An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Ladywell Street, Thomastown
Roll number: 70640I
Date of inspection: 11 May 2006
Date of issue of report: 26 October 2006
This Subject Inspection report
This report has been written following a subject inspection in Grennan 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 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 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.
Grennan College is a co-educational school offering the Junior Certificate, optional Transition Year, Leaving Certificate, Leaving Certificate Vocational Programme and Post-Leaving Certificate to its 327 students. Prospective students are well informed about the programmes and subjects offered by the school. An open evening is arranged for incoming first-year students.
Three teachers teach Mathematics in Grennan College, one of whom is the numeracy-support teacher. In so far as is possible, teachers retain class groupings from first until third year and from fifth until sixth year. Mathematics teachers are currently introducing a system to ensure that a teacher will retain a class grouping from first year to sixth year. Commendable practice has developed that allows the teaching of levels and programmes to be rotated among Mathematics teachers. This ensures that all teachers get an opportunity to teach the different ability levels while developing and maintaining the expertise within the department.
Provision of Mathematics is satisfactory with a weekly allocation of five class periods to all class groupings excluding Transition Year which has three class periods per week. However, one teacher is timetabled for two extra class periods per week for sixth-year Mathematics. During this time students are assisted with the revision of various topics on the syllabus.
Lessons are generally organised to take place daily thus ensuring that all students make steady progress. Additionally, the arrangements for Mathematics instruction time shows clear commitment to and understanding of the requirements of the subject with concurrent timetabling of Mathematics from first year onwards. Such practice facilitates the movement of students to study Mathematics at a level appropriate to their ability.
Prior to entry to Grennan College students sit an entrance assessment. Initially two mixed-ability class groupings are formed and students are offered all optional subjects. At Christmas, first-year students then choose their preferred subject options and are streamed for the core subjects. In first year, generally one higher and one ordinary-level Mathematics class grouping are arranged. Mathematics students remain in these groupings throughout the junior cycle but movement between levels is permitted. In the current school year, as a special measure to accommodate the range of abilities of students, an extra teacher has been assigned to third-year Mathematics. Management is to be commended for such teacher allocation.
As the Transition Year is optional, generally one mixed-ability class grouping is formed each year. Two streamed Mathematics classes are formed in both fifth and sixth year. This has led to the teaching of higher and ordinary-level in one class grouping and to the teaching of ordinary-level with the possibility of some foundation-level students in the second class grouping. Such practice does not promote the uptake of higher-level and is a cause of concern for the Mathematics teachers. Consideration should be given to continually reviewing the allocation of teachers to Mathematics particularly at senior cycle with the possibility of extending the current practice that exists in third year of allocating an extra teacher through to senior cycle, as resources permit.
Management is commended for facilitating teachers to attend inservice. Since the revision of the Junior Certificate Mathematics syllabus teachers have attended relevant inservice and have had a follow-up visit from a member of the Junior Certificate Mathematics Support Service. More recently teachers have attended inservice on areas such as the teaching of geometry at Junior Certificate and teaching reluctant learners. Furthermore some teachers are members of the Irish Mathematics Teachers Association and have attended seminars arranged on topics such as the teaching of higher-level Mathematics.
Resources for teaching are allocated on a request basis to the Mathematics department. Generally, Mathematics teachers are classroom based and are located in close proximity to each other. Teachers had a good range of resources available in their classrooms which are accessible to all Mathematics teachers. Teachers collaborate and have prioritised the acquisition of resources for the department. For example the teachers prioritised the acquisition of whiteboards and graph boards for Mathematics and have acquired them. Furthermore the department is now highlighting the purchasing and licensing of a geometry sketchpad for the teaching of geometry in Mathematics. Teachers are commended for such good practice in the long-term prioritisation of resources for Mathematics. This good practice should continue.
Students are identified for learning support in a number of ways including the entrance assessment, primary school information, psychological reports and parental information. Support is offered in a variety of ways including the withdrawal of students for individual or small-group tuition with the resource/learning-support teacher or through the creation of an additional Mathematics class grouping (currently happening in third year). There is evidence that students’ progress is monitored regularly and to this end all teachers complete a questionnaire each term to review students’ progress.
The college is currently focusing on subject department planning as part of school development planning. To this end the department has used diagnostic templates and has collaborated and developed a long-term plan for first-year Mathematics. This good practice has afforded teachers an opportunity to ground planning in the syllabus as opposed to textbooks. It is recommended that the Mathematics department continue this work and further develop the long-term plan for Mathematics. This plan should include an outline of sections of the syllabus at junior and senior cycle and the advised areas of study under each of these sections. Furthermore the plan should include the aims and objectives for Mathematics education in the school and a suggested range of methodologies. This collaboration should provide Mathematics teachers with the opportunity to identify and share good practice. It should also allow for common assessments to be sustained and extended to other year groupings. Consideration should also be given to including planning for the integration of Information and Communication Technology in the teaching of Mathematics.
Staff presented as a unified team who collaborate on all issues pertaining to Mathematics. Formal planning meetings take place twice or three times per year. Additionally many informal meetings take place more frequently on a needs basis. Minutes from formal meetings are recorded and retained and include an outline of agreed decisions, arrangements and assignment of teachers to each class grouping and some cross-curricular links. This good practice is commended. The department does not have a coordinator. However, an informal arrangement is in place that ensures that all are informed regarding mathematical issues. Consideration should be given to the appointing of a coordinator for the subject. This position should be rotated to ensure that all teachers act as co-ordinator at some stage.
The Transition Year plan for the school is reviewed and updated yearly. This is good practice as it allows Mathematics teachers to devise a programme that takes into account the needs and abilities of the students who choose to follow the Transition Year programme. There is a good balance between topics that consolidate the prior learning of students, some elements from the Leaving Certificate programme and other topics such as nets and tessellations and project work. A unique feature of the Transition Year Mathematics programme is that each student chooses and researches a mathematical topic before teaching it to students in their class grouping. This is commendable practice as it allows students to develop an interest in Mathematics while learning in a different way.
All teachers presented individual comprehensive planning documents that detail the topics to be studied and a general timeframe for their completion. In addition, teachers had developed individual handouts and other supplementary materials and these were accessed and used during lessons visited. This is commendable practice.
All teachers displayed a keen interest and commitment to their teaching and their students. Effective planning ensured that lessons were well structured and presented in a confident manner. An appropriate pace ensured that students remained focused and that time was used effectively. Teachers explicitly stated the purpose of the lessons. This is good practice as it increases student motivation and maintains student interest in the lesson.
Topics such as fractions, calculus and functions featured in some lessons. In other lessons students worked on examination papers. The predominant methodology observed in lessons was traditional whole-class teaching. This was observed where the teacher demonstrated a new technique and students then practised the technique by completing a series of similar exercises while the teacher circulated the room to provide individual assistance. To ensure that all students preferred learning styles are catered for, a range of teaching methodologies should be used in all Mathematics classes. To this end teachers should refer to the methodologies outlined in the Junior Certificate Mathematics Guidelines for Teachers.
There was some good use of group work observed with the teacher acting as a facilitator of learning. In such lessons the teacher set appropriate tasks for students who worked in groups to achieve the desired learning outcomes. Through effective group work students had the opportunity to take responsibility for their learning, were challenged to think for themselves, were encouraged to discuss problems and learned to work collaboratively.
In all lessons observed a range of questioning strategies was used. Recall and closed questions were frequently used to determine students’ level of knowledge and understanding of the topic. Such questions were initially offered to the entire class for consideration before an individual was asked to provide an answer. This is good practice as it ensures that all students’ focus is maintained on the topic. There were some very good examples of teachers using higher-order questioning to develop student answers and understanding by encouraging them to explain and justify their thinking and methods. All teachers should use a greater range of questioning strategies in all classes.
Resources used during lessons observed included the whiteboard and overhead projector. These were all used to good effect. The prior preparation of differentiated worksheets helps aid smooth progression in the learning experience while encouraging all students to work at an appropriate level. Such good practice should be extended to all lessons. There was evidence of good practice in the teaching of Mathematics where teachers frequently reviewed terminology and concepts.
Teachers displayed very good classroom management techniques and all lessons were conducted in a warm, friendly atmosphere which was conducive to a good learning environment. Students’ contributions and questions were welcomed and addressed as part of the lesson. A good teacher-student rapport existed in all lessons observed. When teachers circulated the classrooms to provide individual attention this was done in a sensitive and discreet manner. Teacher-based classrooms were well maintained and supported the teaching and learning of Mathematics through the displays of mathematical posters, which is commendable practice.
Student progress is monitored in a variety of ways. These include class questioning, homework correction, end-of-topic tests and formal school examinations. Examination year groupings sit ‘mock’ exams in the second term. Common assessment takes place at Christmas for first-year students. Consideration should be given to extending this to all year groupings as appropriate.
Parents are kept well informed of their children’s ongoing progress. School reports are issued following formal school examinations and following ‘mock’ examinations for examination classes. Parent-teacher meetings are also convened for all year groupings. Examination students attend these meetings with their parents.
Homework assigned was appropriate in terms of quantity and relevance to topics studied during lessons observed. Homework copies are being monitored. However, it is recommended that further commendations and suggested areas for improvement be included in all copies. Students develop their own revision notes for future reference. This is good practice as it ensures that students take an active role in their learning experience. Furthermore some teachers retain a separate class test copy as a record of student achievement. This is commendable practice.
Teachers retain good records of student progress and attendance. From observation of such records there is evidence to suggest that on occasion attendance for some students can be a problem. In addition it was reported that some students ‘drop out’ of school during the year to take up employment or to follow an apprentice programme. It is recommended that both issues be continually monitored and that a whole-school approach be adopted to address these issues.
Students’ outcomes in terms of knowledge and skills are good. Most students were confident and competent in answering questions put to them during the course of the visit. Recent initiatives to address the uptake of foundation level have been successful and have resulted in a decline in the number of students taking foundation level in both the Junior and Leaving Certificates. Teachers are commended for encouraging students to study Mathematics at the highest level appropriate to their abilities.
The following are the main strengths and areas for development identified in the evaluation:
Teachers displayed a strong commitment to the teaching of Mathematics and to their students.
Mathematic teachers collaborate on all issues pertaining to their subject and are currently working on a long-term plan for Mathematics.
Teachers have developed very good short-term individual plans.
Teachers encourage students to study Mathematics at the highest level appropriate to their abilities.
Management supports Mathematics teachers by facilitating them to attend inservice and by providing resources for the teaching and learning of Mathematics.
There is good communication between parents and the school.
As a means of building on these strengths and to address areas for development, the following recommendations are made:
The school should engage in a whole-school approach to address issues such as attendance and the number of students who ‘drop out’ during the year.
The Mathematics department should continue to develop a long-term plan for Mathematics.
The timetabling of Mathematics should be reviewed to ensure that best practice is used in the allocation of teachers to Mathematics, particularly in senior cycle.
A variety of methodologies and a range of questioning strategies should be used in all lessons.
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.