An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
Drogheda Grammar School
Drogheda, County Louth
Roll number: 63870L
Date of inspection: 2 April 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Drogheda Grammar 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 studentsí work, and had discussions with the teachers. The inspector reviewed school planning documentation and teachersí 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.
Drogheda Grammar School has a current enrolment of 161 boys and 118 girls. Timetable provision for Mathematics is good. Five class periods are allocated to first, second, third, fifth and sixth year groups. Transition year (TY) students receive three mathematics lessons per week. Mathematics lessons for all year groups, except first year, are concurrently timetabled. This good practice allows students to study the highest level possible for as long as possible by facilitating change of level throughout the year.
Students are assigned to mixed-ability class groups in first year which is good practice. There is a higher level class and an ordinary class in each of second, third and fifth years. In TY and in sixth year there is a higher level class and two ordinary level classes. There is a similar range of abilities in each ordinary level class group in both of these year groups. Students are assigned to levels on the basis of performance in formal assessments and in-class tests throughout the year. Student preference and teacher advice also play a part in level choice. Students are encouraged to study Mathematics at the highest possible level for their ability and change of level takes place in consultation with teachers, parents, year heads and the guidance counsellor where necessary. Very good arrangements are in place for level choice.
The mathematics department comprises six teachers. It is mathematics department policy that students retain the same teacher from year to year for the duration of a cycle, as far as possible. Maintaining this continuity is worthwhile. Higher level Mathematics at both junior and senior cycles is the responsibility of one experienced member of the teaching team. It is recommended that the number of teachers teaching higher level Mathematics be increased. As well as guarding against over-dependence on particular members of the teaching staff, this measure would strengthen the departmentís capacity to meet the challenges of the forthcoming revisions to the mathematics syllabuses.
Teachers make use of a very wide range of resources for teaching and learning in Mathematics. Most of these are kept in the mathematics room and are available to all teachers. They include an algebra balance, algebra tiles, tangrams, geostrips, playing cards, clinometers, probability kits, geometry equipment, and a wide range of games and puzzles that are designed to make learning mathematics enjoyable for students. Some 3-D models have been produced to enhance the clarity of explanations in Junior Certificate geometry and Leaving Certificate trigonometry. A wide range of everyday objects has been collected for use in teaching volume and area. Books of general mathematical interest are kept in the mathematics section of the school library. There is a diverse collection of mathematics reference books; these are used to provide mathematics teachers with ideas for enabling students to experience the relevance of Mathematics in their everyday lives and for encouraging them to take an interest in Mathematics outside of the classroom. Posters and student projects are displayed on the walls of the mathematics room and each classroom visited; these are used for reference in mathematical explanations. The mathematics departmentís enthusiasm for and interest in the subject is reflected in the quantity and diversity of the resources available for teaching and learning in Mathematics. The sharing, of this enthusiasm and interest, with their students, is central to the work of the mathematics teaching team.
Teacher continuing professional development (CPD) is fully facilitated and the extensive list of courses attended by mathematics teachers is further evidence of their commitment to the subject. Some mathematics teachers are active members of the Irish Mathematics Teachersí Association (IMTA). They regularly attend events organised by the IMTA and bring this experience back to the classroom.
The mathematics department is well provided for in terms of information and communications technology (ICT). TY students are timetabled for some mathematics lessons in the schoolís computer room and this room is used for other year groups when it is available. The mathematics room and most other classrooms are fitted with fixed data projectors. Broadband internet access is available throughout the school. The mathematics department has acquired a range of computer software to support teaching and learning in Mathematics including Geometerís Sketchpad and Autograph and these are used in lessons where relevant. Mathematics teachers have accessed an extensive range of PowerPoint presentations and these, along with material from a variety of suitable websites, are frequently incorporated into lessons where appropriate. ICT is used regularly to add variety to lessons and to make lessons more interesting for students. †
Students in need of learning support are identified through communication with feeder primary schools, pre-entry assessment, diagnostic testing and ongoing teacher observation and class testing. Support is provided through withdrawal from subjects other than Mathematics and through the team teaching of mathematics lessons. Teachers routinely support students who experience difficulty with Mathematics through the provision of individual attention in class. Individual student plans are kept, by mathematics teachers, on students who have been identified as requiring support with Mathematics. This allows teachers to provide the support students need with greater accuracy and is therefore very worthwhile. Overall there is a very high level of support provided to students who have been identified as requiring learning support in Mathematics.
Students of Mathematics participate in a wide range of extracurricular mathematics-related activities. Students attend events and lectures as part of the celebrations for Maths Week each year. The mathematics department is justifiably proud of its studentsí achievement in the PRISM Maths Challenge, the Hamilton Maths Grand Challenge and the Irish Junior Maths Competition. Photographs taken of students participating in some of these events are proudly displayed on the wall of the mathematics room. Participation in extracurricular mathematics activities is very worthwhile as it provides students with opportunities to experience Mathematics for pleasure and it also raises the profile of Mathematics within the school.
Formal planning time is allocated to Mathematics four times per year as part of the whole-school planning process. Lunchtimes are also frequently used as meeting time for planning for Mathematics. 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. The position of mathematics co-ordinator is currently held by the only member of the department who teaches Mathematics exclusively. There is a high level of collegial support among members of the mathematics department.
It was evident from the review of planning documentation that significant progress has been made on planning for Mathematics. The plan opens with the aims of the mathematics department where the encouragement of an appreciation of Mathematics in the world around us and the development of a positive attitude to the subject through experiencing Mathematics for pleasure feature strongly. The plan includes mathematics department policy on assessment, homework, student assignment to levels, and planning for students with special needs. Cross-curricular planning and planning for cultural diversity are elements of the mathematics plan and they contain many lesson ideas that contribute to the achievement of some of the overall aims of the mathematics department. A list of the CPD courses attended by mathematics teachers and a list of resources are also included in the planning documentation. This is all in keeping with good planning practice.
Schemes of work for each year group are also included in the overall department plan. These comprise a list of topics to be covered; each topic heading is accompanied by a list of resources necessary and modes of assessment. These schemes are representative of very good practice because the list of resources for each topic illustrates a diversity of classroom experience that provides teachers with lesson ideas and students with opportunities to experience Mathematics in a wide variety of ways. For example newspaper cuttings, ĎSmartiesí, PowerPoint presentations and Excel are the resources required to teach first year statistics. It is suggested that a column with a brief description of methodology be added to these very good schemes. This would make these topic plans very accessible to any teacher who was not involved in their creation, for example a substitute teacher. The sharing of expertise and lesson ideas that contributes to the planning process has many benefits for teaching and learning in Mathematics and the continuation of this is recommended. Collaboration in the planning process will ensure that the mathematics department plan continues to reflect and inform the day-to-day work of all members of the mathematics teaching team.
The TY plan is in keeping with the underlying principles of a good TY programme. It comprises a suitable combination of material that is on the Leaving Certificate course and material that is different. The focus of the study of trigonometry and probability in TY is on the practical applications of these topics and many opportunities are provided for students to engage in group work and pair work. Projects on the lives of selected Mathematicians are also carried out. Throughout TY students are exposed to mathematical experiences that aim to generate an appreciation for the subject and to encourage the development of the problem-solving and critical-thinking skills that are essential for success in Mathematics. These experiences include participation in fieldwork, engaging in puzzle solving and playing mathematical games. It is good that a module of Applied Mathematics is also included in the TY plan.†
High quality teaching and learning was evident in all of the lessons observed in Drogheda Grammar School. In all cases lessons had a clear focus and were well structured. It was evident that teachers had set learning objectives in lesson planning and these were, in most cases, shared with the students throughout lessons. It is recommended that the learning objectives be explicitly shared with students at the beginning of lessons and their achievement checked at the end. This practice can encourage students to take more responsibility for their own learning and can increase student motivation by leading to a sense of achievement on reaching the lessonís goal.
Teachersí work on the board, explanations and instructions were very clear. For example in a lesson on polar co-ordinates observed the teacher presented the initial idea using navigational directions. This was ideal as it related previously learned material to the new idea presented and also provided students with a real life example. This topic contains some words that students would not have previously encountered and the teacher paid careful attention to their meaning in explanations. The comprehensive treatment of the material in this lesson contributed to the depth of understanding for students and is therefore commended.
Most lessons took the form of teacher example followed by student exercise. The lively pace and good balance that was achieved between teacher input and student activity made this approach effective. Teachers monitored students while they were working independently and provided individual attention where necessary. In all lessons observed the level of student participation and engagement was high and students were able to demonstrate their learning with confidence. It is clear from the mathematics plan and from some of the lessons observed that active methodologies and ICT are frequently incorporated into lessons and this is encouraged. For example in a lesson on Pythagorasí Theorem the students worked in pairs to solve a puzzle which illustrated the idea of the theorem. Varying the methodology in lessons is very good practice. In some lessons observed there were opportunities to take a more investigative approach. It is recommended that such opportunities be considered. For example, in the initial stages of their study of co-ordinate geometry, students could be encouraged to plot a point for each integer in the given domain when drawing a line and discover for themselves that two points are sufficient.
Teachers used questioning to assess learning and to involve students. In some cases teachers took a higher-order approach by encouraging students to focus on developing the strategy for answering the mathematical questions presented in class. In other cases a more method-focused approach was taken where students were provided with all the strategic steps and were expected to follow each step to answer questions. In order to provide students with an opportunity to develop the strategic thinking and problem solving skills that are essential for success in Mathematics it is recommended that teachers include higher-order approaches more often in lessons. In all cases, teachers differentiated learning by careful questioning. To complement this differentiation strategy, it is recommended that a bank of difficult exercises be kept to provide more challenge for the better able student.
It is evident from the planning documentation that PowerPoint presentations, Autograph and Geometerís Sketchpad are use in lessons where appropriate. The effective use of ICT was observed in a third year lesson on geometry revision. A PowerPoint presentation was used to revise previously learned material. The slides were very well designed to capture student interest and their use made for a very lively and productive lesson. Through questioning the students enthusiastically participated in every aspect of the revision. A second teacher was present in this class to provide in-class support to students who had been identified as requiring it. This was observed to work very well with the support teacher circulating the classroom providing assistance where necessary. The mainstream teacher was also very supportive to students throughout this lesson by providing individual attention and answering questions with great care.†
The TY lesson observed opened with the students working in pairs in an experiment to establish the dealerís advantage in Blackjack. This involved student pairs playing ten games each and recording the outcomes on the worksheet that was provided. This concluded with the collation of outcomes on the board. The results of the experiment were then discussed. This was followed by an exercise to work out the probability of winning or losing when presented with all the different possible Ďhandsí of Blackjack. All of the learning activities were very well managed. This was an excellent lesson because the activities were very well used to explain many of the important concepts in probability. The teacher was also very careful to draw studentsí attention to the mathematical significance of each element of the activities. In addition, the active methodology chosen made this lesson ideal for TY.
The relationship between students and their teachers was observed to be excellent. Students responded well to the affirmation and encouragement provided by their teachers. On the walls 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.
Test-based assessments are carried out at Christmas and in October and March. Formal assessments are carried out in May for first, second and fifth year groups. TY students are continuously assessed throughout the year. Students preparing for the certificate examinations are assessed in October, at Christmas and sit Ďmockí examinations in February. Reports are sent home on foot of these assessments and parent-teacher meetings take place annually. Common examination papers are set within levels which is good practice.
Ongoing assessment takes place in class thorough oral questioning and teacher observation. It is mathematics department policy to set class tests at the end of each topic or chapter studied. In some cases teachers design class tests to provide as many students as possible with an opportunity for success and the resulting sense of achievement contributes to high levels of student motivation. This is all very good practice.
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 practices in all of the lessons observed.
The mathematics department carries out an analysis of the schoolís performance in the certificate examinations compared to the national norms. It is recommended that this analysis be used to inform future planning for Mathematics.
The following are the main strengths identified in the evaluation:
∑ A high level of whole school support is provided for Mathematics.
∑ Concurrent timetabling allows students to study the highest level possible for as long as possible by facilitating change of level throughout the year.
∑ The mathematics departmentís enthusiasm for and interest in the subject is reflected in the quantity and diversity of the resources available for teaching and learning in Mathematics and
the sharing of this enthusiasm and interest with their students is central to the work of the mathematics teaching team.
∑ The mathematics department is well provided for in terms of information and communications technology.
∑ There is a very high level of support provided to students who have been identified as requiring learning support in Mathematics.
∑ Students of Mathematics participate in a wide range of extracurricular mathematics related activities.
∑ Significant progress has been made on planning for Mathematics.
∑ High quality teaching and learning was evident in all of the lessons observed.
∑ Teachersí work on the board, explanations and instructions were very clear.
∑ In all lessons observed the level of student participation and engagement was high and students were able to demonstrate their learning with confidence.
∑ The relationship between students and their teachers was observed to be excellent.
∑ Very good assessment practices are in place.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
∑ The number of teachers teaching higher level Mathematics should be increased.
∑ The sharing of expertise and lesson ideas among teachers has many benefits for teaching and learning in Mathematics and should be continued.
∑ The learning objectives should be explicitly shared with students at the beginning of lessons and their achievement checked at the end.
∑ In order to provide students with an opportunity to develop the strategic thinking and problem-solving skills that are essential for success in Mathematics teachers should include higher-order
approaches more often in lessons.
∑ A bank of difficult exercises should be kept to provide more challenge for the better able student.
∑ An investigative approach should be used more often 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 October 2009