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Sunday 30 June 2019

The Newton-Raphson Method

The Newton-Raphson method is a very efficient algorithm to search for the zero of a real function. Most of the time it converges more quickly than a dichotomy approach. Nevertheless, there are some traps to avoid by studying the function and/or its curve.

It is attributed to the mathematicians Newton and Raphson for their respective contributions in 1685 and 1690. However, it is also the result of a slow maturation during the ages, before and after the Newton era. Its definitive principle as known today is from the mathematician Thomas Simpson in 1740. Before, it is derived from the works of mathematicians as the French François Viète in the 16th centuries, Iranians Sharaf al-Din al-Tusi and Jamshīd al-Kāshī in the 13th and 14th centuries. Finally it is a generalization of the Hero of Alexandria method in the 1st century BC also known as the Babylonian method.

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Monday 3 June 2019

La méthode de Newton-Raphson

La méthode de Newton-Raphson est un procédé très efficace dans la recherche du zéro d’une fonction réelle, sa convergence est généralement bien plus rapide que celle de la méthode dichotomique. Elle comporte cependant des chausse-trappes qu’une étude de la fonction et de sa courbe permettent d’éviter.

Elle est attribuée aux mathématiciens Newton et Raphson pour leur contribution respective en 1685 et 1690. Elle est toutefois le fruit d’une lente maturation au cours des ans, avant et après l’époque de Newton. Son procédé définitif tel qu’utilisé aujourd’hui est attribué au mathématicien Thomas Simpson en 1740. Avant, elle est dérivée des travaux du mathématiciens François Viète et des mathématiciens iraniens Sharaf al-Din al-Tusi et Jamshīd al-Kāshī. Enfin elle est une généralisation de la méthode de Héron ou méthode babylonienne d’extraction d’une racine carrée.

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Wednesday 13 February 2019

Switching between Dark and Light Themes

OK I must write this down lest I should ask Hilaire for help the third time about this simple task. For my poor eyes, the Dr. Geo sketches do not look very clear in the default dark background. This is how you change the background to white: click on the workspace background to bring up the system menu. Open the "settings" dialog. Click on "style". Change the "User Interface Theme" to "Light theme". The change takes effect immediately. Now you have a white background.

To make the change permanent, again bring up the system menu Then click "tools" => "Save Session".

Choosing the light theme

Saturday 12 January 2019

Dynabook, user interface point of view

In our previous writings, we took the point of view of said innovative teaching approaches. It differs from the children's point of view historically taken by A. Kay. This provided us a set of general features, curriculum neutral, we may want for a teacher centered Dynabook; we summarize it in our "Dynabook and learning models, final words" writing.

Three features came out in several learning models: text processor, question tool and tools to collect and represent data. The first one is linked to the human concept of writing and reading, the last one relates to how to represent information: statically or dynamically. They are related to the representation of knowledge and its transport both in space and time. Appearing as key features in a learning system should not be a surprise, though it may seem to be obvious, it is important not to be overlooked.

To enrich our thinking, we want to change our point of view and look from the curriculum and user interface perspectives. Based on our previous thinking, this will be examined with text and representation of knowledge as the two backbones. Later, we will discuss the third feature, the question tool.

In the following paragraphs, we discuss the user interface point of view.

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Tuesday 11 September 2018

Dynabook and learning models, final words

The Dynabook was conceptualized under a constructivism learning perspective. Viewing it from other innovative learning model perspectives brings enriched insights that enhance the original vision.

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Tuesday 4 September 2018

Teaching by competences

What research says

A competence or a skill is the association of a knowledge and a task. A knowledge is an academic resource necessary to perform one or more tasks.

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Thursday 30 August 2018

Flipped classroom

What research says

The idea of flipped classroom is to let the learners study the lesson at home, then, once in the classroom, ask the teacher questions on specific points not fully understood and practiced with exercises. The lessons can be a text, but most of the time the flipped classroom is supported with an approximately 10 min. video lesson.

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Tuesday 21 August 2018

Project based learning

What research says

Students study topics they will not likely learn outside of school. Most of the time, the learned topics are disconnected; students do not see the connection between these different topics or how they are related. Project-based learning tries to address this problem.

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Wednesday 15 August 2018

Authentic learning

What research says

Authentic or experience learning is based on the idea students may have a better learning experience with documents or situations coming from the "real world", at the least the world outside the school.

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Saturday 11 August 2018

Interest based learning

What research says

Getting the students interested or using their points of interest to improve learning seems to be very obvious and it is a very old idea.

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Tuesday 7 August 2018

Learning in group

What research says

The Russian psychologist Lev Vygostki was the first to elaborate that social interactions are essential to human learning. His work induced a lot of research on collaborative learning.

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Sunday 29 July 2018

Learning by doing

Taking a closer look at the often-cited innovative pedagogical approaches helps revisit the design of the Dynabook concept; expanding it from the constructivism approach to a broader and more diverse way of teaching and learning. The writing of this paper, and subsequent writing in the same domain, is deeply influenced by the A. Tricot study, Innovation pédagogique, 2017 on what is considered innovative pedagogy.

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Sunday 22 July 2018

The Dynabook and its learning models

Children using the proposed Dynabook (c) Alan Kay 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?

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Wednesday 18 July 2018

The Dynabook Concept

Dynabook concept, A Personal Computer for Children of All Ages.

A Dynabook technical drawing

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Friday 6 July 2018

Dr. Geo and Dynamic Media

A Dynabook mock up 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.

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Wednesday 4 January 2017

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.

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Tuesday 3 January 2017

Mathematics series

My son came to me with a mathematics series, he need 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.

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Monday 2 January 2017

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.


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Saturday 31 December 2016

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.

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Circumscribed circle

How to write a textual description of a circumscribed circle to a triangle?

With Dr. Geo software, you can write source code describing any sketch. Writing a description of the circumscribed circle to a triangle is pretty simple and short as explained in the following paragraphs.

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