For photocopiable books and books on disk for teachers and parents.
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For photocopiable books and books on disk for teachers and parents.
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METHODS OF TEACHING MATHS TO T1630 –
SAMPLE PAGES
1. Solving the dyscalculia problem This book is about the methodologies that can be
adopted in working with children with dyscalculia.
It does not venture into the area of why some children have dyscalculia,
nor do we deal with where the problem comes from. There are other titles available which focus on these issues. We start from the point of view that most other books on
this subject report: that
irrespective of the origins of dyscalculia, the child with dyscalculic problems
can be helped by a focus on particular methods of teaching and learning.
A central element of this approach lies in knowing which aspects of maths
the dyscalculic child is misunderstanding.
For example, if the child has simply not grasped the concept of
multiplication, then there is little point continuing with any other more
advanced maths teaching, until this fundamental has been understood. You may well be aware with each child what the basic
problems are in terms of maths learning. Where
this is so, the approaches laid down in this volume can guide you towards the
most appropriate forms of teaching and learning for this situation.
If however you are not sure of which bits of basic maths the child has
understood, and which bits are not understood, then you may wish to consult Tests
for Dyscalculia, also published in this series.
It contains numerous straightforward tests which can be administered
within the classroom and which will quickly reveal where the problems lie. Tests for Dyscalculia may suggest, for example, that work needs
to be done on the concept of division. This
volume reveals how the teaching and learning should be structured to overcome
the dyscalculia. Many children, students and adults now use the methods of
teaching and methods of learning that we propose – and not all of them are
dyscalculic. Many of the
ideas that are at the heart of the First and Best approach have been proposed
elsewhere by many others. We see
our special contribution as having been: · To make the approach more user friendly through providing our work as photocopiable masters and on computer disk. · To combine these ideas, some of which were given to us by teachers, and some of which appeared in academic journals and books, into single, immediately usable, volumes. ·
To introduce certain new issues rarely seen in traditional study
skill materials, but which appear very obviously to work. As many academic reports now tell us,
reform of methods of teaching and learning can have an enormous part to play in
raising pupil self-esteem. This
development was first noticed by those involved in literacy skill improvement.
Since then reports have been made in connection to many subjects, showing
that this approach not only aids learning in whichever area it concentrates on,
it also benefits the pupil in general once reformed methods of teaching and
learning are introduced. With study
skills blossoming, the previously stifled pupil gains vitality in all areas of
school work, and begins to enjoy enhanced self-esteem. Nowhere is this more apparent than
with the pupil who is struggling with maths.
Give the child the understanding he or she undoubtedly seeks, and
self-esteem rises dramatically. When
this happens the pupil’s whole life changes. These programmes show to be a myth
once and for all, the notion that changing a school’s outlook on, and approach
to, teaching and learning is too difficult and slow to undertake across a whole
country. For the past ten
years, our approach here with dyscalculia, in classes involving dyslexic
children, and across schools in general, have shown that schools working on
their own, can change their approaches to teaching and learning and make a huge
difference. In this area the First and Best
Teaching and Learning programme can claim to have made a unique contribution.
Success for All in the
United States, along with such UK based reforms as IQEA, all require
considerable additional funding for extra teacher training and improved
pupil-teacher ratios. While schools
using the Success for All programme in the USA have been able to call on
“Title 1” money, UK schools have often been left wondering how to gain
access to school improvement programmes on their limited budgets. By putting the essence of our
programme in one photocopiable book we feel that we have helped UK schools
overcome their funding problem and gain access to a major reform programme with
just one purchase. As Robert Slavin of Success
for All so clearly pointed out, “the key requirement for meaningful
change in school reform is that whatever reform is adopted [it] must profoundly
improve the daily instruction provided to children…. Research and experience
in the US and elsewhere has shown that large scale change in teaching practice
can be brought about through the development, evaluation and dissemination of
proven, replicable programmes.” The widespread dissemination of a
comprehensive, copiable (and, through the computer disc, adaptable) programme
shows that positive developments can be replicated on a large scale in the UK
too. The lack of special funding is
no longer a barrier. An achievable aim for all teachers is
now the rapid eradication of academic failure for all pupils.
All teachers can make an estimate of the grades that their pupils will
probably get in national exams. But
it is also possible that all pupils can get at the very least a 10% higher mark
in all exams, if the best methods of teaching and learning are used.
20% is more likely. Such a target can be easily achieved.
It has nothing to do with reforming the education system, as the
materials are widely available and already in use in many schools.
Additional help from the government will always be welcome, but for most
schools the answer is now within reach. This volume makes a particular
contribution to the work undertaken by the First and Best research team, for
this is believed to be the first single-volume photocopiable book to cover both
methods of learning and methods of teaching maths for children with dyscalculia.
The book is divided into four parts: Methods
of Teaching.
This section for teachers is intended to be photocopied and shared with
staff throughout your department. It
can also be shared across departments – for example between the maths co-ordinator
(or head of maths department) and the special needs co-ordinator.
If you find the methods here helpful and you find that they bring in the
results we predict, that is obviously beneficial.
But if you can copy the text and share it with colleagues who then also
use it, that is better still. Sample
policy statements on Methods of Teaching.
These are intended as a starting point for those who wish to codify the
message of this volume into the structure of the school’s work. Methods
of Learning. We suggest
that as part of your regular teaching, one session is set aside each week to
work with the pupils on their methods of learning.
Some schools will want to let individual teachers handle this, in others
the timetable is arranged so that one member of staff works across the whole
department. Where the latter is the
case each project needs to be explored and explained by the other members of
staff in the department, so that they are fully aware of what is going on. Memory
techniques.
A small project based on specific ways of improving memory. Each part can be read in isolation,
but is obviously intended to be part of the whole project. 5.1.
Using the Methods of Learning Programme What follows is a course in Methods
of Learning for dyscalculic pupils. Our
preferred method, and certainly the most effective method, of using this
material is that each week the pupils following the course have a meeting with
you about one specific method of learning maths. The pupils discuss the method with
you and with each other. It is
vital that you give them enthusiasm, and that they understand what they have to
do. Then, throughout the week they
have to adopt this week’s selected method for as much of the maths work as
possible. The following week you review the
progress made, solving any problems, talking the matter through – allowing all
the pupils to make their own contributions.
Assuming all is going well, you resolve any difficulties, and move on to
the next method of learning. If
however there are quite a few problems, the pupils can stay for a second week on
that particular method of learning maths. The pupils can also be given a set of
blank cards and the methods of learning maths can be written on a card each week.
The whole point is that the children should add the methods of learning
to their understanding of how they learn maths, so that over time they are
picking out the methods that suit them best. 5.2.
Learning as an active skill At the heart of our work is the fact
that learning maths is an active process – it doesn’t happen just because a
pupil is sitting in class, or has a book open at home.
Just because the pupil does a homework correctly does not mean that the
pupil has learned or is learning anything.
(Hence the topic “All homework is learning homework”.) As they work through the exercises
given here the pupils will think (probably for the first time ever) about the
way their brains deal with mathematical concepts. As pupils think about learning they gain confidence in their
control over a process which was previously considered to be fixed and
unchanging. As this progresses learning becomes
an active skill. Only if the
Methods of Learning programme is reduced to an unimportant extra (added in if
there is time) will the message inherent within the programme be lost. To make the most sense of what
follows, pupils should get used to lessons which follow the Structured
Instruction approach outlined in section 3.4.
If it is not possible to follow that approach then the following should
be adopted: · The lesson starts with a warm up – a mental event possibly unrelated to the subject of the lesson. This could well involve focusing on the pupils’ physical presence – getting them upright and smiling, attentive and active. Remember the physical well-being of the pupil is important. They will learn better if they practise smiling as the lesson begins. · The lesson proper then starts with a revision of what is known on a chosen topic. · This early stage involves questioning. Throughout the lesson there must be a lot of questions. ·
As they work through the Methods of Learning activities the pupils
will be ready to apply their new knowledge to each topic being studied, and here
the pupils should have guidance on which methods of learning might be most
appropriate in each case. Dividing learning sessions into
sections is a very important element in our
Methods of Learning work, and pupils will find this easier to grasp if their
lessons are very obviously divided into sections.
In an ideal situation, the structure of the lesson should be on a large
chart, which everyone can see and to which the teacher refers as the lesson
progresses. Here’s an example based on the structured instruction approach. · 0-4 minutes: Active review of previous knowledge. · 5-8 minutes: Active review of the last lesson. · 9-10 minutes: Establish a lesson structure which orientates the pupils. · 11-14 minutes: Discuss the objectives and targets for the lesson. · 15 minutes: Provide clear instructions. Show the materials to be used. · 16-25 minutes: Present new material in small steps. · 26-30 minutes: Review the rule or topic that has been taught. · 31-40 minutes: Discuss the topic with the pupils, check understandings. · 41-45 minutes: Test the knowledge of all students. · 46-50 minutes: Move the pupils towards mastery of the topic. ·
Homework: The pupils undertake independent practice, solving
problems and using shared learning techniques. 5.3
Objections from teachers to the Methods of Learning programme Here are some of the main objections we have heard from
teachers who are not happy with the methods of learning programme, and the
answers we have given. 1.
My own methods of teaching have worked perfectly well until now. This is undoubtedly true, but unless
every dyscalculic pupil is overcoming his or her dyscalculia very quickly there
is room to improve. There is no
knowing how well the pupils can do until we start trying different methods. 2.
I don’t have time – the syllabus is far too long Although we are adding an extra
element to the syllabus in terms of methods of learning we are effectively
reducing the amount of time needed to teach dyscalculic pupils how to handle
maths because the teaching and learning becomes much more efficient and the
dyscalculia is overcome far more quickly. 3.
I am supposed to be doing maths, not teaching skills. Our view (and of course it is just
our view) is that the role of members of the maths department is to teach maths
in such a way that the pupils learn it
– which is what we are talking about here. 4.
Well if you insist I’ll give it a go, but I don’t expect for a moment
it is going to work. It probably won’t with this
attitude. Everyone has the ability
to sabotage a project by treating it with disdain. You have to sell the concept to the teachers first – if
necessary by running the project yourself first and then proving to them it does
work. If you have read this volume
and you feel the project is unlikely to work, but you’ll “give it a go” we
would urge you not to. It is not
going to work under such an attitude, and will probably just serve to prejudice
the pupils against maths even more. 5.
The parents don’t like it. If that is the case then they
haven’t had it explained properly. You
cannot allow the pupils to be your messengers in something as important as this.
Write to the parents, invite them into the school for a meeting –
explain to them that this is going to be of enormous benefit to their pupils. 6.
We’re already doing it. Great – but are you sure?
This process involves far more than just changing the teaching method
according to the topic. 7.
The methods of learning projects are too childish.
What is the point of the pupils making lists of what they learned? In fact major achievements can be
gained just by getting the pupils to think about learning.
The reality is that until they start a course such as this they rarely
think about learning at all. Half
the battle is to get the pupils to focus on learning. 8.
The children I am teaching are too young to use the forms and activities
in the programme. This of course can be a problem – especially in a book of
this nature which aims to explore the issue of failure at maths and which is not
age specific. You may well have to adjust the pages that follow to meet
the needs and abilities of your pupils. This
however does not, in our opinion, invalidate the entire approach.
Help the pupils with each activity.
Guide them through it. Give
them suggestions. Keep working with
them until such time as they grasp the nature of the activity and can do it by
themselves. |
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