Virtual collaborative learning experience for researchers, teachers and students :

Virtual collaborative learning experience for researchers, teachers and students Eugenia Sendova, Iliana Nikolova,
George Gachev
Bulgarian Academy of Sciences University of Sofia, Bulgaria

The WebLabs project:

The WebLabs project Partners: Bulgaria, Cyprus, Italy, Portugal, Sweden and UK.
Goals: Creating virtual laboratory and a community of young learners, teachers and researchers to explore collaboratively mathematical and science phenomena.

The Bulgarian partner:

The Bulgarian partner Sofia University through the Center for Information Society Technologies (CIST) in close cooperation with
the Department of Information Technologies at the Faculty of Mathematics and Informatics,
responsible for pre-service education and in-service training of mathematics and informatics/IT teachers.

The Bulgarian Weblabs team:

The Bulgarian Weblabs team
University (teacher trainers, PhD students)
Bulgarian Academy of Sciences (senior and junior researchers)
Teachers
Children
Parents/Grandparents

WebLabs innovative aspects:

WebLabs innovative aspects bridging science and explorations with children and teachers
adding a virtual dimension to constructionism
innovative didactics, which employs modern ICT and Internet tools to empower learning
development of non-traditional collaborative learning scenarios

Weblabs’ educational aims :

Weblabs’ educational aims To build web-based transparent learning modules
To enable students to share and collaborate through dynamic web reports
To evaluate learning in a context where the community’s ideas are being expressed through web reports.

The focus of WebLabs:

The focus of WebLabs

ToonTalk in a nutshell :

ToonTalk in a nutshell Abstract computational concepts are represented by cartoon-like character
Programs take the form of animated cartoon robots

Slide9:

The ToonTalk instruments

Programming in ToonTalk:

Programming in ToonTalk Now the robot can add 1 to any current number in the box and then pass the result to the bird (forever) The concrete first addend in the robot’s thought bubble is then erased to generalize the process
Training the robot to add 1 to 1

A Counting robot:

A Counting robot

WebReports:

WebReports designed to allow students to share and discuss the models of mathematical objects and processes they have built in ToonTalk.
using a visual on-line editor
to compose reports detailing their work,
to comment on and annotate each others' reports,
to publish working ToonTalk models of their ideas as they develop.

Some examples :

Some examples Guess My Robot Game – A catalyst for children motivation and virtual collaboration
Weblabetics - A graphical language, representing visual programming algorithms (invented and developed by kids)
The challenge of Ivan and Yana

A WebLabs scenario:

A WebLabs scenario

A webreport about WebLabetics - published on Wlplone:

A webreport about WebLabetics - published on Wlplone

Slide16:

Teacher: Can you think of a way to express ToonTalk ideas so that anyone could understand them?

An old friend “in new clothes” :

An old friend “in new clothes” A robot puts 1 in a box, then copies the content, gives it to a bird, which puts it in its nest. Afterwards everything is repeated. Do you see the “:||” sign at the end – this is the music symbol for a repetition.

Slide18:

The atmosphere in class

Slide19:

In Sofia

In Portugal:

In Portugal

Guess my robot game:

Guess my robot game

Proving the equivalence of robots:

Proving the equivalence of robots

Constructive comparing of robots :

Constructive comparing of robots Emmy: I’ll call the comparing robot Themis.
Teddy and Mitty: So, if Themis stops we could be sure that the sequences are not the same.
Teacher: Otherwise? How long should we wait to be sure that the sequences produced by several robots are the same?
Voices: Till the end of the world...
Till we die... Till the electricity is off

A virtual discussion between the kids and the researchers:

A virtual discussion between the kids and the researchers Rita: I could use a robot which makes the difference between the same terms of my sequence and Nasko’s sequence. If the new sequence is a zero’s sequence that shows to us that my robot and Nasko’s robot make the same sequence.
Researcher: How long do you have to run this “machine” to be sure that the sequences are equal?
Rita: I tried “very much” time and it always generated zeros. Clearly this is not a proof, it is only conjecture and though I am 99% sure that they are equal
Researcher: Can a mathematical statement be 99% true? If we have two robots, and they generate two sequences which are equal for the first 100 000 terms, can the 100 001 term be different (Don’t think I know the answer, I am thinking about it as well…)
Rita: I think not! And I hope that some mathematician has demonstrated that. There is no reason for the 100 001 term to be different if the 100 000 previous terms were equal…

Students’ collaboration from a distance:

Students’ collaboration from a distance Rita: Congratulations, you found a solution to my sequence! I can prove that my sequence and your sequence are equal with the algebraic representation used by Sofia group.
yn+1 =(yn + 2).4 = 4 yn + 8
That is the algebraic representation of the Cyprus’s sequence. So I can prove that the two sequences are equal!

The challenge of Ivan and Yana:

The challenge of Ivan and Yana Ivan: Consider these sequences:
1001, 2001, 3001, ...
1, 2, 4, 8, 16, ...
1, 1024, 59049,...
Is it possible for the terms of the second sequence to surpass the corresponding terms of the first one? What about the corresponding terms of the second and the third?
Yana: I have two sequences for you:
1, 16, 81, 256, 625,...
1, 8, 27, 64, 125,...
If you start with the second one it will be easier for you to solve the first one, I think

The researcher’s answer:

The researcher’s answer Very nice challenge. It inspired me to train a simple robot that made the following sequence. I think it grows faster than either Ivan's or Yana's sequences. Can you reason why?
1 4 27 256 3125 46656 823543 16777216
….

More kids take the gauntlet:

More kids take the gauntlet Mitty: So we have to compare:
(1) 2, 4, 8, 16, ...
(2) 1, 1024, 59049, ...
(3) 1, 4, 27, 256,...
Teddy: The number 1024 is 210. So my guess is that the sequence (2) has a general term n10 for n=1, 2, 3, ....
To check this let's compute 310. That's it - just 59049.
The sequence (1) has a general term 2n and it is an old friend of ours. And the sequence (3) is a challenge given by Ken. It is in fact the sequence {nn} - I love it!

Discussing a peer’s solution:

Discussing a peer’s solution

WebLabs’ achievements:

WebLabs’ achievements Collaboration in mathematics and informatics context at various levels
Making knowledge, traditionally considered as difficult and unattainable for young children, accessible, interesting and meaningful for them
Implementing the constructionist approach in ToonTalk context
Symbiosis between web collaboration, visual programming and mathematical modeling
Creating a new culture of communication and collaboration

Our motivation:

Our motivation
We are traditionally faithful to the constructionist philosophy of learning
We have experience in developing and using computer learning environments, supporting this philosophy.
In WebLabs we saw an opportunity and challenge to dig further in this direction and add new dimensions to the constructionist approach.

Main roles of our team:

Main roles of our team Explorations and modeling with ToonTalk in mathematics domain (Sequences, Series, Cardinality) with researchers, teachers and 5 groups of children in two different cities (a total of more than 200 class sessions with kids).
Developing guidance materials, Toon Talk tools and webreports (more than 30 group webreports plus reviews and comments of others’ reports)
Contribution to building and functioning of the WebLabs virtual learning community

Dissemination:

Dissemination

What did the children learn? :

What did the children learn? to generate and verbalize ideas;
to present their results according to a concrete standard;
to share their experience and products face-to-face and from a distance;
to discuss their work and to work in a team
to be (self-)critical to the work published in the virtual environment

What did the researchers learn?:

What did the researchers learn? The students can find ways to talk about deep mathematical ideas
Cultivating the ability of the students to publish their ideas on the web, to comment on others’ reports, and to challenge their partners to extend their ideas is a very important working paradigm of a contemporary scientist
The students could be real partners in the research process and could influence both the development of the computer environment and the design of the educational activities

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