An Roinn
Oideachais agus Eolaíochta
Department
of Education and Science
Subject
Inspection of Mathematics
REPORT
Sligo,
Roll
number: 65181V
Date of
inspection: 6 May 2009
Subject provision and whole school support
Summary of main findings and recommendations
Report on the
Quality of Learning and Teaching in Mathematics
Subject
inspection report
This
report has been written following a subject inspection in
Subject
provision and whole school support
In
first year there are two mixed-ability classes and a small class containing
students who have been identified as requiring support with Mathematics.
Students are assigned to one of these classes on the basis of pre-entry
assessment and further assessment in September, immediately following enrolment
in first year. In second and third year higher-level, ordinary-level and
foundation-level classes are formed and students are assigned to classes on the
basis of achievement in end-of-year examinations, in-class testing and teacher
observation. Students study Mathematics in mixed-ability groups in TY. For
fifth and sixth year, students are assigned to higher or ordinary-level class
groups on the basis of junior certificate results and performance in formal
end-of-year examinations. A small foundation-level class is formed in sixth
year to accommodate students who are experiencing difficulty with
ordinary-level Mathematics. Student preference, parental preference and teacher
advice also have a role in level selection. Concurrent timetabling of
Mathematics occurs from first year through to sixth year. This very good
practice allows for flexibility in changing levels. It is mathematics department
policy that every student is encouraged to study Mathematics at the highest
level possible for as long as possible. The school’s practice in relation to
level choice is very good.
The
mathematics department comprises eleven teachers. Good rotation of levels and
programmes takes place among most members of the teaching team. Students retain
the same mathematics teacher for the duration of a cycle where possible.
Maintaining this continuity is worthwhile.
Teacher
continuing professional development (CPD) is facilitated by management. The
list of CPD courses attended by members of the mathematics department is
evidence that they are committed to maintaining a high level of expertise within
the mathematics department.
Teachers
make use of a range of resources for teaching and learning in Mathematics.
These are kept in a central location and are available to all mathematics
teachers. They include charts and posters, geometry equipment, 3-D solids,
dice, and an overhead projector. It is encouraging that there is also a
mathematics section in the school library.
Geometry Sketchpad, geometry software is currently being used on a pilot
basis and a decision as to whether its purchase is worthwhile will be reached
by the mathematics department in due course. There is a set of Digital Grinds available to assist
higher-level leaving certificate students with revision. Access to information
and communications technology (ICT) for teaching and learning in Mathematics is
limited. There are two computer rooms which can be used on a booking system. A
data projector is available in each of the two computer rooms and three other
classrooms in the school. In order to increase the mathematics department’s
access to ICT it is recommended that these rooms be used on a rotational basis
where possible.
The
procedures for identifying students who need learning support in Mathematics
are good. They included pre-entry assessment, further assessment on entry, communication
with feeder primary schools, diagnostic testing and ongoing teacher observation
and class testing. Support is provided through small group withdrawal, the
creation of small foundation-level classes and team teaching. There is very
good practice in first year where all students follow a common syllabus and sit
common examinations that are differentiated to suit students of varying abilities.
This is done to enable students who require learning support with Mathematics
to be assigned to a small class group while providing the option of moving up a
level at the beginning of second year if this is required. Teachers routinely
provide support to any student experiencing difficulty during lessons through
individual attention. A homework club and after school classes are provided
under the School Completion Programme, these are used to provide additional
opportunities for students to receive support with Mathematics. There is an autism
unit in the school that currently caters for three students. A mathematics
lesson in this unit was observed during the evaluation and it was evident that
valuable learning was taking place and that the students were happy and
confident with Mathematics. Overall high quality learning support in
Mathematics is provided for any student identified with such need.
Planning and preparation
Formal
planning time is allocated to Mathematics once per term as part of the whole-school
planning process. In keeping with good practice minutes are kept. It is
recommended that a copy of the minutes of planning meetings be included in the
planning documentation. Much informal planning also takes place. The
mathematics department and the learning support department work together to
identify difficulties and to facilitate learning for students. It was evident
throughout the evaluation that the members of the mathematics department work
well together as a team and provide a high level of collegial support for each
other. The mathematics department is currently co-ordinated by an experienced
mathematics teacher. Rotation of this position is recommended. This measure,
with the assistance of the current holder of the position, would help the
department to retain current levels of expertise.
The
plan for Mathematics is comprehensive and this is evidence that the mathematics
department has engaged well with the planning process. The plan contains
mathematics department policy on student assignment to levels, timetabling of
Mathematics, planning for students with special needs, homework, assessment, and
access to ICT. In keeping with best practice the policy statements genuinely
reflect current practice in the school and it is clear that meeting student
needs is their central focus. Details of CPD courses attended by mathematics
teachers are also contained in the planning documentation and this is good
practice.
Schemes
of work for each year group and level form part of the mathematics plan. For
most year groups these are set out in terms of topics or chapters of a text
book to be covered within defined timeframes. The scheme of work for first year
describes the content in terms of learning outcomes which is good practice. It
is recommended that, over time, brief sections on methodology, resources
necessary and assessment be added to the first year plans. This measure would
ensure that the plans are accessible to mathematics teachers who had not
participated in their creation. Furthermore it is recommended that this
framework be extended, over time, to the schemes of work for the other year
groups. This approach provides a valuable way for the planning process to
facilitate a sharing of ideas and methodologies that can have a very positive
effect on student experience in the classroom. Active, investigative, discovery
and research methodologies are currently used in teaching and learning in
Mathematics in some cases, particularly in TY and LCA lessons. However these
methodologies transfer well to all year groups and levels and it is recommended
that the planning process be used as a means of extending their use.
The
TY programme comprises a combination of the study of leaving certificate
syllabus content and participation in activities that encourage an alternative
experience of Mathematics. The approach taken to the study of some of the
leaving certificate material involves participation in project work and
activities that take students out of the usual classroom environment. For
example, as part of the school’s healthy eating campaign a survey is carried
out and the resulting data is analysed using Excel. The graphs generated
are displayed on notice boards throughout the school as part of the healthy
eating projects. Teachers use the material from student participation in the TY
mini company as part of the study of arithmetic. In addition TY students engage
in a project on micro-teaching. This involves students teaching a topic of
their choice to their classmates. Students also complete projects on the lives
of famous mathematicians. This approach is in keeping with the underlying
principles of a good TY programme.
Teaching
and learning
All
of the lessons observed provided an effective combination of teacher example
and student exercise. Teachers were well prepared for lessons and had all the
necessary resources available. All handouts used were well chosen and
supportive to learning. The answers to the questions on one handout formed a
puzzle for students to complete. This good practice provided students with
additional motivation. In other cases teachers had prepared supportive study
notes for students preparing for examinations. ICT, in the form of a PowerPoint presentation, was used
effectively in one classroom visited. A good balance was achieved between
teacher input and student activity and the pace of lessons was lively yet appropriate
to the ability level of the students. This ensured that student interest and
engagement were maintained throughout lessons. All lessons were well structured
and had a clear focus. Overall the quality of teaching and learning in all of
the lessons observed was high.
Teacher
instructions and explanations were very clear. Where it was appropriate,
teachers guided students towards deep understanding with well chosen examples
that illustrated the underlying concepts of the lesson clearly. In a lesson on
the Newton-Raphson method of approximating roots the students were initially
asked to find the roots of a cubic equation by trial and error. The teacher was
careful to direct student attention towards the sign change on trying different
values. The students were expected to explain why they thought the sign change
had occurred. The students were given ample time to formulate answers and
opinions. This sequence of examples, questions and discussion enabled the
students to appreciate the significance of each idea presented in the
explanations. This approach is very valuable to learning in Mathematics as it allows
students to build on previously learned material and to develop critical
thinking skills. Its continuation and extension is therefore recommended.
Teaching
concentrated on using straightforward examples of each concept to enable
students to develop the skills that would be required on the concept becoming
more complicated. This was complemented by the adherence to established
routines and methods and the inclusion of all steps in worked examples. Students
were encouraged to pursue their own preferred methods and approaches once they
had understood and become familiar with the ideas. There was evidence of this
valuable approach in many of the lessons observed. Students worked on
individual exercises while teachers provided assistance where necessary. This
arrangement served to differentiate learning by allowing each student scope to
work at a pace suited to her. In one class group visited a small group of
students worked on additional questions while the teacher corrected work with
the remainder of the class group. The teacher carefully monitored the work of
both groups throughout the lesson. It is recommended that the excellent
differentiation practice observed in this case be extended to further lessons.
In
keeping with the time of the inspection visit most lessons involved examination
preparation. This mainly consisted of working through past examination papers. Through
the inspector’s interaction with students it was evident that a conceptual
approach was taken in the study of geometry and the students were able to
demonstrate solid and thorough understanding of the theorems on their course. In
supporting students most teachers encouraged them to tackle the strategic elements
of the questions for themselves. In another case, however, students were
provided with a strategic step-by-step breakdown of each problem and were
expected to follow each step to answer questions. In order to allow students to
develop their own problem-solving skills and to gain confidence in using them
independently it is recommended that students be encouraged at every
opportunity to tackle the strategic elements of mathematical problems.
The
relationship between students and their teachers was characterised by warmth
and good humour. Students responded well to the encouragement, affirmation and
support that they received from their teachers. Teachers have created
stimulating mathematical environments with commercial and student-generated
posters displayed on the walls of their classrooms.
Assessment
All
year groups with the exception of TY are formally assessed at Christmas.
Examinations are held in May for first, second and fifth year students. TY
students are continuously assessed throughout the year. Students preparing for
the certificate examinations sit ‘mock’ examinations in February. Reports are
sent home on foot of these formal assessments and annual parent-teacher
meetings are held. In keeping with good assessment practice it is mathematics
department policy to set common examination papers within levels. There is very
good practice in relation to differentiation on examination papers where the
questions set take account of the variety in ability levels in the class group.
Students’
progress is closely monitored by teacher observation and oral questioning in
class. It is mathematics department policy to set class tests at the end of
each topic or chapter studied. Homework is set regularly and is usually
corrected as part of the following lesson. It was evident from the review of
student copybooks that the standard of presentation of student work is very
high. Teachers routinely monitor student work and this contributes to these
high standards. The standard of presentation of the LCA student folders and the
quality of their key assignments are very high. These folders are kept within
the school and they are evidence of the value placed on the mathematical applications
component of the LCA programme in the school.
The
mathematics department carries out an analysis of the school’s performance in
the certificate examinations each year. In keeping with good practice this
analysis is used to inform planning for Mathematics. The school is justifiably
proud of its students’ achievements in the certificate examinations.
Summary
of main findings and recommendations
The
following are the main strengths identified in the evaluation:
·
The school’s practice in relation to students’ choice of
level for Mathematics is very good.
·
High quality support is provided for any student identified with
such need.
·
Members of the mathematics department work well together as
a team and provide a high level of collegial support for each other.
·
The mathematics department has engaged well with the
planning process and the plan for Mathematics is comprehensive.
·
The TY mathematics programme is very good.
·
The quality of teaching and learning was observed to be
high.
·
The relationship between students and their teachers is very
good.
·
There is very good practice in relation to differentiation
on examination papers where the questions set take account of the variety in
ability levels in the class group.
·
Student work is closely monitored by teachers and it is of a
high standard.
·
The school is justifiably proud of its students’
achievements in the certificate examinations.
As
a means of building on these strengths and to address areas for development,
the following key recommendations are made:
·
The position of mathematics department co-ordinator should
be rotated among members of the teaching team.
·
The schemes of work for Mathematics should be extended over
time to include brief sections on methodology, resources and assessment.
·
Teachers should increase the use of approaches that
encourage students to develop strategic thinking and problem-solving skills.
·
The very good practice of differentiation which allows each
student scope to work at a pace suited to her that was evident in many of the
lessons observed 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 November 2009