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An Roinn Oideachais agus Eolaíochta**

**Department of Education and Science**

**Subject Inspection of Mathematics**

**REPORT **

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**Loreto Secondary School**

**Balbriggan, County Dublin**

**Roll number: 60010P**

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**Date of inspection: 29 September
2009**

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Subject provision and whole school support

Summary of main findings and recommendations

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**Report on the Quality of Learning and Teaching
in Mathematics**

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This report has been written following a subject inspection in Loreto Balbriggan. 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 and examined students’ work. 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. The board of management was given an 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 of this report.

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Loreto Secondary School currently has an enrolment of 1189 girls. Timetable provision for Mathematics is good with five class periods per week allocated to first, second and third year groups. Fifth and sixth years receive six mathematics lessons weekly. In Transition Year (TY) Mathematics is timetabled for three class periods per week. The timetabling arrangements for Mathematics are also good; for example, mathematics lessons are concurrently timetabled for all year groups with the exception of first years.

First years study Mathematics in mixed-ability class groups, this is good practice. In all other year groups, students are assigned to higher and ordinary-level mathematics classes according to their achievement in school examinations and later in the certificate examinations. This means that each class group comprises students considered to be within a particular, and sometimes narrow, range of ability in Mathematics. Concurrent timetabling of mathematics lessons facilitates change of level where necessary. At the beginning of each school year, the mathematics department invests considerable time and effort in dividing students into these ability groupings. It was evident throughout the evaluation that the level of teacher expectation, for each class is determined by its placing within the class groups. So, for example, students in the top higher-level class are expected to do better than those in the second higher-level class and so on. It is recommended that the mathematics department considers dividing students into higher and ordinary levels and then, where there is more than one class group at either level in a year group, assigning them to mixed-ability classes within that level. This measure would contribute to a more individualised determination of expectation based on each student’s achievement and demonstrated ability rather than on the placing of the class as a whole. This, in turn, would enable advantage to be taken of the correlation known to exist between levels of teacher expectation and levels of student achievement and it would mitigate the de-motivating effects on students than can result from being placed in low ability grouping.

The mathematics department comprises thirteen teachers. There is good rotation of levels among members of the mathematics teaching team. Students retain the same mathematics teachers from year to year insofar as possible for the duration of a cycle, maintaining continuity in this way is worthwhile. Teacher continuing professional development (CPD) is encouraged by management. In addition to whole-school CPD on assessment for learning (AfL) for example, some mathematics teachers have recently attended courses on probability, trigonometry, geometry and transition year mathematics. Some members of the mathematics department have also attended evening courses on higher-level leaving certificate Mathematics. This is evidence of the mathematics teachers’ commitment to the subject.

Mathematics teachers use a wide variety of resources in teaching and learning in Mathematics. The resources used in the lessons observed included coloured paper, scissors, glue, shopping catalogues, cylinders and cones, sand, small boxes and raisins. In addition, overhead projectors and calculators, geometry equipment and games are available for mathematics lessons. It is good that everyday objects are used as lesson resources and it is recommended that teachers seek further ways to extend this practice. In each classroom visited number lines, posters and student projects decorated the walls and helped to create stimulating learning environments for students.

The facilities for information and communications technology (ICT) available to mathematics teachers are good. The school’s computer room can be booked for mathematics lessons. Most teachers have laptop computers that can be used for teaching and learning and there are mobile data projectors available on a booking system. The school subscribes to the ‘Mathletics’ website and student subscription is also encouraged. Teachers described this as being successful and supportive to learners. There is a range of mathematics computer software available to students and a list of useful mathematical websites is included in the mathematics plan. However, there is limited use of ICT in teaching and learning in Mathematics and it is recommended that ways in which ICT can become a regular feature of mathematics lessons should be explored.

There are good procedures in place for identifying students who need learning support in Mathematics. Students are identified through communication with feeder primary schools, pre-entry testing, diagnostic testing, communication with parents, psychological assessment and ongoing teacher observation and class testing. Learning support is provided on the basis of withdrawing individual students or small groups from scheduled classes. Teachers routinely provide high quality individual attention and encouragement throughout lessons for any student experiencing difficulty. It was evident in the evaluation that teachers use active learning strategies and games to motivate students who experience difficulty with Mathematics; this was observed to have a very positive effect on student confidence with the subject. Learning support in Mathematics is provided by subject specialists, which is good practice. Overall very good provision is made for students who have been identified as requiring support in Mathematics.

Each
year students are encouraged to participate in training for the *Irish
Mathematical Olympiad *at the National University of Ireland, Maynooth. Students
take part in the *Team Maths* and the *PRISM* mathematics challenges.
Students also represent the school in the *Irish Junior Mathematics *competition.
In addition, *World Maths Day* and *Maths Week* are celebrated as
significant events each year. Participation in extra-curricular mathematics
activities is very worthwhile as it provides students with opportunities to
experience Mathematics for pleasure and it also raises the profile of
Mathematics within the school.

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Time is allocated to planning for Mathematics on school planning days and on a further three occasions per year. The members of the mathematics department also discuss day-to-day issues as they arise. In keeping with good practice minutes are kept of all planning meetings and these are included in the planning documentation. Co-ordination of the mathematics department is currently the responsibility of two mathematics teachers. It is recommended that, in time, these positions be rotated in order to allow other members of the teaching team to gain experience in this area. It was evident from the review of the minutes of planning meetings that time is allocated for teachers who have attended in-service courses to bring that experience back to the remainder of the team. This is very good practice and it is recommended that a similar arrangement for the sharing of lesson ideas and methodologies be established in order to facilitate an increase in the variety of the lesson activities used in teaching and learning in Mathematics.

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Significant
progress has been made on planning for Mathematics. The plan contains policy
documents on areas such as time allocation for Mathematics, student assignment
to class groups, homework, assessment, and provision for students with special
needs. A catalogue of resources and a list of CPD courses attended are also
included in the planning documentation. The mathematics plan is comprehensive
and reflects the decision-making processes engaged in by the mathematics
teachers. The discussions around whether to become a pilot school for *Project
Maths *are recorded in the planning documentation and provide an insight
into how decisions are reached by the mathematics department. The plan also
contains details on how elements of assessment for learning were trialled by
some members of the teaching team and how the findings were then brought back
to the entire team for decision making. These are examples of very good
collaborative planning practice. In addition, it is good that the plan is
reviewed and revised annually.

Programmes of work for each year group form part of the mathematics plan. These are set out in terms of topics to be covered for the year. While it is good that each year group, within levels, follows a common programme, it is recommended that these programmes be developed, over time, to include sections for methodology, resources and assessment. There was much evidence throughout the evaluation that active, research, and discovery methodologies are used in teaching and learning in Mathematics. The involvement of all mathematics teachers in the development of the programmes of work will contribute to the sharing of these very good classroom practices.

The transition year (TY) plan comprises a combination of Leaving Certificate topics and material that is not part of the Leaving Certificate course. While this is characteristic of a good TY programme, the emphasis of the plan is on the Leaving Certificate course work. The content of the one TY lesson observed was ideal for TY; however, this lesson content was not included in the TY plan. It is therefore recommended that the TY plan be revised so that it accurately reflects the spirit of the school’s TY programme for Mathematics and the actual work undertaken in TY mathematics lessons. TY provides a very good opportunity to increase student interest in Mathematics and the TY plan should aim to use this opportunity to full advantage.

It is good that each year an analysis of the school’s performance in the certificate examinations is carried out by school management. It is recommended that the mathematics department compare the school’s performance in Mathematics each year to national norms. This analysis should be used to inform planning for Mathematics.

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During the evaluation nine lessons were observed. In all cases teacher explanations were clear and conceptual. All teachers made very good use of questioning to involve students and to assess learning. Best practice was observed in most lessons where teachers used higher order questions to encourage a deep understanding of the concepts involved. Student engagement was highest where there was a good balance between teacher input and student activity. This was true of most lessons and the benefits of this method should be extended to all. The pace of the majority of lessons was appropriate to the ability level of the students. One lesson, however, progressed at too fast a pace and this resulted in inadequate covering of the lesson content. It is recommended that the good practice in relation to the pacing of lessons that was observed in most cases be extended to all lessons.

A
wide variety of methodologies was used in the lessons observed. These included
pair and group work; games and puzzles; investigation and demonstration as well
as a combination of teacher example and student exercise. Learning was
facilitated best in lessons where activities or games were used to motivate and
encourage students. One such lesson, on algebra, involved students playing a
version of the game ‘*Who wants to be a Millionaire?*’ The teacher had
organised a scenario that closely resembled that of the game show and
individual students were chosen at random to participate as contestants while
the remainder of the class group acted as the audience. This class group
contained students who find Mathematics difficult and the methodology allowed
the teacher and the audience to provide support and encouragement for the
students at the board. Through this format the students were facilitated in
examining the work of the lesson closely and were able to demonstrate high-quality
learning. Considerable thought and effort had been invested in the planning and
preparation of this excellent lesson and it was very rewarding to observe solid
learning taking place in an atmosphere of fun and enjoyment.

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There was much evidence of teachers encouraging students to take responsibility for their own learning. This took the form in some cases, of teachers facilitating students in working independently on exercises and then providing examples to consolidate understanding. In other cases students worked in pairs or groups on activities designed to help them to explore the main ideas of the lessons for themselves. This is representative of very good practice. In a small number of cases, however, teachers over-supported students either by leading students too much through questioning or by providing a conceptual breakdown of the solution to questions before the students had a chance to try them for themselves. It is recommended that strategies that encourage students to take responsibility for their own learning be further included in lessons.

Teachers provide opportunities for students to explore underlying concepts and to reach a deeper understanding of lesson content. An activity that demonstrated recasting, using the transfer of sand from a conical container to a cylindrical one served to illustrate the underlying idea of one lesson very clearly. In another lesson an algebraic explanation was used in combination with a graphical explanation to demonstrate the significance of the solutions to solving non-linear simultaneous equations. Small boxes containing raisins were used to illustrate the relationship between simultaneous equations and their solutions in another excellent lesson on this topic. These are some examples of very good practice with regard to teaching for understanding, although there was evidence of this approach in many more of the lessons observed.

In the TY class visited students worked in small groups to budget for the furnishing of a home. The students were assigned a budget, a type of accommodation and a family type at the beginning of the lesson. The teacher distributed shopping catalogues to each group in preparation for the task. Throughout this very good lesson the students enthusiastically engaged with the task. The methodology used and the content of this lesson made it ideal for TY.

Where the lesson activities were student-centred natural differentiation of learning took place as students were able to find their own pace and work at it. In lessons where the methodology comprised a combination of teacher-example followed by student-exercise, teachers differentiated learning through the provision of individual attention and assistance where necessary. These good practices helped to ensure that individual student needs were met. Wider use of similar differentiation strategies is encouraged.

The quality of learning was observed to be high. This was evident in the high levels of interest and enthusiasm for Mathematics demonstrated by students throughout the evaluation. Furthermore, students engaged and participated very well in the lessons observed. The quality and variety of activities organised by teachers for their lessons is evidence of their commitment to making the subject accessible and enjoyable for students. The active learning strategies observed during the evaluation facilitated, for some class groups, a necessary level of repetition that contributed significantly to understanding for learners. Most lessons were engaging and student attention was optimised by the lively pace and the variety of tasks.

The relationship between students and their teachers was observed to be very good. Students responded well to the affirmation and encouragement provided by their teachers. Teachers have created secure learning environments where students can engage with Mathematics with confidence.

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In-class assessments are held for all groups, with the exception of TY, at Christmas. TY students are assessed in January. First, second, fifth and transition year students sit formal examinations in May. ‘Mock’ examinations are held in spring for students preparing for the certificate examinations. Reports are sent home on foot of all formal examinations and parent-teacher meetings take place annually.

In keeping with good assessment practice common examination papers are set, within levels, for each year group. It is mathematics department policy to differentiate the standard of the questions on examination papers. This very good practice takes account of the variety of ability and helps to ensure that all students have opportunities to achieve. However, it was evident in the review of the assessment test, held for students prior to entry, that the standard of questions is not differentiated in a similar way. It is therefore recommended that the principles applied to the in-house examinations be applied to the pre-entry assessment. This measure will make a positive contribution to the quality of the resultant information.

Homework is regularly given and is corrected as part of the following day’s lesson. Teachers assess student progress through oral questioning in class and observation. In addition, class tests are set at the end of each topic or chapter studied. All of this is good practice. The standard of presentation of student work is high and students are making good progress in Mathematics. Some teachers are including comments and ‘stars’ in the correction of written work. This very good practice provides students with a valuable source of advice and encouragement and allows them to take more responsibility for their own learning. Overall the mathematics department’s practices in relation to assessment are very good.

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The following are the main strengths identified in the evaluation:

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· The timetabling arrangements for Mathematics are good.

· Very good provision is made for students who have been identified as requiring support in Mathematics.

· Significant progress has been made on planning for Mathematics.

· High quality of teaching and learning was evident in the lessons observed. Teacher explanations were clear and conceptual and very good use was made of questioning.

· Teachers provide opportunities for students to explore underlying concepts and to reach a deeper understanding of lesson content.

· Students are encouraged to take responsibility for their own learning.

· There was good evidence of differentiation of learning.

· The mathematics department’s practices in relation to assessment are very good.

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

· The mathematics department should consider dividing students into higher and ordinary levels and then, where there is more than one class group of each level in a year group,

assigning them to mixed-ability classes within these levels.

· Ways in which ICT can become a regular feature of mathematics lessons should be explored.

· Collaborative planning should be used as a mechanism for sharing the variety of methodologies and learning strategies that are used in teaching and learning in Mathematics.

· The TY plan should be revised so that it accurately reflects the spirit of the school’s TY programme for Mathematics and the actual work undertaken in TY mathematics lessons.

· The good practices observed in relation to the pacing of lessons and in relation to the balance between student and teacher activity should be extended to all lessons.

A post-evaluation meeting was held with the principal at the conclusion of the evaluation when the draft findings and recommendations of the evaluation were presented and discussed.

*Published February 2010*

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**Appendix**

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**Submitted by the Board of Management**

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**Area 1: Observations on the content of the inspection report**

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The Board of Management is pleased to note the very affirming comments of the Maths Inspector and thank the school’s Maths teachers for their continued dedication.

**Area 2: Follow-up actions planned or undertaken since the completion
of the inspection activity to implement the findings and recommendations of the
inspection**

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