
The Case Against Computers in K-13 Math Education (1996) - jessup
https://sites.math.washington.edu/~koblitz/mi.html
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curun1r
I don't know about general purpose computers, but my life would be completely
different if my high school hadn't required the use of computers that
masqueraded as calculators.

My school required us to use either a TI-81 or TI-85 and my friends and I
quickly discovered the power of TI-Basic. We started with small games to amuse
ourselves, since this was an era before mobile phones. But I quickly realized
that I could write programs to solve the kinds of problems I expected to see
on my math tests. And I was amazed when I asked my teachers whether I was
allowed to do that and they said yes...it felt like cheating. Suddenly
studying became an altogether different experience where cramming and hoping
I'd learned enough was replaced by writing small scripts that gave me full
confidence I'd ace the tests. It was so much more efficient. The funny part
was, I never actually used my programs during the tests...the act of
programming, I realized, forced me to understand the material in a way that
cramming never did.

From that experience, and a Doom-like game I built on my calculator, that
spurred me to take a computer programming class the summer before college and
eventually major in CS and go into tech. And none of that would have happened
if my math teachers hadn't been so open minded about allowing us to use what
was essentially a computer in class and on tests. So I hope they're not
advocating removing all computers from class, because I'd be sad if the path I
took into tech was closed to today's students.

~~~
dragonshed
I had a very similar experience. I didn't get a computer until I showed my
parents something I'd built on a TI-81. The one difficulty I had was a physics
teacher who would go around and factory reset the calculator prior to tests,
and that was just fine by me until I started making large games and things I
wanted to keep. I ended up making a reset emulator to fake the teacher and
allow me to keep my apps.

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dahart
> We already saw an extreme example of misallocated resources in Peru. But
> even in a ``wealthy'' country one has to be concerned about this problem.
> Many educators in North America share the feeling of betrayal of the teacher
> who said, They can give us the axe, but they can spend thousands on
> computers. We have to fire our music coordinator, we have to fire our music
> teachers, we have shitty libraries. (Lynn, a Canadian schoolteacher, quoted
> in [14, p. 41])

I’ve seen this happen in the relatively wealthy schools my kids are in. They
spend many thousands on smartboards and iPads, and they’ve gotten rid of the
“non-essential” arts and music teachers. Parents are personally funding some
arts educators on a part time basis a couple of days a week. I think it’s an
egregious misuse of funds, wasteful and ultimately damaging to the kids.

What’s worse, the tech is not being used effectively. The teachers don’t have
enough training to incorporate the smartboards and iPads, and they don’t have
the budget for tech training because they spent it on the iPads. Kids play
games on them that they have access to at home, but they’re not being taught
about the technology or being taught to use it to do things they can’t do on
paper.

I don’t mind computers in the classroom, as long as the arts are funded and
the teachers are paid enough. What I’d really love to see more of is using
computers to integrate math and arts together... digital arts with an emphasis
on both rigorous math and rigorous art. Give the mathy students some
aesthetics training, and make sure the art students are capable with
computation.

~~~
20years
"What’s worse, the tech is not being used effectively. The teachers don’t have
enough training to incorporate the smartboards and iPads, and they don’t have
the budget for tech training because they spent it on the iPads."

Yes this is exactly what I see in my sons school. Some of the kids actually
know more than the teachers and end up providing support to the teachers. Then
the kids do silly things like duplicating icons on the home screen 100+ times
and change folder names to things like "poop". The teachers freak out thinking
they hacked into the computers because they have no idea on how those simple
things were done, or how to disable them from doing those things.

"What I’d really love to see more of is using computers to integrate math and
arts together... digital arts with an emphasis on both rigorous math and
rigorous art"

Yes!!!

~~~
applecrazy
I attend high school in the Bay Area and I'm surrounded by this Smartboard
epidemic. Nearly every classroom at our school has one, but only around 10% of
teachers actually use the "smart" portion, even though most of them have
gotten some basic training in their proper usage. Most are used as dumb
projectors for presentations and lectures, and the pens are seldom used. And
keep in mind, this is _Silicon Valley_ , the _" cradle of tech innovation."_

I find this to be an egregious waste of school funds, funds that could have
gone towards funding school plays, improving school facilities, or expanding
the engineering course offerings. And the real kicker is that my HS is an
"arts magnet" school.

¯\\_(ツ)_/¯

~~~
alphydan
teacher here. Most smartboards are rubbish. The calibration fails constantly,
it's really hard to draw on it ... and most "ready made" lessons for
smartboards are usually boring. So I'm afraid it's a projector for me.

~~~
eat_veggies
The ready-made lessons are more shitty tech demos (Amazing! Drag and drop!
Buttons! Computers!) to wow the administrators than actual lessons.

We have smart boards and chromebook carts in every room of my high school, and
yet they canceled our fucking robotics team due to "lack of funding" and fired
our oldest computer science teacher because his experience + degrees meant he
cost them too much to employ [0]. Yes, I'm mad.

[0]
[https://de01903704.schoolwires.net/site/handlers/filedownloa...](https://de01903704.schoolwires.net/site/handlers/filedownload.ashx?moduleinstanceid=1213&dataid=1446&FileName=FY18%20TEACHERS%20PAYSCALE.pdf)

~~~
applecrazy
You’re absolutely right, it’s absolutely admins seeing the “ooh shiny” aspect
of these things. I have a feeling the company pushing these boards has really
good salespeople.

And I’m an officer of a robotics team, so I feel your pain. We get zero
funding from the school. Most money comes from members’ pockets or
fundraisers. Eventually, we want to ease the burden on members by getting
corporate sponsors, since we obviously won’t get any money from the school
district, who’s busy cutting library budgets and buying smart boards.

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perl4ever
Some declarations of the limits of computers jump out to me as dated:

"The inability to develop good translation software has been one of the most
embarrassing failures of Artificial Intelligence. If the best computers in the
world are unable to translate from French into English..."

"in the calculus final exams at my university we usually ask for exact (not
decimal) answers. For example, sin(60°)=\sqrt{3}/2, not 0.866; the
circumference of a circle is 2 pi r, not 6.283r"

Also, the comparison of computers to automobiles in order to dismiss them is
odd, as driver's education _was_ part of school when I attended in the 90s.
And so was auto repair, which I regretted not taking in later years.

A computer from 1996 seems, in today's context, rather ironically like
"simple, unstructured play material like clay, sand, blocks, rag dolls, and
finger-painting sets".

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bocklund
One of the keys to learning is making students engage in the material and to
fix their mistakes. Computers are uniquely able to give individual, rapid
feedback.

Even at the advanced level it would be really cool for students to have access
to and use proof software. I wish I could have had the opportunity to work out
proofs for myself, guided by software, instead of just being given them.

~~~
nmca
Interactive theorem proving is an active area of research, but it's quite hard
to do well, and the main area of focus is on theory atm, as opposed to UX

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Viliam1234
Asking whether "computers" belong to education is like asking whether "books"
belong to education. I can imagine a book that does. I can also imagine a book
that does not. Same for computer programs.

We should debate specific applications, whether they help the education, or
are just shiny toys. Then we should make the cheapest computer which runs
exactly these applications and nothing more, and use that in schools.

If teachers don't know how to use a computer, these two things could fix that
easily: set up the educational computer so that it can only run those selected
educational applications; and write a book about how to use each of those
applications in education.

A debate on the level of "Computers good! No, computers bad! Good! Bad! Good!
Bad!" is not helping anyone.

An example of a useful application in math education could be e.g. something
that shows you how a graph of a function changes when you change the equation.
For example, you could have a quadratic equation, where you can use the mouse
to change each coefficient. When the time is right, bring the computers and
let the kids experiment with this. On other days, do not bring the computers
to the math lesson.

Collect some applications like this, make a Linux DVD which can be installed
or run live, write teachers' manual for each application and put it on the DVD
and online as a PDF file, and that's it. (I suppose someone already did
something like this, although probably without the PDFs.)

The question is not whether to use the computers or not, but how to use them.

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kwhitefoot
The purpose of education should be learning how to think and to apply one's
thoughts. The most important tools in the class are the brains of the teachers
and pupils. Those are really the only tools that are needed. My youngest son
had to have a laptop for the final three years of school (Norwegian
videregående). It was justified on very flimsy grounds. One of the programs
was a geometry program; what he learnt from that could have been taught by
Pythagoras with a sharp stick in the dust on the ground.

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jwatte
The #1 important need in math education is repetition. Repetition with
understanding. If you don't internalize all the simple rules, you can't do it
for yourself when you need to.

Which side of the division line do you put each quantity on? How do you use
unit math to verify your problem statement? Multiplication table, and simple
addition/subtraction. Probability and statistics. Repeat, repeat, repeat.

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dfaigonio
I've long held that, if we want computers in the classroom at all, we should
steer well clear of any modern gee-whiz gadgets. A modern Commodore 64 clone
would teach vastly more about computers than an iPad and would cost maybe $50
total. Modern computers are designed so people _don 't have to understand
them_, which is exactly backwards for a student.

~~~
cmrdporcupine
But it depends on the goal. Most people's interactions with computers is going
to be as a user, even a power user -- but not as a developer. Due to classroom
activities, my 10 year old is quite adept at Google Docs, Slides, etc. and
various authoring tools they use in class. She puts together presentations and
reports with them, and collaborates with her peers using them.

I grew up in the Apple II/Ti-994a in the classroom era. Only a small fraction
of students took the challenge of those machines on such that they learned
software engineering skills later. We had classes teacher BASIC and Logo, but
almost none of my peers went on to do anything with it, and I'm sure retention
generally was very poor.

I'd love for people to learn like you say, but I don't think it would work
that way.

~~~
lr4444lr
That's great they're learning about business applications, which is a valid
part of the curriculum. But they're not about computers, as per the OP's
point.

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Clubber
If I were a professor, I wouldn't allow open laptops or phones. I would
imagine it's a huge distraction and students are there to listen to the
lecture and learn, not goof off with their devices. I'm old and crotchety
though. We had laptops when I went to school, but no one (that I noticed) used
them in non-computer class.

~~~
msangi
I would allow them, but then I'd also shift the focus from learning some
mechanical procedure or facts to more fundamental concepts and increase the
complexity of the problems accordingly.

It's hard to do it right, but I believe it has the potential to to engage
students and increase their understanding by separating the boring parts (that
a computer can easily do) and the challenging parts that the students need to
understand

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rsp1984
Pardon my ignorance but can somebody educate me on what K-13 means? I know
about K-12 and have seen K-14,-16, ... as well but I've never seen K-13 in an
international context.

At my local school in Germany the final year was called K-13 but it's probably
not what's meant in the article.

~~~
bsznjyewgd
I think it just means kindergarten to year 13. At least, Ontario (Canada) used
to have a 13th year, but they phased that out 2 decades ago into just K-12 as
well.

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SamReidHughes
The short argument is make is that learning happens in the brain, when it
thinks about stuff. It doesn't happen in the computer. We can create a faster
pace by having more individualized education, but that's about it.

