An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Baldoyle, Dublin 13
Roll number: 91342R
Date of inspection: 16 September 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Pobalscoil Neasáin, Baldoyle. 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 and subject teachers.
The board of management of the school was given an opportunity to comment on the findings and recommendations of the report; the board chose to accept the report without response.
Pobalscoil Neasáin has a current enrolment of 411 boys and 142 girls. Timetable provision for Mathematics is good with first, second and third year receiving five class periods of Mathematics per week. Transition year students are allocated four periods of Mathematics per week. Fifth and sixth years receive five mathematics lessons per week. Students following the Leaving Certificate Applied (LCA) programme are allocated three mathematics lessons per week. There is good distribution of mathematics lessons throughout the day and the week.
Concurrent timetabling of mathematics lessons is provided for third, fifth and sixth years. This good practice allows students of these year groups the flexibility to change levels as the need arises. Second year mathematics lessons are not concurrently timetabled. This means that second year students who need to change level throughout the year can only do so by changing tutor group which may result in a change of class group in certain other subjects. In order to provide second year students with the flexibility to change levels, it is recommended that that second year mathematics lessons be concurrently timetabled.
In first year three mixed-ability class groups and one smaller ordinary-level class group are formed. This is good practice. For all other years students are assigned to higher and ordinary-level class groups for Mathematics on the basis of achievement in class tests and formal examinations. Teacher observation and student preference also play a role in level choice. There was much evidence in the evaluation of the mathematics department’s policy of encouraging students to study Mathematics at the highest level possible for as long as possible. The school’s commitment to the achievement of this aim is reflected in the high uptake rates for higher-level Mathematics in the certificate examinations.
The mathematics department comprises nine teachers. Teachers are deployed in accordance with their qualifications, experience and expertise. Higher-level mathematics in all year groups is alternated between two members of the mathematics teaching team. Currently there is one higher-level class group in each of second, third, transition, fifth, and sixth years. Therefore, it is possible for the school to meet its current needs with only two members of the mathematics department teaching the higher-level course. It is recommended that the current arrangement be kept under review with a view to increasing the school’s capacity to teach higher level Mathematics. This would have the beneficial effect of permitting a wider contribution to collaborative planning for the subject as well as strengthening the mathematics department’s capacity to meet the changing needs of the students.
The information and communications technology (ICT) facilities that are available for teaching and learning in Mathematics are very good. The mathematics department has exclusive use of six laptop computers. There are a number of mobile data projectors that can be accessed on a booking system. The school’s computer room can also be booked for mathematics lessons. A science room that is used for mathematics lessons is fitted with a ‘Smartboard’. Currently there is limited use of ICT in teaching and learning in Mathematics. This is due mainly to the fact that much of the ICT equipment has been very recently acquired. It is recommended that, over time, mathematics teachers establish the use of ICT as a routine and regular feature of their lessons.
In addition to ICT equipment, there is a good range of resources available for teaching and learning in Mathematics. These include lateral thinking cards, posters, geometry sets, puzzle books, calculators, games, ‘Lego,’ and LCA support material. These are used effectively to provide a variety of learning experiences for students. It is suggested that teachers also make use of everyday objects such as utility bills, containers of various shapes and sizes and shopping catalogues. These can be used in the study of arithmetic and volume and area. ‘Geogebra’ geometry software is available on one laptop computer and it is suggested that this be extended to the remainder of the mathematics department laptop computers so that it may be used in the study of co-ordinate geometry, geometry and trigonometry.
Teacher continuing professional development (CPD) is supported by school management. There are a number of CPD courses planned for mathematics teachers for the coming year. Topics including teaching mixed-ability class groups and teaching LCA Mathematical Applications will be covered. Teachers of Mathematics have recently participated in a workshop on ‘Project Maths’.
There are good procedures in place for identifying students who need learning support in Mathematics. Students are identified through communication with feeder primary schools and parents, pre-entry diagnostic testing and ongoing teacher observation and class testing. Support is provided through individual and small group withdrawal and team teaching. In some year groups smaller classes are created for students who have been identified as requiring support in Mathematics. It is very good that, in general, numeracy support is provided by a qualified mathematics teacher. Teachers routinely provide high quality individual attention throughout lessons for any student experiencing difficulties. Overall students who require support in Mathematics are very well provided for.
Students of Mathematics are encouraged to participate in training for the Irish Mathematical Olympiad each year. It is very good practice for students to get involved in extracurricular mathematics-related activities as they provide opportunities for students to experience Mathematics for pleasure.
Formal meetings of the mathematics department are held monthly. Lunchtimes are often used if additional meetings are needed. Minutes are kept of all formal meetings. In addition, mathematics teachers meet frequently on an informal basis to discuss any day-to-day issues that arise. In keeping with good practice the position of co-ordinator of the mathematics department rotates amongst all mathematics teachers. The members of the mathematics department work well together and provide a high level of collegial support for each other. It is recommended that some time at formal mathematics meetings be given over to the sharing of ideas and methodologies. This measure will support teachers in creating alternative lesson plans and enable them to increase the variety of student experiences in the classroom.
Good progress has been made on planning for Mathematics. The plan contains the mathematics department’s policies including those on homework and assessment. Schemes of work for each year group are also contained within the planning documentation. These are very comprehensive and, in keeping with good planning practice, are set out in terms of learning outcomes to be achieved within agreed timeframes. It is recommended that, over time, brief sections for methodology, resources and assessment be added to these plans. The process this would involve would provide a valuable forum for sharing ideas and expertise. It is good that, at the beginning of each year the mathematics department reflects on the previous year’s work and reviews the plan in the light of this reflection.
The focus of the TY plan is on Leaving Certificate course material. It comprises, predominantly, a list of chapters in a Leaving Certificate text book to be covered for the year. Since this approach is not in keeping with the underpinning principles of TY this plan needs to be reviewed. It is important to take advantage of the opportunity in TY to study different Mathematics or to adopt a different approach to the teaching and learning of Leaving Certificate course material. It is therefore recommended that the current TY plan be extended to incorporate a wider range of course content and of teaching methodologies. A research project on the lives of famous mathematicians and a study of the areas of Mathematics that made them famous would be ideal for TY students. It is suggested that students carry out a survey and use the results to inform their study of statistics. A module of Applied Mathematics focusing on the Mathematics of road safety would also be very suitable for TY. Students could complete a research project on Pascal’s Triangle by exploring its various number patterns and practical applications. The card game ‘Blackjack’ can be used to explore many of the important concepts in Leaving Certificate probability. TY offers a valuable opportunity for students to engage with Mathematics on an enjoyable level and to gain a greater appreciation for the subject; it is therefore recommended that every effort be made to optimise the potential of this opportunity.
The quality of teaching and learning in all of the lessons observed was of a high standard. In all cases the methodology used was teacher exposition. In one lesson observed this was complemented by the use of ICT in the form of a PowerPoint presentation of worked examples. In all cases lessons were purposeful and appropriate to the syllabus and had a clear focus. Teachers were careful to relate new material to the work of previous lessons and this is good practice. Teachers related the work of lessons to students’ own experience where appropriate. A very good example of this was observed in a lesson on ratio and proportion. In this lesson the teacher examples and the student worksheet used very well chosen material that served to help students identify with the lesson content and also to add humour and interest to the lesson.
In general, teachers used a combination of teacher example and student exercise to vary the learning activity throughout lessons. This ensured a good balance between student activity and teacher input. In one lesson, however, although students participated well through answering questions, a reduced level of student engagement was observed towards the end of the lesson. If students had, for example, been expected to complete individual exercises, a better mix of tasks would have been achieved. Since, the practice of varying the learning activity can increase the levels of attention paid by students its extension to all lessons is recommended. The pace of all of the lessons observed was lively yet appropriate to the ability level of the students. In all cases, students demonstrated a good interest in the content of lessons.
The extensive use of questioning to involve students in the learning activities contributed substantially to the success of lessons. In some of the lessons observed students were expected to attempt exercises before seeing a worked example. The extension of this practice is recommended as it provides a good means of encouraging students to take more responsibility for their own learning. In all cases explanations were very clear and in most cases they focused on the conceptual elements of worked examples. Open questions were used, by most teachers, to encourage students to think about the underlying mathematical concepts presented. This is very good practice and an increase in the use of open questions is recommended.
Teachers took an investigative approach in some cases. In a lesson on quadratic graphs observed, the students were encouraged to plot the points of different types of graph and to discuss these differences with reference to each graph’s quadratic equation. Throughout this lesson, as each new idea was presented, the students were expected to use previously learned material to make predictions. These predictions were then investigated to consolidate learning. This is an example of how an investigative approach can very easily be incorporated into teaching and learning in Mathematics. The use of the geometry software that is available on one of the school’s laptop computers would have complemented this very good lesson by facilitating further investigation. It is recommended that teachers build on the very good practices that are already used in teaching and learning by including more variety of methodology in lessons. While increasing the variety of approaches would enhance the learning experience for all students, it is of particular importance for students of the LCA and TY programmes. It is therefore recommended that teachers explore ways in which group work, pair work, project work, ICT, active, investigative, discovery, and research methodologies can be included in mathematics lessons.
The provision of supportive notes, the welcoming of student contributions and the recognition and encouragement provided by teachers contributed to the creation of secure learning environments where students can study Mathematics with confidence. The standard of student behaviour was observed to be very high throughout the evaluation. In all of the classrooms visited the relationships between students and their teachers was observed to be based on mutual respect. Teachers routinely praise students for their efforts and students respond well to this affirmation. The levels of engagement and participation in the work of lessons were high. In interaction with the inspector students demonstrated an interest in and an enthusiasm for Mathematics.
Formal examinations are held at Christmas for all year groups. First, second, fifth and transition year students sit formal examinations in May. In keeping with good assessment practice common examinations are set within levels. Reports are sent home following all formal examinations. ‘Mock’ examinations are held in February for students preparing for the certificate examinations. It is mathematics department policy that ‘mock’ examination papers are corrected by the teachers themselves. The aim of this measure is to provide teachers with a clearer assessment of individual student progress.
Throughout the lessons observed teachers provided clear instructions on the presentation of work. High standards are expected of students and this has contributed to the high standard of presentation of work in the copybooks reviewed. All students are expected to have a separate copybook for examples and notes. This was observed to be used extensively in the classrooms visited. The notes provided by teachers were very comprehensive and should serve as a valuable source of support when students are revising for examinations. This is very good practice.
Homework is set regularly and is usually corrected at the beginning of the following lesson. In most cases observed the correction of homework involved teachers correcting only the parts that students had found difficult and this ensured that the time spent on corrections was appropriately short. Teachers monitor progress through the observation of class work. Some teachers include comments on student work that provide advice and encouragement for students. Since this type of feedback is very valuable for learning, its continuation and extension is encouraged. Ongoing assessment takes the form of oral questioning in class and observation. Class tests are also set at the end of each topic or chapter studied. The school’s practice in relation to assessment is very good.
The school carries out an analysis of its performance in the certificate examinations compared to the national norms. This is used to inform planning for Mathematics. The school is justifiably proud of its high uptake rates for higher-level Mathematics and its students’ achievement in the certificate examinations.
The following are the main strengths identified in the evaluation:
· Timetable provision for Mathematics is good.
· The information and communications technology (ICT) facilities that are available for teaching and learning in Mathematics are very good.
· Students who require learning support in Mathematics are very well provided for.
· Significant progress has been made on planning for Mathematics.
· The quality of teaching and learning in all of the lessons observed was of a high standard.
· Questioning was used to good effect in all lessons.
· Teachers are encouraging, supportive and caring in their dealings with students.
· The school’s practice in relation to assessment is very good.
· The standard of presentation of student work is very high and students are making steady progress in Mathematics.
· The school is justifiably proud of its high uptake rates for higher-level Mathematics and its students’ achievement in the certificate examinations.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· In order to provide second year students with flexibility to change levels, second year mathematics lessons should be concurrently timetabled.
· The arrangements for assigning teachers of Mathematics to levels should be kept under review in order to ensure that adequate capacity within the mathematics department to teach all levels is maintained.
· Mathematics teachers should establish the use of ICT as a routine and regular feature of their lessons.
· The plan for transition year should be reviewed in order to incorporate Mathematics that is different from that of the Leaving Certificate course and to plan for alternative treatment of traditional course material.
· The use of open questions that encourage students to explore the underlying concepts of lessons should be extended.
· Teachers should extend the use of strategies that encourage students to take more responsibility for their own learning.
· Some time at mathematics meetings should be given over to exploring ways of including more variety of learning experience in mathematics 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.
Published January 2010