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Topic: Question 7: Why integrate computer science with high school
math?

Replies: 1   Last Post: Apr 4, 2001 3:50 PM

 Messages: [ Previous | Next ]
 Kirby Urner Posts: 803 Registered: 12/4/04
Question 7: Why integrate computer science with high school
math?

Posted: Apr 3, 2001 4:04 PM

The question of how to better integrate computer science with
mathematics at the introductory level is very important, and
I think many different solutions will be (already have been)
tried, with varying degrees of success.

Because computers are essential to the core functions of large
technological societies, students should have some insight
into how they operate, but these insights should point back
to general ideas in mathematics as well.

The use of computers may add to student understanding of
mathematics completely independently of students' learning
how computers work. However, some discussion of the internals
of computers provides an ideal entry point into many overlapping
topics and historical narratives, all of which will shed light
on the shared world in which our students will be growing to
adulthood and, we hope, prospering and mentally maturing.

I will give three examples of how computer science and mathe-
matics might be taught together, in the same integrated curriculum:

---

1. The use of symbols as primary keys to track objects

The fact that symbols may be permuted in various ways to
form unique strings or symbols, which may, in turn, be used
to identify objects, as in the case of serial numbers or
passport numbers, provides a useful introduction to
cardinality -- the use of numbers as identifiers. This
leads to a discussion of how many permutations might be
required if the only symbols or values at the most
primitive level are 1 and 0. How shall we map all the
symbols in the Chinese language, and other languages, to
permutations of 0 and 1? This question leads to an
investigation of the unicode solution.

Example: http://www.inetarena.com/~pdx4d/ocn/cardinality.html

2. The use of logical operations in circuit function and design

Binary logic with operators such as XOR, AND, OR, NOT make
sense to children, if properly presented. These operators
may be investigated independently of their applications in
the design of integrated circuits, in the form of propositions
which may be true or false. However, the application to
circuit design should be discussed.

Example: http://educ.queensu.ca/~compsci/units/BoolLogic/titlepage.html

3. The use of variables in coded, general purpose algorithms

The coding of an algorithm such that it may be applied to
many cases, depending on what gets passed to it in the
form of parameters or arguments, helps students appreciate
the importance and power of variables. Some exposure to a
programming language, in which variables are used as place-
holders, provides a good foundation in which to later
develop more complex algorithms, such as matrix multiplication
or vector operations. I would go further and suggest that
students should develop an appreciation for the object-oriented
approach to programming, as this will provide many benefits
in math learning, such as when we represent vectors or matrices
as objects defined by their common template or class.

Example: http://www.inetarena.com/~pdx4d/ocn/numeracy0.html

This was not meant to be an exhaustive list of course. One
additional example of an application for computers which is
making a lot of headway in my home state of Oregon at the
high school level is the introduction to dynamic system modeling,
mostly using STELLA software. Sym*Bowl, a regional gathering
for students participating in these classes, is set for May 2nd
at the local science museum.

http://www.clexchange.org/cle_symbowl.html

----

I do not think the integration of computer science and
mathematics teaching will occur overnight and without many
false starts and dead ends. Appropriate teacher training is
currently in short supply, and computer hardware, if available
at all, may not be properly configured for use in the math-
learning classroom.

In the United States, computer science is often taught
completely independently of mathematics courses. To my way
of thinking this promotes waste and redundancy, is a
misallocation of resources, as at the introductory level
there's no good reason to separate these disciplines -- it's
a symptom of overspecialization that we do so today. Math
provides a fertile and interesting territory in which to
apply one's growing programming skills, and comprehension
of the underlying mathematical ideas improves as one is
faced with capturing them in the form of working programs
(we may think of them as "math poems").

Also, whereas computer science teachers of course demand
computers, math teachers seem content to accept their
second class status such that their students must purchase
calculators even when a fully equipped computer lab exists
just down the hall.

I am hopeful that math faculties will eventually break out
of this "calculator ghetto" situation and graduate to
classrooms equipped with real computers, as these will
provide richer educational experiences and opportunities
for their students. Perhaps China is in a position to
leap-frog the calculator phase and go more directly to
the computer-endowed math classroom still on the horizon
in this country. Having one computer for every student is
unnecessary. More important is to have a teacher who knows
how to use the computer effectively, and some way of
projecting the computer's display for the whole class to
see at one time.

If the system is market-driven in the sense that students
and parents have some choice in the matter, then this may
approach in more schools, as the benefits to students will
be obvious, and schools not offering it will find themselves
less attractive to would-be customers.

This economic motivation for moving towards a more techno-
logically-informed curriculum is what will bring about the
necessary reforms. Without these market forces, teachers
will find it comfortable to teach in about the same way next
year as they did this year, and the present day status quo,
which many of us regard as unacceptable, because too
irrelevant to real student needs, will persist indefinitely.

Kirby Urner
Curriculum writer
Oregon Curriculum Network
http://www.inetarena.com/~pdx4d/ocn/

Date Subject Author
4/3/01 Kirby Urner
4/4/01 xiaodong cheng