematical displays. To create a more visually stimulating learning environment for all students, it is recommended, that as a department, teachers display and use students’ mathematical work, project work and mathematical posters.
Students generally retain their work in a homework copy, a class work copy and a notes copy. Progress can be seen in these copybooks. An examination of a sample of students’ mathematical work at Saint Patrick’s Secondary school showed work that was appropriate, relevant and generally well presented. There was evidence of monitoring of student work, with, in some instances, teachers’ positive written comments being used to encourage students’ efforts. This is good practice and in line with the principles of assessment for learning.
As referred to previously the team have adapted and applied the school’s homework policy to mathematics and there is also a school assessment policy in place. Homework was regularly assigned and corrected and student misunderstandings noted in the review of homework was seen to be used to inform teaching.
Students’ ongoing progress is assessed through classroom observation, oral questioning, the assignment and correction of class work and homework. To add to this, regular class topic tests, mid-term and end-of-term examinations are set. Formal examinations for those students who will be participating in the certificate examinations are organised at mid-term and Christmas. There are also mock examinations organised for these students later in the school year. All other year groups are provided with mid-term examinations as well as formal tests at Christmas and at the end of the school year.
Two reports regarding students’ progress are issued for all year groups. The report at Christmas contains the results of the formal Christmas test and the mid-term test. The summer report also contains the results of a mid-term and end-of-year test. There is one parent-teacher meeting per year organised for each year group. The student journal is also used to facilitate communication between teachers and parents. Parents are also facilitated in making appointments with teachers to discuss students’ progress, should the need arise. These arrangements ensure that good lines of communication exist between school and home.
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:
Published, February 2009