history of mathematics - National STEM Centre

IV
Using Nuffield Advanced Mathematics
The book consists mainly of activities through which you can develop your
understanding of mathematical ideas and results, or apply your knowledge and
understanding to problems of various kinds.
The activities are designed so that you can use your graphics calculator fully,
gaining all the advantages that this can bring to your learning of mathematics.
For most of the activities you can work either individually or in a small group of
two to four students, but there are some activities for which individual or group
work is specifically recommended.
You will be working on the activities outside the classroom as well as in class,
sometimes with and sometimes without help from your teacher.
Do not assume that you should work through every activity in a unit. The
Nuffield course is suitable for a variety of students with a variety of
mathematical backgrounds and interests.
Planning your work on each unit is essential, as you will need to decide
together with your teacher, which activities to work on, and whether to work on
them in class or as part of your independent study time.
The information in unit and chapter introductions will help with your planning.
The chapter summaries and practice exercises at the end of the book will also
be useful for this purpose. For example, you might already know all of the
results that are developed in some particular chapter, in which case it might be
appropriate to skip that chapter.
On several occasions during your study of a unit, you will take part in a review.
Reviews can take a number of forms: their main purpose is for you to take
stock, through discussion with your teacher and other students, of what you
have learned so far.
To assist with the review process, the end of every chapter contains some
specific suggestions which might form the basis for discussion; there is also a
list headed What you should know. This list is a reminder of the main ideas of
the chapter and of any new mathematics terms that it has introduced. New
mathematical terms are written in bold type the first time they are explained in
the unit. Most chapters end with some check questions for you to tackle to make
sure you have grasped the main ideas of the chapter. There are no answers
provided for these questions, but answers are provided for nearly all the other
questions on which you will work.
You will find messages at various stages in the materials suggesting for example
that you consult your teacher, or should retain the results of a particular activity
for later use. These will be printed in a different typeface so that you can
recognise them. In addition, there will be general mathematical comments
which appear in shaded boxes. These are usually to give you extra background
information.
Towards the back of the book there is a chapter of hints for various activities if
you need help in getting started. You will find the hint symbol ^^ in the margin
next to the particular question for which there is a hint. You should only look up
the hint if you find you are unable to solve the question without it.