An Roinn Oideachais agus Eolaíochta
Department of Education and Science
Subject Inspection of Mathematics
Mercy Secondary School,
Ozanam Street, Waterford
Roll number: 64971W
Date of inspection: 7 and 8 April 2008
Report on the Quality of Learning and Teaching in Mathematics
This report has been written following a subject inspection in Mercy Secondary School, Waterford. 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 timetabling provision for Mathematics is very good. All junior cycle and senior cycle classes have five periods of forty minutes duration each week. Sixth-year, higher-level classes are allocated one additional period each week. The Transition Year (TY) class and the Leaving Certificate Applied classes have four periods of Mathematics each week. In addition to this, classes are spread evenly throughout the school week. In a small number of instances classes have a majority of their lessons in the afternoon. This should be avoided if possible in future timetabling. Mathematics classes from first year onwards are timetabled concurrently to allow separate classes for higher-level and ordinary-level students. In the interests of maintaining high levels of continuity, the good practice of teachers remaining with the same class groups from second year to third year and from fifth year to sixth year, where possible, was noted.
Teachers are assigned to classes following consultation with management. The mathematics team is commended for its policy of encouraging and supporting all members to teach the topic to all levels. To date almost all have taught the subject to higher, Leaving Certificate level.
Students are assigned to mixed-ability classes in first year and follow an agreed common course for the year. At the beginning of second year, classes are reformed to allow students to follow the higher or ordinary level syllabus. This is good practice as it encourages students to follow the highest level possible for as long as possible. In the second-year and third-year classes, as well as for the senior years, the commendable practice is to have mixed ability within levels. Mixed-ability teaching within levels takes account of varying rates of student development and exploits the correlation between levels of teacher expectation and levels of student achievement.
TY is optional for students within the school. Either one or two class groups are formed depending on the number of students who undertake the year. At the beginning of fifth year students opt for higher or ordinary level Mathematics. Again the classes are formed on a mixed ability basis within levels.
Incoming first-year students are assessed prior to entry to the school in a number of areas including Mathematics. Students who find the subject particularly challenging are identified through this pre-entry assessment, contact with the local primary schools and parents, and teacher monitoring and assessment during first year. These students are generally supported through a system of withdrawal from mathematics classes, for some periods each week, for small group or individual tuition for as long as required. Close informal contact is maintained between the learning support teacher and the classroom teachers. As a further support, an extra mathematics class group has been created in second year to allow a smaller number of students to progress at an appropriate pace.
Information and communication technology (ICT) is currently used mainly in the production of materials to enhance the teaching of Mathematics and to a lesser extent in classroom teaching. There was evidence of the use of ICT in TY project work and in LCA assignment work. All classrooms are now networked and have broadband internet access. It is recommended that, in order to support the teaching and learning of the subject, strategies to integrate ICT more directly into the lessons should be discussed and included within future reviews of the team’s plan.
Management is commended for supporting the continuous professional development (CPD) of teachers by facilitating opportunities to attend in-service in Mathematics during school time. Some teachers have attended and plan to attend a range of in-service courses organised by the Mathematics Support Service in a number of topics. Those who attend specific courses provide a report to the next team meeting. This practice is commended.
The mathematics department in the school has been in existence on an informal basis for quite some time. In recent years, the structure has become more formal following input from the School Development Planning Initiative (SDPI) service. Currently the department is co-ordinated, on a voluntary basis, by an experienced member of the team. The teachers work collaboratively and responsibility for specific tasks and year groups is delegated to individual team members as needs arise. There is a strong sense of co-operation, openness and collegiality within the team. This is supported by the practice of full rotation of levels, common assessments at first year and within levels thereafter and the shared resources available to all.
Formal planning and review meetings are scheduled around staff meeting and school planning days and occur about three times a year. There are also shorter, formal meetings each month and informal contact is regularly maintained. The good practice of record keeping at formal meetings has begun and these records show evidence of ongoing collaboration and review among mathematics teachers.
The mathematics team have made commendable progress in planning. They have used diagnostic templates and have collaborated and developed a comprehensive long-term plan for Mathematics along School Development Planning Initiative (SDPI) guidelines. The department plan includes a mission statement, overall aims and objectives for mathematics education within the school, organisational details of classes and teachers, the school homework policy and forms of assessment, an inventory of resources, comprehensive topic based programmes of work for each year group and level, reference to a variety of methodologies, and a description of provision for students with special educational needs, which is in line with good practice and is commended.
There is a Transition Year plan for the school. There is a balance between topics that consolidate the prior learning of students, some work that introduces elements of the Leaving Certificate programme in an innovative way and other topics such as puzzles, student survey and project work around the history of Mathematics.
All teachers made individual planning and preparation materials available during the inspection. Included in these materials were some individual lesson plans, schemes of work, resources including worksheets and handouts, teacher notes, assessments and marking schemes, test papers, examination questions and solutions. Teachers also had support service materials including worksheets and loop cards. This level of preparation for teaching is commended.
In lessons observed, teachers’ preparation for teaching was evident, and the mathematics content was appropriate. The presentation of work to students was challenging but clear and students responded to their teacher’s expectations. While classroom activities were generally of a passive nature, students were generally attentive to their work and, on occasion, interest in and enthusiasm for the subject were apparent. Classroom management was generally good and students were kept on task. There was a sense of mutual respect between teachers and students, creating an atmosphere that was conducive to learning. Teachers were aware of and attentive to the needs of individual students and devoted class time to working with students who were experiencing difficulty. Students’ progress and effort were affirmed in an atmosphere that created confidence and encouraged students’ use of appropriate mathematical language.
Examples of good practice in the teaching of Mathematics included the use of Algebra Tiles as a concrete way to introduce factorisation, the use of a fold out model in the teaching of area and volume, the use of pair work, students explaining procedures to one another, the use of ICT for assignment work and the appropriate use of mathematical language by students and teachers.
Lessons generally began with the correction of homework at the board by the teacher. In some instances the purpose of the lesson was then shared with the students. This is good practice as it stimulates interest in the lesson and captures students’ attention. 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. Within this traditional style, teaching was effective, lesson content was appropriate and in line with agreed programmes of work and syllabus requirements.
To complement this general, teacher-directed, whole-class teaching style, it is recommended that a wider range of teaching methodologies be explored and developed, to engage students more fully in their own learning. Some examples could include investigation, practical work, discussion, group work, pair work, consolidation activities, quiz activities and greater use of ICT. It is also important, where possible, to link the mathematical concepts being taught to the students’ own experiences. The inclusion of such strategies into the lessons observed should address the widely accepted benefits for students of being actively involved in their own learning. In addition students’ different preferred learning styles are engaged by using a range of methodologies. 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 all contribute to this task.
Interactions between teachers and students typically took the form of brief answers to questions posed to individual students or to the class group by the teacher. There were also examples of students asking questions, reflecting their engagement with learning in the lessons. Teacher questions were generally of the “next step” or “fill in” type. There were also some good examples of teachers posing more challenging questions, encouraging students to justify their methods, to encourage students to probe new material being presented and to create links to previous learning. The use by all teachers of some probing questions in mathematics lessons is recommended. Such questions should appropriately challenge students and assist them in developing their skills in the area of problem analysis, mathematical thinking and mathematical communication.
In Mercy Secondary School classes have been allocated their own base classrooms. Despite this a wide range of commercial posters and student generated work had been used to enhance the rooms. This is commended as it has created a visually stimulating mathematical environment.
In interactions with the inspector, the students could make connections to previous learning and displayed clear mathematical knowledge. They were able to demonstrate understanding of the concepts they had learned and how to apply them to problems.
Students’ progress is assessed on an ongoing basis by questioning in class, through correction and monitoring of homework and student work during class and through monitoring of students during lessons. Students’ progress is also monitored throughout the year by means of a series of tests administered at the end of a topic and results are recorded in the Teacher’s Diary. Non examination classes have formal assessments twice a year at Christmas and summer. Third-year and sixth-year students are continuously assessed and also sit ‘mock’ examinations during the second term.
The school maintains good communication with parents. Two school reports are issued for each student during the year. Parent-teacher meetings are held for each year group. Additionally the student diary can be used as an effective means of communication between the school and home and vice-versa.
Common examinations enable comparisons to be made across the student cohort. It can also serve a useful purpose in informing students’ choice, or in providing advice to students in relation to levels. Teachers are commended for the high level of co-ordination associated with the testing of students. All first-year students complete the same end-of-year test, and term tests within levels in all other year groups are common.
An analysis of students’ performance in the State examinations over the last four years indicates that uptake rates at higher and ordinary levels are good at both Junior and Leaving Certificate level. It is noted that discussion and review of uptake rates, as well as results, have begun to be discussed at department planning meetings. This is good practice and should be used as a regular and natural part of the planning activities of the mathematics department.
Students are encouraged to participate in a range of co-curricular activities pertaining to Mathematics. These activities include the Team Maths competition, the Prism competition and Maths week activities. This very good practice is commended as it allows students to have an interest in Mathematics outside of the classroom, raises the profile of the subject within the school, gives students the opportunity to enjoy Mathematics and see it applied to problem solving in a new and stimulating way. All those involved in these activities are commended.
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:
Published, September 2008