An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
Bridgetown Vocational College,
Bridgetown, County Wexford
Roll number: 71610E
Date of inspection: 10 December 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Bridgetown Vocational 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 studentsí work, and had discussions with the teachers. The inspector reviewed school planning documentation and teachersí 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.† 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 Mathematics in Bridgetown Vocational College is good. Mathematics classes are generally forty minutes in duration. At junior cycle each year group is allocated five class periods per week of Mathematics. There is a minimum of five class periods per week for fifth and sixth-year Mathematics students with a sixth class period per week allocated to higher-level Mathematics students. Management endeavours to provide six lessons to all classes in fifth and sixth year but not all ordinary and foundation level classes receive a sixth Mathematics lesson. While the efforts towards a high level of provision are recognised there is an issue regarding the equity of provision in fifth and sixth year and it is advisable that this be addressed. Leaving Certificate Applied (LCA) is allocated three class periods per week.
The distribution of Mathematics lessons is generally good and facilitates daily contact with the subject. However, on occasion two class periods are assigned on one day per week, resulting in students not having Mathematics on one day of the week. This should be reviewed to ensure insofar as is possible that daily exposure to Mathematics is facilitated.
On entry to the school, first-year students are assigned to one of two bands for Mathematics based on the Drumcondra Reasoning tests. Three class groups are formed within the upper band for Mathematics and are taught in mixed-ability setting. Students in the lower band are assigned to their class group based on results from the NFER Nelson France Maths Test. Resource hours are used to create a small Mathematics class group within this band for students who find Mathematics difficult. Students remain within these bands throughout junior cycle. In second year students in the upper band generally follow higher or ordinary level with ordinary or foundation level offered to the lower band. Management is commended for facilitating concurrent timetabling within each band from second year as it affords students the opportunity to access the most appropriate level.
At senior cycle, one class group of LCA is established each year. Students who follow the established Leaving Certificate are assigned to Mathematics classes based on their Junior Certificate level and results. Concurrent timetabling of Mathematics takes place for fifth and sixth year students thus providing optimal access to appropriate levels for students.
Ten teachers teach the Mathematics classes in the school with an additional three Mathematics teachers providing support classes to students in Mathematics. Management is commended for the allocation of extra teachers to Mathematics for each year group. In general teachers remain with a class group within each cycle and on occasion from first year through to sixth year, and this is good practice. In junior cycle the practice is to rotate the teaching of levels and programmes among all Mathematics teachers. In senior cycle, two teachers share the rotation of higher-level Mathematics, but other teachers can be included in this rotation. It is good practice that rotation is facilitated as it ensures that opportunities to develop expertise among all members of the Mathematics department are encouraged.
Communication and collaboration between the learning support, resource and Mathematics teachers within the school is very good, as evidenced in the minutes of Mathematics meetings and through the establishment of support structures to assist students for whom Mathematics is challenging. Further evidence was the development of a strategy to reduce the number of students choosing foundation level particularly for Junior Certificate. This has been successful.
A wide range of resources is available for the teaching of Mathematics in the school. For example, probability kits, geosolids and mathematical sets are available for use by all. Requests for additional resources are forwarded to the principal by the subject contact person. Teachers are facilitated by management to engage with in-service and many have attended Mathematics-specific in-service. In addition, whole staff in-service has included topics such as assessment for learning and mixed-ability teaching. Management also pays the annual subscription for membership of the Irish Mathematics Teachers Association (IMTA). Such support by management is commendable.
Students have been invited to participate in the Irish Mathematical Olympiad. It was reported that teachers offer additional voluntary Mathematics lessons to students throughout the year.
Management facilitates formal planning time to subject departments with regular informal meeting also arranged. The voluntary position of subject contact person is decided upon on a rotational basis among members of the department. This position involves liaising with management and arranging department meetings. Records of Mathematics meetings are retained and show clear evidence of ongoing collaboration and review among teachers. Furthermore, there is evidence that Mathematics teachers discuss the most appropriate approaches for students with special educational needs, and this is good practice.
The Mathematics department has made commendable progress in planning. The department has a comprehensive document that comprises a Mathematics plan and supplementary materials that include relevant syllabuses and resources sourced at relevant in-services. The department plan includes the overall aims and objectives for Mathematics, subject organisational details, a list of mathematical resources and a scheme of work for each year group and level. To further progress the work already completed, it is recommended that the schemes of work be reviewed to include learning outcomes for students. Furthermore, the proportion of geometry studied in third year particularly at higher level should be reviewed. A scheme that will allow for students to study geometry on a continuous basis from first year should be considered.
Teachers followed the long-term plan for the subject when planning individual lessons. Many teachers prepared supplementary materials for lessons observed, including student worksheets, PowerPoint presentations and transparencies for overhead projectors. The prior preparation of materials and good planning allowed for good progress and smooth transition within lessons.
Topics in the lessons observed included calculus, algebra, numbers and co-ordinate geometry. Lesson content was appropriate to the range of studentsí abilities and in line with syllabus requirements. Commendably, links between topics on the syllabus were established. In addition, links between mathematical topics and associated real-life situations added to the enjoyment of learning Mathematics.
Terminology used in lessons by both teachers and students was very good and appropriate to the topics. Lessons observed were appropriately paced and time was used effectively. Students were attentive and there was, in general, a positive atmosphere in lessons. High expectations were set by many teachers and students strove to reach these standards.
A very good variety of methodologies was observed in lessons. For example, traditional whole-class teaching was effectively used in some lessons; this is a combination of teacher demonstrations to the whole class and students completing a series of examples while the teacher assists individuals. Team teaching was very successfully used: both teachers shared equal responsibility for the teaching of the class and the provision of individual attention to students. Commendably, both teachersí styles complemented each other and the lesson progressed seamlessly. In another lesson, the use of paired work to consolidate learning was effective as it allowed students to share in the responsibility for their learning. Other methods observed, such as practical work and peer learning, allowed students to work independently with the teacher acting as facilitator. It is commendable that students experience a range of methodologies as it ensures that studentsí preferred learning styles are catered for.
Questioning styles varied in lessons. For example, the common practice was to begin with a global question to the entire class followed by more directed individual questions. This is good practice as it ensures that all students remain on task and focused on the topic. Questions prompting recall were used to find the next step in a solution to a question or to recap on previous material. Higher-order questions were used to a lesser extent to challenge studentsí understanding of a topic. It is recommended that teachers vary the types of questions in lessons and increase their use of higher-order questions.
Textbooks, worksheets, concrete materials, laptops and data projectors were among the resources used in lessons. Laptop, data projector and overhead projector were used effectively as a learning aid at key junctures in the lessons to recap on the main points of the lesson, correct homework, or provide a variety of different types of examples. The use of teacher-developed task cards to reinforce concepts was very effective. These task cards were set in context and allowed students to complete a variety of exercises independently at a pace appropriate to their ability while the teacher circulated to provide assistance. The use of the whiteboard by teachers was effective as it allowed for the recording of key points and for teachers to model best practice in the presentation of Mathematics.
Some teachers are classroom based and in most classrooms an array of commercially sourced mathematical posters and studentsí work was displayed. This is good practice as it provides a stimulating environment for learning: for example, the use of posters as a teaching aid, as was observed here. However, the use of the demonstration room for Mathematics classes does not facilitate movement by the teacher to provide individual support to a student and should be avoided for this reason.
Studentsí inputs were frequently affirmed. Interactions between the students were positive and many were capable of answering questions posed to them by the inspector.
Formal assessments are arranged for non-examination years at Christmas and summer and for examination years at Christmas with Ďmocksí in the second term. Commendably, the Mathematics department has agreed to set common assessments at Christmas and summer for first-year and fifth-year students and this practice will be extended where relevant to other year groups. This practice will allow for studentsí achievements within levels to be compared with the entire year group.
Homework assigned was appropriate in terms of the quantity and relevance to the topics encountered during the lesson. An inspection of student journals suggested that not all students record homework systematically. Closer monitoring is required to ensure that students accurately record homework. A review of studentsí Mathematics copies and in-house examination papers indicated that many teachers include formative assessment particularly on exam papers. This is commendable as it provides students with clear procedures as to how they can progress with their work.
The school issues reports following formal school examinations. Progress reports are also issued to the home to advise parents about studentsí performance should a subject teacher have concerns. Parent-teacher meetings are convened for each year group. It is established practice that Mathematics teachers contact the home to discuss studentsí progress should they have concerns about a studentís attainment. The student journal is also used as means of communication between home and the school by subject teachers and parents. Evening events are arranged for JCSP students to celebrate studentsí achievements.
Teachers retain very good records of studentsí attendance and performance in assessments. Teachers also retain LCA Mathematics key assignments and relevant work for past and current modules, and Mathematics statements for JCSP students were presented during the evaluation.†
A review of teachersí records of attendance indicated that some studentsí attendance is poor, and this results in gaps in their mathematical education. Management indicated its awareness of studentsí poor attendance and systems are in place to make daily contact with relevant parents to highlight concerns. Ongoing efforts to encourage greater attendance by all students should be made to ensure that they benefit from the education provided within the school.
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:
Post-evaluation meetings were held with the teachers of Mathematics and with the principal and deputy principal, at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published October 2009