An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Ardee Community School
Ardee, County Louth
Roll number: 91441T
Date of inspection: 24 February 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Ardee Community School. 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 was given an opportunity to comment in writing on the findings and recommendations of the report; a response was not received from the board.
Ardee Community School caters for 345 boys and 262 girls. Timetable provision for Mathematics is very good. In the junior cycle five Mathematics lessons per week are allocated to first, second and third year groups. Leaving Certificate Applied (LCA) students receive three mathematics lessons per week during year one and year two of their programme. In the case of the Leaving Certificate (Established) fifth year students receive five mathematics lessons per week and sixth years receive six lessons per week.
Mathematics lessons are well distributed throughout the week, allowing students contact with the subject each day. This is good practice. For all year groups with the exception of fifth year, mathematics lessons take place at different times of the day, with some in the morning which is the most preferable. In fifth year, however, mathematics lessons are predominantly timetabled for the afternoon. It is recommended that future timetabling should aim for some morning mathematics lessons for all year groups. Concurrent timetabling of mathematics lessons occurs from first year through to sixth year. This is good practice as it provides students with a high degree of flexibility in changing levels and allows the mathematics department to adopt a student-centred approach to level choice.
In first year there is a higher level band and an ordinary level band. Students are assigned to class groups in one of these bands mainly on the basis of pre-entry assessments. Abilities are mixed within the level bands. It is good that throughout first year students who need to change levels have the opportunity to do so. Mathematics classes are set from second year onwards. This means that students are assigned to higher, ordinary and foundation level classes on the basis of performance during in-house testing and, later, in the Junior Certificate examination. It is recommended that the method of assigning first year students to a higher or ordinary level band at entry point be monitored and reviewed. Consideration could be given to mixed-ability first-year classes, which would allow for a settling in period before level decisions are made.
It is mathematics department policy that students study the highest level possible for as long as possible and that change of level takes place in consultation with students, teachers and parents. This is good practice.
The mathematics department comprises eleven teachers. Class levels taught in the junior cycle are rotated among all members of the mathematics teaching team. The responsibility for teaching higher-level Mathematics in the senior cycle is rotated between two mathematics teachers. It is recommended that more members of the mathematics teaching team become involved in teaching higher level Mathematics for Leaving Certificate class groups. This measure would enable the mathematics department to retain the high level of expertise that currently exists and to meet the challenges of the forthcoming revisions to the mathematics syllabuses.
The mathematics department has access to information and communications technology (ICT). There are two computer rooms in the school and access to these can be arranged through a booking system. Demand for these facilities is high and this limits the possibility of regular use of a computer room for mathematics lessons. The science laboratories and some classrooms are fitted with ceiling-mounted data projectors and some mathematics classes are timetabled for these rooms. Since all mathematics classes are concurrently timetabled, the opportunity for mathematics teachers to organise an exchange between, for example, a science laboratory and a mainstream classroom exists. This provides one possibility for gaining further access to ICT facilities. The school has recently acquired a number of data projectors and it is good that there are plans to assign some of these to mathematics classrooms. It is recommended that ways in which ICT can be integrated into mathematics lessons be actively explored.
A range of resources is available for teaching and learning in Mathematics. These include geometry equipment, grouping circles, 3-D solids, and overhead projectors. It is encouraging to see that some teachers have collected everyday objects such as containers to be used for teaching volume and area. It is suggested that this be extended to the sourcing of, for example train timetables, actual household bills, and holiday brochures for particular use in teaching and learning in LCA Mathematical Applications. Staff continuing professional development (CPD) is facilitated by school management and the school funds teacher membership of the Irish Mathematics Teachers’ Association.
Students in need of learning support are identified through communication with feeder primary schools, pre-entry assessment, diagnostic testing, ongoing teacher observation and class testing. Support is provided through small group withdrawal from subjects other than Mathematics and the creation of smaller foundation level classes. The school has some experience with team teaching and is encouraged to reconsider it as a method of delivering learning support. Mainstream teachers provide ongoing in-class support to students experiencing difficulty with Mathematics through careful monitoring and individual attention. It was evident in the evaluation that a high level of learning support in Mathematics is provided to students.
A number of fifth year students have participated in training for the Irish Mathematical Olympiad at the National University of Ireland, Maynooth (NUIM). This is very beneficial as participation in mathematical activities outside of the classroom encourages students to experience Mathematics for pleasure.
Formal planning time is allocated at least once per term as part of the school planning process. Records are maintained of all planning meetings and minutes are kept. Mathematics teachers also meet informally on a day-to-day basis to discuss issues that arise. Currently one experienced mathematics teacher co-ordinates the mathematics department. It is recommended that this position be rotated among more members of the mathematics department. This would allow other mathematics teachers to gain experience in this area. It is very good that teachers new to the school benefit from the support of their more experienced colleagues through the mentoring system that is in operation. Overall it was clear during the evaluation that the members of the mathematics department work very well as a team.
Good progress is being made on planning for Mathematics and a comprehensive mathematics plan is in place. The plan includes mathematics department policy on homework, assessment, student access to levels, and planning for students with special educational needs. The plan also contains schemes of work in terms of topics to be covered within agreed timeframes. In keeping with best practice the mathematics department engages in self-evaluation. The result of this self evaluation is evident in the plan as it provides an accurate account of the strengths of the mathematics department, the challenges that have been identified and the rationale employed in decisions made. It is recommended, in order to build on the good reflective practice that takes place, that teachers extend discussions at planning meetings to include classroom practice. This would involve exploring lesson ideas and planning for variety in the methodologies used.
High quality teaching and learning was evident in all of the lessons observed in Ardee Community School. In all cases the lessons were well planned, purposeful and appropriate to the syllabus. All lessons were well structured and had a clear focus and it was evident that teachers had set learning objectives in lesson planning. It is recommended that these learning objectives be shared with the students at the beginning of each lesson and their achievement be checked at the end of the lesson. This practice can increase student motivation, encourage students to take more personal responsibility for their own learning, and provide a sense of accomplishment on achieving the lesson’s goal.
Teachers’ work on the white board and their explanations were very clear in all cases. Great care was taken to include all steps in worked examples and attention was routinely paid to detail. These high standards were reflected in student work. Teachers related the new material presented to the work of previous lessons and in some cases to other areas of the course. For example in one lesson observed, students were reminded of aspects of co-ordinate geometry in their study of functions and graphs. In another case the teacher clarified an explanation on the simplification of surds by using the example of simplifying a fraction. This good practice helps students to situate new ideas, to reinforce learning and to appreciate the inter-connections between different areas of Mathematics. The pace of lessons was lively yet appropriate to the ability level of the students.
Classroom practice 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 involved. 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. These additional methodologies should 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.
In the LCA lesson observed the students worked on exercises following teacher examples. The content chosen was suitable for the group and the lively presentation of the examples ensured that the students were engaged throughout the lesson. However it is recommended that alternative methodologies be explored for teaching and learning in LCA Mathematical Applications. It is recommended that active methodologies, ICT, and research methodologies be incorporated into LCA mathematics lessons. Real-life examples and materials, and content of student interest should also be used wherever possible.
A thoughtful approach is taken to the delivery of learning support in Mathematics. During the course of the evaluation one learning support class was visited. The content of the lesson was specifically chosen to address the anticipated difficulties encountered in the ‘pre-Leaving Certificate’ examinations. The lesson was very well designed to address student needs. A supportive handout was provided that gradually increased in difficulty and enabled the students to explore the best approach to take in tackling difficult problems for themselves. The main outcome of this lesson was that students were provided with an opportunity to discover that they could rely on previously learned material to solve unfamiliar problems. This lesson represents very good practice because while the teacher did provide support where it was necessary, the choice of questions on the handout encouraged the students to develop their own ability to work through difficult questions.
Through very good classroom management teachers have established strong classroom routines and have created very secure learning environments where students can engage with their course material with confidence. On the walls of each of the classrooms visited student projects were proudly displayed and teachers have created stimulating mathematical environments. Throughout the evaluation it was evident that mathematics teachers are very committed to providing high quality learning experiences for their students and the conscientious approach that they take to the planning and delivery of lessons contributes to the achievement of this aim. Teachers are also very accommodating in providing assistance to students outside of class time in preparation for the certificate examinations. The relationships between students and their teachers were observed to be mutually respectful. This has contributed to the high standards of student behaviour that were evident in the classes visited. Teachers are very affirming and encouraging of student effort.
Formal examinations are held for first, second and fifth years at Christmas and in May. Third and sixth year groups are assessed in November through in-class testing and sit ‘pre-certificate’ examinations in February. Reports are sent home on foot of these assessments and parent-teacher meetings take place annually. Common examination papers within levels are set for all formal examinations. In the review of these common examination papers it was evident that the questions that are set are differentiated so that their component parts increase in difficulty. This is in keeping with best practice as it contributes to the quality of the information gained from examination results. The continuation of this sound practice is encouraged.
Ongoing assessment takes place in class through oral questioning and teacher observation. A high level of in-class student monitoring was observed during the evaluation. It is mathematics department policy to set class tests at the end of each topic or chapter studied. Frequent class testing is a good means of providing motivation for students and it is suggested that tests be designed to ensure that all students have a real chance of success. Some teachers have developed ways, such as reward charts, to celebrate student achievement in class tests; this good practice also provides a source of motivation for students and is encouraged. In some cases teachers have developed very good study notes for students who are preparing for examinations. These are very comprehensive and provide valuable support for students. It is recommended that the sharing of expertise that takes place through the planning process should include discussion around sharing assessment practices with a particular emphasis on using assessment to provide additional motivation for students.
Homework is set regularly and usually corrected as part of the following lesson. It was evident from the review of student copybooks that the standard of presentation of student work is generally very high. The careful monitoring of student work by teachers contributes to these high standards. There was evidence of very good assessment practice in all of the lessons observed, some of which reflected assessment for learning (AfL) principles. Further information on AfL is available on the National Council for Curriculum and Assessment website (www.ncca.ie).
The mathematics department analyses the school’s results in the certificate examinations each year and uses this analysis to inform planning. This good practice has contributed to ensuring, through careful monitoring of uptake rates, that students study Mathematics at a level appropriate to their ability.
The following are the main strengths identified in the evaluation:
· Whole-school provision for Mathematics is good.
· It is mathematics department policy that students study the highest level possible for as long as possible.
· High quality learning support is provided for students who experience difficulty with Mathematics.
· The members of the mathematics department work very well as a team.
· Teachers new to the school benefit from the support of their more experienced colleagues through the mentoring system that is in operation.
· Good progress is being made on planning for Mathematics and a comprehensive mathematics plan is in place. A reflective approach is taken, where mathematics teachers engage in evaluation of
the work of the mathematics department.
· High quality teaching and learning was evident in all of the lessons observed.
· In all cases explanations were clear, attention was paid to detail, new work was related to prior learning and the pace of lessons was lively.
· The good balance that was achieved between teacher input and student activity kept lessons interesting and students engaged.
· All teachers made very good use of questioning to assess, differentiate and reinforce learning. Higher order questions were used to help students explore difficult concepts.
· Through very good classroom management teachers have established clear classroom routines and have created very secure learning environments where students can engage with their course
material with confidence.
· Mathematics teachers are very committed to providing high quality learning experiences for their students and the conscientious approach that they take to the planning and delivery of lessons
contributes to the achievement of this aim.
· High standards of student behaviour were evident in the classes visited. Teachers are very affirming and encouraging of student effort.
· There are very good practices in relation to assessment.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· The method of assigning first year students to a higher or ordinary level band at entry point should be monitored and reviewed.
· More members of the mathematics teaching team should become involved in teaching higher level Mathematics to Leaving Certificate class groups.
· Ways in which ICT can be incorporated into mathematics lessons should be actively explored.
· The position of mathematics department co-ordinator should rotate among more members of the mathematics department.
· Teachers should include discussions around classroom practice and assessment practice at planning meetings. This should involve exploring lesson ideas, planning for variety in methodologies
and exploring ways in which class tests can be used to encourage and motivate students.
· The learning objectives should be shared with the students at the beginning of each lesson and their achievement checked at the end of the lesson.
· For students of LCA Mathematical Applications, more active methodologies, ICT, and research methodologies should be incorporated into lessons. Real-life examples and materials along with
content of student interest should also be used wherever possible.
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 October 2009