PROTOTYPE (1/9/04): ADDITIONAL RESOURCES FOR
DELIVERABLE 1.1.2 (TO INFORM DISCUSSION AT LISBON
PROJECT MEETING 19/9/04)
Activity Sequence: Modelling in
Ecoliteracy & Randomness
Aims of activity sequence
This activity sequence is the result of merging two existing ones: Ecoliteracy and
Randomness. The focus is on collaboration and modelling, with the provision of joint
activities, common tool kits and a weblabspaedia site.
1. Ecoliteracy
The goal of this activity sequence is to learn concepts and techniques of modelling and
how to construct dynamic systems on a computer. This activity sequence has evolved
from previously focussing on learning about ecological and complex systems to focus
now on modelling and construction of dynamic systems. Ecological and complex systems
still play an important role in the activity sequence since these serve the role of providing
domains with properties that are interesting to construct computational models of. As
application domains they also provide a means of fostering collaboration between
children in the different sites of the project.
The activity sequence is designed to provide tools that let children learn to model – and
also construct their own – dynamic representations of real world phenomena. The
sequence aims to provide means for children to control some of the expressive properties
of computation and at the same time get insights into how a complex phenomena in the
real world can be expressed through computer modelling in different forms. The domain
holds properties that we find particularly interesting for the purpose of the project.
The modelling, construction, exchange, and modification of dynamic systems provide
new means for children to communicate with each other, even though they are not able to
understand each others’ spoken and written languages. One challenge that has emerged
during the second year of the project has been that of achieving the kind of collaboration
between children across sites that fosters the knowledge building processes that the
project has set as one of as its central goals. Simply finding technical solutions for how to
manage translation of children’s webreports will not be sufficient in reaching this goal.
Especially since the project has set out to also provide children with other than pure
language based means of communicating their knowledge. When developing the activity
sequence we presupposed that animals, nature and environmental issues would be topics
that many children at this age are interested in, and also that the geographical differences
between the sites in the project would make it particularly interesting for students to
exchange models were such issues were central aspects.
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Moreover, another goal of the Weblabs project is to explore how transparent modules of
programming code or more generally, computational processes, could be used for
modelling and programming activities in order to express and communicate ideas within
particular knowledge domains. Behaviours of – and relations between – organisms are
aspects that we find to be very well suited for the exploration of such programming
structures while also being interesting and engaging for the targeted age group.
2. Randomness
What is randomness?
What is a random phenomenon?
Given a phenomenon how can we judge if it is random or not?
These questions are still open in the sense that there is not yet a universally accepted
definition of randomness. Probability (in which we include the concept of randomness) is
a quite young subject; in fact historians chose 1654 as a convenient landmark for the birth
of mathematical probability, due to the contents of the correspondence of Pascal and
Fermat regarding games of chance. Furthermore its first universally accepted
axiomatisation was proposed by Kolmogorov in 1933. However, humans have been
coping with randomness for thousands of years, for instance in chance games, thus it is
only its mathematical interpretations that are relatively new. Drawing from history, the
peculiarity of mathematical formalizations of randomness is that they are based either on
common sense, either on key ideas derived from different scientific contexts. In fact we
can find interpretations, and related attempts of formalizations, of the word “random” for
instance as: “unpredictable”, “lawless”, “incomputable”, “uncompressible”, “not
deterministic”, etc. Any of such characterisation can be ascribed to the idea of
randomness, and contributed to define its key aspects, as shown by the historical
evolution of the definitions of randomness. Our activity sequence relies on the idea of
building meanings for some of the key words associated to randomness, taking into
account of issues highlighted by research in mathematics education such as:
1. cultural biases concerning randomness (for instance in Lotto games, people’s
belief that the less a numbers is extracted, the more chances to be extracted it
has);
2. gap between intuitions and probabilistic formalizations;
3. difficulties in gathering together different random related experiences; literature
shows examples of pupils being able to cope with different random phenomenon,
but being unable to individuate a common denominator linking the different
experiences.
The activity sequence that we designed, approaches the idea of randomness on the one
hand by exploring some key dichotomies such as “predictability vs. unpredictability”,
“presence of pattern vs. lack of pattern”, “rule based vs. not rule based”, “fairness vs.
unfairness”, “determinism vs. indeterminism”; on the other hand some key properties of
randomness are explored, such as the properties of random walk, and independence of
events from events’ history, etc.. The study of such dichotomies, and properties, is to be
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intended as a means to explore and define the dichotomy “random vs. non-random”,
which is the core of our educational goal.
An additional goal of the randomness activity is a qualitative understanding of some
aspects of probability such as sample space and law of large numbers: Probability at
school is usually introduced via sample activities with coins, dices or spinners. RCXLego tangibles might provide another set of tools that augment physical devices with
computational power and link them to the computer based ones. Constructing and using
tangible random devices offers an opportunity to make pupils experience concepts of
randomness and probability starting from their intuitions. It also allows us to discuss
interesting advanced concepts, such as the verification of a random source and the
properties of random walks. To support the related activities we will introduce modelling
of LEGO robots and other phenomena focusing on random strategy and modification
and/or replacement of the random generator used into the model.
Role of collaboration
Within the development of the proposed activities, collaboration between the participants
concerns pedagogical, cultural and source related aspects that we will discuss partially in
this section. Other detail will be given along activities descriptions. In the following we
are going to describe, in general lines, how collaboration shell be set up in standard
school situations, where we have a teacher and a group of pupils. Such general lines, with
slight changes, apply to any situation characterized by a group of learners and one person
(or a few) orchestrating their activities; thus they apply to any of the specific settings
within the project.
Collaboration will occur at the following levels:
 Group work: within a single class collaboration will happen within subjects
participating to activities with different and well defined roles. For instance in some
cases some pupils will be involved in the production of a phenomenon, while others
will participate as active observers (making conjectures, taking notes, etc.).
 Webreports: among different classes, participants may collaborate communicating
both as single persons and as whole classes via web tools.
Group work
Collaboration within single classes will happen both in the form of small group of pupils
activities and in the form of class discussion under the guidance of the teacher.
The aim of the former is to stimulate each pupils’ verbalization, and reciprocal help,
concerning what is being observed and done during the development of the activity.
On the other hand the aim of the latter is both, to compare and socialize the outcomes of
the small groups’ works, and to stimulate individuals’ further advances and inquires.
Here it is part of the teacher’s role to let emerge pupils’ intuitions and guide them toward
the focusing on, and the command of, some key aspects of the considered knowledge
domain (randomness in this case). In particular the teacher may act as: concepts’
mediator that pupils are not able to construct neither individually nor in collaboration;
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provocative agent of the emergence of new concepts; mediator for making new concepts
explicit.
Pupils will be required to produce both reports of what they will have individually done,
and reports of what they will have learnt through collective activities. We hypothesize
that pupil will learn to better express themselves, and to improve their capability to talk
about meaningful contents.
On the basis of the mentioned reports, the class as a whole (teacher and pupils) will
produce a “group webreport” which will represent the status and the evolution of the
knowledge which is shared within the class.
The activity of producing such individual reports, and collective notebook, together with
its extension to a larger community, pupils will be introduced to a meaningful cultural
experience; namely the process of knowledge sharing, which is a fundamental step in the
construction of adults’ scientific knowledge.
Weblabspaedia
In order to orchestrate the process of knowledge sharing, pupils within the different sites
will be involved in the production of a common “Weblabspaedia”, where the concepts of
the activity will be explored in terms of significant examples, words, ideas, and sayings.
Each class (or local group of pupils), will be involved in the production of a local
“collective notebook”, which will be published on the web (perhaps with researchers’
technical help), written in the pupils’ mother tongue. Such documents will represent the
cultures of each local group.
Concerning the languages to be used to write both the local documents and the common
“Weblabspaedia”, firstly we need a language which is powerful as an expressive tool and
as a tool for thinking, for each pupil to approach new concepts. Secondly, we need a
common language to share knowledge across sites. Finally we want each group to be
integrated, with its culture, in the community with equal importance and dignity.
Therefore the common “Weblabspaedia” will be written in English, whilst the local
“collective notebooks” will be written in native languages, which are more familiar to the
single groups. Thanks to a common language, and several native languages, we plan to
exploit linguistic and cultural differences as a propellant for the evolution of common
activities.
Given their collective notebooks, local groups will be required to choose some of their
contents to be proposed to the other groups as “candidates” for the edition of the common
Weblabspaedia. This step will require: choice of contents to be shared production of a
document containing such contents (for all groups); and translation of such documents in
English (for all non-native English speakers). We will call such documents “proposal
documents”.
Although a common language is chosen, it may be the case that different groups will give
different meanings to the same words, thus we will foster a process of comparison which
will be orchestrated by teachers (or researchers) in order to reach agreements on the
possible meanings of each word.
Starting from the proposal documents, local and cross sites debates will be set up, in
order to choose what of the proposed contents will be included in the official “common
Weblabspaedia”. Along with such debate the Weblabspaedia will be edited, possibly with
researchers’ technical help.
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In the case of randomness, at the core of the designed activities, there are some key words
and sayings (see aims in this document), and the exploration of their meanings. This
exploration is rooted in pupils’ cultures, and in the specific practical experience proposed.
This approach is supported by the literature review, with particular attention to the
cultural historical evolution of the meaning of randomness. We choose the metaphor of
the Weblabspaedia, as a cultural instrument that, for each item, may contain a wide
variety of relevant material that represent the cultural meaning of the item.
The contents of our Weblabspaedia, for each item, will contain key words, sayings,
examples, questions, relevant problems, etc.. We believe that, the cultural diversity of the
groups will bring to each item different elements that, shared within the community, will
enrich the shared meanings of to the item. Each element used to describe en item, will be
considered an items itself and will have its dedicated documents.
For each of these items there will be a dedicated web document. The single pages will
evolve along with the sequence of activities. In particular, for each item of the
Weblabspaedia, we will have as many proposal documents and local Weblabspaedia
items, as the number of the involved groups.
To conclude, the main idea is that of setting up an activity of collaboration, which goes
through the whole duration of the experimentation and that unifies all participants under a
common aim, the construction of a Weblabspaedia. Furthermore, the Weblabspaedia will
function also a means for sharing experiences and knowledge. Thus, in case pupils will
be involved in different practical activities, they will have a chance to learn from what
others will have been doing.
Models
An important part of the collaboration in this activity sequence should evolve around the
models that the children construct (models created on the computer as well as on paper).
The most important reason for this is that it is the actual artefacts that are an expression
of the children’s understanding of the phenomena under study. By allowing children to
try out, change, and extend each other’s models, they are allowed to investigate different
ways of understanding and expressing knowledge. In addition, collaboration through
model exchange provides a way of overcoming the language barrier between children in
different countries.
Assessment criteria
In our view the assessment of the students’ learning should be conducted within a
“situated” framework where assessment is integrated with the students’ daily and weekly
learning activities. This is especially important in tool-intense activities where learning
cannot be separated from the use of the involved tools. Therefore we will focus the
assessment around the character of the models that children create and the way they talk
about their models, as they construct them and explain their workings to each other in the
weekly sessions. In order to find indications of how the children’s understandings
develop throughout their work we will compare their models and explanations at different
stages in the activity sequence. Hence, we will not create particular assessment activities,
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for instance, in the form of pre- and post-tests, since we find that these run the risk of
getting detached from the children’s actual learning activities and thereby not measuring
what actually is intended.
We will use student’s models and conversations, field notes and video recordings as the
main data sources. In the analysis these will be used in the following way:

Researchers field notes and reflective reports
These will serve as reflective material for the researchers to develop rich descriptions
of the aspects that are focused upon in the students’ models and conversations.

Students’ models
The content and functionality of the students’ models will be analysed. The analysis
will cover the dynamics of the model, how real world phenomena are represented,
how relations and dependencies between species are represented, how behaviours are
defined, etc.

Analysing students’ webreports and weblabspaedia
Analysing how characteristics of the students’ models are described and discussed in
reports and weblabspaedia,

Students’ conversations
Higher level analysis of students’ conversation and argumentation will investigate
what the students focus upon, e.g. dynamics, function, looks, etc.

Video recordings
This will be used to conduct detailed analysis and zoom into particular issues found in
the analysis of conversations and models.
As collaboration is a central element in the children’s activities we will need to assess
both individual and collaborative learning. Most data collected will be based on the
children’s collaborative activities, especially since they will not be working with
individual projects but mostly in pairs or in groups. Moreover, all activities will be
conducted in collaborative settings with children and teachers working together. Hence,
we will initially take a collaborative point of view with respect to assessment, and as the
analysis evolves search for indications and evidence of learning at the individual level.
Tools
The following tables lists all the tools current available on the WebReports site for
randomness.
Tool
Random jump
ToonTalk Sweeper Bot
(Random Bot 2D)
Description
Behaviour that moves jumping
randomly around.
A vehicle that moves in a 2D area
and sweeps balls away, or
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Animation tool
Animation tool
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Stream bar graph
Stream counter
Remove duplicates
Nest to box
Box to nest
Random gardens tools
Coin
disintegrates them.
Plots a bar graph of the elements of
a stream
Counts how many times an object is
present in a stream
Removes all duplicated elements of
a box.
Converts a stack of objects on a nest
into a box.
Converts a box of objects into a
stack on top of a nest.
ToonTalks tools for exploring
random numbers generators.
coin you can toss by hitting t
Destructive random garden Picks at random one of the parts
(i.e. pictures, texts and numbers) of
the white picture.
Random Garden
Picks at random one of the parts
(i.e. pictures, texts and numbers) of
the green picture.
ToonaTalk Shaker
It is a tool that can contain one or
more balls, when it is shaked, the
balls begins moving, bouncing on
the sides of the shaker, and slowing
down according to a predefined
friction
Bounce Random Garden
Extracts an element from its
contents whenever it is touched by
another ToonTalk object.
Copy touched
this little gadget sends a copy of
whatever it touches to a nest.
Data Analysis
tool
Data Analysis
tool
Generic tool
Generic tool
Generic tool
Notebook
Random
Generator
Random
Generator
Random
Generator
Random
Generator
Random
Generator
Random
Generator
Table 1. List of Randomness Toon Talk tools.
Tool
The Random Bot 2D
(Sweeper Bot)
ShakerHarvester
The RandomBot1D
(Drunk Bot 1D)
ShakerBot
Description
Description and building instructions of the Random
Bot 2D also called Drunk Bot 2D or "Berto" (as pupils
of Class2A suggested)
Description of the RCX tool ShakerHarvester, with
images, instructions, and NQC file.
Description of the RandomBot1D with instructions for
building and running it.
ShakerBot RCX Robot
Table 2. List of RCX tools.
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Tool
Description
Used in
Defined in
Ecoliteracy1.tt Example simulation where
not all objects are
programmed.
Random
motion
A new behaviour for
random movement.
Ecoliteracy1.tt
Systems TM
spec
Move with
arrows
A new behaviour for
moving with arrows.
Ecoliteracy1.tt
Systems TM
spec
Dive
Object make a “dive” at
regular intervals.
Behaviour consist of sub
behaviours
- Start dive
- Turn at bottom
- Stop dive
Ecoliteracy1.tt
Systems TM
spec
Eat
Object "eats" food-object Ecoliteracy1.tt
upon collision. Consist of
sub behaviours:
- grow when
touching
- remove objects
collided with
Systems TM
spec
Starve
Keeps making the object
smaller and smaller
(starving). Contains subbehaviours:
- Shrink sometimes
- Starve to death
Ecoliteracy1.tt
Systems TM
spec
Grow when
touching
User defines the amount
with which the object
grows when touching the
specified object.
Eat (Ecoliteracy1.tt)
Systems TM
spec
Shrink
sometimes
Uses the tool
- seconds counter
Starve (Ecoliteracy1.tt)
Systems TM
spec
Starve (Ecoliteracy1.tt)
Systems TM
spec
Starve to death If width or height is
smaller than zero, the
whole object is removed
from memory. Subbehaviours:
- remove when
width=0
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Tool
Description
-
Used in
Defined in
remove when
height=0
Remove
objects
collided with
Transfers the behaviour of Eat (Ecoliteracy1.tt)
removing oneself to the
object colliding with.
Systems TM
spec
Seconds
counter
Repeats counting seconds Shrink sometimes
from a number that users (Starve)
define down to zero.
Dive
Systems TM
spec
Behaviour
cards
Playing-style cards
representing the animal
gadgets
Role playing activities
Table 3. List of Toon Talk Ecoliteracy tools.
The merging of the tools from the two activities implies modifying the movement
behaviours in the animal gadget to decouple the random generator from the actual update
of the position and velocity of an object. Furthermore, by enabling some behaviours (e.g.
eat) to be executed in a probabilistic fashion (by including a random garden as a trigger)
will make possible to explore random strategies in the ecoliteracy domain as well.
Overview of activity sequence
The merge of the activity sequence will be based on a spiral approach where key
concepts are visited more times from a variety of point of views. Here we outline the
joint planned activities; for what concerns the other activities in the specific domains
(ecoliteracy, randomness) we refer to the existing documents detailing them.
We will start by introducing ToonTalk via the animal gadgets for example exploring last
year children models (see: Our new animal gadget webreport) and building new ones.
Some children would then continue on the ecomodelling parts (e.g. Sweden) while others
might focus on Randomness for example modelling the behaviour of LEGO robots such
as the shakerbot or the sweeperbot (by the way the two model share the same LEGO
vehicle, the random generator is different).
The exchange and collaborative development of models will be based on the “guess and
modify my model” activity were children will examine a model constructed using the
animal gadget’s toolkit and modify it introducing non-determinism.
To provide a common language to discuss the randomness aspect of children model we
will jointly organize a guess my garden activity.
At the end of each of those activities the classes involved in the field-testing will update a
common weblabspaedia.
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