[Edu-sig] a non-rhetorical question

Michel Paul mpaul at bhusd.k12.ca.us
Sat Jul 7 19:49:58 CEST 2007

I was very happy to see this book come out recently:

"Mathematics for the Digital Age" 

This is still in its preliminary stages, finished version will appear in February.

The preface is delightful - they explain there how Donald Knuth realized that the mathematics he needed in computer science was not quite what he had studied in the traditional math major.  This led him to create "Concrete Mathematics" (CONtinous + disCRETE).

>I think it's impossible to teach CS to kids who are afraid of math.

More and more I believe high school math teachers have a responsibility to emphasize to students that computers only exist BECAUSE of mathematics.  What makes something a computer is not the material from which it is constructed - that material could even be plumbing - what makes something a computer is its organization.  When a student asks, "When am I ever going to use this stuff?" the answer is - "Every friggin time you use your computer!"

Many math students are actually surprised to hear that - it's weird, but they just do NOT realize that computers have their roots in mathematics!  I really believe that has to change - the whole math curriculum needs to be upgraded for the 21st century.

>here we are in 2007 and most high school
>math classes are stuck in the calculator era.  What happened?

Marketing.  Cleverly appropriating teachers to perform free advertising and sell product by calling them 'leaders'.  Getting textbook publishers to feature calculator sections in each chapter, thereby creating a status quo where technological integration has "already been handled".

Also, I believe part of the problem is the perceived division between CS and mathematics.  CS has grown to become its own discipline and its own department at the university level, so when we talk about integrating CS into math classes, people are apprehensive, thinking we're adding some "other subject", some "additional layer", to the math curriculum.  

The difficulty is getting people to realize that it's really the other way around.  When you introduce gadgets - calculators, software "packages", etc. that students then have to learn to use - THAT'S where you get additional layers to the already-existing curriculum.  When you use a high-level computational language, like Python, to express algebraic concepts, the algebra and the technology can be presented as ONE THING.  For example:  >>> for x in domain: x, f(x)  There's actually LESS layering going on there.

There's actually an interesting contrast here between
    emphasizing the unity of CS/mathematics and 
    getting kids to program in "fun" (i.e. "non-mathematical") ways.  

It does make sense in our math-phobic educational climate to show beginning programming students how they can do fun things without having to worry about the algebra, and quite a lot of good effort has gone into this.

But simultaneously, I think it makes tremendous sense to show students how a kind of algebraic thinking is fundamental to our technology and to weave this into math classes.

- Michel


"Shall I tell you what it is to know?
To say you know when you know, and 
to say you do not when you do not, 
that is knowledge."

- Confucius


-----Original Message-----
From: edu-sig-bounces at python.org on behalf of kirby urner
Sent: Sat 07/07/07 02:52 AM
To: Ivan Krstic
Cc: edu-sig at python.org
Subject: Re: [Edu-sig] a non-rhetorical question
On 7/7/07, Ivan Krstic <krstic at solarsail.hcs.harvard.edu> wrote:

> Bottom line: terminology matters. I think it's impossible to teach CS
> to kids who are afraid of math. Teaching *programming* is something
> else entirely. I'd submit that what Andy can expect from his students
> depends largely on which of the two he's trying to teach.
> Cheers,
> --
> Ivan Krstic <krstic at solarsail.hcs.harvard.edu> | GPG: 0x147C722D

You're correct that math has a terrible reputation in many corners.
As mathematician Keith Devlin puts it, math is about making the
invisible visible -- a meme he invented to try countering the negative
perceptions people have about math.

On the other hand, if you're sitting in front of a computer, connected
to the Internet especially, there's a sense of possibility, as well as of
community.  Technology has "sex appeal" including the allure of a more
positive future (a meaning captured by the South African word 'kusasa').
Bridging the digital divide is another way of saying we're working to
spread analytical skills to those who could use them.

So a question confronting a lot of us is how to "rescue" mathematics
by means of technology, which in part means restoring a sense of
fun (Papert: "hard fun") and play.  In the 1980s, it seemed K-12 math
curricula were on the verge of incorporating more technology in the
form of BASIC and Logo, but here we are in 2007 and most high school
math classes are stuck in the calculator era.  What happened?

I think what a lot of kids find accessible and meaningful is a "how
things work" approach (which connects to Keith Devlin's meme).  We
want to explain real stuff in the real world, and that takes mathematical
concepts, analytical thinking and the like.  Little things like indexing,
data structures like trees (document object model, xml) make a huge
difference.  Databases are behind the scenes in so many walks of life.
In the traditional curriculum, that means branching off from Venn
Diagrams, plus talking about data in tabular formats.  When we talk
about Venn Diagrams would be a good place to put some intro to

A problem in the mathematics culture is there's a lot of pride at having
made it through certain "filters" and a wish to impose those filters on
newcomers, to see who "makes it" through these difficult obstacle
courses.  Whereas I recognize every profession has standards, and
not everyone is cut out to be just anything, I think math's poor
reputation is in many ways a result of too much pride among the
math savvy.  There's a lot of protectionism, not to mention
overspecialization that goes on.  I see the infusion of computer
savvy as helping to break up some of the old patterns of specialization.
Restoring the reputation of mathematics does not have to mean
returning to some past status quo.

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