**
An Roinn Oideachais agus Eolaíochta**

**Department
of Education and Science**

**Subject
Inspection of Mathematics**

**REPORT **

**Ashbourne****
Community School**

**Ashbourne****,
**

**Roll number:
91495T**

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**Date of
inspection: 17 September 2008**

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

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The mathematics department has invested considerable
effort in devising the optimum system for allocating students to class groups,
one that allows each student to maximise his or her potential. At present,
first year students are assigned to one of seven mixed-ability classes. In
second and third year there are seven class groups three at higher level, three
at ordinary level and one at foundation level. At the beginning of second year,
students are assigned to one of these class groups, based on the results from
common first year examinations. TY comprises four mixed-ability classes. In
each of fifth and sixth year, there are two higher level classes, four ordinary
level classes and one foundation level class. In these years, students are
assigned to class groups according to performance and to any personal
preferences they have regarding levels. The method of dividing students into
classes is subject to regular review and can be revised to suit the requirements
of a particular year group. Students are encouraged to study the highest level
possible for as long as possible. Change of level takes place in consultation
with class teachers, parents, the mathematics department co-ordinator and the
guidance counsellor where necessary.

The mathematics department comprises thirteen
teachers. Management assigns teachers to class groups in close consultation
with the teachers themselves. It is mathematics department policy and practice
that levels, at both junior and senior cycle, are rotated among all members of
the mathematics teaching team. Each mathematics teacher is also given the
opportunity to teach TY and LCA mathematics classes. The enabling of all
mathematics teachers to gain experience of teaching all levels and programmes
in Mathematics is very worthwhile since it helps to maintain high levels of
expertise within the mathematics department. Teachers retain the same class
groups from second year to third year and from fifth year to sixth year. Such
continuity is good practice.

Teachers make use of a wide variety of teaching
resources. These include overhead projectors and calculators, Venn diagram
sets, algebra tiles, geometry equipment, clinometer, theodolite, probability kits, and number lines. The members
of the mathematics teaching team are currently compiling a bank of notes and
handouts that will be used as a shared resource in the teaching and learning of
Mathematics. Mathematics teachers have access to information and communications
technology (ICT) through the timetabling of mathematics lessons for the
school’s computer rooms. Laptops and data projectors are also regularly used to
incorporate ICT into mathematics lessons. Formal induction is provided for
newly appointed teachers and a mentoring system has been established to support
new teachers in their first year in the school. Teacher continuing professional
development (CPD) is fully facilitated. Teachers are encouraged by management
to attend in-service courses and time is allocated at subject meetings for the
provision of feedback from CPD courses. The school provides a high level of
support for Mathematics.

Students who require learning support in Mathematics
are identified through pre-entry assessment, communication with feeder primary
schools and ongoing teacher observation. Support for students experiencing
difficulty with Mathematics is provided through individual and small group
withdrawal from subjects other than Mathematics and the creation of smaller
class groups. Commendably, in-class support is also provided in mathematics
lessons, this is of particular benefit to students since they can discreetly
receive the help they need in a timely and accurate way while remaining with
their peers. Students who need numeracy support have
access to a wide range of puzzles, games and computer software, all designed to
support learning in Mathematics. Very good communication exists between members
of the mathematics department and the teachers providing numeracy
support. This takes place formally at subject department meetings and also on a
regular informal basis. Reassessment takes the form of in-house testing and
ongoing teacher observation. A high level of support is provided, by members of
the mathematics teaching team and the learning support team, to students who
find Mathematics challenging.

The mathematics plan is reviewed and updated at formal
planning meetings held on school planning days at the beginning and the end of
the academic year. In addition, frequent mathematics department meetings are
scheduled throughout the school year. Planning meetings for Mathematics also
take place at lunchtime where necessary. Records are maintained of all formal
meetings that take place. Copies of the minutes of meetings are kept by the
principal and deputy principal. The role of mathematics co-ordinator rotates
among members of the teaching team. Mathematics teachers routinely collaborate
and co-operate, this has created a strong spirit of collegial support within the
subject department. It is evident that some sharing of ideas and discussion of
teaching strategies and methodologies takes place. This is commended as it can
be of particular benefit to new teachers or to teachers new to areas of the
curriculum, for example LCA or TY. It is recommended that the collaboration
around classroom activity that takes place be continued and built upon over
time.

It was evident from the review of the subject
department plan that good progress is being made on planning for Mathematics.
The plan contains policy documents on allocation to levels, assessment,
homework and learning support. The minutes of mathematics department meetings,
lists of resources and details of extra-curricular mathematics activities are
also contained within the planning document. Following the certificate
examinations the mathematics department compares the results achieved in the
school in Mathematics to the national norms and they use this analysis to
inform future planning for Mathematics. All of this is good practice. It is
recommended however that planning for teaching Mathematics to students for whom
English is an additional language be further developed and that the resulting
policy be included in the mathematics department planning documentation.

The mathematics department plan contains schemes of
work for each year group. These consist of lists of topics to be covered within
agreed time frames. It is recommended that the schemes for higher and ordinary
levels in each year group be co-ordinated so that the same topics are studied
by students at both levels at the same time, where it is feasible. This will
ensure that students who need to change level will have covered the same course
material as the group they are joining. It is clear from the observation of
lessons and the wide range of resources available that active, discovery and
investigative teaching methodologies are used in practice. ICT was also
observed to be used effectively in teaching and learning in Mathematics. It is
therefore recommended that this variety in teaching strategy be reflected in
the subject department planning documentation.

The TY plan comprises eight modular units. Each
teacher teaches two units and classes rotate every four weeks. The mathematics
department has created a course designed to be taught in a mixed-ability
setting. The TY plan strikes a good balance between Leaving Certificate course
content and material that is not on the Leaving Certificate course. The schemes
of work for TY are set out in terms of lesson objectives, learning outcomes and
strategies to be employed. All of this is excellent practice as the TY plan is
clearly in keeping with the underpinning principles of TY. It is evident from
the TY plan that students are encouraged to experience Mathematics for pleasure
and gain an appreciation for the real life applications of the subject. It is
suggested that, in the further development of this very good plan, a module of
Applied Mathematics might be considered.

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In all of the lessons observed there was evidence of
good advance planning. Teachers had prepared handouts, *PowerPoint
presentations*, and a variety of materials necessary for the active lesson
activities organised for the students. In all cases the materials were well
chosen and supportive of learning. Lessons had a clear aim and good continuity
was maintained with previous lessons by linking with and building on students’
prior knowledge. At the beginning of most of the lessons observed the teacher
shared the learning objectives with the students. Best practice in this regard
occurs where the lesson objectives are written on the board at the start of the
lesson and checked at the end to ensure that they have been achieved. This can
encourage students to take personal responsibility for their own learning and
can help to increase motivation and a sense of achievement on reaching the
lesson goals. It can also alert the teacher to any areas that have proven
difficult for some students and need to be revisited in the next lesson. It is
therefore recommended that the learning objectives be explicitly shared in this
way.

Teacher instructions and explanations were very clear
in all of the lessons observed. The pace of lessons was lively yet appropriate
to the ability level of the students. Teachers used a variety of questioning
strategies to involve students and to assess learning in class. There was
evidence of teachers using higher-order questions, requiring reflection and
consideration to help students to engage with their course material. Since this
type of questioning is so beneficial to learning in Mathematics it is
recommended that it be employed at every opportunity. In general there was a
good balance between teacher input and student activity. Allowing students
plenty of time to solve mathematical problems independently is very worthwhile
since it can enable students to develop confidence in their own problem-solving
skills and can lead to a great sense of personal satisfaction. Teachers covered
lesson content in a comprehensive way. This was particularly evident in a
lesson on integration where the teacher was careful to accept the wide variety
of correct student answers presented and to work each through fully, with student
contribution, without showing preference for any one method. This very good
practice helped the students to thoroughly explore and to gain a deep
understanding of the ideas covered in the lesson.

During the majority of the lessons observed, students were
given opportunities to actively engage in the learning process. The LCA class
visited provides a very good example of this. The lesson opened with an
introduction to probability presented in *PowerPoint*. The students were
then expected to mathematically calculate the probability of throwing a certain
number on the roll of a die and then to experimentally investigate the same
probability. The students participated enthusiastically and fully in this
activity and were supported with a well-designed handout that guided them
through the exercise with ease. This handout also served to consolidate the
mathematical aspect of the activity and with individual help from their teacher
each student was able to complete the task. In this lesson the teacher very
patiently ensured that all of the students were completely involved and engaged
in the activity throughout the lesson.

Teachers make effective use of ICT in teaching and
learning in Mathematics. In the TY lesson observed the students worked in pairs
to research the life of a famous mathematician that they had chosen for their
projects. This module in TY will conclude with student presentations on the
lives of their chosen mathematicians. This type of methodology is in keeping
with the spirit of the TY programme and is commended. TY in

Teachers demonstrated a genuine concern for students’
understanding of the concepts taught and considerable effort was made to
ascertain individual student perspective and to build explanations around the
students’ own interpretation of particular problems. The Junior Certificate
geometry lesson observed provided an excellent example of this. The study of
geometry theorems can provide students with a very good opportunity to develop
their reasoning and thinking skills. In the lesson observed the teacher
maximised the potential of this opportunity by taking the students carefully
through each thought process with probing questions and by encouraging the class
to engage in logical argument and discussion. Throughout this lesson,
individual students worked at the board and engaged with the remainder of the
class group to tease out the ideas presented. The teacher facilitated learning
by guiding the students towards the full understanding of each concept and by
persisting until the students could demonstrate that full understanding had
been achieved. The content of this lesson was specifically chosen to address
difficulties that had arisen out of the previous night’s homework and the
lesson concluded with a consolidating physical demonstration to illustrate the
concept in a concrete way. The learner-centred focus and the comprehensive
treatment of the lesson content observed in this case were exemplary.

Classroom management was generally good. The
atmosphere in the classrooms was warm and the rapport between teachers and
students and among the students themselves was very good in all cases. Teachers
tended to move around the classroom to give individual attention; in most
cases, they were careful to simultaneously monitor the class group as a whole,
a practice which is essential for successful class management. Students
responded well to the affirming manner of their teachers in all cases and in
one class students demonstrated a good sense of fun in their approach to the
subject.

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It is evident from the review of student copybooks
that the standard of student work is high and that the majority of students are
making steady progress in Mathematics. Teachers model good presentation and
include all the steps of worked examples. This attention to detail is reflected
in student work. Teachers routinely monitor student work in class. Homework is
set regularly and usually corrected as part of the following lesson. Some
teachers are taking this valuable opportunity to provide students with critical
feedback and positive reinforcement. The use of *assessment for learning*
(AfL) principles in this way
is very good practice and it is recommended that AfL
practices be extended to all mathematics classes. More information on AfL is available on the NCCA
website (www.ncca.ie).

All students with the exception of those in third,
sixth and TY year groups are formally assessed at Christmas and in May.
Examination classes are formally assessed in October and sit ‘mock’
examinations in spring. TY students are continuously assessed throughout the
year. Reports are sent home on foot of these formal examinations and
parent-teacher meetings take place once a year. Achievement is routinely
assessed through end-of-topic tests, oral questioning in class and ongoing
teacher observation.

The mathematics department organise *Maths Week *events
in the school, including participation in the *PRISM* mathematics
challenge. Mathematics students in the school take part in training for the
International Mathematics Olympiad. The mathematics department are also engaged
in the setting up of a mathematics web link within the school’s internet
website. Participation in mathematics-related extra-curricular activities is
good practice as it can help to generate interest in the subject and can
encourage students to experience mathematics for pleasure.

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The following are the main strengths identified in the
evaluation:

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·
Mathematics is well supported in the school and timetable provision for
the subject is very good.

·
A high level
of support is provided, by members of the mathematics teaching team and the
learning support team, to students who find Mathematics challenging.

·
Good progress is being made on planning for Mathematics.

·
The TY programme for Mathematics is very good and is in keeping with the
spirit of TY.

·
High-quality teaching and learning was evident in the lessons observed
and student participation and engagement were high.

·
The
relationship between students and teachers was observed to be mutually
respectful.

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

·
A policy for
teaching Mathematics to students for whom English is an additional language
should be developed.

·
The employment
of active, investigative and discovery methodologies and the incorporation of
ICT, group work and pair work in lessons should be continued and extended over
time.

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

*Published January 2009*

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