An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Ballinteer Community School
Ballinteer, Dublin 16
Roll number: 91305L
Date of inspection: 26 October 2006
Date of issue of report: 21 June 2007
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Ballinteer Community 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, deputy principal and subject teachers.
Ballinteer Community School is a co-educational school offering the Junior Certificate, Transition Year, Leaving Certificate Applied and Leaving Certificate programmes to its 331 students.
Prior to entry students sit an assessment and, based on these results, are assigned to one of three streamed class groupings. The level a student follows in junior cycle depends on the stream to which he/she is assigned. The top stream follows higher level, the middle follows ordinary level and the third stream follows foundation level. The concurrent timetabling of Mathematics permits movement but generally this only happens between the top two streams. Streaming then continues for all Mathematics class groupings throughout senior cycle excluding the Leaving Certificate Applied class grouping. It is recommended that a review of this practice be undertaken to ensure a more flexible system of assigning students to classes so that the potential of all students is met. Furthermore, consideration should be given to placing students in mixed-ability class groups for Mathematics in first year. Students could then be set from second year onwards for Mathematics.
The Mathematics department comprises seven Mathematics teachers. Teachers are assigned to Junior Certificate classes on a rotational basis. At senior cycle the teaching of higher-level Mathematics is rotated but not on a yearly basis. The rotation of levels and programmes is good practice as it allows for the expertise to be maintained in the Mathematics department while ensuring that no one person is associated with a particular level or programme. Teachers generally retain the same class grouping from year to year.
An extra Mathematics teacher is assigned in both third-year and sixth-year. It is questionable whether this intervention is appropriate as classes have already been streamed from first year and such and intervention may lead to a fragmentation of the learning experience for students. In addition even though it is commendable that extra support is provided in Mathematics to the lowest streams from first to third year, on occasion this can result in these classes having two Mathematics teachers. A review of such practices is recommended.
Time allocated to Mathematics at junior cycle varies according to class grouping. For example, all Junior Certificate students have four class periods per week with extra classes assigned to the third stream. This is resulting in some second and third-year class groupings not having daily contact with the subject. It is therefore recommended that a review of timetabling be undertaken to increase the number of class periods for second and third year class groupings especially for the top two streams.
Three streamed class groupings are arranged in Transition Year; each having four class periods per week. The review of streaming mentioned earlier should also take place for Transition Year. One class grouping of Leaving Certificate Applied is arranged in fifth and sixth year and each has four class periods per week assigned to Mathematics, which is adequate to fulfil the requirements of the syllabus. Fifth and sixth-year classes have five class periods per week and classes are in general well distributed throughout the week.
Management is commended for supporting the continual professional development of teachers by facilitating opportunities to attend inservice in Mathematics. Mathematic teachers with particular expertise are commended for giving inservice on occasion to the Mathematics department. Furthermore, some members of the department have been on the executive committee of the Irish Mathematics Teachers Association (IMTA) and continue to have a connection with the association.
While there is no specific budget for Mathematics, teachers have access to resources such as overhead projectors, mathematical equipment and occasionally a data projector. Reasonable requests for purchase of resources are granted. As teachers are classroom based resources tend to be developed independently but on occasion some teachers have collaborated to develop a bank of resources, which they share. Consideration should be given to extending this practice to all within the department.
Students have opportunities to participate in extra-curricular and co-curricular activities associated with Mathematics. For example, an “Open night in Dunsink Observatory” has been organised for senior cycle students studying Mathematics and Applied Mathematics. In addition, students have also competed in the IMTA run TeamMath and first-year Mathematics competitions. A unique feature of the school is the setting each week of a Mathematical puzzle for consideration by students. Such support for and encouragement of Mathematics is highly commendable as it promotes the subject while offering students an opportunity to experience Mathematics in a variety of different learning situations.
Teachers are facilitated to meet formally twice per year. The position of coordination of the subject is rotated on an annual basis among Mathematics teachers. In the current year, two teachers act as coordinator of the subject. Minutes from meetings are retained and issues discussed include the sequencing of Mathematics topics for each year, discussion regarding policy documents and analysis of student entrance results. Further consideration at such meetings should be given by teachers to collaborating to develop a prioritised list of resources to meet the ongoing needs for the teaching of Mathematics; such resources should be retained in a central location to allow for ease of access for all teachers. Discussions should also address the uptake of levels in Mathematics and strategies to ensure that students take a level appropriate to their abilities.
The long-term plan for Mathematics includes plans for each year grouping, a Transition Year plan and a Leaving Certificate Applied plan. A policy document for Mathematics, an outline of the aims and objectives for the subject, are also included in the plan. Work to date on planning is commendable. However, in the interest of furthering such good practice it is recommended that individual plans be consolidated into a succinct whole school department plan for Mathematics. Planning for Mathematics should be as a department rather than a compilation of individual plans. This will ensure that a common structure is placed on all year plans while avoiding duplication of some aspects of the plan. It will also provide all teachers with an opportunity to collaborate and share best practice.
The integration of Information and Communication Technology (ICT) should be included within all year groupings’ plans to support the teaching and learning of the subject. To this end consideration should be given to including some of the materials and suggestions engaged with through the Teaching and Learning 21 project.
The Transition Year plan for Mathematics is divided into a higher and ordinary-level section. The ordinary-level plan includes topics such as problem solving using sudoku and other activities, arithmetic, geometry and statistics. The higher-level plan focuses entirely on the Algebra section from the higher-level Leaving Certificate syllabus. One of the four higher-level Transition Year Mathematics class periods is used to introduce Applied Mathematics during which topics such as kinematics and problem solving are covered. It was reported that on occasion other elements are included in the programme. Circular M1/00 The Transition Year Programme states that: “A Transition Year programme is not part of the Leaving Certificate programme, and should not be seen as an opportunity for spending three years rather than two studying Leaving Certificate material.” It is therefore recommended that aspects of the Transition Year programme for Mathematics be reviewed to ensure compliance with the circular.
When reviewing the Transition Year Mathematics programme reference should be made to the support available on the website www.slss.ie where access can be made to resources and newsletters, which outline teaching and learning strategies, interdisciplinary links and curriculum ideas pertaining to Transition Year Mathematics.
Individual lessons plans presented were very good. For example the use of a flow chart in the planning for a lesson is highly commendable and ensured that steady progression was made in lessons and that time was effectively managed throughout lessons. In general teachers worked from the individual year group plan and made the necessary modifications to suit the needs of the cohort of students that they were teaching. Prior preparation of materials and necessary handouts aided the smooth transition between stages of the lesson.
Topics such as statistics, probability and geometry featured in lessons observed. Lessons were presented in a confident, coherent manner. Best practice was observed when teachers explicitly stated the aims and objectives of the lesson in advance. This had the effect of focusing students and engaging them from the outset and should be extended to all classes.
Teachers used Mathematics terminology appropriate to the relevant topics and students’ ability. Best practice observed included the setting in context of key mathematical terms or phrases for students thus aiding their understanding. Such practices are commendable and should be extended to all classes.
Teaching was, in general, of a high standard. Some very good examples of methodologies observed in lessons gave students an opportunity to work in groups or undertake investigative work. For example students used the mathematical data available on products to discuss the merits of purchasing. In addition, the use of a dominos game at the beginning of a lesson to reinforce and check students understanding of percentages, decimals and fractions was very effective. Such good practices are commendable as they provide students with an opportunity to share in the responsibility for their learning. Many lessons were taught in a traditional manner; that is the teacher demonstrates a technique and then the students practise it by completing exercises from a textbook. As not all students benefit from traditional teaching it is recommended that a greater range of methodologies be used where appropriate in lessons.
Teachers engaged students through a range of questioning techniques. For example, good use was made of a combination of recall questions and higher-order questions. Generally recall questions were used to ascertain students’ understanding or to make connections with a previous lesson. Higher-order questioning was used to encourage students to develop, justify and think through an answer. This is good practice as the capacity to reason, explain and prove is paramount to being successful in Mathematics.
Resources used in lessons included textbook, prepared
worksheets, a data projector and handouts. The use of sudoku puzzles allowed
students to fully engage with a range of concepts in an enjoyable manner. The
presentation by a student of work that linked Leaving Certificate Applied
Mathematics and ICT was commendable. In addition, the overhead projector was used to
good effect to explain a variety of questions or show suggested solutions to
questions. However, the use of some mathematical equipment in other lessons
would have been effective, as a means of demonstrating appropriate techniques
to students and should be planned for in all lessons.
Classroom management was very good and generally there were very positive interactions between teachers and students. The evidence suggested that the practice of affirming students’ effort worked most effectively. Frequently teachers circulated to provide support and immediate feedback to students and this was done effectively and sensitively. In general, students used mathematical terminology appropriate to the topic when questioned by their teachers and this should be encouraged in all lessons.
In many classrooms the learning environment was enhanced with mathematical materials and students’ mathematical displays. On occasion reference to such posters was made to good effect when teaching or referring to aspects of the curriculum.
Students’ outcomes in terms of knowledge and skills are varied. Some students demonstrated capability in answering and justifying questions put to them during the course of the visit. There is evidence to suggest that a significant proportion of students are taking foundation level at Junior Certificate and achieving high results. This suggests that some students should strive for a higher level. Furthermore, the number of students taking higher level in Junior Certificate Mathematics is low and this will inevitably have consequences for the uptake of higher level at Leaving Certificate. It is therefore recommended that the Mathematics department collaborate to review the uptake of levels and adopt a strategy to ensure that all students are reaching their full potential.
Assessment is ongoing and takes many forms; class questioning, homework and end-of-topic examinations. Formal examinations take place at Christmas and summer for non-examination year groupings and there are Christmas and ‘mock’ exams for examination year. Leaving Certificate Applied students do not sit ‘mock’ exams.
There was commendable use of a student self-assessment sheet observed in a particular lesson. The use of such an assessment provided students with clear criteria for success at the outset of a topic in addition to providing students with an opportunity to participate fully in their own learning. This is good practice and could be used more extensively.
Communication between home and school is maintained through school reports which are issued twice per year, school newsletter and when necessary contact via a phone call. Students’ school diaries are used to record reasons for absences. Parent-teacher meetings are also convened for each year grouping.
Homework is a valuable part of students’ learning and was assigned in most lessons observed. The relevance and quantity assigned was appropriate in terms of students’ abilities. The assignment of homework provides students with an opportunity to practise newly acquired skills and techniques. The practice of students accurately recording their homework in their student journal is sporadic and consequently should be monitored more carefully.
Teachers retain very good records of students’ attendance and record student achievements following examinations. Furthermore, there was evidence that many teachers monitored students’ homework and provided appropriate commendations and suggested areas of improvement, which is commendable practice and should be used by all teachers. Management has provided a computer in each classroom and staff is currently working on recording student attendance via the computer through a system called Pinnacle.
The following are the main strengths identified in the evaluation:
· Good communication between the school and home is maintained in a variety of ways.
· Teachers have developed good individual short-term plans for Mathematics and have also developed materials in preparation of their lessons.
· There were some very good examples of group work, pair work and investigative methods used in some lessons. A good range of questioning by teachers was used in most lessons.
· There were good mathematical displays in some classrooms.
· The inclusion of a range of co-curricular and extra-curricular activities pertaining to Mathematics is commendable.
· There were some good examples of formative assessment in students’ copies.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· The practice of streaming students on entry to the school should be reviewed. Consideration should be given to mixed ability in first year and banding of Mathematics classes from second year onwards.
· A review of timetabling to increase the number of class periods in Mathematics allocated to junior cycle class grouping should be undertaken.
· The long-term plan for Mathematics should be reviewed and one succinct plan for the subject developed. Furthermore, a review of the Transition Year Mathematics programme should be undertaken to ensure compliance with circular M1/00.
· A greater range of differentiated methodologies should be used in lessons to complement the learning styles of all students.
· A whole school approach should be taken to develop strategies to ensure that students take the highest level most appropriate to their ability.
Post-evaluation meetings were held with the teachers of Mathematics and with the principal, deputy principal, at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.