An Roinn Oideachais agus Scileanna
Department of Education and Skills
Subject Inspection of Mathematics
Carrickmacross, County Monaghan
Roll number: 72180K
Date of inspection: 27 November 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Inver College, conducted as part of a whole-school evaluation. 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.
Inver College has a current enrolment of 206 girls and 321 boys. Timetable provision for Mathematics in the junior cycle is good with first year groups receiving four mathematics lessons per week. Second and third year students are allocated five class periods of Mathematics per week. Transition year (TY) students are timetabled for four mathematics lessons per week. Six mathematics lessons are allocated to fifth years and sixth years receive five lessons per week. Leaving Certificate Applied (LCA) students receive three mathematical applications lessons each week for year one and year two of the programme. The school offers the Junior Certificate School Programme (JCSP) and students availing of this option benefit from one extra mathematics lesson per week in first year and two extra lessons per week in second year.
Incoming first year students are assigned to one of three mixed-ability class groups or the JCSP class group. In October of first year students are assigned to higher and ordinary levels. This is done on the basis of achievement in common tests, teacher assessment, and parental and student preference. While mathematics lessons for the higher level class group and an ordinary level class are concurrently timetabled to allow students of these groups the flexibility to change level should the need arise, students of the remaining ordinary level class group do not have this flexibility. It is very early to make decisions regarding levels in October. The main reason is that October allows students very little time to settle in and display their true potential in the subject. However, another is that the current arrangement does not allow a sizable group of students any scope to reverse their decision to move to ordinary should they discover that it was a wrong decision. Prior to this current year students were assigned to mixed ability class groups or the JCSP group for the full year. It is recommended that the mathematics department conducts a review of the recent changes to the method of dividing students for first year mathematics class groups. During this review consideration should be given to returning to the method of assigning students to the mixed-ability groups for the full duration of first year.
Mathematics lessons for all third, fifth and sixth year groups are concurrently timetabled. This is very good practice. There is some concurrent timetabling of mathematics lessons provided for second year class groups which is good, however, mathematics lessons for one ordinary level class group are timetabled at different times to those of the other groups. This means that students of this class group who are identified as requiring a change of level can only do so by changing base class group. It is recommended that mathematics lessons for this ordinary level group be timetabled at the same times as mathematics lessons for the other two groups. In general mathematics lessons are well distributed across the week and day, however, this is not the case for all year groups. It is recommended that timetabling should aim for a lesson per day with the avoidance of double periods where possible.
The mathematics department comprises eleven teachers. Teachers are deployed in accordance with their qualifications, experience and expertise. There is good rotation of levels and programmes amongst members of the teaching team. Teacher continuing professional development (CPD) is well supported by school management. In addition to whole-school courses, for example, on classroom management, organised by the National Behaviour Support Service (NBSS), mathematics teachers have participated in a range of mathematics-related courses. This is evidence of the mathematics department’s commitment to the development of the subject within the school.
The information and communications technology (ICT) facilities available for teaching and learning in Mathematics are very good. Most classrooms have a personal computer and data projector. TY students are timetabled for the computer room once a week. The computer room can be booked for mathematics lessons; however access is limited by high demand. Two science rooms that are used by mathematics teachers are fitted with interactive whiteboards. While ICT is currently being used for teaching and learning in Mathematics there is scope for this level to be increased. It is recommended that the concurrent timetabling of mathematics lesson be exploited to facilitate greater access to ICT. In particular science rooms containing interactive whiteboards could be used on a rotational basis thus allowing the mathematics department to derive optimum value from the ICT facilities in the school.
In addition to ICT equipment, there is a wide range of resources available for mathematics lessons. These include overhead projectors and calculators, geometry sets, dice, playing cards, games, puzzles, books of mathematical interest, and ‘Flashmasters’. Everyday items such as utility bills, pay slips, shopping lists, newspapers, objects of various shapes and sizes, and the internet are used to encourage students to appreciate the relevance of Mathematics in the world around them. Teachers also use science equipment such as trundle wheels, opisometers, callipers, overflow cans, electronic balances and weights to make mathematics lessons more active for learners. Teachers prepare handouts and worksheets to complement the text book; the examples used throughout the evaluation were very well designed to challenge students and to support learning. In addition, students make models of different shapes and use these in their study of volume and area and geometry. These resources are kept in a central location and are shared amongst the members of the teaching team. ‘Geogebra’ geometry software is available on one of the school’s computers and it is recommended that this be extended to the rest of the classroom-based computers so that it may be used in the study of geometry, co-ordinate geometry and trigonometry. There is good practice in relation to the collection, sharing and use of concrete materials and resources in teaching and learning in Mathematics.
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 addition smaller classes are created for students who have been identified as requiring support in Mathematics. It is very good that numeracy support is provided by qualified mathematics teachers. It is also good that mathematics teachers who supervise the school’s homework club use this very valuable opportunity to provide additional assistance to students. These teachers routinely provide high quality individual attention throughout lessons for any student experiencing difficulties. Overall students who require assistance in Mathematics are very well supported.
Students of Mathematics are encouraged to participate in the PRISM Maths Challenge. 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.
Meetings of the mathematics department are held once every six weeks. In addition, mathematics teachers meet frequently on an informal basis to discuss day-to-day issues that arise. The position of co-ordinator of the mathematics department is currently held by an experienced member of the teaching team. In keeping with good practice this position 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 a section of formal mathematics meetings be given over to the sharing of ideas and methodologies. This would support teachers in creating alternative lesson plans and enable them to increase the variety of student experiences in the classroom.
The mathematics department teachers have engaged with the planning process and some progress has been made. The plan opens with the aims and objectives of the mathematics department which focus on encouraging students to gain confidence with the subject and to develop an appreciation for Mathematics. The plan includes mathematics department policy on student allocation to levels, timetabling, homework, assessment and planning for students with additional learning needs. Some of the policies genuinely reflect current practice, for example the policy on student assignment to levels. However others should be further developed so that they relate more closely to the actual work of mathematics teachers. These include; the list of effective teaching methodologies, the range and variety of resources and the availability and use of ICT.
The mathematics plan contains programmes of work for each year group and level. With the exception of the TY plan these comprise a list of chapters of the textbook to be covered within defined timeframes. While it is good that each year group, within levels, follows a common programme these programmes do not adequately reflect the very good work taking place in teaching and learning on a day-to-day basis. The programme for each year group and level should be set out in terms of expected learning outcomes, resources necessary, methodologies used, and modes of assessment. The format of the TY plan provides a good example of the recommended approach. In addition, a section should also be included for reflection and review. While it is acknowledged that this will involve considerable effort on the part of the members of the mathematics teaching team, it is recommended that they begin to engage in this process. Over time, with the collaboration of the entire team, the programmes of work for mathematics should facilitate a very worthwhile sharing of experience and expertise. This approach would contribute to plans that genuinely reflect the valuable approaches and methodologies used in teaching and learning in Mathematics in Inver College.
The focus of the TY plan is on developing student confidence with Mathematics by using a hands-on approach to make the subject more relevant to students. The plan describes a good combination of Leaving Certificate course content and topics that are not on the Leaving Certificate course. Real life materials and active methodologies are used to help students to develop their understanding of mathematical concepts. TY students complete a project on the mathematical codes described in the novel ‘The Da Vinci Code’ and a study of the Fibonacci sequence. Students make models to use as concrete materials for the study of geometry and volume and area. These are then used as resources for TY students to use in teaching these topics to second year students. This experience should be of great benefit to the second year students who will get the opportunity to explore these topics in a concrete way. The TY students should also derive benefits from having the opportunity to gain alternative insights into the learning process. The LCA lesson that was observed in the evaluation is suggested as an ideal addition to the current TY plan. Furthermore a project to create clinometers and to use them to find the heights of structures around the school is suggested as an idea that would also fit well into this very good TY plan. Further information on how to approach this is available in the Mathematics Junior Certificate Guidelines for Teachers produced by the National Council for Curriculum and Assessment (NCCA).
The quality of teaching and learning in all of the seven lessons observed was of a high standard. Teachers’ work on the board, explanations and instructions were very clear. All of the lessons observed had a clear focus, were well structured and most lessons progressed at a pace that was appropriate to the ability level of the students. The pace of one lesson, however, was a little too fast. In general there was a good balance between student activity and teacher input as teachers were careful to vary the learning activity regularly throughout lessons. This very good practice should also be extended to all lessons. While ICT was used in some lessons the main methodology used was teacher example followed by student exercise. Some teachers have already attended the Project Maths workshops organised by the Second Level Support Service and there was much enthusiasm expressed about the variety of approaches promoted there. It is recommended that the experience gained from attendance at the workshops be used to increase the variety of methodologies used in mathematics lessons on a day-to-day basis.
The learning objective of each lesson was shared with the students through teachers providing a comprehensive introduction to lessons. This very good practice ensured that students knew what was expected of them from the outset. Lessons closed with very good consolidating activities such as high quality open discussion of material covered, student completion of exercises and in some cases teachers asking students to describe what they had learned from the lesson. These very good practices helped students to take responsibility for their own learning by contributing to a sense of student-teacher partnership and by allowing students to have an appreciation of the progress that they made in the lesson.
Teachers made very good use of questioning to assess learning and to engage and involve students. In all cases higher-order questions, that required students to focus on the reasons for the steps in worked examples, were used to help students to explore ideas and concepts. Teachers used many valuable strategies when explaining mathematical concepts to provide students with opportunities to fully understand lesson material. In the case of a lesson on solving linear equations the teacher first explained the main concept through an explanation on the board and then explained it again using a balance which was very well illustrated on the interactive white board. In another lesson, after an initial example on the board followed by students completing exercises the teacher engaged students in a quick oral revision of the work of the lesson; this focused on the strategy necessary rather than the answers to questions. While providing individual assistance for students teachers were very creative in the variety of explanations used; this was of particular note when teachers explained very basic concepts. These are a sample of some of the best practice observed in this regard; however in all cases teachers invested considerable effort in helping students to genuinely understand their course material.
There was much evidence that mathematics teachers have high expectations for student achievement. The second year higher level class visited provides a good example of this. The students’ abilities in this class group ranged from those who were very well able for the higher level syllabus to those who would certainly benefit from the challenge of higher level but would be likely to take the ordinary level paper in the junior certificate examination. It is mathematics department policy to encourage every student who takes higher level junior certificate Mathematics to attempt higher level in fifth year. Providing students with the opportunity to participate at the highest level possible in Mathematics for as long as possible is very worthwhile. In addition, the handouts and worksheets prepared by teachers to support lessons were graduated to cater for a variety of abilities and included questions that were quite challenging. Through questioning students in class, teachers encouraged students to think for themselves. These examples illustrate the very good strategies employed by the mathematics department to encourage students to reach their potential.
The effective use of ICT was observed throughout the evaluation. The students of the JCSP class group visited engaged in a competition using ‘Flashmasters’. The students of this group worked individually on completing six tasks while their teacher provided individual assistance where necessary and recorded their scores using Excel. The competitive nature of this activity facilitated the high degree of repetition required for the students to achieve the learning objectives of the lesson. The students participated very well and enjoyed this lesson. The teacher very discreetly differentiated learning by choosing different tasks for some students in the group thus allowing all students to experience success and ensuring that all students were challenged by the exercise. PowerPoint presentations were used to provide an alternative focus for student attention in some cases. The interactive white board was used effectively to demonstrate equality in a lesson on algebra. As an alternative approach it is suggested that the students be encouraged to complete the exercise on the interactive white board themselves.
The students of the LCA class group visited worked on an exercise to explore the proportional representation electoral system. The teacher chose, for this excellent lesson, the results of the voting from the Carrickmacross local elections that were held in June 2009. The students worked through a worksheet that included exercises to calculate the valid poll, the quota, and each candidate’s first preference votes as a percentage of the total valid poll. A printout of the count details for each of the seven counts was provided for each student. The main activity of the lesson involved lively discussion around the concepts of valid poll, quota, transfers, surpluses, elimination and election. Higher order questioning strategies were used to facilitate each student’s exploration of these difficult ideas on a very deep level. The quality of student contributions demonstrated that deep understanding had been achieved. This lesson was ideal for LCA and also for the particular class group. By choosing the local elections the teacher took advantage of students’ genuine interest in the topic as most of the election candidates were personally familiar to the students. Meticulous planning, excellent choice of material, enthusiastic presentation, and the collaborative approach taken ensured that high quality learning took place in this lesson.
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. Students demonstrated an interest in and an enthusiasm for Mathematics.
First, second and fifth year students are formally assessed at Christmas and in May. TY students are continuously assessed throughout the year. Students preparing for the certificate examinations sit ‘mock’ examinations in spring and are assessed in October. Reports are sent home on foot of these formal assessments and annual parent-teacher meetings are held. In keeping with good assessment practice it is mathematics department policy to set common examination papers within levels.
Students’ progress is closely monitored by teacher observation and oral questioning in class. It is mathematics department policy to set class tests at the end of each topic or chapter studied. Homework is set regularly and is 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 very high. Teachers routinely monitor student work and this contributes to these high standards. It is good that each student is provided with the programme of work for their year group and level. The students of one third year class group visited use this to plan their revision for the certificate examinations. This is a very valuable approach as it enables students to break the course into manageable sections and helps to prevent students from becoming overwhelmed in the preparation for examinations.
The following are the main strengths identified in the evaluation:
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
Post-evaluation meetings were held with the teachers of Mathematics and with the principal and deputy principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published June 2010