An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Blackwater Community School
Lismore, County Waterford
Roll number: 91509E
Date of inspection: 27 November 2007
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Blackwater Community School. It presents the findings of an evaluation of the quality of teaching and learning in Mathematics and Applied Mathematics and makes recommendations for the further development of the teaching of these subjects 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.
Blackwater Community School was formed from the amalgamation of three local post-primary schools. The school opened in September 2003. School management is committed to the use of information and communication technology (ICT) in teaching within the school. All teachers have received training in the use of ICT in their teaching and further training is available on request. Teachers have the option of having an interactive whiteboard placed in their classrooms in the school. To date twelve classrooms have had this technology installed and its use was observed in a number of mathematics lessons during the visit. All involved in this innovative scheme are commended.
The time allocated to the subject and the concurrent timetabling of classes is evidence of the commitment of school management to the promotion of Mathematics within the school. Mathematics lessons for all year groups from second year on are timetabled concurrently. This allows for the creation of level-specific classes and students can follow the highest level possible for as long as possible while still retaining the option of changing levels where appropriate. The time allocated to Mathematics is also good. All second-year, third-year and fifth-year classes have five class periods per week. Sixth-year classes have six periods each week.
First-year classes have four periods of Mathematics each week. Students are allocated to first-year classes on a mixed ability basis. This allows all students to experience Post-primary Mathematics equally following the transition from primary school. Students are assessed on their progress during their first year through two formal common assessments at Christmas and summer, as well as ongoing teacher monitoring and topic tests. Students are then allocated to level-specific groups from second year on.
In line with accepted good practice, mathematics classes are generally distributed evenly throughout the school day and the school week. However, due to reported timetabling constraints, one first-year class has all four mathematics lessons in the afternoon. It is recommended that, where possible, future timetabling try to ensure that all classes enjoy the benefits of an even spread of classes through the school day and the week.
Transition Year (TY) is optional in the school. A majority of students avail of this option and the three class groups are timetabled concurrently for four periods of Mathematics each week. Students who have completed the higher level syllabus at junior cycle form one group and two other mixed-ability groups are formed. This structure allows for flexibility within the teaching arrangements and it is suggested that this flexibility could be exploited to allow for some rotation of teachers among the classes, creating the option of teaching short modules to each group.
Students assessed as needing resource hours in Mathematics are supported in first year through one-to-one tuition during resources classes. The mathematical ability of all incoming first-year students is formally assessed prior to entry to the school and again early in September of their first year. These assessments, along with ongoing teacher observation and monitoring, identify students who find the subject particularly challenging. Support in the form of extra tuition for these students is provided in first year, through withdrawal for one-to-one and small group tuition from classes other than mathematics classes. In all cases the resource teacher or learning-support teacher maintains informal contact with the mathematics teacher. It is suggested that the current strategies for learning support and resources provision for Mathematics at Blackwater Community School be reviewed to examine the possibilities offered by team-teaching or in-class support to complement the good practice already in place.
From first year on, support is provided as needs are identified. Currently, in both second and third year a small class group is created. This group studies a limited range of subjects and individual students receive support in a range of subjects including Mathematics. Currently, in sixth year, a smaller class has also been created to cater specifically for those students who wish to follow the foundation level syllabus. It is suggested that the learning support and resources provision for Mathematics at Blackwater Community School be reviewed to ensure that the available resources are employed to achieve the maximum benefits for the students concerned.
The option of studying Applied Mathematics as an extra Leaving Certificate subject has been offered to students since the school opened in 2003. Students are taught the subject for five periods each week in fifth and sixth year. Uptake rates in the subject have increased steadily since the subject was introduced. All involved in promoting the subject in the school are commended.
The mathematics department is co-ordinated on an ongoing basis. The present co-ordinator was appointed in the beginning of the current school year. It is reported that the running of the department is reviewed annually and the position of co-ordinator may rotate between members of the team. This is good practice as each member of the team will benefit from the experience of the issues involved in the running of their subject department.
Formal subject-specific team meetings for planning and review are held at the beginning and end of the school year as part of ongoing school development planning. This is positive and the good practice of keeping records of these meetings is in place. The school also has scheduled forty-five minute staff meeting each week on a Monday afternoon. Approximately one in four of these meetings is devoted to subject-department planning. Mathematics teachers also meet informally outside of these times.
Commendable progress has been made with the mathematics department plan. The current plan contains a mission statement along with the aims and objectives of mathematics teaching in the school. It also contains organisational details along with a long-term yearly plan, in the form of chapter headings, for each year group and level. There is clear evidence that the department works collaboratively on planning and review.
It is recommended that the mathematics department continue this good work and further develop the long-term plan for Mathematics. This revised plan should include an outline of sections of the syllabus at junior and senior cycle and the key skills for students to acquire under each of these sections. The yearly plan should be divided into sections by term, or half year, to allow greater co-ordination within levels. This collaboration should provide mathematics teachers with more opportunities to identify and share good practice. It should also allow for common assessments or common questions in assessments to be sustained and extended to other year groups.
The current model of continuous professional development (CPD) in Mathematics includes one-day seminars in local education centres, where schools are invited to send one or two members of the team as appropriate. These representatives then report back to colleagues as appropriate. The school’s mathematics plan should contain details of the teachers who have attended such in-service and the topics covered.
Mathematics teachers currently using the interactive whiteboards are creating and saving resources on an ongoing basis. Resources are also being accessed on the web. It would be useful for all members of the department if a list of these and other ICT resources, updated on a regular basis, was available within the plan.
Individual plans made available by all members of the team during the inspection were good. Teachers used the long-term plan for the department to plan their individual programme of work. Some teachers also maintain a record of the work covered by, and homework given to, their classes. Many teachers have developed supplementary materials such as handouts, ICT resources, charts and acetates for use in the teaching and learning of Mathematics.
The content of lessons visited was appropriate in all cases and in line with agreed programmes of work and syllabus requirements. Teachers’ presentation of work, using interactive whiteboard, whiteboard or blackboard was generally clear, suited to the task and linked to previous work. Teachers were prepared for their teaching and students were attentive and engaged in the work at hand. In some cases the topic of the class, in the form of what the students were expected to be able to do at the end of the lesson, was stated. This is in keeping with the principles of Assessment for Learning and it is recommended that each lesson have a structured opening, where the learning intention would be explicitly communicated, and a closing, where the achievement of the intention would be reviewed.
Classroom interactions generally took the form of brief answers, by students, to questions posed by the teacher. The emphasis of much of the questioning was on finding the next steps in the solution to a problem or on ‘fill in’ type questions. There were, however, in line with good practice, some cases of teachers using more open questioning to extend students’ understanding and encourage the expression of mathematical ideas. This commendable practice can help students become more involved in their learning, maintain engagement with the topic and foster a problem-solving approach. It is recommended, therefore, that all teachers make more use of a variety of questioning styles including probing questions to appropriately challenge students and support them in developing the skills of mathematical thinking and communication.
Teaching observed was predominantly conducted through the presentation of work on the board followed by the setting of exercises for practice while the teacher provided help to individual students. A characteristic of this teaching style is that students are generally passive and see their role as reproducing the method of solution in similar type problems from the textbook. To complement this ‘traditional’ approach, it is recommended that a broader range of teaching methodologies and materials be explored and developed. Some examples could include pair work, group work, investigation, consolidation activities, use of concrete materials, discussion, and quiz activities, more use of ICT and student project work. The incorporation of these methodologies into lessons acknowledges students’ different preferred learning styles and engages students more actively in their own learning.
There were many commendable examples where teachers had appropriately high expectations of students’ capabilities, and in all cases students responded accordingly. Mutual respect among students and between teachers and students was observed.
Examples of good practice observed during lesson visits included teachers affirming students’ efforts, teachers and students making appropriate use of mathematics terminology, encouraging students to explain how answers were reached, an emphasis on the visual interpretation of solving simultaneous equations in algebra and taking specific measures to include all students in the lesson.
A minority of classrooms visited had displays of students’ work or of mathematical posters which enhanced the visual learning environment. The display of such posters and students’ project work can be effectively used to remind students of key mathematical concepts or formulae. It is recommended that the purchase or creation and use of such displays be more widely adopted by the team.
In interactions with the inspector, it was evident that in the majority of lessons, students had a clear understanding of the work in which they were involved. They were able to discuss solutions to questions posed to them in appropriate mathematical language. Appropriate student progress was also evident from an examination of the written work being done by students, during the lessons inspected. The standard of this work showed that they had understood procedures taught during the lessons and were able to apply them to similar problems from the textbook.
Students’ progress is assessed through oral questioning, the assignment and correction of homework, class tests and term examinations. Teachers keep records of students’ achievements in assessments. First-year students are commonly assessed at Christmas and summer and there is some reported use of common exams for classes studying at the same levels in other years. Progress is formally reported to parents four times each year. All classes are informally assessed at Halloween and non-examination classes have formal assessments at Christmas, Easter and summer. Examination classes have ‘mock’ examinations in February as well as assessments at Halloween, Christmas and Easter. Each year group has a parent-teacher meeting once per year. This high level of communication with parents is commended.
The team analyse students’ performance in the Certificate examinations each year. Teachers are aware of the school’s standing in this regard and use is made of this data to inform planning. The school’s efforts to increase uptake rates at higher level in both junior and senior cycle are commended.
To recognise students’ success the school organises an awards ceremony which acknowledges academic achievements and endeavours in each subject. There is a medal presentation to the highest achieving student in both Mathematics and Applied Mathematics. Students have the opportunity to participate in a range of extracurricular activities pertaining to Mathematics. Mathematics students have been invited to participate in Mathematics Olympiad training and in talented-youth training on the basis of their performance in State examinations. Furthermore, students participate in a variety of co-curricular activities such as the ESAT Young Scientist exhibition.
A number of national mathematics competitions are currently available to schools. The Irish Mathematics Teachers Association (IMTA) organise the Team Maths competition for senior students and Irish Junior Mathematics Competition for first-year students. Problem Solving for Irish Second Level Mathematicians (PRISM) competitions, organised nationally as part of Maths Week Ireland held in October for second-year and fifth-year students are also available. It is recommended that the school investigate the potential of national mathematics competitions to engage and encourage students.
Homework has an important role in the learning process and was assigned in all lessons observed. Students’ copybooks revealed that regular homework is assigned which is good practice. There was evidence that teachers generally monitor students’ copybooks. Good practice was evident where teachers, through the use of comments, encourage students’ efforts and direct them on ways to correct and improve their work.
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 Applied 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, June 2008