An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
St Kieran’s College,
College Street, Kilkenny
Roll number: 61560J
Date of inspection: 16 January 2009
This report has been written following a subject inspection in St.Kieran’s College. 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; a response was not received from the board.
Time allocated to Mathematic is very good. All junior cycle classes have five periods of Mathematics per week. Three periods per week are allocated to Transition Year (TY) Mathematics. Fifth and sixth-year Mathematics students are allocated five class periods per week with an additional sixth Mathematics period allocated to higher-level Mathematics in both years.
In general Mathematics classes are distributed evenly throughout the week allowing for daily contact with the subject. However, two second-year class groups have two of their five Mathematics classes timetabled on one day of the week. As this is not ideal it is recommended that this issue be reviewed to ensure that all students have continuity in the learning experience.
First-year students are assigned to one of two bands based on perceived ability following the pre-entrance assessment in the core subjects. Two classes are formed within each band and students generally remain within these bands throughout junior cycle. Two concurrently timetabled Mathematics classes are created in each band. Students in the upper band pursue the higher-level course. In the lower band on occasion, both the higher and ordinary level syllabuses are taught within the one class, as is the case with the third-year groups this year. To address this, management has provided additional Mathematics lessons to higher-level students in the mixed-level grouping. Senior management reported that the current practice of class formation will be reviewed for the next academic year. This is to be welcomed. In the course of this review issues of timetabling and staff deployment as well as class formation should be considered to create the best possible provision.
Students following the Transition Year (TY) programme are assigned to one of four classes for Mathematics. In TY two bands are formed for Mathematics with concurrent timetabling facilitated within each band. Concurrent timetabling of Mathematics takes place in both fifth and sixth year. Management is commended for deploying additional teachers to fifth and sixth year Mathematics classes. This has resulted in the formation of six class groups in both fifth and sixth year for Mathematics. At the beginning of fifth year, three higher-level and three ordinary level Mathematics classes are formed. Praiseworthy efforts are made to retain students in the higher-level groups.
Eleven teachers provide Mathematics education in the school with an additional teacher providing support in Mathematics. A high level of co-operation exists among the team of committed Mathematics teachers. Teachers generally remain with a class grouping throughout a cycle, which is commendable. On occasion a teacher has retained a class grouping from first to sixth year also. The principal takes responsibility for the assignment of Mathematics teachers to levels and programmes. The stated goal of senior management to build capacity and to retain expertise within the department is commended.
Teachers’ continuous professional development is supported by management, for example, by facilitating attendance at relevant Mathematics in-service. In addition, members of the Mathematics department have provided in-school training to fellow members of the department in the use of a computer software, with plans in place to provide training in the Mathematics package “Autograph”. This is highly commendable and is evidence of the commitment of the Mathematics department to sharing best practice.
Following discussion within the Mathematic department, the co-ordinator of Mathematics puts requests for resources to the Principal. Resources available within the department are listed in the department’s Mathematics plan and include algetiles, geostrips, mathematical equipment for teachers, overhead projectors and more recently some data projectors. In addition many teachers use pen tablets, data projectors and laptops for the teaching and learning of Mathematics. Shared resources are retained in a central location where teachers can access them when necessary.
Additional support for students who find Mathematics difficult is arranged in a number of ways. For example, some support is offered to students on a withdrawal basis or in small class groups. Additionally, this year the school is piloting team teaching for a second-year class grouping for two of the five Mathematics classes per week. In line with best practice, it is envisaged that this pilot model of provision will be reviewed to assess its effectiveness. It is commendable that a variety of models are explored to enable students to benefit from supports most suitable to their needs.
Mathematics students in St.Kieran’s College are encouraged and facilitated to participate in a range of co-curricular Mathematics activities. Students have participated in the Problem Solving for Irish Second Level Mathematicians (PRISM) competitions, Irish Mathematics Teachers Association TeamMath quiz and Maths Week. Additionally, many students have been invited to participate in the Irish Mathematics Olympiads. The opportunities offered to students to participate in such activities add to the positive atmosphere among students regarding their Mathematics education. They highlight teachers’ enthusiasm and commitment to the subject and their commendable desire that students experience Mathematics in different contexts.
Subject planning is facilitated by management throughout the school year. The position of co-ordinator is rotated among Mathematics teachers. Minutes of Mathematics meetings are retained and they outline issues discussed and suggestions for further development. There is evidence that an analysis of state examination results is undertaken which is used to inform planning for the subject. This is commendable. Additionally, there is evidence of long-term planning for the subject and planning for the acquisition of resources for the department. The evident collaboration among members of the department and their planning for the future development of the subject are highly commendable.
The Mathematics department is commended for its work to date on the development of a subject plan. The plan includes the aims and objectives and the organisational details for the department. However, the curriculum content for each year group is limited to chapters from a textbook and is not syllabus based. It is therefore recommended that a more detailed programme of work be included for each year group with the desired learning outcomes for sections included, guided by the relevant syllabuses and with timeframes for each section. Commendably, the Mathematics plan includes a list of “improvement strategies for the year” identified by the Mathematics department. Actions on many of the highlighted issues are recorded in the minutes of the Mathematics department. Such evidence suggests that the Mathematics department is well organised and functions effectively.
The TY Mathematics plan presented is diverse and offers students the opportunity to consolidate concepts from the Junior Certificate, study some new material from the Leaving Certificate and study modules of Mathematics such as Applied Mathematics, Cryptography and Application of Mathematics. The TY Mathematics teachers are collaborating to develop a set of worksheets and learning aids that will be used to teach each of the modular sections of the TY Mathematics programme. Such collaboration and sharing of best practice among Mathematics teachers is to be commended.
The principal requires all teachers to prepare and submit individual schemes of work for each Mathematics class they teach. These individual schemes made available during the inspection are based on the long-term department plan for Mathematics. Further supplementary materials presented by teachers included prepared worksheets, learning aids and PowerPoint presentations for use in many of the lessons observed. Individual planning for lessons was very good.
Some of the Mathematics teachers have become proficient in the area of Information and Communication Technologies (ICT). For example, samples of recordings of some Mathematics lessons were presented. Students can access these multimedia recordings at a later stage, not least as an aid in their revision work. Furthermore, the use of the pen tablets and a laptop has afforded teachers the opportunity to save classwork and print relevant examples for students who may be absent on a particular day, or to return to a question for further discussion at a later stage. Teachers are highly commended for the integration of such technologies in the teaching of the subject.
The policy to encourage students to remain with the highest possible level for as long as possible has been very successful. A review of the state examination results indicates that many students choose higher level for both Junior and Leaving Certificates. Student achievement in both Junior and Leaving Certificate examinations at all levels but particularly at higher level is very good. Mathematics teachers are to be commended for setting high expectations for their students, as observed during the course of the evaluation.
Lessons were well presented and content was in line with relevant syllabuses. Topics observed included trigonometry, algebra and statistics. The material studied during the lessons was appropriate to the abilities of the students. Efforts to set Mathematics in context were very good and added to the enjoyment of the topics for students. In addition teachers’ knowledge of and enthusiasm for the subject contributed to the positive Mathematics classes and to student engagement in the lessons. Teaching methods observed, while largely traditional, were very competently managed and effective.
Time management in lessons was very good. Well-paced lessons allowed for the desired planned content to be completed in an efficient manner. Teachers had excellent rapport with their students. Interactions with students were engaging and purposeful and mutually respectful. Students’ responses were affirmed and in many instances were used to progress the topic in hand. When necessary and where appropriate individual attention was provided in a sensitive manner. Teachers set high expectations in lessons observed and students responded accordingly. Students were engaged throughout the lessons observed, due mainly to very good lesson structure and pace being established by their teachers.
The main teaching method observed consisted of the teachers demonstrating an example with students completing an exercise. This traditional approach was effectively used. However, on occasion the use of an alternative method would have been more appropriate to ensure that the learning needs of all students were catered for. It is therefore recommended that the range of methods used in lessons be extended
In many lessons teachers skilfully included a range of questioning strategies throughout the lesson. Recall type questions were utilised to make connections between previous and current work. Effective use was made of higher-order questions within many lessons observed, prompting students to provide a rationale for the answer or to develop other students’ answers. This allowed students to be more involved in their learning and to discuss and address any misconceptions that they had. This is highly desirable and commendable practice and should be followed in all lessons.
The use in many lessons of supplementary material prepared in advance was appropriate and commendable. In some lessons the overhead projector and television were effectively used at key junctures to reinforce key areas and to demonstrate accuracy when completing an exercise. Effective use of ICT also allowed teachers to model best practice in the presentation of work, to position themselves in front of students where they could observe student engagement, and to store and retrieve completed exercises which were used during key stages of a lesson.
In many lessons students were eager to learn and frequently questioned their teachers in a way that demonstrated engagement with the topic and with their own learning processes. Through interactions with the inspector it was evident that students have very positive attitudes towards Mathematics and strive to achieve to the best of their abilities. Frequently, students used appropriate mathematical terminology and were capable and confident when answering questions posed to them.
Many teachers are based in their own classrooms with samples of student work on display, and this is commendable. Additionally, good practice was observed in the use of displays in the teaching of Mathematics topics.
Students are regularly assessed, with tests on completion of a topic and formal assessments thrice yearly in examination years and four times for other years. Common assessments are used by some teachers for end-of-topic tests and this practice should be extended where appropriate.
Parents are informed of students’ performance in assessments through the issuing of individual reports following formal school assessments, and parent-teacher meetings. Additionally, teachers are encouraged to contact parents if they have a concern regarding a student’s performance or achievement.
Teachers retain good records of students’ achievement and attendance. All junior cycle students are required to record their homework within the school journal. The school journal can also be used for communication between school and parents. However, the use of the journal to record homework was observed not to be consistent. It is recommended that a review of the intended use of the journal be considered as a whole-school matter.
Homework assigned was appropriate to the work engaged with during the lesson and was suitably challenging for students to allow for the practising of newly acquired techniques. There was evidence that homework is regularly assigned to students. However, observation of students’ Mathematics copies indicated that students in some classes are not modelling the best practice that their teachers indicated in the presentation of their work and greater care is needed. There is evidence that some teachers are reviewing students’ work and providing annotations to assist students in their work. However, it was not always clear if students were sharing in the responsibility for the correction and amendments of their own work. Greater consistency in this practice should be encouraged as it would complement one of the “improvement strategies for the year” highlighted in the Mathematics plan. In addition to homework copies, students retain a separate hardback copy in which they record definitions and examples covered in class. This practice is commendable as it provides students with a learning resource that they have created.
The following are the main strengths identified in the evaluation:
· There is very good whole school support by management for Mathematics.
· Teachers have very good subject knowledge, were enthusiastic about their work, very well prepared for their lessons and presented lessons in a
· The uptake of levels and achievement of students in state examinations is very good.
· The Mathematics department is very active in its promotion of the subject, in its identification of areas for improvement and in developing actions to
· There were some very good examples of teaching and learning in lessons, with a very good range of questioning strategies and resources.
· Teachers set high standard for their students and students in turn strive to achieve.
· There are very good opportunities for students to engage with Mathematics through the promotion by teachers of a range of co-curricular activities.
· Individual teachers have developed skills in the area of ICT which they are using effectively in the teaching of Mathematics.
· The practice of providing in-service to fellow members of the Mathematics department is commended.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· Ongoing work on the long-term plan is necessary to develop the curriculum content for each year grouping into desired learning outcomes for students.
· Where appropriate a wider range of methodologies should be explored to ensure that the learning needs of all students are catered for.
· Increased use of higher-order questions in some lessons should be encouraged to prompt students to support and develop the answers they offer.
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