The Dynabook and its learning models

On learning-by-doing...

In Alan Kay's Dynabook it is best to learn something kinesthetically, then iconically, and finally the intuitive knowledge will be in place to allow the more powerful but less vivid symbolic processes to work at their strongest(Kay1990).

What said scientific studies on the field of learning by doing and other related pedagogical approaches?

The Dynabook Concept

Dynabook concept, A Personal Computer for Children of All Ages[1], [2], is to provide to learners a computing service to facilitate children learning the world by constructing it via an interactive graphical interface..

Dr. Geo and Dynamic Media

Alan Kay coined the term Dynabook, the expressions Dynamic media and Active Essays. How does Dr. Geo connects to the underneath concepts behind these words? This is what we explain in the following paragraphs.

Cercle inscrit

Dans un article précédent, nous montrions comment écrire une description textuelle du cercle circonscrit à un triangle. Cette fois-ci nous expliquons comment écrire une description textuelle du cercle inscrit à un triangle Cette description sera toujours en français, et légèrement plus complexe.

Mathematics series

My son came to me with a mathematics series, he needs to find its convergence. After the mathematics work is done, we want to confirm by calculus the found limit. Dr. Geo can be of some help here.

The series is S = Sum 1 / (k * (k + 1) * (k + 2)).
Once cut in three parts it is established it converges toward 1/4.

Then we fired up Dr. Geo to compute a few ten of thousand terms and its sum.

In a Workspace we wrote this tiny script:

| u s |
u := [ :k| 1 / (k * (k + 1) * (k + 2) ) ].
s := 0.
1 to: 100000 do: [ :k | s := s + (u value: k) ].
Transcript show: s; tab; show: s asFloat; cr

...and we got the confirmation of our finding:

(1250037500/5000150001) 0.2499999999500015

What is interesting is the exact result Pharo gave us as a fraction number. That's why we also asked for a float version of the sum to more easily realize how close we were to 1/4.

Model with perpendicular bisector

How to resolve a real world problem with perpendicular bisector?

Mathematics is the tool of the mind to build simplified model of a real world problem situation. Then within its model, the mathematics toolset helps to build solutions. We present in the following paragraphs a very simple example of this process with the use of the Dr. Geo software.

Cercle circonscrit

Comment écrire une description textuelle du cercle circonscrit à un triangle

Avec le logiciel Dr. Geo, il est possible d'écrire un code source en français décrivant n'importe quelle figure. Ecrire une telle description pour le cercle circonscrit d'un triangle est assez simple et court comme expliqué dans les paragraphes suivants.