An Roinn Oideachais agus Eolaíochta

Department of Education and Science



Subject Inspection of Mathematics




Good Counsel College

New Ross, County Wexford

Roll number: 63610I



Date of inspection: 31 March 2006

Date of issue of report: 15 December 2006



Report on the Quality of Learning and Teaching in Mathematics

Subject Provision and Whole School Support

Planning and Preparation

Teaching and Learning

Assessment and Achievement

Summary of Main Findings and Recommendations


Report on the Quality of Learning and Teaching in Mathematics



This Subject Inspection report


This report has been written following a subject inspection in Good Counsel College, 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 one day 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, deputy principal and subject teachers.


Subject Provision and Whole School Support


There are seven teachers in the Mathematics department at Good Counsel College. In addition, there are four teachers providing learning support in Mathematics in the school. At junior cycle, teachers have an opportunity to rotate programmes and levels. In recent years this custom has also been introduced into the senior cycle. This is good practice as it develops the expertise within the subject department. In general, teachers retain the same class groupings through each cycle.


There are nine class periods, five days per week. Each class is forty minutes in duration. This results in good time allocation to Mathematics.  In general classes are well distributed throughout the day. However not all classes have daily lessons in Mathematics. It is recommended that the timetabling of Mathematics be reviewed to include Mathematics each day, therefore promoting continuity in learning.


Since September 2005 the school has introduced mixed-ability class groups in first year. The school reported that from second year onwards, excluding Transition Year, classes are banded. However, this is not the case for all classes as both higher and ordinary level are taught in one class grouping. Consideration is currently being given to the setting of classes for the next school year. It is recommended that co-timetabling of Mathematics from second year be considered, with a view to offering all levels simultaneously.


Learning support is provided on a withdrawal basis.  Small groups are formed.  This is good practice as students have an opportunity to receive more individual tuition.  Furthermore, all learning support students are strongly encouraged to follow the ordinary level programme with foundation level on offer in exceptional circumstances.


There is no specific budget for Mathematics. Nonetheless, any requests for equipment are met. Recent purchases include a class set of calculators, geometry sets and geometry sketchpad. It is recommended that teachers collaborate to identify and develop a prioritised list of resources for the teaching and learning of Mathematics, based on their teaching programmes. They should make the necessary arrangements for their acquisition. Furthermore, all resources should be retained in a central location for use in the teaching and learning of Mathematics.


Teachers are facilitated to attend inservice, and have attended the revised Junior Certificate syllabus inservice.  Since then there has been an in-school follow up by a member of the Junior Certificate Mathematics Support Service.  The most recent inservice in the area of geometry has also been attended.


The school is currently involved in the National Induction Pilot Project in conjunction with University College Dublin. As part of this project a member of the school staff acts as mentor for a newly qualified teacher. The newly qualified teachers and mentors observe each others teaching with a view to improving practice. Such support by the school for newly qualified teachers is to be commended.


Planning and Preparation


Management is to be commended for facilitating subject meetings for Mathematics during school staff meetings and/or during school development planning meetings. Informal meetings take place on a needs basis. There is no coordinator of Mathematics and currently no minutes of meetings are retained. It is therefore recommended that a Mathematics coordinator be appointed and this position should be rotated among the Mathematics team. Furthermore, agendas for subject department meetings should be prepared, decisions on issues discussed at meetings recorded and minutes of meetings retained.


The Mathematics department has developed a three-page document outlining the long-term objectives of the department and cross-curricular links. However, there are a number of omissions from this document.   There are no references to curriculum content, methodologies or learning outcomes. It is therefore recommended in the context of school development planning that the Mathematics department should develop a long-term plan for Mathematics. This plan should outline the aims, objectives and the sections of the syllabus at junior and senior cycle, and the advised areas of study under each of these sections. It should also include a list of varied methodologies and a range of resources and learning outcomes to be achieved. General organisation details of the department and the system of allocating students to Mathematics classes and levels should also be included in the plan. The development of a common plan for Mathematics will give teachers an opportunity to identify and share good practice. In this context the web site of the SDPI has useful resource material that may assist in this regard. 


The current Transition Year Mathematics programme is based on Leaving Certificate material. The Transition Year Mathematics module should be used to give students the opportunity to learn Mathematics in different situations. It is therefore recommended that the Mathematics team collaborate to review the Transition Year Mathematics programme to ensure compliance with Circular M1/00.  To this end a useful support is available at where teachers can access resources and newsletters, which outline teaching and learning strategies, interdisciplinary links and curriculum ideas pertaining to Transition Year Mathematics.


Management is to be commended for providing the “Curriculum Content Planning” document to all staff at the start of the school year. This planning document template allows teachers to divide their programme of work into term plans. Some teachers have used this template for their plans while others have developed good short-term plans of work for Mathematics with prior preparation of supplementary material and handouts for the lessons. In general teachers develop resources independently and consideration should be given to sharing of such resources


Teaching and Learning


Topics such as co-ordinate geometry, metric systems, geometry, and calculus featured in lessons observed. Some lessons opened with the correction of homework from the previous day and with the continuation of topics. Classes were conducted in a warm friendly atmosphere, conducive to a good learning environment. In general lessons were presented in a confident and coherent manner. In most cases classes were well structured and lessons were paced at a level appropriate to the needs and ability of each class grouping. Such lessons allowed for a clear and focused lesson to take place.


Terminology used during lessons was good and appropriate to the level and abilities of each class grouping. When necessary, students were corrected and reminded of appropriate use of terminology.


The predominant methodology used in lessons was traditional whole-class teaching. This is a combination of teachers demonstrating to the class while students worked independently on an assignment and the teacher circulating to provide individual attention. To a lesser extent students were given the opportunity to learn through investigation.  This is good practice and should be encouraged in all classes. Where teacher-talk dominated the lesson, this had a negative effect and students became passive for some time. It is recommended that students experience a variety of appropriate methodologies, which should include for example group work and quiz activities as outlined in the Junior Certificate Mathematics Guidelines for Teachers. In this way, all students are sure to be involved in the class, to take personal responsibility for their learning, to think independently and to become more involved in the learning process. 


Generally, interactions between teachers and students took the form of recall type questions or brief answers to lower-order questions. Oral exchanges focused mostly on steps in the solution to a problem. However, there were some very good examples where teachers skilfully varied their questioning to include a balance of higher and lower-order questioning. One such example of this was when questioning built on students’ answers, thus probing and extending the students’ understanding. This encouraged them to explain and justify their thinking and methods. In other lessons this generated discussion about the topic and was an excellent example of students engaging fully with the topic in hand. Such good practice is to be commended and should be extended to all lessons. It is recommended that a more varied range of questioning strategies should be employed in all lessons.


In most lessons the textbook was used appropriately as a source of reference.  This was  supplemented by graded worksheets which helped to support learning activities.  Such preparation ensured the smooth transition in the learning experience. There were instances where the appropriate use of other resources would have allowed for greater student participation. For example the use of an overhead projector to illustrate a variety of examples would help to develop the concepts being engaged in during the lesson. It is therefore recommended that consideration be given to using the OHP and other appropriate resources through lessons.


In most lessons students demonstrated a clear understanding of concepts engaged with during the lesson.  Generally, students answered questions in a confident manner, justified solutions to questions posed to them and demonstrated an appropriate knowledge of the topic. Students were capable of using terminology appropriate to the topic.


Some mathematical posters were displayed in classes. It is important to surround students with a print-rich environment which displays students’ work and other mathematical materials. It is therefore recommended that mathematical displays be designed or sourced to provide a stimulating environment for students.


Assessment and Achievement


Ongoing assessment takes place through class questioning, at the end of a topic and through homework. Formal examinations take place for non-examination years at Christmas and again at the summer. Third and sixth-year students sit Christmas and ‘mock’ examinations in the second term.


The Mathematics department currently operates common assessments for first-year students. The development of a long term plan for the department should further facilitate the extension of common assessments for subsequent year groupings


Communication between parents and the college is maintained in a number of ways. The college issues reports following formal examinations. Letters are regularly sent to parents informing them of upcoming events in the school. Parent-teacher meetings are convened for all year groups. The student school journal has a dual purpose. Students use it to record homework and parents use it as a means of communication to explain a student’s non-attendance at school. However, during the course of the inspection, the success of the journal was questionable. While there was evidence to suggest that parents are using it to record absences, not all students recorded their homework in the journal in a systematic manner. It is therefore recommended that a review of the effectiveness of the student journal be undertaken.


Homework assigned was appropriate in terms of quantity and relevance to topics and material covered in lessons. The monitoring of Mathematics copies varied. There were some very good examples of students’ copies that included commendations and suggested areas for improvements. This good practice should be extended to all classes. Furthermore, students should also be encouraged to monitor and amend their own work.


In general teachers maintain good records of student assessment and on occasion extensive records were maintained of student homework and revision work. Such practice is to be commended. The monitoring of attendance was generally good but in some situations a daily record of attendance for each class needs to be taken.


Students are encouraged to follow either higher level or ordinary level in Mathematics and if necessary foundation level is provided.  Teachers are commended for the good practice that has developed of keeping the number of students doing foundation level to a minimum. 


Mathematics students have opportunities to participate in co-curricular activities. For example students have competed in TeamMath organised by the Irish Mathematics Teachers Association and have been invited to compete in Mathematics Olympiads. Additionally, a number of students have participated in Scholastic Aptitude Tests (SAT) organised by the Irish Centre for Talented Youth (CTYI). Participation in such events is to be commended as it provides students with an opportunity to experience Mathematics and to develop their interest and skills in Mathematics while experiencing the subject in a different learning environment.




Summary of Main Findings and Recommendations


The following are the main strengths and areas for development identified in the evaluation:


§        There is good time provision for Mathematics in the school.

§        Teachers are given an opportunity to attend inservice in the area of Mathematics.

§        Learning support for Mathematics is well organised and classes run parallel to Mathematics classes.

§        Management facilitates staff to plan by providing formal planning time.

§        There were examples of some very good record keeping of student assessments, monitoring of copies and feedback to students.

§        All classes were conducted in an atmosphere of mutual respect.

§        Students participate in co-curricular activities in Mathematics.


As a means of building on these strengths and to address areas for development, the following recommendations are made:


§        The Mathematics department should collaborate to develop a long-term plan for Mathematics. A coordinator of Mathematics should be appointed and this position should be rotated. Agendas should be established for subject department meetings with minutes of meetings formally recorded.

§        The Transition Year Mathematics programme should be reviewed to ensure compliance with Circular M1/00.

§        The timetabling of Mathematics should be reviewed to include daily contact for all class groupings with Mathematics and consideration given to the co-timetabling of Mathematics from second year onwards.

§        A variety of appropriate methodologies and a varied range of questioning strategies should be employed in all lessons.

§        A review of the effectiveness of the student journal should be undertaken.

§        Consideration should be given to using the OHP and other appropriate resources in lessons.


Post-evaluation meetings were held with the principal and with the teachers of Mathematics at the conclusion of the evaluation at which the draft findings and recommendations of the evaluation were presented and discussed.