[Edu-sig] Programming in High School

[Gregor Lingl]

Daniel Ajoy schrieb:
>>> But the criteria of "relevant problems, easily solved with a quickie
>>> program" is tough to meet.  
>>>       
...
>>> And another point is that some problems cannot be solved using algebra or trig. I believe this is one:
>>>
>>> http://neoparaiso.com/logo/problema-triangulos.html
>>>
>>> It asks the student to determine the values of the segments a and b.
This is a nice problem, which could also find an easy solution in 
Python, not only in Logo, of course ;-)
Like the on attached one, for instance.

I'd only like to add a few remarks to the problem discussed in this 
thread - which I also know very well as a high school teacher in Vienna, 
Austria.

(1) One root of the problem seems to be that whatever "relevant problem" 
we pose, there are *a lot* of different adequate tools to approach it in 
these modern times and it is by no means clear that programming is the 
'natural' approach. See for instance

http://www.rg16.at/~glingl/triangle/

for a different solution to Daniel's problem.

(2) To profit from beeing able to program needs continuous practice. So 
as a teacher of a math class you had to convince *all* of your students 
to do it continually.

(3) This - at least here in Austria - seems to be impossible as long as 
programming is not part of the official math curriculum (like for 
instance the appropriate use of a pocket calculator). Even core math is 
not done by *all* students on their own free will, because they enjoy 
it, or they are interested in it, but by some of them often only because 
they *need* it for their gradutation. And I suppose that programming 
will  never be part of the standard curriculum, even if only because 
only a small part of the maths teachers are proficient in programming. 
So they naturally would oppose such a change.

(4) Moreover it seems to me, that even in the area of computer science 
or computer technology the part which is occupied by programming is 
getting smaller. 25 years ago, if you wanted to do some interesting 
things with a computer, you *had* to be able to program, while nowadays 
there are so many interesting things you can do without programming. For 
instance what do you think, which part of the people working in the 
comuter game industry are programmers? I suppose, this trend also 
diminishes the young people's interest in programming (as well as the 
school authorities interest in putting programming into the mainstream 
curricula.)

(5) Despite all of this I'd also like to contribute a problem, I 
stumbled over yersterday, incidentally. It might not be 'relevant' but 
it's also one that most probably couldn't be solved without computers 
and which without doubt has the potential to stimulate the student's 
interest in math as well as computing:

Christian Goldbach (1690-1783), stated several number theoretical 
conjectures, among them the famous Goldbach conjecture, concerning the 
set of even numbers > 2.

An other (similar) one is the following: every odd positive integer 
could be written in the form p + 2*a**2, where p is a prime (or 1, then 
considered a prime) and a >=0 is an integer. Example: 23 = 5 + 2*3**2 
(to use Python notation). Euler checked this conjecture for odd numbers 
up to 2500 and he didn't find a counter example. Only a century later 
two counter examples were found in the range below 10000.  What are 
these two numbers?
The curious thing is, that to this day these two numbers remain the only 
ones found.

Regards

Gregor




>>> Daniel
>>>
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