An Roinn Oideachais agus Eolaíochta

Department of Education and Science

 

Subject Inspection of Mathematics

REPORT

 

Vocational School Muinebheag

Co Carlow

Roll number: 70430U

 

Date of inspection: 4 April 2006

Date of issue of report: 26 October 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 Vocational School Muinebheag. 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.  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.

 

 

Subject Provision and Whole School Support

 

Opened in 1963 Muinebheag Vocational School offers the Junior Certificate, Leaving Certificate, and Leaving Certificate Vocational Programme to 146 second-level students and offers Post Leaving Certificate Courses to 134 students. Prospective second-level students and their parents are well informed about the programmes and subjects that the school offers. Parents of second-level students are invited to an information evening while incoming first-year students attend a series of induction events.

 

The school operates a nine-lesson day, each lesson being of thirty-five minutes duration. This results in a significant shortfall in the minimum instruction time for students. Management is aware that the school is not in compliance with Circular M29/95, Time in School and has indicated that it will address this matter. It is therefore recommended that the school address this compliance issue as a matter of urgency.

 

Five teachers teach Mathematics in the school, one of whom is the numeracy-support teacher. Generally Mathematics teachers rotate the teaching of levels. This is good practice as it ensures that the expertise within the department is shared. Commendable practice has developed whereby teachers generally retain a class from first year through to third year and again from fourth year through to fifth year.

 

Prior to entry to the school students sit an assessment examination and in first year are arranged into mixed-ability classes. In general, two Mathematics class groupings are formed in each year. The allocation of teachers to Mathematics is good and this leads to small class sizes. Management is to be commended for such allocation. Following the results of the first-year summer examination students choose their level for the Junior Certificate. Generally, one class group of ordinary-level students and one class group of foundation-level students is formed in each year. However, those who choose to follow higher level at junior cycle are facilitated. Even though Mathematics classes are concurrently timetabled there is little movement between levels and classes.

 

Time allocated to Mathematics is good. In general, junior cycle classes are allocated five class periods per week with senior cycle classes having six class periods of Mathematics per week. Extra classes are allocated to some class groupings. While acknowledging that all efforts are made to provide students with many opportunities to have extra Mathematics tuition, some difficulties have arisen with the timetabling of Mathematics. For example, the allocation of two teachers to some classes is not good practice as it does not promote continuity of the learning experience for the student.  Additionally, it is important that students engage with Mathematics regularly to increase numeracy skills. However a number of class groupings do not have Mathematics timetabled daily. It is therefore recommended that a review of the timetabling of Mathematics be undertaken to address these issues.

 

Students in receipt of learning support are identified based on the incoming assessment test for first years and from information provided by the primary schools and from parents. The school offers numeracy support to students in a variety of ways. For example, team teaching takes place in some classes or students are withdrawn from classes for extra support. It is recommended that a review of the provision of numeracy support be undertaken. Best practice would suggest that the concurrent timetabling of numeracy-support classes with Mathematics classes provides the most suitable learning experience for students.

 

Teachers are given an opportunity to attend inservice, for example, on the revised Junior Certificate Mathematics syllabus. Additionally, the school has also had a follow-up visit from a member of the Junior Certificate Mathematics Support Service.   While there is no specific budget allocated to Mathematics, requested resources are provided. Recent purchases include mathematical games and puzzles and these are retained centrally for use by all involved in the teaching and learning of Mathematics.

 

The school offers a homework club to some first and second-year students. A member of the Mathematics department coordinates this club and some students take the opportunity to receive help in the area of Mathematics. Furthermore the school through the home-school community-liaison programme has introduced ‘Maths for Fun’. Such initiatives are to be commended as they promote Mathematics in different learning environments.

 

The school indicated that it has ongoing difficulties with students’ attendance. This was evident in Mathematics classes and from teachers’ records. The school has introduced a system of monitoring students’ attendance in the morning and again in the afternoon. It is recommended that a whole school approach be adopted to address this issue as a matter of urgency. Furthermore, it was reported that a number of students have ‘dropped out’ of school during the school year. Given the student profile and the school’s designated disadvantaged status it is recommended that the school give consideration to the introduction of alternative programmes of study at both junior and senior cycle for students that would best suit their needs.

 

 

Planning and Preparation

 

There is evidence to suggest that the Mathematics department works as a unified cohesive team. The department has a coordinator and this position is rotated yearly. Teachers are facilitated to meet formally approximately twice a year with informal meetings taking place on a needs basis. Minutes of formal meetings are retained by each teacher which is commendable practice. Issues discussed include progress of students and the setting of internal examinations. Agendas for further meetings are documented. This is good practice as it provides a focus and direction for these meetings.

 

It was reported that work on a long-term plan for Mathematics is ongoing.  In this context the department has developed a ‘Mathematics Subject Policy’ (which is included in the school plan) and ‘A Whole School Plan for Mathematics’ retained by Mathematics teachers. Both documents have similar content and include a description of aims, approaches and methodologies, and staff development. Both documents need to be reviewed and updated as they contain a number of shortcomings particularly in the ‘Whole School Plan for Mathematics’. For example there is no reference to the programme of study for each year group.  It is therefore recommended that the Mathematics department collaborate to further develop the long-term plan for Mathematics. This plan should include an outline of sections of the syllabus at junior and senior cycle and the advised areas of study under each of these sections. Such planning should ensure that teachers follow an agreed programme of work and that the particular students in third year who change from foundation to ordinary level are facilitated to study in a class grouping appropriate to their desired level. 

 

Collaborating to develop a common plan for Mathematics should give teachers an opportunity to identify and share good practice and should include the development of common assessments. Furthermore, consideration should be given to planning for the integration of Information and Communication Technology (ICT) into Mathematics. In this context the web site of the School Development Planning Initiative (SDPI) www.sdpi.ie has useful resource material that may assist in this regard. 

 

Teachers have developed good individual short-term plans for Mathematics. Some of these plans are extensive in their scope. Teachers had prepared well for lessons as was shown from the prior preparation of material such as handouts and other supplementary materials. In general teachers develop resources individually.

 

 

Teaching and Learning

 

Topics such as arithmetic, statistics, and geometry featured in the lessons observed. In general lessons began with the teacher correcting homework from the previous day and continued with the development of the topics. Teachers used Mathematics terminology appropriate to the relevant topics and students’ ability. A clear purpose was established at the beginning of lessons. Generally, pace and time management were appropriate to the students’ needs and abilities, however this was not so in all lessons. Teachers should ensure that time is used effectively and that lessons are paced properly to ensure that the specific objectives set for the lesson are achieved.

 

The predominant methodology used in lessons was traditional whole-class teaching. This is a combination of the teacher demonstrating to the class and the students working alone on tasks while the teacher assists individuals. Less frequently observed was the use of learning aids to teach a particular concept in Mathematics. When used this had the effect of allowing students to become engaged fully in the activity and to develop a genuine interest in the topic. Such practices are commendable and should be extended to all classes. Students would have benefited greatly from a variety of methodologies in lessons. For example the use of strategies such as investigation, consolidation activities, practical work, discussion, group work and quiz activities would have enhanced learning. It is therefore recommended that teachers review methodologies used in lessons and add variety to their approaches.

 

In general, teachers asked lower-order or recall type questions. Less frequently, teachers built on students’ answers by encouraging them to explain and justify their thinking and methods. It is therefore recommended that a varied range of questioning strategies be used to ensure that a balance between lower and higher-order questions are used in all classes.

 

In general, textbooks, handouts and to a lesser extent learning aids were the main resources used in lessons. There were some good examples observed of the use of differentiated worksheets. Such good practice ensures that all students are encouraged to work to the best of their abilities and to consolidate the learning activities in a lesson.

 

When specific tasks were set for students, teachers had an opportunity to circulate to monitor student progress and provided individual attention to students. In all cases this was done discretely and sensitively.

 

Teachers displayed very good classroom management skills. All classes were conducted in an environment of mutual respect where teachers gave varied and appropriate encouragement to all students.  Teachers were always affirming of students. Most teachers are classroom based and rooms were bright and tidy. Commendable practice was observed where mathematical posters were displayed in classrooms.

 

Students’ outcomes in terms of knowledge and understanding varied. Some students ably and confidently answered questions put to them during the course of the visit while others were less forthcoming.

 

 

Assessment and Achievement

 

Ongoing assessment is carried out through class questioning, the setting of homework and end-of-topic examinations. Formal assessments take place for all non-examination years at Christmas and in the summer. Examination years sit Christmas and ‘mock’ examinations.

 

Communication with parents is maintained in a number of ways. School reports are issued following formal examinations. A student record book includes notes from parents outlining reasons for absences or permission to leave the school during the school day. This record book is monitored daily by the deputy principal. Parents are also required to sign the student homework journal each evening. Parents receive regular letters providing information about school events. Furthermore parent-teacher meetings are convened for all year groupings.

 

Currently, when students decide to change their level of study a variety of practices are used to inform parents. It is recommended that an agreed procedure be introduced to formally inform parents and students of the long-term consequences of changing levels in Mathematics.

 

Homework assigned was appropriate in terms of quantity and relevance to the topic engaged with during the lesson. There was evidence to indicate that teachers monitor copies. There were some very good examples of teachers providing formative assessment to students. Such good practice should be extended so that all teachers, when correcting students’ work, include commendations and suggested areas of improvement.

 

While acknowledging that the school is designated disadvantaged the uptake of foundation level at both junior and senior cycle is significantly high. Few students take higher level at either the junior or senior cycle. Furthermore there is a gender imbalance in the uptake of Mathematics.  It is recommended that the Mathematics department work on a strategy to address the uptake of levels and gender balance issues that have arisen in Mathematics.

 

Awards ceremonies are arranged in the last term to acknowledge students’ academic and sporting achievements. Mathematics teachers are commended for their availability to meet students to give extra help as needed. However, students’ absenteeism suggests that responsibility should be put on students to improve their attendance and benefit more from formal class teaching.

 

 

Summary of Main Findings and Recommendations

 

The following are the main strengths and areas for development 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.