An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Roll number: 68068R
Date of inspection: 18 September 2009
Report on the Quality of Learning and Teaching in Mathematics
Subject inspection report
This report has been written following a subject inspection in Coláiste Íosagáin. 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. Following the evaluation visit, the inspector provided oral feedback on the outcomes of the evaluation to the principal and deputy principal. 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.
Subject provision and whole school support
Coláiste Íosagáin is one of the twenty-four schools participating in the pilot phase of Project Maths. Participation in the project has presented the school and in particular the mathematics department with many challenges and opportunities. The teachers of Mathematics have embraced the project with enthusiasm and have worked hard to ensure that the project is successfully integrated into the operation of the mathematics department and into the delivery of the mathematics curriculum.
The amount of time allocated to Mathematics on the school’s timetable is very good. All mainstream junior cycle classes are provided with five periods of Mathematics per week. There is one learning-support class group in each year in junior cycle and these classes are provided with an additional period of Mathematics each week. Upon completion of junior cycle, students can opt to enter transition year (TY) or go directly into fifth year. There are four periods of Mathematics per week in TY, six periods per week in fifth year and five in sixth year.
The scheduling of mathematics classes in Junior Certificate is in need of review. Apart from the learning-support classes, mathematics classes in first and second year are mixed ability. The classes are timetabled independently within each year group. Mathematics classes are set in third year and are timetabled concurrently. In order to facilitate the formation of higher-level and ordinary-level classes at an earlier stage, it is recommended that mathematics classes are set at the end of first year and are timetabled concurrently in each year group for the remainder of the junior cycle. In order to provide concurrent timetabling of mathematics classes, consideration may need to be given to the creation of two separate bands in second and third year, with setting within each band.
Students with special educational needs or in need of learning support in Mathematics are very well catered for in the school. The learning-support class is created in first year following standardised assessments and consultation with the learning-support and class teachers in the feeder primary schools. The learning-support class receives additional support in Mathematics and follow the ordinary-level curriculum. Some of the students may eventually opt to take foundation level Mathematics in the Junior Certificate examinations while students who wish to follow higher level are also facilitated. The learning-support co-ordinator is also a member of the mathematics department and this is particularly beneficial in preparing schemes of work and in monitoring the students’ progress in relation to the overall cohort. Learning support in Mathematics is also provided by withdrawal in small groups from subjects from which the students are exempt.
Students with completed psychological assessments are identified upon enrolment and the arrangements for collecting the assessments and submitting them to the Department of Education and Science for consideration are timely and effective. If it is deemed necessary, additional assessments for some students are also arranged through the National Educational Psychological Service.
The mathematics department comprises ten teachers all of whom have an appropriate qualification in Mathematics. The teachers are assigned to levels by agreement within the department and following consultation with management. This good practice is indicative of the teamwork evident in the operation of the department. However, a number of the members of the department teach Mathematics to just one class group. In order to further enhance the collaboration within the department and to facilitate more cohesive curriculum delivery, it is recommended that this practice be reviewed.
The mathematics department is well resourced. The department has an annual budget and procedures for ordering new equipment and materials are in place and are followed with care. The funding provided to support the school’s participation in Project Maths has been used to purchase a range of materials to facilitate active teaching and learning. These and other resources are accessible to all of the members of the department and are detailed in the subject department plan. Management has been proactive in developing the school’s information and communications technology (ICT) infrastructure. The school boasts one principal computer room, a multimedia language facility and a significant number of computers and data projectors are distributed throughout the school. The staffroom also contains a networked bank of computers.
Management is fully supportive of teacher attendance at continuing professional development (CPD) courses. The school’s board of management gives significant financial support to teachers attending CPD courses in their own time. This is very good practice. Owing to the school’s participation in Project Maths, the members of the mathematics department have attended a significant number of CPD courses in the last two years. Management and staff have collaborated effectively to ensure teacher attendance at the requisite courses and the members of the department have successfully integrated the materials presented at these courses in lesson delivery and department planning.
Planning and preparation
Subject department planning in Mathematics is very well advanced. The department is ably co-ordinated, regular meetings are held and very good records of the proceedings of department meetings are maintained. Co-ordination of the department’s activities has been the responsibility of one of the teachers for the last number of years. It would be preferable if the post of co-ordinator were to rotate between the members of the department as this would develop capacity within the department and provide each member with an opportunity to lead the development of the department. However, any decision to change the co-ordinator should wait until the pilot phase of Project Maths has ended. Recent planning in the department has focused on the challenges presented by the school’s participation in Project Maths and great credit is due to the department for the manner in which it has risen to the challenge. Once this phase has passed, it is advised that the department use one of its planning meetings annually to engage in an analysis of the students’ performance in the state examinations compared to national norms. The analysis should inform planning, and strategies to address any issues that emerge from the analysis should be put in place.
A comprehensive subject department plan for Mathematics is in place and it is evident that a great deal of collaboration has taken place in developing the plan, particularly in creating schemes of work, in agreeing assessment schedules, and in developing innovative modes of assessment. The schemes of work, which are in keeping with the curriculum strands in the revised syllabuses, have a very welcome focus on learning outcomes. Classroom practices and modes of assessment are closely informed by the schemes of work contained in the plan. This is very good practice. The very good work evident in subject planning in Mathematics could be further enhanced by detailing, in the plan, the most effective methodologies to be employed in realising the identified learning outcomes.
There are very good links between the mathematics department and the learning-support teachers. As a result, planning for students with special educational needs is an integral part of the department planning in Mathematics and the special educational needs section of the subject department plan is comprehensive. Future planning meetings should consider mainstreaming the teaching methods currently employed in learning-support classes, particularly in relation to group and pair work and in the integration of resources in lesson delivery.
A separate plan for Mathematics in TY is in place. The plan outlines the content to be covered in the form of topic lists and refers to the types of teaching methods to be employed in delivering the programme. The plan also lists the various co-curricular and extracurricular activities available to the students taking TY. In order to develop the existing plan, it is recommended that it be redrafted with reference to clearly stated aims and objectives and that the content of the mathematics programme be modified accordingly. In carrying out the review, due cognisance should be given to the context-based framework and the teaching methods advocated in Project Maths.
Teaching and learning
The lessons observed during the inspection were well planned and the content in each case was in keeping with the schedule outlined in the subject department plan. The teachers were well prepared for the lessons, were knowledgeable, and taught with enthusiasm. The lessons proceeded at a suitable pace and, in general, the time management of the lessons was appropriate. However, care should be taken to ensure that the amount of time spent correcting homework is not excessive. In some instances, the lesson’s objectives were discussed with the students at the outset of the lesson. This is very good practice and should be adopted as standard across the department. The auxiliary whiteboard present in many of the rooms could be used to record the agreed objectives. A brief review of how successfully the objectives were met should then take place prior to the end of the lesson.
A number of teaching methods were in evidence. In many lessons, the textbook was the primary teaching resource and, in such instances, the preferred teaching method involved teacher exposition at the board followed by the students working individually on assigned tasks. While these classes worked well, they did not provide opportunities for student collaboration and self-directed learning. However, a number of innovative approaches were also in evidence and there were some particularly good examples of group and pair work, supported by excellent teacher movement and appropriate graduated worksheets. The group and pair work was made possible by flexible seating arrangements that allowed the students to collaborate and to work at their own pace. The resulting lessons were models of good practice and the methods used could be exploited very successfully in mixed-ability classes.
ICT was integrated into lesson delivery in a number of cases. It was seen to best effect where dynamic software was used to explore the features of quadratic graphs and to enable the students to immediately establish if their proposed solutions were correct. The technology was supported by excellent teacher questioning and written resource materials designed to facilitate collaborative learning and exploration. However, in another case, ICT, in the form of a web-based video broadcast, merely served to carry out the teaching function and brought very little additional benefit. As this material is very useful for revision and is available free of charge, students were advised to access it at home as a study aid. This is good practice. It is suggested that the students continue to be directed to the content on the site, where appropriate, but that the site should not be an ongoing focus of lesson delivery.
The innovative use of resources was seen to very good effect where students engaged in experiments to record the outcomes when a pair of dice was thrown. The students worked in pairs and carried out an agreed number of trials. The results of the trials were recorded by each pair. Very interesting conversations followed as anomalies in the results achieved by the different pairs, when compared to the expected outcomes, became apparent. The results were then collated and the effect of increasing the sample size was explored. The lesson was engaging and challenging and served to introduce probability in a realistic and accessible fashion.
Very effective use was made of teacher questioning. The questions were used to elicit answers to specific problems and also served to engage the students in higher-order thinking and to encourage them to speculate and hypothesise. Teacher questioning was also used to enable students to interpret questions and to discuss the best approaches to problem solving.
Classroom management was, in all cases, very good. The interactions between teachers and students, and between the students themselves, were respectful and the students engaged productively with the lessons and contributed in a positive fashion when opportunities arose. Many of the rooms contained posters and other visually stimulating materials. These materials were relevant to the curriculum and were often referred to during the lessons. Moreover, they helped to highlight the importance of Mathematics in the academic and wider world.
The quality of student learning was, in almost all cases, very good. The students responded readily and with confidence when questioned by the teachers and the quality of their written work was, in most instances, also very satisfactory. Analysis of student attainment in the state examinations suggests that while student attainment in higher-level and ordinary-level Mathematics in the Junior Certificate is good, it is evident that work needs to be done in ensuring that students taking higher-level Mathematics in the Junior Certificate examination continue at higher level in senior cycle. Participation in Project Maths is an ideal vehicle by which the school can begin to address this issue.
Practices in relation to assessing student progress in Mathematics are very good. The members of the Mathematics department have worked very closely in developing cohesive assessment procedures. Class groups within each year and level sit common classroom-based assessments, with agreed marking schemes, upon completion of each topic. The tests, developed by the teachers, are innovative in design, student friendly and are differentiated to meet the needs of all of the students in the year group. The effect of such careful planning is that all of the mathematics teachers work to an agreed schedule and that an examination of the outcome of the various tests offers a very clear picture of how the cohort as a whole is performing and how individual performances within the cohort varies from test to test. Ongoing assessment also occurs through the assignment and correction of homework and through teacher questioning in class. The students’ homework copies are monitored appropriately.
In addition to the ongoing classroom-based tests, all students sit class tests at Halloween and sit more formal examinations at Christmas. The mathematics tests in both instances are common within levels in each year group. A written report issues to parents at Christmas detailing student performance in both assessments. A similar assessment and reporting model operates for non-examination classes in the second term each year, with class-based tests in March and formal examinations just prior to the summer holidays. Examination classes sit mock examinations in March each year.
Practices in relation to monitoring student attendance and attainment in class and in formal examinations are very good. Roll call is taken at the beginning of each lesson and the results of class and formal tests, and compliance with homework assignments, are kept in the teachers’ diaries.
The school promotes student participation in co-curricular and extracurricular activities and students are facilitated to participate in the BT Young Scientist & Technology Exhibition, junior cycle mathematics students participate in Problem Solving for Irish Second Level Mathematicians (PRISM) competitions, organised nationally as part of Maths Week Ireland, while senior cycle mathematics students participate in Team Maths.
Summary of main findings and recommendations
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 principal and deputy principal, at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published, January 2010