An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Roll number: 70010V
Date of inspection: 10 March 2009
Report on the Quality of Learning and Teaching in Mathematics
Subject inspection report
has been written following a subject inspection in
Subject provision and whole school support
In first and second year, students are assigned for Mathematics to class groups designated to take higher level, ordinary level or the JCSP. In second year an additional group is formed for foundation level. Students are assigned to class groups on the basis of discussion with feeder primary schools, pre-entry assessment and diagnostic testing. All the students taking one particular level are distributed across the class groups taking that level, thus ensuring a range of abilities in each class. Mathematics lessons are not concurrently timetabled and therefore movement between levels throughout the year is not possible. It is recommended that first year and second year mathematics lessons be concurrently timetabled so as to allow some changing of levels for students during the year.
Third, fourth and fifth year students are assigned to a higher level class, an ordinary level band or a foundation level band; abilities are mixed within the level bands. Levels are decided on the basis of achievement in in-house examinations and the certificate examinations. In keeping with good practice student preference and teacher advice also play a part in level selection. Concurrent timetabling of Mathematics occurs from third year through to fifth year. This is highly beneficial to students in these year groups as it provides them with flexibility in changing levels and allows the mathematics department to take a student-centred approach to level choice.
The mathematics department comprises ten teachers, each of whom teaches at least one other main subject. In the junior cycle higher-level Mathematics is rotated among most members of the teaching team. Higher-level Mathematics in the senior cycle is currently the responsibility of one mathematics teacher. It is recommended that more teachers become involved in teaching higher-level Leaving Certificate Mathematics. This is necessary to ensure that the mathematics department maintains the expertise necessary to deliver the subject into the future.
The mathematics department has good access to information and communications technology (ICT). The computer room is regularly used for teaching and learning in Mathematics and this is accessed through a booking system. Data projectors are available in some classrooms and teachers have the use of the school’s laptop computers. It is recommended that these classrooms be used on a rotational basis to allow for an increase in the use of ICT in teaching and learning in Mathematics. The mathematics department has acquired a range of computer software and teaching resources that are used to make lessons more interactive for students. All teachers have access to resources including geometry equipment, probability sets and meter sticks. In addition, teachers use everyday materials, such as bank giro forms, to illustrate the relevance of Mathematics in everyday life. Mobile phones are also used to clarify explanations of the twenty-four hour clock or as stop watches in outdoor mathematics activities. This very good practice is encouraged and it is suggested that teachers explore further ways in which everyday materials and objects can be incorporated into mathematics lessons. Staff continuing professional development (CPD) is facilitated by school management.
Students who are in need of learning support are identified through pre-entry assessment, diagnostic testing, ongoing teacher observation, in-class testing, and information from feeder primary schools. Support is provided through small group withdrawal from subjects other than Mathematics and the creation of small foundation level classes from second year onwards. Students following the JCSP programme are taught in smaller class groups and receive six or seven mathematics lessons per week, depending on the year. ICT is regularly used to make Mathematics more accessible for students who require support with the subject and suitable computer software is used to make learning fun. These students are well supported through careful monitoring by their teachers and individual attention. Overall it was evident during the evaluation that a very high level of learning support is provided to students who are identified as needing support with Mathematics.
Maths Week is celebrated in the school each year and students are encouraged to participate in the Irish Junior Mathematics Competitions. Such activities are very worthwhile as they allow students to experience Mathematics for pleasure and the new learning that results enhances their understanding of the subject.
Planning and preparation
Mathematics teachers meet regularly on an informal
basis to discuss the day-to-day issues that arise. Good informal communication
takes place among members of the mathematics department and they are supportive
of each other and work well together. However, members of the mathematics
department do not meet formally. Consequently, very little progress has been
made in planning for Mathematics. It is recommended that this process be
formalised with the objective of developing the mathematics plan. This plan
will be an essential tool for
The challenges of creating a cohesive, collaborative mathematics department are heightened by the fact that each teacher of Mathematics teaches another main subject and engages in the planning process for that other subject. There is currently no co-ordinator for the mathematics department. It is recommended that a co-ordinator be appointed to oversee the planning process for Mathematics. Over time, this position should rotate amongst the members of the teaching team. The involvement of the entire team in these ways would contribute to the development of expertise within the department. Furthermore, the contribution of each member’s unique perspective would add to the quality and value of the plan.
The current mathematics plan consists of schemes of work for each class group; these are in terms of topics to be covered within given timeframes. Within year groups, each class should, as far as possible, follow the same scheme. This would enable the mathematics department to set common in-house examination papers, within levels, and would facilitate students who need to change level. It is recommended that the co-ordination of these schemes of work be a focus of future planning. The planning process should also be used to develop policies on areas of importance to teaching and learning in Mathematics. These could include policies on student assignment to levels, assessment, homework, teaching methodologies and provision of learning support.
In the classes visited, individual lessons were well prepared and teachers had all the necessary resources available. During the evaluation a variety of methodologies was observed. The mathematics plan should reflect this variety, should inform classroom practice and should put the student at the centre of planning. It is strongly encouraged that members of the mathematics department engage in open collaboration and share expertise and experience. The creation, over time, of a shared folder of lesson ideas that are set out in terms of learning objectives, preferred methodologies, resources necessary, assessment methods, and review comments would contribute to the achievement of a mathematics plan that has a very real and positive impact on students’ learning experience in the classroom.
In keeping with best practice, the mathematics department members carry out a comprehensive analysis of the school’s performance in the certificate examinations and compare it to the national norms. This analysis should inform the mathematics department policy on student access to levels.
Teaching and learning
High quality teaching and learning was evident in the lessons observed. 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. Most teachers shared the learning objectives with the students at the beginning of the lessons. Best practice in this regard was observed where the lesson objectives were written on the board at the start of the lesson and checked at the end to ensure that they had been achieved. The extension of this to all lessons is recommended.
Teacher explanations and instructions were very clear in all cases. In a lesson on vertically opposite angles the teacher explanation exploited the proof of the theorem by calculating the angles using a combination of straight angles. This very clear explanation enabled the students to calculate the angles with ease, see the underlying concept clearly, and acted as very good preparation for studying the actual theorem. In another lesson on volumes of rotation, the teacher used a very clear, simple explanation of the underlying idea to enhance student understanding. These are examples of very good practice because the clarity of the explanations was the result of taking a basic concept that every student understood and building towards a more difficult concept.
Where teaching predominantly consisted of teacher example followed by student exercise, the good balance that was achieved between teacher input and student activity kept lessons interesting and students engaged. Teachers monitored students while they were working independently and provided help and encouragement where necessary. In all of the lessons observed the level of student participation and engagement was high. It is recommended that teachers gradually incorporate more active, discovery, investigative and research methodologies into lessons. The sharing of ideas that arises from engagement with the planning process might make it easier to include greater variety of methodologies in lessons. Some additional methodologies would complement the very good practices that are already used in teaching and learning in Mathematics.
All teachers made very good use of questioning to assess, differentiate and reinforce learning. Questioning was also used frequently to keep students fully involved in lessons. Best practice was observed in most lessons where teachers used higher-order questions to encourage students to explore difficult concepts or ideas. The further use of higher-order questioning is encouraged. Most teachers were very careful to differentiate learning. In one case this was achieved by providing alternative approaches for students to take to the lesson activities. This meant that students could choose the approach that suited them best and ensured the full participation of all students. In another case learning was differentiated by the provision of a task that gradually increased in difficulty so as to provide exercises at which all students could succeed and also to provide challenge for the more able students. In addition, wherever possible, students were encouraged to work ahead at a pace that is appropriate to his or her level of ability. These are examples of very good practice in relation to differentiation of learning.
Two lessons in the computer room were observed as part of the evaluation and in both cases ICT was used very effectively to enhance student learning. In one of these lessons, LCA students were working on an exercise on tallying that will form part of a key assignment. This involved creating a spreadsheet to collate and tally the takings from a business. A well designed handout and very clear instructions provided all the information needed for students to independently tackle the assignment, with teacher assistance where necessary. Throughout this lesson the students took responsibility for their own learning by engaging fully with the task and by the end all had completed the exercise to a very high standard. The realistic nature of the lesson content and the use of ICT and real life materials meant that students had an appreciation of the relevance of the lesson in their everyday lives. The other lesson involved JCSP students working through a game that helped them to work on an exercise involving time in various formats. The use of a game to achieve this facilitated the high degree of repetition that was necessary to achieve the learning objectives of the lesson. These lessons were very well planned and the students were actively and enthusiastically involved in their own learning. Throughout these excellent lessons students were provided with support as needed but were encouraged to work on the exercises for themselves, as much as possible. This best practice ensured that students had an opportunity to develop their own mathematical ability and confidence.
Some teachers made very effective use of active methodologies. In one lesson on measure the students were expected to measure items in the classroom. Throughout this lesson reference was frequently made to day-to-day examples that would be relevant to students’ lives. As well as deepening learners’ understanding, these practices contributed to the high level of student engagement with the lesson material.
The relationships between the students and their teachers were characterised by warmth, humour, encouragement and affirmation. Teachers were very respectful of students and were very supportive and caring in their dealings with them. In all of the lessons observed the students were lively and in most cases well behaved. Some minor instances of challenging behaviour were observed. Classroom management tended to be best where teachers had established strong classroom routines and had set clear boundaries for student behaviour. Such boundaries included teachers waiting for students to settle down before teaching began, expecting students to raise their hands when they wanted to make a contribution in class and maintaining good eye contact with students throughout lessons. Good lesson planning and strong lesson structure also had a positive effect on the management of lessons. Where good classroom management was observed the students had a clear understanding of the behaviour that was expected of them and the teacher adhered consistently to the established routines. It is recommended that the members of the mathematics department discuss and share classroom management practices that have proved effective and that they agree common approaches.
Formal examinations are held for all year groups at Christmas. In February students preparing for the certificate examinations sit ‘mock’ examinations and formal assessments take place for all other year groups. First, second and fourth year students are formally assessed in May. Reports are sent home on foot of these formal assessments and parent-teacher meetings take place annually. From a review of formal examination papers it is evident that the questions are differentiated so that their component parts increase in difficulty. This is in keeping with best practice. A supportive format is chosen for students who find Mathematics difficult, where for example number lines are provided to assist with numeracy. The continuation of such practices is encouraged.
Ongoing assessment takes the form of questioning in class and teacher observation. Students’ work is well monitored by teachers through the provision of individual attention in class. It was evident from the review of student copybooks that the standard of student work is generally high. LCA student assignments are well maintained. Homework is set regularly and usually corrected as part of the following lesson and this is good practice. Overall, good assessment practices are in place.
Summary of main findings and recommendations
The following are the main strengths identified in the evaluation:
· The mathematics department has good access to information and communications technology.
· A very high level of learning support is provided to students who are identified as needing support with Mathematics.
· Good informal communication takes place among members of the mathematics department and they are supportive of each other and work well together.
· Individual lessons were well prepared and teachers had all the necessary resources available.
· High quality teaching and learning was evident in the lessons observed. Teacher instructions and explanation were very clear in all cases.
· The good balance that was achieved between teacher input and student activity kept lessons interesting.
· In all of the lessons observed the level of student participation and engagement was high.
· ICT was used very effectively to enhance student learning.
· The relationships between the students and their teachers were characterised by warmth, humour, encouragement and affirmation. Teachers were very respectful of students and were very
supportive and caring in their dealings with them.
· There are good assessment practices in place for Mathematics. Students’ work is well monitored by teachers through the provision of individual attention in class.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· First year and second year mathematics lessons should be concurrently timetabled to allow students to move between levels.
· More teachers should become involved in teaching higher-level Leaving Certificate Mathematics.
· A mathematics plan should be developed collaboratively by all the teachers of Mathematics.
· A co-ordinator should be appointed to oversee the planning process for Mathematics.
· Within year groups, each class should, as far as possible, follow the same scheme of work.
· Teachers should gradually incorporate more active, discovery, investigative and research methodologies into lessons.
· The members of the mathematics department should discuss and share classroom management practices that have proved effective and they should agree common approaches.
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 November 2009