An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Árdscoil na mBráithre
Clonmel, County Tipperary
Roll number: 65320J
Date of inspection: 1 October 2007
Date of issue of report: 21 February 2008
the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Árdscoil na mBráithre. 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. The board of management was given the opportunity to comment in writing on the findings and recommendations of the report, and the response of the board will be found in the appendix to this report.
The time allocated to Mathematics in Árdscoil na mBráithre is in line with national norms at junior cycle. Each junior cycle grouping has two years with four periods per week and one year with five periods per week, over the three years. All lesson periods are of forty minutes duration. The year in which the five periods occur rotates each year. Transition Year (TY) which is optional for students, is limited to one class group each year. The TY class has three class periods of Mathematics per week. Provision at Leaving Certificate level is good and classes have six periods per week in both fifth year and sixth year.
First year classes are arranged on a mixed-ability basis and there is a common assessment for all students at the end of their first year. In second and third year, two bands of classes are formed. The classes within each band are timetabled concurrently. This allows students to study the subject at higher level for as long as possible and still retain the option of moving to ordinary level. All fifth- and sixth-year classes are timetabled concurrently. At present, each year has one higher level class. In fifth year, one smaller class grouping has been created to cater for students identified as finding the subject difficult. Students are allocated to the other classes on a mixed-ability basis.
The school is commended for its structures to identify and support incoming students who may have difficulties with Mathematics. Incoming students who may find the subject particularly challenging are identified through a pre-entry assessment, contact with the local feeder primary schools and ongoing teacher monitoring during first year. Support is provided through a variety of mechanisms, including individual and small group withdrawal from classes, other than mathematics class, for one or two periods per week. In one instance, in-class support is provided by another teacher. In all instances the teacher providing the support is one of the mathematics team. Support in Mathematics is also provided to newcomer students where their command of English prevents them from benefiting fully from the mathematics classes. It is reported that there is a high level of informal co-operation between the support teachers and the class teacher and this is commended. This support is continued throughout junior cycle as students’ needs dictate.
Teachers are assigned to classes and levels on a rotating basis by school management. It is policy and practice within the school for teachers to remain with the same class groups from second to third year and from fifth to sixth year, where possible, thus maintaining high levels of continuity.
Teachers are facilitated to attend continuous professional development courses and a number of teachers have availed of courses, during and outside of school time, offered this year and in previous years. Furthermore, some teachers are or have been members of their subject association and the cost of membership is funded by management. Each year the mathematics department submits a budget for the following year, to the board of management, for approval and requests for additional funding during the year are considered.
The mathematics department is co-ordinated, on a voluntary basis, by a long-standing teacher. It is recommended that the role of co-ordinator be rotated among members of the team, perhaps on an annual basis. This system would allow each member of the team to gain a deeper understanding of the issues involved in the workings of their subject department. The mathematics team is facilitated to meet formally twice per year. Time is made available for year-group meetings during the year, if requested, and other informal meetings also take place. The good practice of recording minutes of formal meetings has begun.
School development planning is ongoing. In addition to the ongoing review and updating of the school plan, subject-specific planning is also progressing. Current work involves developing mathematics-specific guidelines in line with the school’s homework policy. The mathematics team members have collaborated on a long-term plan for Mathematics that includes a list of topics for each year grouping, classroom teaching activities and assessment methodologies. A short TY plan lists areas of Mathematics to be completed during the year. Work to date on planning is commendable. However, in the interest of furthering this good practice, it is recommended that the mathematics team review and expanded all programmes of work to include not only lists of topics, but also key skills and key terms for students to know and understand within the topics. Resources, to assist students in acquiring such key skills, should then be identified and obtained by the Mathematics department. The website http://maths.slss.ie and the publications Junior Certificate Mathematics Guidelines for Teachers and Calculators: Guidelines for Post Primary Schools could make a significant contribution in this area.
Most teachers made individual planning and preparation documentation available during the inspection. These included detailed individual long-term and weekly work plans, assessment and attendance records, lists of daily work completed, worksheets, handouts, class assessment material and marking schemes and a set of differentiated mathematics questions for a planned table quiz to be given to a mixed-ability TY group.
Currently the information and communication technology (ICT) resources available within the school include the geometry software package The Geometer’s Sketchpad, which is installed on the network of computers in the school’s computer room. A broadband connection is available in each classroom. A number of computers are available in the staff room for teachers who wish to use ICT in the preparation of classroom materials. To ensure that these resources are utilised to a greater extent, it is recommended that the integration of ICT, to support teaching and learning, should be included in all year-group plans.
In all classes visited, lesson content was appropriate and teachers were prepared for their teaching. Lessons began with the correction of homework. There was mutual respect evident between students and teachers and classroom management was good. Students were attentive and engaged in the work at hand. In one instance, students were asked to create their own problems based on the topic being discussed and they responded with eagerness and enthusiasm.
In the classes visited, the students maintained a notebook into which they copied key examples taken from the blackboard, as well as notes dictated or written by the teacher and important points to remember in each topic. This is good practice, as the work observed in students’ copybooks was clear, well presented and of a high standard. It is suggested that this practice could be enhanced if occasionally students were encouraged to discuss and agree what should go into the notebooks. This would stimulate mathematical discussion, problem analysis and create a focus on problem solving in the classroom.
Teachers had appropriately high expectations of their students and students responded in line with these. Other examples of good practice noted in mathematics teaching included: affirming students’ efforts, appropriate use of mathematical terminology, providing individual attention to students and the clear use of board work as a template for students’ own work.
Trigonometry, algebra, co-ordinate geometry and arithmetic were among the topics studied in lessons observed. Lessons were presented in a confident and coherent manner. A good pace was maintained in all lessons. Best practice was observed when the mathematical concepts underlying the procedures being taught were clearly and explicitly stated. In this way, students’ focus and interest was maintained. This practice should be extended to all lessons.
In all cases teaching was traditional in style. Textbooks, the blackboard and worksheets were the main resources used during lessons. This involved teacher demonstrations to the full class group and the students then working alone on assigned tasks while the teacher assisted individuals. To cater for students’ different preferred learning styles, it is recommended that a broader range of teaching methodologies be investigated and combined with the current teaching style. Some examples could include pair work, group work, investigation, consolidation activities, the use of concrete materials, discussion, quiz activities, ICT and student project work. The classrooms visited had no displays of student work or of mathematical posters which can enhance the visual learning environment and remind students of key mathematical concepts or formulae. It is recommended that such a display be given consideration.
Interaction between teachers and students generally took the form of brief answers by the students to ‘fill in’ type questions from the teachers. Questioning focused mostly on finding the next steps in the solution to a problem. In some instances, teachers posed more probing questions where students had to explain and justify their answers or create their own questions. It is suggested that the good practice of having such a range of questioning strategies be extended to all classes.
In interactions with the inspector, it was evident that the majority of students had a clear understanding of the work in which they were involved and were able to discuss solutions to questions posed to them in appropriate mathematical language. Appropriate student progress was also evident from an examination of the written work being done by students, during the lessons inspected. The quality of this work indicated that they had understood procedures taught during the lessons and were able to apply them to problems set by their teachers.
Homework has an important role in the learning process and was assigned in all lessons observed. As previously stated, the mathematics team have prepared guidelines on homework in line with the school’s homework policy. These guidelines relate to frequency, amount and monitoring.
Student progress is assessed by class questioning, the monitoring of homework and class work, regular topic tests and end of term examinations. Teachers keep records of student attendance and test results. It is good practice that there is a common assessment for all students at the end of first year. Thereafter there is some coordination within levels up to Junior Certificate but not generally after that. It is recommended that the team move towards more use of common assessments within levels for all year groups. Communication with parents is maintained through a yearly parent teacher meeting for each year group. Reports on students’ progress are issued twice each year following formal assessments.
An examination of a sample of mathematics copybooks showed work that was appropriate, relevant and well presented. There was evidence of teacher monitoring with, in one instance, comments being written to inform student learning. This is in line with the principles of ‘assessment for learning’ and is commended.
Students participate in a range of extra-curricular activities pertaining to Mathematics. These activities include: the Junior Maths competition, the Team Maths competition and attendance by the TY class at ‘Maths Week’ activities.
The following are the main strengths identified in the evaluation:
· The time allocated to Mathematics is in line with national norms at junior cycle. Provision at Leaving Certificate level is good.
· The school is commended for its structures to identify and support incoming students who may have difficulties with Mathematics. Students are facilitated and encouraged to follow the highest level possible for as long as possible.
· There is a high level of continuity in the allocation of teachers to classes.
· Teachers are facilitated to attend continuous professional development courses.
· The mathematics department has an annual budget.
· The mathematics department has a designated co-ordinator.
· School development planning is ongoing. The mathematics team members have collaborated to produce a long-term mathematics plan.
· In all classes visited, lesson content was appropriate and teachers were prepared for their teaching.
· Work observed in students’ copybooks was clear, well presented and of a high standard.
· Teachers keep records of student attendance and test results.
· There is a common assessment for all students at the end of first year.
As a means of building on these strengths and to address areas for development, the following key recommendations are made:
· It is recommended that the role of co-ordinator be rotated among members of the mathematics team.
· It is recommended that the mathematics team review and expanded the programmes of work to include key skills and key terms for students to know and understand.
· It is recommended that the team move towards more use of common assessments within levels for all year groups.
· It is recommended that the integration of ICT should be included within all year group plans.
· It is recommended that a broader range of teaching methodologies be investigated and combined with current teaching styles.
Post-evaluation meetings were held with the teachers of Mathematics, except one who was absent on the day of the inspection, and with the principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.
School Response to the Report
Submitted by the Board of Management
Inspection Report School Response Form
Area 1 Observations on the content of the Inspection Report
The Board of Management of Ardscoil na mBráithre welcome the very positive comments regarding the teaching of mathematics within the school. The identification of good teaching practice and a caring environment of mutual respect within the school concurs with the views of the Board of Management.
The Board would also make the following observations:
· While all classrooms have access to Broadband the integration of ICT in mathematics classes is dependent on additional funding from the DES so that all staff would have access to individual laptops and software. It is also necessary to have ongoing technical support.
· Teacher based classrooms are not an option within Ardscoil na mBráithre at present due to shortage of classroom space. As a result it is very difficult to display student work or mathematical posters.
Area 2 Follow-up actions planned or undertaken since the completion of the inspection activity to implement the findings and recommendations of the inspection
The Board and staff will consider the recommendations and areas for development in due course.