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parts of the problem to be solved. These procedures are given names that
can then be used within other procedures. In some programming
environments, the word macro is used to describe a sequence of instructions
that can be named so that the programmer can use the macro without having
to think about the details of its definition. In the computer programming
world, there are often standard ways of solving particular problems, for
example, the problem of sorting a set of numbers. The word algorithm is
often used to describe a series of instructions to solve a specific problem.
From a programming point of view, some algorithms are more efficient than
others (e.g., in terms of time and memory). An emphasis on standard algo-
rithms, pre-written macros and efficiency is clearly important for effective
computer programming, but is not, I suggest, where the emphasis should be
placed when programming in the mathematics classroom.
My own personal experience of computer programming illustrates the
dramatic way in which it has changed over the last 25 years. In 1966, as a
university student, I attended a one-week Algol programming workshop,
which consisted of lectures and hands-on experience. This hands-on experi-
ence involved spending hours typing a program on a set of punched cards (a
Rosamund Sutherland
London
1. INTRODUCTION AND BACKGROUND
R. Biehler, R. W. Scholz, R. Sträßer, B. Winkelmann (Eds.),
Didactics of Mathematics as a Scientific Discipline, 177-187.
© 1994 Dordrecht: Kluwer Academic Publishers. Printed in the Netherlands.

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piece of card containing data in the form of punched holes) and waiting at
least overnight for the program to run only to discover that typing errors had
been made, errors that were difficult to identify because the punched code
had to be translated into the computer language before it could be read. So,
at this time, it was very important to plan a program in advance, and it was
very important not to make syntax errors because these cost time. In no way
was it possible to interact with the computer code as it was interpreted and
evaluated by the machine. Things began to change with teletype terminals,
which were attached to mainframe computers, but these were very un-
friendly, feedback could be slow, and the link to the mainframe computer
was often fragile. Nowadays, we can write sophisticated programs on a
portable computer, interacting with the language in a negotiating way.
Professional programmers have responded to these technological changes,
but in the educational world (i.e., the world of teaching and learning pro-
gramming), a "mainframe mentality" often prevails. This can result in an
over-emphasis on planning away from the computer and an over-emphasis
on a directed form of teaching. Nowadays, there are many possible ways of
interacting with a computer program, and so it is interesting to question why
so many university computer programming courses are still taught in ways
that are similar to those used 25 years ago. Lack of computer provision, or
student numbers, is often given as a reason, but, in my opinion, the reason is
more related to the need of the teacher to hold onto knowledge as a means
of power and control. Also, if, as a teacher, you have a strong model of
learning as being related to both the ability and developmental stage of a
student (possibly influenced by Piaget's theories), then you have more or
less rid yourself of the responsibility of changing your teaching method. We
now know that elementary school children can program in Logo (Noss,
1985). This knowledge has not revolutionized the teaching of programming,
it has merely resulted in the marginalization of Logo as a programming lan-
guage.
178
THE ROLE OF PROGRAMMING
2. PROGRAMMING IN THE UK MATHEMATICS CLASSROOM
In the UK, programming in school was firstly the province of school com-
puter science courses, a new subject taught and examined to 14- to 16-year-
olds. This subject was often taught by the mathematics teacher, and the pro-
gramming language used was almost always BASIC. So there developed, in
the UK, a body of secondary school mathematics/computer science teachers
with an expertise in BASIC programming. Most of these teachers were men
and most of the students studying computer science were boys. BASIC pro-
gramming began to be used by mathematics teachers in the mathematics
classroom, and it was this activity that was greeted with such enthusiasm by
the mathematics inspectorate as expressed by Fletcher:
Some years ago I saw the heartening, indeed amazing, response when microcom-
puters were first introduced into schools . . . excellent work was done when stu-

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ROSAMUND SUTHERLAND
dents were encouraged to explore, to investigate things which interested them and
to find their own way forward. (Fletcher, 1992, p. 1)
When Logo became available on small computers (in about 1982) and
started to be used in schools, it challenged the BASIC programming com-
munity for a number of reasons: Firstly, young children began to learn com-
puter programming, and, secondly, Logo was difficult to learn for those
who had previously programmed only in BASIC. This relates to the recur-
sive control structure of Logo, which cannot easily be followed in a step-by-
step way. Thirdly, Logo came with a whole set of ideas about the philoso-
phy of teaching, ideas that have become polarized as learning by discovery.
Many of us who have carried out research and development with Logo no
longer accept this polarized view of learning and have extensively written
about the issues surrounding the teaching and learning of Logo (Noss &
Hoyles, 1992; Sutherland, 1993).
The tensions and debates about the relative value of Logo and BASIC in
the UK mathematics curriculum, which now seem very outdated, have nev-
ertheless resulted in an equal share being given to both programming lan-
guages in the new National Curriculum for Mathematics. For example, in
the strand related to algebra, it states that students are expected to follow