An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
Curragh Post Primary School
The Curragh, County Kildare
Roll number: 70660O
†††††††††Date of inspection: 10 December 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Curragh Post Primary 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, deputy 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.
The mathematics department in Curragh Post Primary School is comprised of four teachers who work in an atmosphere of close collaboration and where the student is firmly the focus of the departmentís activities. The mathematics department is very well resourced. Co. Kildare VEC has made a considerable investment in the schoolís information and communications technology (ICT) infrastructure and, as a result, there are seven interactive whiteboards located in different classrooms around the school and each teacher has been given a laptop, which can be used in lesson planning and delivery. Access to such facilities provides the mathematics team with a great opportunity and also poses considerable challenges. The team has embraced these challenges and ICT integration was evident in many of the lessons observed during the inspection. In order to enhance the benefits accruing from the schoolís facilities, it is recommended that a member of the team be chosen to identify suitable resources that could be used in teaching and learning Mathematics. It would be best if these resources could be used to engage students in active and self-directed learning rather than simply providing additional avenues for teacher-led lesson delivery. The second level support service (www.slss.ie) is available to assist with this work.
Curragh Post Primary School draws its students from a small number of primary schools in the surrounding area. The deputy principal, accompanied by a colleague, visits each of these schools to inform prospective students about the curricular and extra-curricular programmes available in the school, to distribute application forms and to detail the enrolment procedures. An enrolment afternoon is held shortly afterwards. Once the incoming cohort has been identified, the parents and students are invited to private meetings with the principal. The schoolís policies and procedures are outlined, the studentís needs, aptitudes and interests are established and details regarding the day-to-day running of the school are discussed at these meetings.
All incoming students are assessed using a number of standardised tests. These tests measure the studentsí visual, numerical and verbal reasoning. It emerged during the inspection that the school was reviewing some of the tests being used and, in order to inform this process, it is recommended that the school liaise with the National Educational Psychological Service (NEPS) and refer to Circular 0008/2007 www.education.gov.ie, to ensure that the standardised tests selected during the review are included in the list of approved tests contained therein. Consideration should also be given to providing incoming students with a competency test in Mathematics, to identify their weaknesses and strengths. The results of the test should then inform the material to be covered in the first-year mathematics programme.
The procedures for identifying and supporting students who need learning support in Mathematics are very good. Class teachers in the feeder primary schools are contacted by telephone and the profiles of incoming students are discussed. Incoming students who have had their learning or other needs already formally assessed by NEPS in primary school are identified, and applications for extra resources are then submitted by the school to the Department of Education and Science for consideration. If it is deemed necessary, additional assessments for some students are also arranged through NEPS or through a special programme funded by Co. Kildare VEC.
There is one core class group in each year and learning support in Mathematics is provided by withdrawal in small groups, from subjects from which the students have an exemption and through the provision of an additional mathematics class in second and third year. These additional classes are timetabled concurrently with the mainstream class in each year, in order to facilitate ease of movement between levels and to facilitate access to additional short-term support when the need arises. Ongoing liaison takes place between the class and learning-support teachers and procedures for returning students to mainstream are in place.
Mathematics classes are mixed ability in junior cycle and there are four periods of Mathematics per week in each year. Mathematics classes are set in senior cycle and there are five periods per week in fifth year, and six per week in sixth year. All classes are forty minutes long. The distribution of mathematics classes throughout the week and the balance of provision between morning and evening, are very good.† It is recommended that, as part of school development planning, the timetabling provision for Mathematics in junior cycle be kept under review, with a view to increasing the provision to five periods of Mathematics per week in each year.
Subject development planning in Mathematics is well underway and the department is capably co-ordinated by one of the teachers. Regular meetings of the department take place and minutes of the meetings are available in the subject development plan for Mathematics. It is intended that responsibility for co-ordinating the department will rotate between the members of the department. However, it is suggested that the present co-ordinator remain in place until the impending changes in the mathematics curriculum are in place.
A subject development plan for Mathematics has been developed. The plan contains a statement of the departmentís aims and objectives, timetabling arrangements for Mathematics, arrangements for student access to programmes and levels, lists of textbooks and course materials and long-term schemes of work. In order to build on this good work, it is recommended that the department collaborate in developing the subject plan to detail effective teaching methods, learning outcomes, strategies for integrating ICT and other resources in teaching and learning, and agreed procedures to be followed in carrying out core mathematical operations.
Individual teacher planning is very good. All of the teachers visited during the inspection made their planning documentation available to the inspector and, in all cases, it was found to be comprehensive, relevant and student friendly. Planning for the inclusion of ICT resources was particularly good and, as a result, they were seamlessly integrated into the lessons and served to create a learning environment that was visually stimulating and provided opportunities for effective teacher movement. The use of subject-specific software to illustrate key concepts, and to develop the studentsí understanding of basic principles, would greatly enhance existing good practice. Such software should be identified as part of the engagement with the SLSS suggested earlier in this report.
The school is rightly proud of the attainment of its students in the state examinations and an informal analysis of student uptake and performance takes place annually. This very good practice would be greatly enhanced if the mathematics team were to engage with the principal, at the beginning of each year, to analyse the studentsí performance with reference to the statistics available from the state examinations commission and also to review the chief examinerís report for Mathematics. The meeting could act as a forum to examine any measures that might be taken to enhance the uptake of higher-level mathematics in both junior and senior cycle.
Management is very supportive of attendance at continuing professional development (CPD) courses and teachers have attended a wide range of such courses in the recent past. All of the teachers are members of the Irish Mathematics Teachers Association (IMTA) and the school pays the cost of membership.
The lessons observed during the inspection were very well planned. The material covered was appropriate to the curriculum and was in keeping with the subject departmentís long-term schemes of work. Resources, including graduated worksheets, had been prepared in advance of all of the lessons and were skilfully used to support the lessons objectives and to engage the students in the lessonís subject matter. The teachers taught with enthusiasm, were mindful of the needs and aptitudes of the students and were careful to insist on the correct use of mathematical language. Furthermore, every effort was made to create links to the studentsí earlier learning and to their everyday experiences.
Pair work, small group work, ICT integration, the use of worksheets, and the more traditional teaching style, were all in evidence during the inspection. In one instance, a class on introductory geometry was supported by a graduated worksheet, which engaged the students in actively measuring angles, learning the correct terminology for the angles being measured, calculating the sizes of angles, and carrying out various constructions. The students were actively engaged throughout and the teacherís use of questioning served to reinforce the lessonís objectives and to prepare the ground for the more difficult material that they would meet in subsequent lessons. The studentsí ability to solve the equations that emerged naturally as part of their investigations was very impressive, and indicated that their knowledge of algebra was very satisfactory.
Pair work was used very effectively to enable students to investigate and graph quadratic functions. The teacher paired those students who had been absent from the previous lesson with those who had been in attendance. The students were asked to predict the type of graph that would emerge and to reflect upon the graphs of linear functions they had encountered in earlier classes. The teacher asked them to suggest the correct expressions associated with linear and quadratic functions and to outline the steps involved in graphing them. Furthermore, the teacher insisted that those who had been absent were to the fore in suggesting approaches and in carrying out calculations. The lesson was purposeful and student centered and the quality of student engagement was very good throughout.
The interactive whiteboard was very skilfully integrated in a lesson where students were being introduced to fractions. The teacher explicitly outlined the lessonís goals at the outset and proceeded to demonstrate the correct procedures for adding and subtracting fractions. The lesson was characterised by an insistence on the use of correct language and the adherence to correct procedures when carrying out calculations. The use of ICT supported the achievement of the lessonís objectives, enabled the teacher to circulate around the room, and allowed easy review of earlier examples to assist students when difficulties arose. The use of a graduated worksheet, to allow the more able students to develop their skills and to investigate more intricate problems, while the teacher provided assistance to individuals, would have offered a valuable enhancement to an otherwise excellent lesson.
Classroom management was very good. The teachers had very high expectations of the studentsí engagement and attainment and, in most cases, these expectations were met. Teacher questioning was very good. It was not only designed to elicit factual responses, but to encourage the students to speculate, to suggest solutions to problems and to engage in higher-order thinking. The students responded positively and were anxious to please and to assist the teachers in achieving the lessonsí goals. The teachers were affirming of the studentsí efforts and the classroom atmosphere was warm, respectful and busy.
Teacher questioning also served to reinforce student learning and it was evident, from their response to such questions, that the studentsí knowledge of the material being covered was very good, as was their ability to recall material covered in earlier lessons. Evidence of student learning was also available from the studentsí homework copies, from their performance in class tests and from their confident responses when interacting with the inspector.
Ongoing assessment occurs through the use of teacher questioning in class, the provision of class tests upon completion of each chapter, and through the use of revision worksheets. Homework is assigned and corrected regularly and the homework copies examined during the inspection were in very good order. The studentsí work was neat and tidy and there was some evidence of teacher corrections and comments, and of the students amending their own work.† In order that the good practice in assigning and correcting homework, evident in some instance, be adopted across the entire department, it is suggested that the homework policy be reviewed and that the amended policy be included in the subject development plan for Mathematics. The review should address the role of homework in providing opportunities for independent, collaborative and shared learning, the role of the different stakeholders in setting, monitoring and amending homework, and the adoption of assessment for learning, already in evidence in some instances, as a key medium in assessing studentsí work.
Formal examinations are provided for non-examination classes at Christmas and just prior to the summer holidays, while students in third and sixth year sit formal examinations at Christmas and take mock examinations early in the second term. Students in receipt of reasonable accommodation in the state examinations receive similar consideration in all formal examinations. In order to reflect current practice and to inform future planning, the subject development plan for Mathematics should be amended to include the schoolís assessment policy and to specify the frequency of, and arrangements for, in-class tests and formal examinations and to outline any other assessment vehicles to be employed in evaluating studentsí work.
Ongoing communication with parents occurs through the use of the student diary and telephone contact, and formal letters are also issued if the need arises. In addition, each class group has one parent-teacher meeting per year. Other, less formal, meetings can also be arranged if required. An awards evening to celebrate student attainment, endeavour and contribution to the life of the school, is held in the final term of each year.
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 2009