An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Stillorgan Road, County Dublin
Roll number: 60042F
Date of inspection: 25 September 2008
REPORT ON THE QUALITY OF LEARNING AND TEACHING IN MATHEMATICS
This report has been written following a subject inspection in Coláiste Íosagáin, 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.
Students are assigned to mixed-ability classes in first year and follow an agreed common course for the first two years. Classes are timetabled concurrently from third year onwards. At the beginning of third year, an extra class group is created in the band to cater for the small group of students wishing to follow the ordinary level syllabus. This is good practice, in the context of the school, as it encourages students to follow the highest level possible for as long as possible. An extra class in the band at fifth year allows Mathematics to be taught to smaller groups. The timetabling provision for Mathematics is good. Almost all junior cycle and fifth-year classes have five periods of forty minutes duration each week. The third year ordinary level class has four periods each week. In sixth year, all classes have six periods of Mathematics each week. The Transition Year (TY) classes have three periods of Mathematics each week. In addition to this, classes are generally spread evenly throughout the school day and the school week. In one instance, a second year class has the majority of its lessons in the afternoon. This should be avoided, if possible, in future timetabling.
In the interests of maintaining high levels of continuity, the good practice of teachers remaining with the same class groups from first year to third year and from fifth year to sixth year, where possible, was noted. There is full rotation within levels in the junior cycle and at senior cycle it is planned that in coming years more members of the mathematics team will teach the subject to higher level. This is a commendable development.
In the third-year classes, as well as for the senior years, the school operates the good practice of having mixed ability within levels. Mixed-ability teaching within levels allows for varying rates of student development and acknowledges the connection between levels of teacher expectation and levels of student achievement.
Classrooms are student based and to date nine rooms have been equipped with interactive whiteboards. In some instances teachers have begun to integrate the use of information and communication technology (ICT) into their teaching. Formal training will continue to be provided to all staff on their use. It is suggested that the mathematics team cooperate on the sharing of created and acquired resources on an ongoing basis. While there is no specific budget for Mathematics reasonable requests for purchase of resources are granted.
Teacher attendance at continuous professional development courses is facilitated and it is reported that in the past the board of management of the school has supported teachers involved in further study.
Student involvement in a range of co-curricular activities pertaining to Mathematics is promoted within the school. These activities include the Junior Mathematics competition, the Team Maths competition, the Prism competition and Maths week activities. This good practice allows students to have an interest in Mathematics outside of the classroom and raises the profile of the subject within the school. This practice also gives students the opportunity to enjoy Mathematics and apply it to problem solving in a new and non-formal way. All those involved in these activities are commended.
Students identified as finding Mathematics particularly challenging are supported in a number of ways. In first, second and fifth years, where necessary, a small number of students are withdrawn from a lesson, other than their mathematics lessons for one period per week of extra tuition. This extra tuition is provided by a member of the mathematics team. The extra class group in third year and fifth year which allows for the creation of smaller class groups, and the extra period each week in sixth year, also contribute to the support of students.
An analysis of students’ performance in the State Examinations over the last three years indicates that the uptake and achievement rates at higher level are good at both Junior and Leaving Certificate level. It is noted that discussion and review of uptake rates, as well as results, are conducted within the school. This is good practice and should be used as a regular and natural part of the planning activities of the mathematics department in particular having regard to issues raised during the inspection.
Students wishing to study Applied Mathematics are accommodated by the provision of after school classes in conjunction with other schools in the locality.
The mathematics department in the school currently consists of seven members. The task of co-ordinating the team is undertaken by the convenor of the department. One member of the team undertakes this role on a voluntary basis and the position rotates every two years. There is a strong sense of collaboration, co-operation, openness and collegiality within the team. This is supported by the practice of rotation of levels within junior cycle, the following of similar programmes of work and having common formal assessments at first and second year and within levels thereafter.
Formal planning and review meetings are scheduled around staff meeting and school planning days, and occur about three times a year. It is reported that ongoing informal contact is also maintained. The good practice of record keeping at formal meetings has begun and these records show evidence of ongoing collaboration and review within the team.
There is a comprehensive written plan for Mathematics. The department plan includes overall aims and objectives for mathematics education within the school for junior and senior cycle. It also includes organisational details, including timetables, of classes and teachers. The plan contains an outline programme of work for each year group by term, reference to a variety of methodologies, and a description of provision for students with special educational needs, which is in line with good practice. It also includes procedures for homework, assessment, record keeping and reporting.
There is a Transition Year plan for the school. TY classes have three mathematics lessons each week. The current plan envisages that two lessons per week would be used for the introduction of elements of the Leaving Certificate programme. The remaining period each week would be devoted to other topics such as puzzles, student survey and project work in the area of Mathematics. It is recommended that the programme for TY Mathematics be reviewed to ensure that the good practices and teaching approaches seen in the previously mentioned lesson are applied to all topics and learning during the year. The team should explore the possibility of “doing maths differently” through teaching modules to different groups and accessing resources and materials available on the Maths section of the website www.slss.ie.
All teachers made individual planning materials available for inspection. Generally, the department plan had been customised into monthly, weekly and in some cases daily work to be covered by class groups. This good practice allowed for individual flexibility to respond to the needs of students while still maintaining the coverage required by the overall plan.
Lessons observed were purposeful and syllabus content was appropriate to the ability levels of the students. Topics were presented in a confident, clear and coherent manner, and preparation for teaching was evident. Effective use was made of time to ensure that a good pace to all lessons was maintained. While classroom activities were generally of a passive nature, students were attentive to their work. Best practice was observed when the objectives for the lessons were explicitly shared with the students at an appropriate point of the lesson and reviewed at the end of the lesson. This practice should be extended to all lessons.
The language of instruction and communication, in all lessons visited, was Irish. The use of Irish mathematical terminology by teachers and students was a natural part of the lesson. Students’ progress and efforts were affirmed in an atmosphere that created confidence and encouraged students’ use of such appropriate mathematical language.
Lessons generally began with the correction of homework at the board by the teacher. Teaching was then predominantly conducted through the presentation of work at the board followed by the setting of similar problems from the textbook for individual students to practice what they had observed. Teachers were aware of and attentive to the needs of individual students and they devoted class time to working with students who were experiencing difficulty. Within this traditional style, teaching was effective and students were learning.
To add to this general, teacher-directed, whole-class teaching style, it is recommended that a wider range of teaching methodologies be explored and developed with a view to actively engaging students more in their own learning. The sharing of the experiences of the members of the mathematics team along with the courses and website of the Mathematics Support Service (MSS) and the publication Junior Certificate Mathematics Guidelines for Teachers could aid in this endeavour. Some possibilities might be the inclusion of student generated questions, pair work, group work, investigation, practical work, discussion, consolidation activities, quiz activities and greater use of ICT. The inclusion of a range of methodologies takes advantage of students’ different preferred learning styles.
The main exchanges between teachers and students took the form of brief answers to questions posed to named students or to the class group by the teacher. Students also asked questions, reflecting their engagement with learning in the lessons. Teacher questions were generally of the “next step” or “fill in” type. In addition, there were also some good examples of teachers posing more challenging questions to encourage students to engage with new material and to create links to previous learning. The use of such questioning to appropriately challenge students, assist them in developing their skills in the area of problem analysis, mathematical thinking and mathematical communication is good.
In interactions with the inspector, the students displayed clear mathematical knowledge and could make connections to previously learned topics. They were able to demonstrate knowledge and understanding of the concepts they had learned and were confidently able to apply them to problems. A further feature of these discussions was the competence of the students in the Irish language and their ability to appropriately use the Irish version of mathematics terminology. This was also noticeable in all classroom communications. Students’ written work also indicated a high standard of learning.
Classroom management was effective and discipline was sensitively maintained. The teachers had appropriately high expectations of the students commensurate with their abilities. There was a sense of mutual respect between teachers and students, creating an atmosphere that was conducive to learning.
The classrooms in Coláiste Íosagáin are student based. In one instance, to enhance the visual impact of a room, the good practice of having teacher prepared posters and a number line on display was noted. During the lesson, to highlight a key point for students to remember, a further item was added to the display. In other instances the classroom environment was not adequately stimulating and the opportunity for displays of student and teacher work had not been availed of. It is recommended that a visually stimulating mathematical environment would be created within each classroom.
An agreed subject department homework policy is implemented by the team. Appropriate homework was assigned in all lessons thus providing students with an opportunity to develop and consolidate mathematical concepts engaged with during the lesson. Students’ work was monitored by the teachers. Homework copies were well maintained and work was well presented.
The school maintains good communication with parents. Two school reports are issued for each student during the year. Assessment is carried out on an ongoing basis through monitoring of class work, questioning in class and a written examination following the completion of each topic. The cumulative results of these tests, taken during the first term, form the basis of a report to parents, of all students, at the end of that term. Examination years sit their ‘mock’ exams during the second term. Results of these tests are communicated to parents in a second report. Formal assessment of non-examination students takes place at the end of the school year and
parents receive an assessment of students’ progress at that time. In addition a parent-teacher meeting for each year group is held annually. The student diary is also used as a means of communication between the school and home and vice-versa.
The team engage in good practices in the area of co-ordination associated with the testing of students. All first-year and second-year students complete the same end-of-term and end-of-year tests, and term tests within levels in all other year groups are common. Flexibility is maintained in relation to end of topic tests and in some instances common testing occurs. Common examinations enable comparisons to be made across the whole year group. They can also serve a useful purpose in informing students’ choice, or in providing advice to students in relation to levels.
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 at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
Published October 2009