An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Roll number: 72360M
Date of inspection: 8 May 2009
Report on the Quality of Learning and Teaching in Mathematics
Subject inspection report
This report has been written following a subject
Subject provision and whole school support
There are two class groups in first year and also in second year; comprising one mixed-ability group and one foundation-level group. Students are assigned to higher level, ordinary level or foundation-level class groups in third year. The school offers the Junior Certificate School Programme (JCSP) and all first and second year students follow this programme and benefit from the methodologies and additional support associated with it. In the current fourth year there is a higher-level class and an ordinary-level class. The current fifth year comprises one ordinary level class group. Students are encouraged to study Mathematics at the highest level possible for as long as possible. Concurrent timetabling of mathematics lessons allows the mathematics department to take a student-centred approach to level choice. The mathematics department arrangements for level choice are very good.
The mathematics department comprises six teachers. There is good rotation of levels among members of the teaching team. School management facilitates teacher continuing professional development and teachers engage in such activities on an ongoing basis. Each member of the mathematics department has attended courses in the last school year. These include courses that focus on provision for students with special needs such as ‘Mood Watchers’, ‘Conflict Resolution in the Classroom’, JCSP numeracy courses, dyslexia seminars and co-operative learning courses. Most mathematics teachers have received Smartboard training. Other courses attended include ‘ideas to enhance teaching and learning of Maths parts 1 and 2’ and ‘teaching methodologies for LCA parts 1 and 2’. The range and quantity of courses attended reflects mathematics teachers’ openness to developments in mathematics teaching and interest in making mathematics accessible to students of all ability levels.
The facilities for information and communications technology (ICT) are very good and are also effectively used in practice. There is a computer and data projector in most classrooms. A laptop computer has been provided for mathematics department use. One mathematics room is fitted with a Smartboard and a further two rooms have a computer with internet access and a data projector. The interactive whiteboard and the computers have Autograph software installed. These rooms are used on a rotational basis by mathematics teachers. EBeam, an alternative interactive whiteboard, has been recently acquired by the school and is also available for use in teaching and learning in Mathematics. The internet is regularly used to source suitable lesson material. Through the quality and frequency of the ICT used in teaching and learning in Mathematics it is evident that the mathematics department are committed to finding ways to make lessons both interesting and enjoyable for students.
Teachers use a wide variety of resources for teaching and learning in Mathematics. These include probability kits, geometry equipment, geostrips, algebra tiles, overhead projectors and a range of mathematical games and puzzles. Resources that support numeracy, for example fraction sets, number dominoes, euro coins and notes, and Venn diagram posters are routinely used to enhance the clarity of explanations and to make mathematics more relevant to students. Teachers use the walls of their classrooms to display student projects and posters and have created stimulating mathematical environments. The variety of resources used in lessons is evidence of the department’s focus on encouraging students to appreciate the relevance of Mathematics in their everyday lives and on facilitating positive experiences with Mathematics for students.
Students with learning support needs in Mathematics are identified through communication with feeder primary schools, psychological assessments, pre-entrance assessments and diagnostic testing. Teacher observation and class testing provide additional information. Support is provided through the formation of small class groups and withdrawal from subjects other than Mathematics. The small number of students in all class groups means that students receive a very high level of individual support and attention in mathematics lessons from their class teachers. The members of the learning support department and the mathematics department work together to create learning plans for students and to ensure that individual learning support needs are met. It is suggested that team teaching be considered as an additional method of providing learning support for students. This would complement the very good supports that are currently in place. There is, overall, a very high level of support provided for any student experiencing difficulty with Mathematics.
Mathematics students are provided with many opportunities of participating in extracurricular mathematics-related activities. Maths Week and World Maths Day are celebrated as significant events in the life of the school. The school takes part in the mathematics quiz organised between schools in the County Sligo Vocational Education Committee (VEC) scheme. Photographs of students participating in this event are prominently displayed on classroom walls. Participation in activities such as these provides students with valuable opportunities to experience mathematics for pleasure.
Planning and preparation
The mathematics department meets at the beginning and end of the school year as part of the whole-school planning process and then once per term throughout the year. There is a high level of informal planning and collegial support among members of the teaching team. The department is co-ordinated by an experienced mathematics teacher on a voluntary basis and this is working very well. It was evident from the review of the minutes of planning meetings and the observation of classroom practice that mathematics teachers share lesson ideas and methodologies. Teachers are also involved in the development of the Mathematics Teachers’ Network within Co. Sligo VEC. Such a valuable sharing of expertise has a positive effect on student experience in the classroom.
Significant progress has been made on planning for Mathematics. The subject plan opens with aims and objectives that focus on providing a mathematical experience for students that is relevant, accessible and positive. The plan includes mathematics department policy on student allocation to class groups, planning for students with special needs, homework, assessment and ICT usage. Sections on cross-curricular planning and planning for cultural diversity are also included. Considerable effort has clearly been invested in policy development to ensure that the plan reflects the work of the mathematics department. However, a strong common feature of the lessons observed was the focus on teaching for a deep understanding of mathematical concepts. It is therefore recommended that this valuable approach be reflected in mathematics department written policy. In keeping with good practice the plan is regularly reviewed and evaluated and changes are made accordingly.
Schemes of work are maintained in terms of topics to be covered within defined timeframes and student learning outcomes. Some also include sections on methodology, resources and assessment. This is in keeping with very good planning practice and it is recommended that over time this format be gradually extended to ensure that the schemes of work reflect the variety in methodology and classroom experience evidenced in the evaluation.
The plan for LCA Mathematical Applications is detailed and comprehensive. It is set out in terms of student learning outcomes and work plans. For each topic the plan of work describes activities and methodologies that are ideal for LCA. Examples include: estimating and then accurately measuring objects; discovering, by experiment, the relationship between the circumference and the diameter of a circle; using and setting timing devices; and applying the skills of Mathematics to household repairs. Active, investigative, discovery, and research methodologies are outlined in this plan. It is clear from the plan that good cross-curricular collaboration takes place. It is evident from the list of resources in each section that real life materials such as bank forms, newspapers, brochures, catalogues, and menus are used wherever possible. LCA lessons include ICT in the form of PowerPoint presentations, internet research and using Excel to tabulate numerical data. This plan provides a very good LCA programme.
Four lessons were observed during the evaluation and in all cases the quality of teaching and learning was very high. Each lesson observed was very well planned and teachers provided students with a clear outline of the lesson’s learning objectives. In one very successful lesson the teacher had prepared a number of tasks for the students to complete and a mathematical game for them to participate in once the main work of the lesson was done. The teacher shared the learning objectives clearly with the students in this case. This was very valuable as the students benefited from the security of knowing exactly what was expected of them throughout the lesson. Some teachers shared the learning objective orally while others wrote them on the board at the beginning of the lesson. In order to derive full benefit from this practice it is recommended that teachers explicitly share the learning objectives at the beginning of lessons with students by writing them on the board. These can be marked off as they are achieved by students during the lesson.
There was a variety of teaching methodologies used in each lesson. An investigative approach was taken to calculating the value of loan repayments in the LCA lesson observed. The students were asked to estimate the repayments in order to pay off a loan over various different time periods. Once they had made their original estimate they were expected to refine it by trial and error to arrive at the correct value. The students worked in pairs and engaged in lively discussion throughout the lesson. A very well-designed PowerPoint presentation was used to illustrate the main ideas. This lesson was successful because the content was chosen to reflect student interest and, by approximating the values, the students’ focus was drawn to the significance of the amounts of the repayments. The teacher was very careful to provide any support needed while allowing students to work out the answers for themselves. Throughout this lesson the teacher encouraged and motivated students to complete the task and the levels of student attention and participation were high due to the variety of the learning activities.
Providing for the individual needs of students is a central focus of the work of the mathematics department. This was particularly evident in the junior cycle class visited. This excellent lesson involved the students completing an exercise involving money. Concrete materials were used to provide activities that illustrated the ideas of the lesson. The teacher supported student learning by close monitoring and the provision of individual attention. The lesson activities were well supported by the presence of the special needs assistant (SNA). The levels of student concentration and engagement were very high with students working hard to ensure that all elements of the task were completed correctly. The students were encouraged to persist when the exercise proved difficult and were supported in using the concrete materials to enable them to reach understanding. The students demonstrated considerable respect for the work of the lesson and a sense of achievement on completion of the learning activities. By the end of the lesson all of the students had achieved the learning objectives. Furthermore, the provision of positive mathematical experiences for students was clearly a parallel objective of the lesson and it was evident that this was being achieved through well-planned activities and the encouragement, support and affirmation provided.
It is evident in all the lessons visited that teachers are enabling students to take responsibility for their own learning through providing opportunities for collaboration and by encouraging students to think for themselves. This was best illustrated by practice observed in a junior-cycle algebra lesson. In this lesson the students and their teacher worked together as a team to solve word problems in algebra. The students were expected to explain the reason for each step taken and through the use of higher-order questions were encouraged to examine the underlying concepts of the lesson. Where necessary, the teacher provided support in terms of general problem-solving advice. This approach allowed the students to effectively develop the problem-solving skills that are essential to learning in Mathematics.
In three of the four lessons observed ICT was used. In all cases it was effective. Autograph was used on the Smartboard in a senior-cycle lesson on co-ordinate geometry. In this lesson the students were expected to identify the equations of given lines from the diagrams presented on Autograph. This lesson followed on from a lesson in the computer room where students used Autograph to explore the relationship between the physical representation of a line and its slope and y-intercept and were able to demonstrate a solid understanding of the concepts involved. The teacher then distributed envelopes containing cards, some with diagrams of lines and others with equations of lines printed on them. The students worked in groups to match the lines with their equations. The variety and student-centred nature of the learning activities ensured that learning was differentiated. Further differentiation occurred when a handout describing the previous lesson and additional attention was provided for any student who had been absent and was experiencing difficulties. This is very good practice. Throughout this excellent lesson the teacher used higher-order questions to encourage students to discuss their observations and examine the concepts thoroughly. Student seating was arranged to facilitate group work and this contributed to very high levels of participation in the learning activities.
The relationship between students and their teachers was characterised by warmth and good humour. A caring learning environment existed in all of the classrooms visited. Every effort was made to ensure that student experience with Mathematics was positive and that students could develop confidence with the subject. Students contributed fully and freely to lessons and it was evident that they were enjoying Mathematics.
Formal examinations are held for each year group at Christmas. Students preparing for the certificate examinations sit ‘mock’ examinations in March. First, second and fourth year students are formally assessed in May. Reports are sent home following each of these formal assessments and parent-teacher meetings take place annually. In keeping with very good practice any student who qualifies for reasonable accommodations in the certificate examinations receives similar support for formal in-house examinations.
Teachers monitor progress on an ongoing basis through observation and oral questioning. In some cases a ‘traffic lights’ system is used to assess student understanding. This involves students declaring their understanding of the lesson content in terms of green, yellow, or red with each colour representing a different level of understanding. This was observed to work very well. It is mathematics department policy that class tests are given at the end of each topic or chapter studied. Homework is set regularly and usually corrected as part of the following lesson. It was evident from the review of student work that the standard of presentation is generally high and that students are making good progress. The practice in relation to assessment is very good.
Summary of main findings and recommendations
The following are the main strengths identified in the evaluation:
· Timetable allocation for Mathematics is good and the mathematics department arrangements for level choice are very good.
· The range and quantity of continuing professional development courses attended reflects mathematics teachers’ openness to developments in mathematics teaching and interest in making
mathematics accessible to students of all ability levels.
· The facilities for information and communications technology are very good.
· Teachers use a wide variety of resources for teaching and learning in Mathematics.
· Significant progress has been made on planning for Mathematics.
· The quality of teaching and learning was very high; there was a variety of teaching methodologies used in each lesson.
· Providing for the individual needs of students is a central focus of the work of the mathematics department and there is a very high level of support provided for any student experiencing difficulty
· Teachers are enabling students to take responsibility for their own learning through providing opportunities for collaboration and by encouraging students to think for themselves.
· The caring environment that was evident in all of the classrooms visited reflects the excellent relationships that exist between students and their teachers.
· The school’s practice in relation to assessment in Mathematics is very good.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· Over time all schemes of work should be set out in terms of learning objectives, methodologies, resources necessary and modes of assessment.
· Teachers should explicitly share the learning objectives at the beginning of lessons with students by writing them on the board. These can be marked off as they are achieved by students
during the lesson.
Post-evaluation meetings were held 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