An Roinn Oideachais agus EolaŪochta
Department of Education and Science
Subject Inspection of Mathematics
Cnoc Mhuire Secondary School
Granard, County Longford
Roll number: 63730S
Date of inspection: 27 April 2009
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Cnoc Mhuire Secondary 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 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.
Timetabling provision for Mathematics in Cnoc Mhuire Secondary School is very good.† Students entering the school in first year are placed in mixed-ability classes and are provided with five classes of Mathematics per week. A common programme is followed throughout first year and following a common assessment at the end of the year, mathematics classes are set for the remainder of the junior cycle. In order that the common first-year programme addresses more closely the identified needs of the students, it is recommended that all incoming students sit a competency test in Mathematics and that the outcomes are analysed and used to inform the content of the first-year programme. The students should then be provided with a number of common examinations during the year, the results of which should be used to determine the composition of the classes when setting takes place.
Students in second and third year are provided with five periods of Mathematics per week at higher and ordinary level. Upon completion of the junior cycle, students can apply to enter transition year (TY) or go directly into fifth year. One mixed-ability class is formed in TY and there are three periods of Mathematics per week. Mathematics is followed at higher and ordinary level in fifth and sixth year and there are six periods of Mathematics per week in each year.
Mathematics classes are timetabled concurrently in each year. This is very good practice as it allows students to change level should the need arise and enables them to follow the highest level possible for as long as possible. The distribution of Mathematics classes throughout the week is mostly satisfactory. However, the provision in first year needs to be kept under review to ensure that the situation where class groups are provided with two periods of mathematics on the same day should not continue in future years.††
Students with special educational needs or in need of learning support are identified as part of the enrolment process. Members of the special educational needs team attend the schoolís open and enrolment evenings and meet with parents to discuss the needs and aptitudes of the incoming students. A small learning-support group, timetabled concurrently with the mainstream mathematics classes, is formed in each year of junior cycle. Close liaison is maintained between the learning-support teachers and the members of the mathematics department. These links serve to ensure that the material being covered in the learning-support classes, while addressing identified underlying weaknesses, is in line with the programme in the mainstream classes.
Incoming students who have already had their learning or other needs formally assessed by the National Educational Psychological Service (NEPS) in primary school are also identified during the transfer programme, and applications for extra resources are then submitted by the school to the Department of Education and Science for consideration. These students receive additional support in Mathematics during individual or small-group withdrawal from subjects from which they are exempt. If it is deemed necessary, additional assessments for some students are also arranged through NEPS.
The progress of each student in receipt of learning support or with resource hours is tracked by monitoring their performance in class tests and in formal examinations. The special educational needs team have recently received in-service training in the development and use of individual education plans (IEPs) and it is intended that IEPs will be developed for each student with identified special educational needs. This development will enhance the design, delivery and assessment of the learning-support and resource programme and is commended.
As part of the ongoing development of the schoolís special educational needs programme, special provision should be made in the schoolís transfer and enrolment processes to identify students with exceptional abilities in Mathematics and appropriate initiatives should be undertaken to provide them with relevant supports throughout their time in the school. In designing these initiatives, reference should be made to Exceptionally Able Students-Draft Guidelines for Teachers, which is available from the National Council for Curriculum and Assessment.
Management have been proactive in building the capacity of the mathematics department. The department comprises nine teachers all of whom have an appropriate qualification in Mathematics. Teachers are assigned to levels by rotation and four of the teachers share responsibility for teaching Mathematics to higher level in senior cycle. It is policy that teachers retain the same classes from second to third year and from fifth to sixth year. This is very good practice as it ensures continuity of provision and facilitates long-term planning. It is clear that many of the department members collaborate closely in developing resources and in subject planning. It is equally obvious that they share an enthusiasm for Mathematics and contribute to a sense of vibrancy within the department.
The mathematics department is very well resourced. The mathematics teachers have ready access to the schoolís extensive information and communication technologies (ICT) facilities. Laptops, data projectors, interactive whiteboards and educational software were extensively used in the lessons observed during the inspection. Locally produced and other ICT resources are stored on a computer in the ICT room and are available to all of the members of the department. Members of the department have also been very innovative in producing and procuring additional resources to aid in teaching and learning.
Subject department planning in Mathematics is at an advanced stage. The mathematics department is very ably co-ordinated. Regular planning meetings are held, the details of which are contained in the subject department plan for Mathematics. A great deal of informal planning also takes place and many of the departmentís members collaborate in preparing lesson plans and appropriate classroom materials. The mathematics department also engages in an annual review of the performance of the students in the certificate examinations with reference to the statistics made available by the State Examinations Commission. This informed and enlightened approach to subject planning is very good practice. To further inform the outcomes of this practice, it is suggested that a suitable metric be devised to determine the underlying trends in student uptake and performance.
A comprehensive subject department plan for Mathematics is in place. The plan includes an ethos statement for the department, a statement of aims and objectives, resource lists, arrangements for student access to levels, the departmentís calculator policy, a comprehensive section on special educational needs and strategies for integrating different areas of the schoolís curriculum in teaching and learning. The plan also includes very thorough schemes of work for each year and level. The schemes of work give, in great detail, the material to be covered by each class group and the intended delivery schedule.
In order to build on the existing very good practice in planning, it is recommended that the schemes of work be extended to include key deliverables in the form of learning outcomes in each section. The most appropriate methodologies to achieve the specified outcomes should also be detailed. It is further recommended that the members of the department agree common approaches to teaching core mathematical operations and for integrating different areas of the course in lesson delivery. These should also be included in the subject department plan for Mathematics.†
A separate plan detailing the mathematics programme in TY is in place. The programme is in line with the aims and objectives of TY and specifies the content to be covered and the teaching and learning strategies to be employed in delivering the programme. However, it is recommended that the curricular content outlined in the plan be reviewed to include an agreed core of material and a number of modules. The content should address the studentsí competence in carrying out key operations, and should provide enhanced opportunities for active learning and promote cross-curricular links. Furthermore, the modules chosen should reflect the needs of the students and the expertise and interests of the members of the department.
Individual teacher planning is, in nearly all cases, very good. Resources prepared in advance of the lessons were integrated very effectively into lesson delivery. The resources were relevant and appropriate to the needs of the students and facilitated a range of teaching and learning styles.† A striking feature of the most effective planning was the degree to which reliance on the textbook as the primary teaching tool was reduced and the flexibility this afforded the teacher in responding to any issues that arose during the lessons.
Management is very supportive of teachers attending relevant continuing professional development courses and members of the mathematics department have attended an impressive number of subject-specific courses in the last number of years. In addition, the mathematics support service has delivered on-site training to the entire mathematics department in the recent past.† Newly appointed teachers benefit from the schoolís induction programme and are fully briefed on the schoolís policies and procedures.
The lessons observed during the inspection were, in almost all cases, very well planned. The material covered was appropriate to the curriculum and was in keeping with the subject department plan for Mathematics. The lessons had a very good structure and proceeded at a suitable pace. In one instance, the very good practice of the teacher explicitly sharing the lessonís objectives with the students at the outset of the lesson was in evidence. This very good practice should be adopted as standard practice by all of the members of the department.
A variety of teaching methods, including ICT integration, group work, the use of the overhead projector and teacher exposition was in evidence during the inspection. These teaching methods, allied to enthusiastic lesson delivery, allowed the teachers to impart the subject matter effectively and to facilitate lessons that were enjoyable, challenging and productive. The teachers were very knowledgeable. In nearly every case, they provided the students with reliable procedures for solving problems and with effective strategies to identify the most appropriate method to use in carrying out core mathematical operations. In addition, they presented the students with unambiguous explanations of key concepts and gave comprehensive and accurate answers in response to studentsí questions.
Group work, supported by excellent resources and innovative teaching, was used to very good effect in a lesson where students were investigating simple inequalities. The students were arranged in groups of five and each group was given a number line together with a set of small discs, washers and strips of paper. The students were asked to indicate on the number line the region represented by given inequalities and were expected to defend their reasoning. Students were selected to design problems to be attempted by a neighbouring group and to give feedback on the outcomes.† The students also had to represent the solutions using appropriate symbols on the marker board and to explain their solutions to the class. The lesson, facilitated by occasional and effective teacher interventions, provided the students with a range of learning opportunities and was a very impressive example of how resources can be successfully integrated into lesson delivery.
ICT was very effectively integrated into a lesson where students were revising set theory.† Presentation software was used to review the key points and the use of animation ensured that the material was presented in a visually simulating fashion. The use of ICT also allowed the teacher to move around the room assisting individuals and to replay the content as often as was required to ensure that each student understood the material in hand. Very good teacher questioning, which encouraged the students to make suggestions and to engage in higher-order thinking, further enhanced the studentsí experience of the lesson and served to create an environment that was challenging and rewarding.
Plotting the quadratic function featured in a number of the lessons observed during the inspection. The most effective approach to teaching the topic was seen where the overhead projector (OHP), supported by a graduated worksheet, was incorporated in the delivery of the lesson. The students worked collaboratively to determine the points to be plotted. An acetate sheet, containing the co-ordinate axes was placed on the OHP and was used to illustrate how the graph should be drawn.† The use of the OHP meant that each student could see the location of each point on the curve and could gain an appreciation of the best approach to adopt in plotting the graph. Furthermore, the group could engage in discussions as to how the outcome matched their expectations.† This approach was in stark contrast to the alternatives, which involved the teacher describing from the textbook the approach the students should adopt and then allowing them to work individually in plotting the graphs. In these instances the students had no real understanding of the purpose of the exercise and had little appreciation of the significance of the outcomes.
The very good practice evident in lesson delivery and detailed above reflects very favourably on the enthusiasm and commitment of the members of the department. In order to build on the existing practice, it is recommended that the innovative teaching methods currently being employed in the majority of cases be adopted as standard across the department and that the growing expertise in the department be harnessed to facilitate this process.
Classroom management is very good. It was evident during the inspection that there is very good rapport between the teachers and students. Student engagement with the lessons was very good and there were some excellent examples of differentiated teaching. In such instances the teacher took great care to ensure that all of the students were productively involved in the lesson and that they understood clearly the material being covered.† The teachers and students had adorned many of the classrooms with curricular materials and subject-specific posters. A0-size posters of the key pages from the Mathematics Tables were particularly effective examples of this. These were frequently referred to during lessons and served to reduce the time spent in using the tables when the need arose.
The quality of student learning is very good. They successfully carried out the various tasks assigned during the lessons and displayed a very good knowledge of the material being covered. The quality of the studentsí homework copies and their performance in class tests is most satisfactory. Uptake rates at higher level and student attainment in the certificate examinations offer further evidence of the high quality of student learning.†
Assessment practices in Mathematics are very good. Homework is regularly assigned and corrected. The studentsí homework copies are monitored appropriately and comprehensive verbal and written feedback is provided in a timely fashion. Leaving Certificate higher-level students receive particularly good support in designing, implementing and monitoring their revision programmes. Each student is provided with an individualised revision schedule and receives suggested solutions to every revision exercise they submit.† This is very good practice.
Students in non-examination classes are continually assessed in the first term and sit formal examinations just prior to the summer holidays. Common papers corrected with reference to agreed marking schemes are set where appropriate in all formal examinations and care is taken to ensure that the papers follow the format and standard of the certificate examinations. Consideration should be given to extending the process of continuous assessment for non-examination classes into the second term.
Students in examination classes sit mock examinations early in the second term. In order to enhance the quality of feedback provided to the students, to identify common problems and to inform planning, the members of the department correct the papers themselves. This is very good practice as it ensures that systemic weaknesses can be targeted in the short term to meet the needs of the examination students and that steps to address them in the long term can also be identified and included in the subject department plan for Mathematics. The results of these assessments should be collated and form the basis of a report that would issue to parents when the results of the mock examinations are being issued.
Reports issue to parents at Christmas, following the mock examinations and following the formal examinations in the summer.
Practices in relation to monitoring student attendance and attainment in class and 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 teachersí diaries. The teachersí diaries are also very effectively used to record any difficulties encountered by students.
Ongoing communication with parents occurs through the use of the student journal and telephone contact, and formal letters are also issued if the need arises. Each class group has one parent-teacher meeting per year. Other, less formal meetings can also be arranged if required.
The following are the main strengths identified in the evaluation:
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, October 2009