[squeakland] Etoys, is it difficult or easy?

[Carlos Rabassa]

There was,  recently,  a very active discussion on this subject in the spanish language forums in which we participate.

Today we posted a sort of summary,  we translate below.

The project

How Many Pizzas  (2010-sep-07 18:35 EDT)
por Carlos Rabassa based on ideas by Daniel Ajoy and Paolo Benini <carlos> 

Resolving 2-variable equation              


contains details of the problem someone proposed,  that originated the thread,  and the solutions found by members of the forum.


Here is the translation of today´s post:



================



One project,  three names,  three levels of perceived difficulty



I am referring to the pizzas problem.

I quote it here from the post of a few days ago by Daniel Ajoy:

"A small pizza costs 120 pesos. 

A large pizza costs 160 pesos. 

You spent a total of 920 pesos. 

How many small pizzas and how many large ones did you buy?"




A first solution was proposed [in the forum].

Only multiplication and addition knowledge was required to explain it or to understand it.

The level of difficulty perceived by the members of the forum,  was that of the middle level courses in elementary school,  when we were given problems to solve as homework.

¿Do you remember?

[the problems] had three parts:  Pose,  Resolution and Response




A second solution was then offered.

It used an XO computer like the ones elementary school children use.

It used SocialCalc,  a program distributed in the computers that allows users to create tables and do calculations.

The perceived difficulty level was still suitable for elementary school,  maybe high school students.

It was still a problem to be solved by those students receiving Plan Ceibal's computers.





During the following days,  while we were trying to find out how to resolve it using Etoys,  there was an active exchange of messages in the forums.

We were trying to write something in a format adaptable to Etoys while reading several messages per day.

Our mind was still floating on the memories from elementary school days.

We recalled the advice from our third grade (??) teacher for solving the problems she assigned as homework.

"Keep reading the pose of the problem I gave you,  repeatedly,   until you understand it".

Great,  the pose of the problem was clearly stated in Daniel's message.

We read his message time and again.

As the next step,  we tried to write as we did in our elementary school days,  the worksheet we had to present to the teacher when the homework was due.  We were thinking of the "resolution" section,  between the posing of the problem and the statement of the solution.  Otherwise,  the teacher would return it to us marked "Incomplete, resolution is missing".

What we were writting was getting closer and closer to what,  years later,  in high school,  we used to call "an equation".



When the time came up to fill in the Etoys card for the new project adding "labels" to help those searching for projects,  the word "equation" was already embedded in my mind.

At that point I had no doubts left,  after all my reading in the forums,  that I was in front of a 2-variable equation with more than one solution.

The same original problem,  posed by Daniel with very simple words just a few days earlier,  had already gone up to a perceived difficulty level that would not allow anyone to get close to it without having completed at least high school.  

It would also require to remember well what we learned in math,  no longer called arithmetic,  maybe in courses including the word algebra.



It was good that when I read messages in the forums mentioning  "Diophantine equations",  I checked Wikipedia right away.

This is the definition I found:

"In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only".

I thought,  "I shouldn´t introduce unnecessary complications.  It basically says they are the same thing as a 2-variable equation".  

And this is how my thoughts of including this fancy words in the name of the project or among the tags,  ended.

Within a few more days,  I will have completely forgotten,  for the second time in my life,  that diophantine equations exist.



If we had called the pizzas project "Resolution of Diophantine Equations",  no one would have had any doubts about how difficult Etoys is.

Someone would have proposed without finding any opposition,  to remove Etoys from the Plan Ceibal computers and to recommend its use only with post grade mathematics university students.

Imagine now what if,  we had taken Daniel´s original pose of the problem and to be politically correct and help our friends at INDA, National Nutrition Institute,  we had removed the word pizza,  generally associated with fast food,  and replaced it with apples and oranges,  like the ones we should eat five servings per day.

We would have had no doubts we were dealing with an elementary school level program.  

At least this would have been the case for those from my times,  who had to resolve an endless number of problems involving apples and oranges.


Conclusion:

If we start a discussion on whether resolving a certain problem is easy or difficult,  rather than attempting to resolve it,   the conclusion will depend entirely on those we talk to and the words they use,  rather than on the problem itself.


This is nothing more than my personal opinion.  

I am open to listen to other opinions.

I clearly understand and accept this is not the ultimate and only truth.

As usual,  we would be particularly interested in hearing opinions from teachers and other educators.

Very special thanks,  once again to:


	Daniel Ajoy who brought the problem for the first time to one of our forums and to

	Paolo Benini who offered the first solution using the XO computer through SocialCalc.

"Y se va la segunda ..."

Till soon,

Carlos Rabassa
Voluntario
Red de Apoyo al Plan Ceibal
Montevideo, Uruguay

================

Note: 

The expression "Y se va la segunda ..." is used in a form of art typical of Uruguay, called "Payada".

Is a contest between two guitar players.

Player #1 starts the match by reciting some improvised story,  accompanied by his own guitar playing.

All of a sudden he poses a question to the other player and goes into dead silence.

The other player has to listen very carefully,  understanding the story,  waiting for this unexpected stop.

At that point he has to start reciting his response to the question,  without delays and without hesitation.

The one who stops for too long or who doesn't come up with a response that answers the question with words that go well with the music he is playing,  is declared the loser without any further considerations.

The literal translation of the above expression is,  

"And the second one [second step of this contest] starts here ..."

He is inviting the second player to continue.

There might be some inaccuracies in my explanation,  I'm not an expert on this subject.


Comments,  are still very much welcome,  on the subject of this thread.


Carlos Rabassa
Volunteer
Plan Ceibal Support Network
Montevideo, Uruguay



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