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"Modern" mathematics with Morphic

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Alain Busser

"Modern" mathematics with Morphic

Hi,

when I was a child the times were to what was called "modern mathematics". It was quite strange, and we children had to draw Venn diagrams around pentagons (amongst other polygons) or the like.

Now modern mathematics have become quite ancient (much like me) and everybody forgot about these "patatoids" (that's how we used to call them in french). Yet nowadays with tablets, exercises can be designed where, instead of drawing a Venn diagram *around* pentagons, the pupil could *move* the pentagons *inside* their Venn diagram (for a linguistic example, imagine moving the letters here: http://en.wikipedia.org/wiki/File:Venn_diagram_gr_la_ru.svg). These exercises where the pupil is to categorize objects or concepts, would be useful also in biology or grammar, if only...

Well, ahem, I found out how to devise such exercises in JavaScript with jQuery UI (just declare any element as "draggable", then the sets as "droppable"). But I found out that it seems easy to drop a Morph (element) to another one (set), then make some set theory with "serious games". After all, that's what is shown in "Pharo by example" (drag and drop, and devise one's own method as to what can be dropped or not).

Hence my question: Am I the first "genius" to think about this (doubtful) or (more probably) who did already this kind of exercises about set theory? Maybe in Etoys? Maybe not in mathematics but linguistics or other?

A short bibliography on the subject:
*http://www.cut-the-knot.org/LewisCarroll/tridiagram.shtml (was actually sold in wood with checkers pieces and an instruction book)
*<a href="http://www.college-de-france.fr/site/stanislas-dehaene/course-2013-01-29-09h30.htm#|q=../stanislas-dehaene/course-2012-2013.htm|p=../stanislas-dehaene/course-2013-01-29-09h30.htm|">http://www.college-de-france.fr/site/stanislas-dehaene/course-2013-01-29-09h30.htm#|q=../stanislas-dehaene/course-2012-2013.htm|p=../stanislas-dehaene/course-2013-01-29-09h30.htm| (how the baby learns to speak: There is classification to grasp vocabulary)
*<a href="http://www.college-de-france.fr/site/stanislas-dehaene/course-2013-02-12-09h30.htm#|q=../stanislas-dehaene/course-2012-2013.htm|p=../stanislas-dehaene/course-2013-02-12-09h30.htm|">http://www.college-de-france.fr/site/stanislas-dehaene/course-2013-02-12-09h30.htm#|q=../stanislas-dehaene/course-2012-2013.htm|p=../stanislas-dehaene/course-2013-02-12-09h30.htm| (the following: The baby uses bayesian inference to solve these kind of problems). If I understand well, the minimum age to play to these games is, after Dehaene, 6 months (!)

Alain

philippeback

Re: "Modern" mathematics with Morphic

Hi,

I did that in school as well (and happen to have a bunch of super old math books over that from the sixties - from my mother in law, she was a maths teacher, as is my wife (there is a stream there)).

Anyway, I did a pharo Morphic little app with drag and drop in areas where one drags and drops numbers and signs from one area to another, so doing that kind of thing is pretty doable.

My app runs on the iPad with the StackVM. Drag and drop works perfectly well on it.

Regards,
Phil

2013/5/7 Alain Busser <[hidden email]>

Hi,

when I was a child the times were to what was called "modern mathematics". It was quite strange, and we children had to draw Venn diagrams around pentagons (amongst other polygons) or the like.

Now modern mathematics have become quite ancient (much like me) and everybody forgot about these "patatoids" (that's how we used to call them in french). Yet nowadays with tablets, exercises can be designed where, instead of drawing a Venn diagram *around* pentagons, the pupil could *move* the pentagons *inside* their Venn diagram (for a linguistic example, imagine moving the letters here: http://en.wikipedia.org/wiki/File:Venn_diagram_gr_la_ru.svg). These exercises where the pupil is to categorize objects or concepts, would be useful also in biology or grammar, if only...

Well, ahem, I found out how to devise such exercises in JavaScript with jQuery UI (just declare any element as "draggable", then the sets as "droppable"). But I found out that it seems easy to drop a Morph (element) to another one (set), then make some set theory with "serious games". After all, that's what is shown in "Pharo by example" (drag and drop, and devise one's own method as to what can be dropped or not).

Hence my question: Am I the first "genius" to think about this (doubtful) or (more probably) who did already this kind of exercises about set theory? Maybe in Etoys? Maybe not in mathematics but linguistics or other?

A short bibliography on the subject:
*http://www.cut-the-knot.org/LewisCarroll/tridiagram.shtml (was actually sold in wood with checkers pieces and an instruction book)
*http://www.college-de-france.fr/site/stanislas-dehaene/course-2013-01-29-09h30.htm#|q=../stanislas-dehaene/course-2012-2013.htm|p=../stanislas-dehaene/course-2013-01-29-09h30.htm| (how the baby learns to speak: There is classification to grasp vocabulary)
*http://www.college-de-france.fr/site/stanislas-dehaene/course-2013-02-12-09h30.htm#|q=../stanislas-dehaene/course-2012-2013.htm|p=../stanislas-dehaene/course-2013-02-12-09h30.htm| (the following: The baby uses bayesian inference to solve these kind of problems). If I understand well, the minimum age to play to these games is, after Dehaene, 6 months (!)

Alain