An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
REPORT
Presentation De La Salle College
Bagenalstown, County Carlow
Roll number: 61150N
Date of inspection: 29 November 2006
Date of issue of report: 21 June 2007
Subject provision and whole school support
Summary of main findings and recommendations
Report on the Quality of Learning and Teaching in Mathematics
Subject inspection report
This report has been written following a subject inspection in Presentation De La Salle College, Bagenalstown. 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.
Subject provision and whole school support
Presentation De La Salle College, Bagenalstown, is a co-educational school that offers the Junior Certificate, Transition Year, Leaving Certificate Vocational Programme and Leaving Certificate to its 413 students.
The Mathematics department comprises six teachers and, in addition, a higher diploma student shares the teaching of some of the junior cycle classes. Teachers are given the opportunity to rotate the teaching of levels and programmes at junior cycle. At senior cycle good practice has been developed whereby two teachers rotate the teaching of higher level. Such practice ensures that no one person is associated with a particular level or programme and that the expertise within the department is maintained.
On entry to the school, students are assigned to one of three mixed-ability class groupings for Mathematics. In second year, two higher-level class groupings are arranged. Ongoing monitoring of student progress in Mathematics throughout second year allows for the creation of one higher-level and two ordinary-level class groupings for third year. In Transition Year, one class grouping of students with an interest in attempting higher level at Leaving Certificate is formed, and the remaining students are assigned to one of two class groupings. In the remaining two years of senior cycle, generally one higher and two ordinary-level class groupings are formed. Foundation level is offered when necessary at both junior and senior cycle.
There are three class groupings in each junior cycle year. One teacher is assigned to each class grouping for Mathematics. However, in an effort to facilitate students to follow a level appropriate to their ability, the current third year higher-level Mathematics class has a large number of students. While it is acknowledged that teachers encourage all students to strive for the highest level, the large class grouping is not an ideal situation and should be reviewed to ensure that all students are being effectively catered for. Three Mathematics teachers are allocated to each year grouping at senior cycle, with a fourth teacher assigned in the second term to sixth-year Mathematics. This allocation facilitates those students who wish to follow foundation level.
Time allocated to Mathematics is, in general, good. Four class periods are allocated to first and Transition Year students. Concurrent timetabling of Mathematics classes takes place from second year onwards and this is commendable practice. Second-year, third-year and fifth-year students each have five class periods and sixth-year students are allocated six class periods per week. This year a seventh timetabled class period has been allocated to sixth-year higher-level Mathematics. It was reported that teachers of sixth-year higher-level Mathematics students frequently give extra classes to students during their own time and they are commended for such commitment.
Mathematics classes are, in general, well distributed throughout the week. However, third-year and fourth-year students have two class periods assigned one day and none on another day. It is recommended that a review of the timetabling of Mathematics be undertaken to ensure that students encounter Mathematics on a daily basis.
Management facilitates teachers in attending relevant inservice in Mathematics. In the past a member of the Junior Certificate Support Service has provided in-school inservice to Mathematics teachers. Furthermore, a member of the Mathematics department has on occasion given inservice to staff in the use of software such as Geometry Sketchpad. Even though there is no specific budget for Mathematics, it was reported that reasonable requests from the Mathematics teachers are granted. Teachers have access to an overhead projector (OHP), a data projector and to mathematical equipment. Mathematics teachers should collaborate to ensure that all have access to such equipment for use in the teaching and learning of Mathematics.
Students are encouraged to participate in co-curricular and extra-curricular activities relating to Mathematics. For example, students have competed in the TeamMath table quiz arranged by the Irish Mathematics Teachers Association (IMTA) and have also been invited to take part in the Irish Mathematics Olympiads. Furthermore, students have been informed about the Scholastic Aptitude Tests (SAT) organised by the Irish Centre for Talented Youth (CTYI). Such support for Mathematics is commendable as it provides students with an opportunity to encounter Mathematics in different contexts.
Planning and preparation
Teachers are facilitated by management in meeting formally twice or three times per year. In addition informal meetings take place on a regular basis. At each of the formal meetings the position of facilitator is rotated. Minutes from meetings indicate that issues discussed include division of class groupings and resources needed in the department. In addition teachers discuss issues regarding common assessment for year groupings, agreed usage of calculators when teaching fractions, and an agreed method when teaching factorisation in algebra. Such practice is commendable as it provides teachers with an opportunity to share good practice.
The Mathematics teachers reported that work on a long-term plan for Mathematics has been progressed and formalised with help from a regional coordinator from the School Development Planning Initiative. The Mathematics department’s long-term plan includes a mission statement, aims and objectives and an outline of the division of classes. In addition, a plan for each year grouping is included, with a suggested timeframe for each topic. The Mathematics department indicated that the long-term plan will be reviewed at the end of the school year, which is good practice. At this juncture consideration should be given to identifying and documenting learning outcomes associated with each topic.
Documentation pertaining to Mathematics is retained in the staff workroom, which is good practice. Teachers reported that the use of common assessments has been extended to end-of-topic class tests for many year groupings. Such practice is commendable as it allows for a similar standard to be established within levels in Mathematics.
The TY Mathematics programme contains two plans, one for more able students and the second for students who intend taking ordinary level in the Leaving Certificate. The programme is imaginative and provides all with an opportunity to encounter Mathematics topics in different ways. Topics included allow for the consolidation of Junior Certificate material and non-syllabus- based Mathematics. For example, topics such as Euler formula, ICT such as Excel and Geometry Sketchpad, and investigation work, are also included in the programme. A further commendable feature of this programme is the collaborative approach whereby two teachers rotate class groupings approximately every six weeks.
In general individual planning for lessons was good. Some teachers have adapted the long-term plan to develop individual monthly schemes of work. In addition, there was evidence that teachers shared monthly plans for the same year grouping and that they also had developed individual handouts and other supplementary materials. The latter were accessed and used during lessons visited, which is commendable. However, on occasion, greater care in the development of worksheets should be taken, to ensure that an appropriate number of questions be developed to match the learning objectives for the topic.
Teaching and learning
Topics such as integration, trigonometry, Simpson’s rule and fractions featured in lessons observed. In many cases, teachers explicitly stated the objectives for the lesson. However this practice should be extended to all lessons as it engages students with the lesson from the outset. Most lessons were paced appropriately to allow for a balance between teacher and students’ input and for engagement with new material.
The methodology most frequently used in lessons was question-and-answer sessions. Questioning of students varied between recall type and higher-order questioning. Higher-order questions were predominantly used in higher-level class groupings, were effective in allowing students to justify their thinking, and engaged students fully in such lessons. This is good practice as the capacity to reason, explain and prove is important to be successful in Mathematics. The practice of directing questions to individual students, which was used by most teachers, is good, and it is recommended that this be continued and further developed where appropriate. To ensure that the learning styles of all students are catered for, it is recommended that a greater range of appropriate methodologies be included in lessons, for example, group work or paired work.
In some lessons, effective use was made of resources such as the overhead projector to assist in the demonstration of solutions to answers or in the use of three-dimensional shapes to explain the angles in objects. The use of differentiated worksheets as the predominant resource in another lesson was very effective and allowed students to take an active part in their learning. However, on occasion, the use of a differentiated worksheet would have been more beneficial than using a textbook as the predominant resource in a lesson.
In most lessons, teachers’ classroom management was good even though some students presented as being challenging. In many classes teachers circulated during the lesson to check students’ work or to provide assistance. However there were instances where greater circulation of teachers during the lesson would have ensured that all students remained on task and this practice should be included more frequently where appropriate.
There were very good examples of imaginative mathematical displays or mathematical puzzles in a classroom, which greatly added to the learning experience for students. To this end it is recommended that mathematical displays or student mathematical work should be included in all classrooms to ensure that students are surrounded by visually stimulating materials. These can also be utilised as learning tools within the classroom.
Through observation of state examinations documentation, there is evidence that student uptake and achievement are very good. In addition, in more recent years, the number the number of students taking foundation level in Mathematics has declined.
Assessment
Ongoing assessment of students’ progress takes place and includes class questioning and end-of-topic examinations. Formal examinations take place for students twice per year, at Christmas and summer for non-examination year groupings. Examination year groupings sit formal Christmas tests, with ‘mock’ examinations in February.
Communication between home and school is maintained in many ways. Two school reports are issued following formal examinations and include a grade and a comment from teachers regarding student progress. Parent-teacher meetings are convened for each of the class groupings. Furthermore, teachers frequently contact home by phone to discuss student progress, and a letter is issued to parents in the event of a student changing a level in the subject.
Homework assigned was relevant to the syllabus. At senior cycle the use of a revision copy was monitored very frequently and formative assessment within copies provides students with details of errors and suggested areas for improvement. Homework copies particularly at senior cycle were well maintained and work was well presented. However, as not all students’ work was presented in a systematic and tidy manner, it is recommended that greater individual monitoring of copies be undertaken. Students should take greater care in the presentation of their work and should write up corrections in their copies.
Summary of main findings and recommendations
The following are the main strengths identified in the evaluation:
- Management facilitates time for Mathematics department meetings and minutes of such meetings are recorded.
- The Mathematics department has developed a long-term plan for Mathematics.
- Student participation and achievement in State examinations is very good.
- The inclusion of Mathematical displays and mathematical puzzles, as observed in one classroom, is good practice and adds to the learning experience of students.
- There was very good use of formative assessment in some student copies.
- Teachers use common assessments where appropriate.
- The Transition Year Mathematics programme is creative and offers all students an opportunity to experience Mathematics in different contexts.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
- A range of appropriate methodologies should be used in lessons to ensure that the learning needs of all students are addressed.
- A review of the timetabling of Mathematics for third years should be undertaken to allow students to encounter Mathematics on a daily basis.
- The practice developed by some teachers of including formative assessment in student copies should be extended to all copies.
- Mathematical posters or students’ mathematical work should be displayed in more classrooms.
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.