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This article is in a large part a synthesis of Rieber 1996
{{comment|This article is in a large part a synthesis of Rieber 1996}}


==Definitions==
== Introduction ==


* Microworlds are based on very different principles:  invention, play, and discovery.  
'''Microworlds''' are a kind of [[educational technologies | educational technology]] used in [[constructionism | constructionist]] [[instructional design]]s.


* '''Microworlds''' are central to some forms of [[exploratory learning]]
See also:
* [[Programming microworld]]s and [[End-user programming]]
* [[Expressive digital medium]]
* [[Computer-based manipulative]]


* The aim is to give students the resources to build and refine their own knowledge in personal and meaningful ways.  
Brent Wilson (1995) implicitly classifies microworlds as a kind of '''learning environment''', which is an "idea" expressed as follows:
{{quotationbox|
Like the classroom metaphor, thinking of instruction as an environment gives emphasis to the "place" or "space" where learning occurs. At a minimum, a learning environment contains:
* the learner;
* a setting or "space" wherein the learner acts--using tools and devices, collecting and interpreting information, interacting perhaps with others, etc. This metaphor holds considerable potential because instructional designers like to think that effective instruction requires a degree of student initiative and choice. An environment wherein students are given room to explore, and determine goals and learning activities seems an attractive concept. Students who are given generous access to information resources-- books, print and video materials, etc.--and tools--word-processing programs, e-mail, search tools, etc.--are likely to learn something if they are also given proper support and guidance. Under this conception, learning is fostered and supported, but not controlled or dictated in any strict fashion.}}


* Microworlds are based on constructivism (Jonassen, 1991).  
Microworlds emerged in the 1980's together with pedagogical [[constructivism]] as defined by Wilson (1995) as:
{{quotationbox|
*  a place where learners may work together and support each other
* as they use a variety of tools and information resources
* in their pursuit of learning goals and problem-solving activities.  
}}


* In [[educational technology]] and [[instructional design]], a microworld implements a [[Constructivism|constructivist]] [[instructional design model]] that lets the learner "play" within an artificial or real (e.g. a Sandbox) environment and learn by building things.
Microwords continue to be developped in various forms. On major current debate focusses on the question of how much structure or scenarization is required in effective [[learning design]]s. See also [[Scaffolding]] and [[pedagogical scenario]], [[discovery learning]] vs. [[guided discovery learning]].


* Rieber (1996:583) defines microworlds as collection of software, that << is based on very different principles, those of invention, play, and discovery. Instead of seeking to give students knowledge passed donw from one generation to the next as effeciently as possible, the aime is to give students the resources to build and refine their own knowledge in personal and meaningful ways. >>
==Definitions==


* Clements (1989:86) cited by Rieber (1996:587): A microworld is a small playground of the mind
* Microworlds are '''small playground of the mind''' (Clements, 1989, p. 86 cited by Rieber, 1996:587),
(p. 86).


* Alternative names according to Rieber (1996:583) are: computational media (diSessa, 1989), interactive simulations (White, 1992), participatory simulations (Wilensky & Stroup, 2002), and computer-based manipulatives (Horwitz & Christie, 2002)
* Microworlds are tiny worlds inside which a student can explore alternatives, test hypotheses, and discover facts that are true about that world. ([http://www.umcs.maine.edu/~larry/microworlds/microworld.html Larry Latour]).


* We agree with Rieber (1996) that microworlds are ''not'' the same as [[simulation]]s: "However, microworlds have two important characteristics that may not be present in a simulation. First, a microworld presents the learner with the "simplest case" of the domain, even though the learner would usually be given the means to reshape the microworld to explore increasingly more sophisticated and complex ideas. Second, a microworld must match the learner's cognitive and affective state. Learners immediately know what to do with a microworld - little or no training is necessary to begin using it (imagine first "training" a child how to use a sandbox)." (Rieber, 1996)
* Microworlds are [[expressive digital medium | expressive digital media]] based on principles such as invention, play and discovery.


* " A Microworld is a term coined at the MIT Media Lab Learning and Common Sense Group . It means, literally, a tiny world inside which a student can explore alternatives, test hypotheses, and discover facts that are true about that world. It differs from a simulation in that the student is encouraged to think about it as a "real" world, and not simply as a simulation of another world (for example, the one in which we physically move about in). " quoted from [http://www.umcs.maine.edu/~larry/microworlds/microworld.html Microworlds]
* A microworld implements a [[Constructivism|constructivist]] [[instructional design model]] that lets the learner "play" within an artificial or real (e.g. a Sandbox) environment and learn by building things. The purpose is to give students the resources to build and refine their own knowledge.


Computer-based microworlds offer the means to allow a much greater number of people, starting at a much younger age, to understand highly significant and applicable concepts and principles underlying all complex systems. Two scientific principles deserve special mention: the vast array of rate of change problems common to all dynamic systems (Ogborn, 1999; Roschelle, Kaput, & Stroup, 2000) and decentralized systems, such as economics, ecosystems, ant colonies, and traffic jams (to name just a few), which operate on the basis of local objects or elements following relatively simple rules as they interact, rather than being based on a centralized leader or plan (Resnick, 1991, 1999).
* {{quotation| A microworld is a type of computational document aimed at embedding important ideas in a form that students can readily explore. The best microworlds have an easy-to-understand set of operations that students can use to engage tasks of value to them, and in doing so, they come to understanding powerful underlying principles. You might come to understand ecology, for example, by building your own little creatures that compete with and are dependent on each other.}} (diSessa, 2000, p.47)


==History==
==History==


In 1980 Paper published his book "Mindstorms" and that made popular concepts developped around the programming language Logo whose design was influenced by a particular [[constructionism | constructionist]] vision of education. Logo included "turtle geometry", a drawing pen in the form of a turtle that children could move and draw around on the screen or the floor. The turtle is an "object to think with", i.e. a [[cognitive tool]].
In 1980, Papert made popular concepts developped around the programming language [[Logo]] whose design was influenced by a particular [[constructionism | constructionist]] vision of education. Logo included "turtle geometry", a drawing pen in the form of a turtle that children could move and draw around on the screen or the floor. The turtle is an "object to think with", i.e. a [[cognitive tool]].
Since Logo many other environments in the same spirit have been built. E.g. MIT Lego-Logo that adds a more physical dimension in the spirit of augmented reality.
Since Logo many other environments in the same spirit have been built, but the scope of modern micro-worlds goes much beyound programming environments for children.


Papert (1980) gave a first formal definition of a microworld as a:  
Papert (1980) gave a first formal definition of a microworld as a:{{quotation |  ...subset of reality or a constructed reality whose structure matches that of a given cognitive  mechanism so as to provide an environment where the latter can operate effectively. The concept leads to the project of inventing microworlds so structured as to allow a human learner to exercise particular powerful ideas or intellectual skills. }}(p. 204)  
...subset of reality or a constructed reality whose structure matches that of a given cognitive  mechanism so as to provide an environment where the latter can operate effectively. The concept leads to the project of inventing microworlds so structured as to allow a human learner to exercise particular powerful ideas or intellectual skills. (p. 204)  


For Papert, a microworld is based to a large degree on the way in which an individual is able to use a technological tool for the kinds of thinking and cognitive exploration that would not be possible without the technology.  
For Papert, a microworld is based to a large degree on the way in which an individual is able to use a technological tool for the kinds of thinking and cognitive exploration that would not be possible without the technology.  


But Papert knew that a learner need support structures:  
But Papert knew that a learner needs support structures: {{quotation | ...The use of the microworld provides a model of a learning theory in which active learning consists of exploration by the learner of a microworld sufficiently bounded and transparent for constructive exploration and yet sufficiently rich for significant discovery. }}(p. 208)
...The use of the microworlds provides a model of a learning theory in which active learning consists of exploration by the learner of a microworld sufficiently bounded and transparent for constructive exploration and yet sufficiently rich for significant discovery. (p. 208)
 
While it demonstrates the importance Papert placed on exploration and [[discovery learning]], it also shows the need for a teacher or a microworld designer to identify boundaries for learning. Papert has maybe underestimated the difficulty of designing such boundaries, especially identifying where the boundaries lie for a particular child in a particular domain, but he certainly recognized the need for guidance, both in the microworld itself and in the teacher’s assistance to a child using it. As Papert (1980) writes,
...The construction of a network of microworlds provides a vision of education planning that is in important respects “opposite” to the concept of “curriculum.” This does not mean that no teaching is necessary or that there are no “behavioral objectives.” But the relationship of the teacher to learner is very different: the  teacher introduces the learner to the microworld in which discoveries will be made, rather than to the discovery itself. (p. 209)
 
Mindstorms contained several fundamental ideas that continue to thrive in the vocabulary and thinking of current [[constructivism | constructivist]] conceptions of learning. Among the most profound is the idea of an object to think with, the Logo turtle, of course, being a prime example. Thus, the turtle becomes a way for the child to grapple with mathematical ideas usually considered too difficult or abstract. A prime role served by the turtle is the way it “concretizes” abstract ideas.
 
Another important microworld idea is that of debugging. Unlike conventional education, where errors are to be avoided at all costs, errors in problem-solving tasks such as programming are unavoidable and therefore expected. Errors actually become a rich source of information, without which a correct solution could not be found. The use of an external artifact, such as a computational microworld, as an object to think with to extend our intellectual capabilities, coupled with a learning strategy of expecting and using errors made as a route to successful problem solving, is an integral part of all contemporary learning theories (Norman, 1993; Salomon, Perkins, & Globerson, 1991).
 
So, the concept of a microworld became firmly established as a place for people of all ages to explore in personally satisfying ways complex ideas from domains usually considered intellectually inaccessible to them. These same ideas continue to be championed today, as the following contemporary definition of a microworld by Andy diSessa (2000) shows:


A microworld is a genre of computational document aimed at embedding important ideas in a formthat students can readily explore. The best microworlds have an easy-to-understand set of operations that students can use to engage tasks of value to them, and in doing so, they come to understanding powerful underlying principles. You might come to understand ecology, for example, by building your own little creatures that compete with and are dependent on each other. (p. 47)
While it demonstrates the importance Papert placed on exploration and [[discovery learning]], it also shows the need for a teacher or a microworld designer to identify boundaries for learning. Papert has maybe underestimated the difficulty of designing such boundaries, especially identifying where the boundaries lie for a particular child in a particular domain, but he certainly recognized the need for guidance, both in the microworld itself and in the teacher’s assistance to a child using it. As Papert (1980) writes,{{quotation | ...The construction of a network of microworlds provides a vision of education planning that is in important respects “opposite” to the concept of “curriculum.” This does not mean that no teaching is necessary or that there are no “behavioral objectives.” But the relationship of the teacher to learner is very different: the  teacher introduces the learner to the microworld in which discoveries will be made, rather than to the discovery itself. }}(p. 209)


==General characteristics of microworlds==
Initially LOGO-like environments, were confined to the computer and the individual users. More recent developments (e.g. in MIT's [http://llk.media.mit.edu/ Lifelong Kindergarten] group) concern a wide range of [[constructionist learning object]]s such as:
* [[end-user programming]] environments to produce animated stories, simulations, interactive art, video games.
* smart objects, toys
* online communities where learners can build, e.g. variants of [[MUD]]s or [[3D interactive environments]]
* collaborative construction environments
* construction kits
* [[mixed reality]] kits
* ...


All exploratory learning approaches are based on the following 4 principles:
==Features of microworlds==
# Learners can and should take control of their own learning;
# Knowledge is rich and multidimensional;
# Learners approach the learning task in very diverse ways; and
# It is possible for learning to feel natural and uncoaxed, that is, it does not have to be forced or contrived.


For Edwards (1995), a microworld would consist of:
;A microworld would consist of (Edwards, 1995):
* A set of computational objects that model the mathematical or physical properties of the microworld’s domain
* A set of computational objects that model the mathematical or physical properties of the microworld’s domain
* Links to multiple representations of the underlying properties of the model
* Links to multiple representations of the underlying properties of the model
* The ability to combine objects or operations in complexways, similar to the idea of combining words and sentences in a language
* The ability to combine objects or operations in complex ways, similar to the idea of combining words and sentences in a language
* A set of activities or challenges that are inherent or preprogrammed in the microworld; the student is challenged to solve problems, reach a goal, etc.
* A set of activities or challenges that are inherent or preprogrammed in the microworld; the student is challenged to solve problems, reach a goal, etc.


While such structural affordances are important, the true tests of a microworld are functional—whether it provides a legitimate and appropriate doorway to a domain for a person in a way that captures the person’s interest and curiosity (Edwards, 1995). In other words, for an interactive learning environment to be considered a microworld, a person must “get it” almost immediately—understand a simple aspect of the domain very quickly with the microworld—and then want to explore the domain further with the microworld (Rieber, 1996).  
;So microworlds
* allow more and younger people to understand highly significant and applicable concepts and principles underlying all complex systems.
* are objects to think with to extend our intellectual capabilities. the Logo turtle is an example: the turtle becomes a way for the child to grapple with mathematical ideas usually considered too difficult or abstract. A prime role served by the turtle is the way it “concretizes” abstract ideas.
* are central to some forms of [[exploratory learning]].
* have the idea of debugging: errors in problem-solving tasks become a rich source of information, without which a correct solution could not be found.


A functional view is based on the dynamic relationship among the software, the student, and the setting. Whether or not the software can be considered a microworld depends on this interrelationship when the software is actually used. Students are expected to be able to manipulate the objects and features of the microworld “with the purpose of inducing or discovering their properties and the functioning of the system as a whole” (Edwards, 1995, p. 144). Students are also expected to be able to interpret the feedback generated by the software based on their actions and modify the microworld to achieve their goal (i.e., debugging). And students are expected to “use the objects and operations in the microworld either to create new entities or to solve specific problems or challenges (or both)” (Edwards, 1995, p. 144).
;A software can be considered as a microworld...or not
Whether or not the software can be considered a microworld depends on this interrelationship when the software is actually used. Student have to:
* understand a simple aspect of the domain very quickly (Rieber, 1996b);
* explore the domain further with the microworld (Rieber, 1996b);
* be able to manipulate the objects and features of the microworld “with the purpose of inducing or discovering their properties and the functioning of the system as a whole” (Edwards, 1995, p. 144).  
* be able to interpret the feedback generated by the software based on their actions and modify the microworld to achieve their goal (i.e., debugging).  
* “use the objects and operations in the microworld either to create new entities or to solve specific problems or challenges (or both)” (Edwards, 1995, p. 144).


Therefore, a microworld must be defined at the interface between an individual user in a social context and a software tool possessing the following five functional attributes:
Therefore, a microworld must be defined at the interface between an individual user in a social context and a software tool possessing the following five functional attributes:
* It is domain specific;
* domain specific;
* it provides a doorway to the domain for the user by offering a simple example of the domain that is immediately understandable by the user;
* provides a doorway to the domain for the user by offering a simple example of the domain that is immediately understandable by the user;
* it leads to activity that can be intrinsically motivating to the user—the user wants to participate and persist at the task for some time;
* leads to activity that can be intrinsically motivating to the user—the user wants to participate and persist at the task for some time;
* it leads to immersive activity best characterized bywords such as play, inquiry, and invention; and
* leads to immersive activity best characterized by words such as play, inquiry, and invention; and
* it is situated in a constructivist philosophy of learning.
* situated in a constructivist philosophy of learning (demands a very able teacher serving a dual role: teacher-asfacilitator and teacher-as-learner).


The fifth and final attribute demands that successful learning with a microworld assumes a conducive classroom environment with a very able teacher serving a dual role: teacher-asfacilitator and teacher-as-learner. The teacher’s role is critical in supporting and challenging student learning while at the same
; Simulations are not necessarily microworlds
time modeling the learning process with the microworld.  
Microworlds have two important characteristics that may not be present in a simulation (Rieber, 1996).
# a microworld presents the learner with the "simplest case" of the domain, even though the learner would usually be given the means to reshape the microworld to explore increasingly more sophisticated and complex ideas.  
# a microworld must match the learner's cognitive and affective state. Learners immediately know what to do with a microworld - little or no training is necessary to begin using it (imagine first "training" a child how to use a sandbox).


In summary, while both structures and functions of a microworld are important, a functional orientation is closer to the constructivist ideals of understanding interactions with technology from the learner’s point of view. This means that the same software program may be a microworld for one person and not another. Microworlds can be classified as a type of cognitive tool in that they extend our limited cognitive abilities, similar to the way in which a physical tool, like a hammer or saw, extends our limited physical abilities (Jonassen,1996; Salomon et al., 1991). However, microworlds are domain specific and carry curricular assumptions and pedagogical recommendations for how the domain, such as mathematics or physics, ought to be taught.
the student is encouraged to think about it as a "real" world, and not simply as a simulation of another world. (http://www.umcs.maine.edu/~larry/microworlds/microworld.html)


==Examples of microworlds==
;Alternative names and/or specialized kinds (see Rieber, 1996, p. 583):
* computational media (diSessa, 1989),
* interactive simulations (White, 1992),
* participatory simulations (Wilensky & Stroup, 2002),
* [[computer-based manipulative]]s (Horwitz & Christie, 2002).
* [[expressive digital medium | expressive digital media]]
* [[participatory learning environment]]s (Barab, Hay, Barnett and Squire, 2001)


Many microworlds have become available since 1980:
==Theorical basis for learning in a microworld==
* [[Logo]] and variants like Lego-LOGO, Starlogo
* [[Boxer]] (diSessa, Abelson, & Ploger, 1991),
* [[ThinkerTools]] (White, 1993),
* [[SimCalc]] (Roschelle et al., 2000),
* GenScope (Horwitz & Christie, 2000),
* [[Model-IT]] (Jackson, Stratford, Krajcik, & Soloway, 1996; Spitulnik, Krajcik, & Soloway, 1999),
* StarLogo (Resnick, 1991, 1999),
* Geometer’s Sketchpad (Olive, 1998),
* Function Machine (Feurzeig, 1999),
* Stella (Forrester, 1989; Richmond & Peterson, 1996).


===LOGO===
Representations assist problem solving activities in 3 ways:
 
# the right representation reduces the cognitive load and allows students to use their precious working memory for higher-order tasks.  
* emerged in the mid-1960s
# representations clarify the problem space for students, such as by organizing the problem and the search path.  
* name for a philosophy of education and for a continually evolving family of computer languages that aid its realization.  
# a good representation reveals immediate implications.  
* Its learning environments articulate the principle that giving people personal control over powerful computational resources can enable them to establish intimate contact with profound ideas from science, from mathematics, and from the art of intellectual model building.
* Its computer languages are designed to transform computers into flexible tools to aid in learning, in playing, and in exploring. (Abelson, 1982, p. ix)
 
Logo was particularly distinguished from other programming languages by its use of turtle geometry. Users, as young as preschoolers, successfully learned to communicate with an object called a “turtle,” commanding it to move around the screen or on the floor using commands such as FORWARD, BACK, LEFT, and RIGHT. As the turtle moved, it could leave a trail, thus combining the user’s control of the computer with geometry and aesthetics. Logo was deliberately designed to map onto a child’s own bodily movements in space. By encouraging children to “play turtle,” thousands of children learned to control the turtle successfully in this way.
 
===Boxer===
 
Boxer “is the name for a multipurpose computational medium intended to be used by people who are not computer specialists. Boxer incorporates a broad spectrum of functions—from hypertext processing, to dynamic and interactive graphics, to databases and programming—all within a uniform and easily learned framework” (diSessa et al., 1991, p. 3).  


Boxer’s roots are closely tied to those of Logo. Boxer originated while diSessa was at MIT and part of the Logo team. Despite diSessa’s admiration of Logo and what it represented, he soon became dissatisfied with Logo’s limitations. For example, Logo, though an easy language to start using, is difficult to master. Children quickly learn how to use turtle geometry commands to draw simple shapes, such as squares and triangles, and even complex shapes consisting of a long series of turtle commands, but it is difficult for most children to progress to advanced features of the language, such as writing procedures, combining procedures, and using variables. Another drawback of Logo is that it is essentially just a computer programming language, though with special features, such as turtle geometry. It is difficult to learn Logo well enough to program it to do other meaningful things (journal keeping, database applications,...) . Finally, although Logo enjoyed much success with elementaryand middle-school students, it was difficult to “grow up” using Logo for advanced computational problems. Similarly, Logo was rarely viewed by teachers as a tool that they should use for their own personal learning or professional tasks.  
Microworlds offer the means of maximizing all 3 benefits of representations, when used in the context of an appropriate science teaching pedagogy, such as one based on the scientific method of hypothesis generating and hypothesis testing. For example, in the [[ThinkerTools |ThinkerTools microworld]], students directly interact with a dynamic object while having the discrete forces they impart on the object horizontally or vertically displayed on a simple, yet effective datacross. Students can also manipulate various parameters in the microworld, such as gravity and friction. ThinkerTools ably creates a problem space in which numeric, qualitative, and visual representations consistently work together.


diSessa sought to design a new tool to overcome these difficulties by creating not just another programming language, but a “computational medium.” So Boxer was meant as a successor to Logo, not just a variant.
Furthermore, Perkins and Unger (1994) suggest that microworlds afford the integration of structuremapping frameworks based on analogies and metaphors. Similarly, a microworld can be designed so as to provide a representation that purposefully directs a student to focus on the most salient relationships of the phenomena being studied. Of course, such benefits do not come without certain costs or risks. For example, if the users do not correctly understand the mapping structure of the analogy, then the benefits will be lost and the students may potentially form misconceptions. Just providing a microworld to students, without the pedagogical underpinnings, should not be expected to lead to learning. The role of the teacher and the resulting classroom practice is crucial here. Microworlds rely on a culture of learning in which students are expected to inquire, test, and justify their understanding. “Students needs to be actively engaged in the construction and assessment of their understandings by working thoughtfully in challenging and reflective problem contexts” (p. 27).  As Perkins and Unger (1994) point out, microworld designers have to articulate adequately the components and relationships among components of the domain to be learned. Next they have to construct an illustrative world exemplifying that targeted domain. Finally, the illustrative world should provide natural or familiar referents that, when placed in correspondence with one another and mapped to the target domain, yield a better understanding of the domain. (p. 30)
 
Boxer was designed based on two major principles related to learning:
* concreteness: implies that all aspects and functions of the system should be visible and directly manipulable.  
* the use of a spatial metaphor: capitalizes on a person’s spatial abilities for relating objects or processes. For example, the principal object is a box, hence the name Boxer. A box can contain any element or data structure, such as text, graphics, programs, or even other boxes. The use of boxes allows a person to use intuitive spatial relations such as “outside,” “inside,” and “next” directly in the programming.  


==Constructionism: microworld research evolves==
==Constructionism: microworld research evolves==
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Constructionism is strongly rooted in student-generated projects. Projects offer a way critically to relate motivation and thinking and can be defined as “relatively long-term, problemfocused, and meaningful units of instruction that integrate concepts from a number of disciplines or fields of study” (Blumenfeld et al., 1991, p. 370). Projects have 2 essential components: a driving question or problem and activities that result in one or more artifacts (Blumenfeld et al., 1991). Artifacts are “sharable and critiquable externalizations of students’ cognitive work in classrooms” and “proceed through intermediate phases and are continuously subject to revision and improvement” (Blumenfeld et al., 1991, pp. 370–371).
Constructionism is strongly rooted in student-generated projects. Projects offer a way critically to relate motivation and thinking and can be defined as “relatively long-term, problemfocused, and meaningful units of instruction that integrate concepts from a number of disciplines or fields of study” (Blumenfeld et al., 1991, p. 370). Projects have 2 essential components: a driving question or problem and activities that result in one or more artifacts (Blumenfeld et al., 1991). Artifacts are “sharable and critiquable externalizations of students’ cognitive work in classrooms” and “proceed through intermediate phases and are continuously subject to revision and improvement” (Blumenfeld et al., 1991, pp. 370–371).


It is important that the driving question not be overly constrained by the teacher. Instead, students need much room to create and use their own approaches to designing and developing the project. Projects, as external artifacts, are public representations of the students’ solution. The artifacts, developed over time, reflect their understanding of the problem over time aswell. In contrast, traditional school tasks, such asworksheets, have no driving question and, thus, no authentic purpose to motivate the student to draw or rally the difficult cognitive processes necessary for complex problem- solving.
It is important that the driving question not be overly constrained by the teacher. Instead, students need much room to create and use their own approaches to designing and developing the project. Projects, as external artifacts, are public representations of the students’ solution. The artifacts, developed over time, reflect their understanding of the problem over time aswell. In contrast, traditional school tasks have no driving question and, thus, no authentic purpose to motivate the student to draw or rally the difficult cognitive processes necessary for complex problem- solving.


In an early constructionnism research, Harel and Papert (1991) strongly suggest that what made a difference was not Logo or any particular group of strategies but, rather, that a “total learning environment” (p. 70) was created that permitted a culture of design work to flourish. They particularly point to the affective influences of this environment. These students developed a different “relationship with fractions” (p. 71), that is, they came to like fractions and saw the relevancy of this mathematics to their everyday lives. Many reported “seeing fractions everywhere.” Harel and Papert resist any tendency to report the success as being “caused” by Logo. Instead, “learning how to program and using Logo enabled these students to become more involved in thinking about fractions knowledge” (p. 73). They point to Logo’s allowing such constructions about fractions to take place.  
In an early constructionnism research, Harel and Papert (1991) strongly suggest that what made a difference was not Logo or any particular group of strategies but, rather, that a “total learning environment” (p. 70) was created that permitted a culture of design work to flourish. They particularly point to the affective influences of this environment. These students developed a different “relationship with fractions” (p. 71), that is, they came to like fractions and saw the relevancy of this mathematics to their everyday lives. Many reported “seeing fractions everywhere.” Harel and Papert resist any tendency to report the success as being “caused” by Logo. Instead, “learning how to program and using Logo enabled these students to become more involved in thinking about fractions knowledge” (p. 73). They point to Logo’s allowing such constructions about fractions to take place.  
Line 136: Line 135:
* their own understanding of the content embedded in projects,  
* their own understanding of the content embedded in projects,  
* their ability to teach and recognition of student difficulty in learning the content (i.e., pedagogical awarenesses),  
* their ability to teach and recognition of student difficulty in learning the content (i.e., pedagogical awarenesses),  
* their willingness to assume a constructivist culture in their classrooms.  
* their willingness to assume a constructivist culture in their classrooms.
 
==Theorical basis for learning in a microworld==


Representations aid problem solving in 3 ways:  
[[Category:microworlds]]
# the right representation reduces the cognitive load and allows students to use their precious working memory for higher-order tasks.
# representations clarify the problem space for students, such as by organizing the problem and the search path.
# a good representation reveals immediate implications.


Microworlds offer the means of maximizing all 3 benefits of representations, when used in the context of an appropriate science teaching pedagogy, such as one based on the scientific method of hypothesis generating and hypothesis testing. For example, in the ThinkerTools microworld, students directly interact with a dynamic object while having the discrete forces they impart on the object horizontally or vertically displayed on a simple, yet effective datacross. Students can also manipulate various parameters in the microworld, such as gravity and friction. ThinkerTools ably creates a problem space in which numeric, qualitative, and visual representations consistently work together.
==Examples of microworlds==


Furthermore, Perkins and Unger (1994) suggest that microworlds afford the integration of structuremapping frameworks based on analogies and metaphors. Similarly, a microworld can be designed so as to provide a representation that purposefully directs a student to focus on the most salient relationships of the phenomena being studied. Of course, such benefits do not come without certain costs or risks. For example, if the users do not correctly understand the mapping structure of the analogy, then the benefits will be lost and the students may potentially form misconceptions. Just providing a microworld to students, without the pedagogical underpinnings, should not be expected to lead to learning. The role of the teacher and the resulting classroom practice is crucial here. Microworlds rely on a culture of learning in which students are expected to inquire, test, and justify their understanding. “Students needs to be actively engaged in the construction and assessment of their understandings by working thoughtfully in challenging and reflective problem contexts” (p. 27).  As Perkins and Unger (1994) point out, microworld designers have to articulate adequately the components and relationships among components of the domain to be learned. Next they have to construct an illustrative world exemplifying that targeted domain. Finally, the illustrativeworld should provide natural or familiar referents that, when placed in correspondence with one another and mapped to the target domain, yield a better understanding of the domain. (p. 30)
Many microworlds have become available since 1980:


==Microworlds more broadly conceived: going beyond programming langages==
* [[AgentSheets]]
* [[Beguile]] (Reiser et al.)
* [[BioLogica]]
* [[Boxer]] (diSessa, Abelson, & Ploger, 1991),
* [[Construit]] (series of "construals")
* [[Cool Modes]] (Hoppe et al.)
* [[Crickets]] (Resnick)
* [[Crocodile ICT]]
* [[E-Slate]] (Kynigos et al.)
* Function Machine (Feurzeig, 1999),
* [[GenScope]] (Horwitz & Christie, 2000),
* Geometer’s Sketchpad (Olive, 1998),
* [http://www.geogebra.org/ GeoGebra] (multi-platform dynamic mathematics software for learning and teaching)
* [[LEGO Mindstorms]]
* [[Logo]] and variants like Lego-LOGO, Starlogo
* Model-IT (Jackson, Stratford, Krajcik, & Soloway, 1996; Spitulnik, Krajcik, & Soloway, 1999),
* [[NetLogo]]
* [[Scratch]]
* [[SimCalc]] (Roschelle et al., 2000),
* [[SimQuest]] (Van Joolingen, King and de Jong, 1997)
* [[Squeak]]-based systems
* StarLogo (Resnick, 1991, 1999),
* Stella (Forrester, 1989; Richmond & Peterson, 1996).
* [http://www.strategydynamics.com/shop/ Strategy Dynamics microworlds] (commercial kits for business education)
* [[Teaching genetics with dragons]] (Geniverse, GeniGame, GeniVille)
* [[ThinkerTools]] (White, 1993),
* [[ToonTalk]]
* [[Virtual Water]]
* [[WISE]]


===ThinkerTools===
See also
(http://thinkertools.soe.berkeley.edu/)
* [[programming microworld]]s
* [[computer simulation]]


* ThinkerTools is both a computer-based modeling tool for physics and a pedagogy for science education based on scientific inquiry: “. . . an approach to science education that enables sixth graders to learn principles underlying Newtonian mechanics, and to apply them in unfamiliar problem solving contexts. The students’ learning is centered around problem solving and experimentation within a set of computer microworlds (i.e., interactive simulations)” (White & Horowitz, 1987, abstract).
; Repositories
* one of the earliest examples of how to include interactions and model building within “interactive simulations.”
* [http://mathforum.org/mathtools/ MathTools] at Math Form. This is a large library (not just for microworlds)


In ThinkerTools:
==References==
* students explore interactive models of Newtonian mechanics.
* They can build their own models,
* or they can interact with a variety of ready-made models that accompany the software.
* A variety of symbolic visual representations is used.
* Simple objects, in the shape of balls (called “dots”), can be added to the model, each with parameters directly under the student’s control. For example, each dot’s initial mass, elasticity (bouncy or fragile), or velocity can be manipulated.
* Variables of the model’s environment itself can be modified, such as the presence and strength of gravity and air friction.
* Other elements can be added to the model, such as barriers and targets.
* Forces affecting the motion of the balls can be directly controlled, if desired, by the keyboard or a joy stick, such as by giving the ball kicks in the four directions (i.e., up, down, left, right). This adds a video- game-like feature to the model.


ThinkerTools also includes a variety of measurement tools with which students can accurately observe distance, time, and velocity. Another symbol, called a datacross, can be used to show graphically the motion variables of the object. A datacross shows the current horizontal and vertical motion of the ball in terms of the sum of all of the forces that have acted on the ball. The motion of the object over time can also be depicted by having the object leave a trail of small, stationary dots. When the object moves slowly, the trail of dots is closely spaced, but  when the object moves faster, the space between the trailing dots increases. Students can also use a “step through time” feature, in which the simulation can be frozen in time, allowing students to proceed step by step through time. This gives them a powerful means of analyzing the object’s motion and also of predicting the object’s future motion. The point of all of these tools is to give students the means of determining and understanding the laws of motion in an interactive, exploratory way: “In this way, such dynamic interactive simulations can provide a transition from students’ intuitive ways of reasoning about the world to the more abstract, formal methods that scientists use for representing and reasoning about the behavior of a system” (White & Frederiksen, 2000, pp. 326–327).  
* Abelson, H. (1982). Logo for the Apple II. Peterborough. NH: BYTE/McGraw Hill.


ThinkerTools acts as a bridge between concrete, qualitative reasoning of realworld examples and the highly abstract world of scientific formalism where laws are expressed mathematically in the form of equations.
* Barab, Sasha A. ,Kenneth E. Hay, Michael Barnett and Kurt Squire (2001). Constructing Virtual Worlds: Tracing the Historical Development of Learner Practices, Cognition And Instruction, 19(1), 47-94. [http://inkido.indiana.edu/research/onlinemanu/papers/cogin.pdf PDF]


ThinkerTools is best used with an instructional approach to inquiry and modeling called the ThinkerTools Inquiry Curriculum. The goal of this curriculum is to develop students’ metacognitive knowledge, that is, “their knowledge about the nature of scientific laws and models, their knowledge about the processes of modeling and inquiry, and their ability to monitor and reflect on these processes so they can improve them” (White & Frederiksen, 2000, p. 327). White and her colleagues predicted that such a pedagogical approach used in the context of powerful tools such as the ThinkerTools software should make learning science possible for all students. The curriculum largely follows the scientific method, involving the following steps:
* Blumenfeld, P. C., Soloway, E., Marx, R. W., Krajcik, J. S., Guzdial, M., & Palinscar, A. (1991). Motivating project-based learning: Sustaining the doing, supporting the learning. Educational Psychologist, 26(3 & 4), 369–398.
# question—students start by constructing a research question, perhaps the hardest part of the model;
# hypothesize—students generate hypotheses related to their question;
# investigate—students carry out experiments, both with the ThinkerTools software and in the real world, the goal of which is to gather empirical evidence about which hypotheses (if any) are accurate;
# analyze—after the experiments are run, students analyze the resulting data;
# model—based on their analysis, students articulate a causal model, in the form of a scientific law, to explain the findings; and
# evaluate—the final step is to test whether their laws and causal modelsworkwell in real-world situations, which, in turn, often leads to new research questions.


===SimCalc===
* Clements, D. (1989). Computers in elementary mathematics education. Englewood Cliffs, NJ: Prentice Hall.
(http://www.simcalc.umassd.edu/)


* is concerned with the mathematics of change and variation (MCV).  
* diSessa, A. A. (1989). Computational media as a foundation for new learning cultures. Technical Report G5. Berkeley: University of California.
* to give ordinary children the opportunities, experiences,and resources they need to develop an extraordinary understanding of and skill with MCV (Roschelle et al., 2000).  
* based on 3 lines of innovation.
*# a deep reconstruction of the calculus curriculum, both its subject matter and the way in which it is taught. The goal is to allow all children, even those in elementary school, to access the mathematical principles of change and variation. The developers assert that this is possible through the design of visualizations and simulations for collaborative inquiry. The most notable innovation in the SimCalc curriculum is the use of piecewise linear functions as the basis of student exploration. In a velocity graph, for example, a student can build a function by putting together line segments, each of the same time duration A series of joined horizontal segments denotes constant velocity and a set of rising or falling segments denotes increasing or decreasing speed.
*# to root the learning of these mathematics principles in meaningful experiences of students. Students bring with them a wealth of mathematical understanding that is largely untapped in traditional methods of learning calculus. The SimCalc project does not require students  to understand algebra before exploring calculus principles.  
*# creative use of technology, namely, special software called MathWorlds.
*#* makes extensive use of concrete visual representations, coupled with graphs that students can directly manipulate and control.
*# * graphs can be based on data sets generated by computer-based simulations (animated clowns, ducks, and elevators), laboratory experiments, and even the students’ own body movements by capturing their movements with microcomputer-based (or calculatorbased) motion sensors, then importing these data into the computer.


The SimCalc project
* diSessa, A. A. (2000). Changing minds: Computers, learning, and literacy. Cambridge, MA: MIT Press.
# has reconceptualized the teaching of mathematics at all grade levels, starting with elementary school.  
# has put its focus on meaningful student experience based on graphs of interesting visual phenomena that students can manipulate directly.  


The SimCalc project places much value on students experiencing phenomena as the basis for their mathematical explorations. The SimCalc curriculum is based on 4 strategies that counter traditional teaching of calculus;
* diSessa, A. A., Abelson, H., & Ploger, D. (1991). An overview of Boxer. Journal of Mathematical Behavior, 10, 3–15.
# phenomena are studied and understood before delving into mathematical formalisms.  
# the mathematics are based on discrete variation before turning to continuous variation.  
# the mathematics of accumulation and integrals are taught before rates of change and derivatives.
# students learn to master graphs before algebraic symbolism. So, instead of requiring algebra as a prerequisite skill for studying calculus, the SimCalc project using students’ grasp of visual problem solving with graphs to enter the mathematical world of change and varying quantities.


===GenScope===
* Edwards, L. D. (1995). Microworlds as representations. In A. A. diSessa, C. Hoyles, R. Noss, & L. D. Edwards (Eds.), Computers and exploratory learning (pp. 127–154). New York: Springer.
(http://genscope.concord.org/)  


* exploratory software environment “designed to help students learn to reason and solve problems in the domain of genetics” (Horwitz &Christie, 2000, p. 163).  
* Feurzeig, W., & Roberts, N. (1999). Introduction. In W. Feurzeig & N. Roberts (Eds.), Modeling and simulation in science and mathematics education (pp. xv–xviii). New York: Springer-Verlag.
* help students understand scientific explanations and also to gain insight into the nature of the scientific process.  
* describe as a “computer-based manipulative”, that it is neither a simulation nor a modeling tool.
* Interestingly, their intent is to have students use it to try to determine, largely through inductive reasoning, the software’s underlying model (i.e., genetics). This is precisely the aim of much research on educational uses of simulations.
* emphasis on qualitative understanding of the domain.
* gives students a way to represent genetic problems and derive solutions interactively.
* not require students to master the vocabulary of genetics before effectively using genetic concepts and principles.  


Another significant barrier in understanding genetics, according to Horwitz, is the mismatch between how scientists actually study genetics and how it is taught:
* Freeman, M.A. and J.M. Capper (2000), “Obstacles and opportunities for technological innovation in business teaching and learning”, International Journal of Management Education, 1, 37-47.
* Understanding genetics is largely an inductive exercise, trying to determine the cause from an observed set of effects.  
* In contrast, most science teaching is deductive, teaching the rule, followed by students having to deduce the results.  
* Moreover, the skills that a scientist uses are rarely taught in the classroom (i.e., using the scientific method to reason inductively).
* Instead, most classroom practice activities are meant to let students rehearse factual information and solve similar problem sets.
* Of course, knowing a correct answer on a worksheet does not mean that a student actually understands the underlying concepts and principles.
* The GenScope curriculum was designed to have students use the GenScope tool in ways that mirror closely the methods used by actual scientists.


Genetics is the study of how an organism inherits physical characteristics from its ancestors and passes them on to its descendants. Learning genetics is challenging because descriptions of how changes occur can be formulated at many different levels. GenScope provides students with 6 interdependent levels:  
* Forrester, J.W. (1989). The beginning of system dynamics. International meeting of the System Dynamics Society, Stuttgart, Germany [online]. Available: http://sysdyn.mit.edu/sdep/papers/D-4165-1.pdf.
# molecules,
# chromosomes,
# cells,
# organisms,
# pedigrees,
# populations.  


GenScope provides students with a simplified model of genetics for them to manipulate, beginning with the imaginary species of dragons. GenScope provides individual computer windows for each of the levels—students can interact with one of the levels, say via a DNA window to show the genes of an organism (i.e., genes that control whether a dragon has wings), and then see the results of their manipulation in the organism window (i.e., a dragon sprouting wings).
* Harel, I., & Papert, S. (1991). Software design as a learning environment. In I. Harel & S. Papert (Eds.), Constructionism (pp. 41–84). Norwood, NJ: Ablex.


Students start by focusing on the relationships between the organism and the chromosome levels using the fictitious dragon species, progressively working up to higher levels of relationships dealing with real animals. After getting familiar with the GenScope interface for a few minutes, students are immediately given a challenge (e.g., a fire-breathing green dragon with legs, horns, and a tail but no wings). Students quickly master the ability to manipulate the genes at the chromosomal level to produce such an animal. Interestingly, the next step is to switch to a paper-and-pencil activity where students are asked to describe what a dragon would look like given printed screen shots of chromosomes. After students construct an answer, they are encouraged to use GenScope to verify, or correct, their answers. Students then progress to interrelating the DNA level to the chromosome and organism level. Students come to learn about how recessive and dominant genes can be combined to produce certain characteristics. For example, if wings are a recessive trait, a dragonwould have to possess two recessive genes to be born with wings. Students then progress to the cell level and consider how two parents may pass traits to their offspring. As shown, the pedagogical approach used here is to challenge students with problems to solve in GenScope, then give them time to work alone or in pairs to solve the problems through experimentation.
* Horwitz, P., & Christie, M. A. (2000). Computer-based manipulatives for teaching scientific reasoning: An example. In M. J. Jacobson & R. B. Kozma (Eds.), Learning the sciences of the 21st century: Research, design, and implementing advanced technology learning environments (pp. 163–191). Mahwah, NJ: Lawrence Erlbaum Associates.


==References==
* Horwitz, P., & Christie, M. A. (2002, April). Hypermodels: Embedding curriculum and assessment in computer-based manipulatives. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.


Abelson, H. (1982). Logo for the Apple II. Peterborough. NH: BYTE/McGraw Hill.
* Jackson, S., Stratford, S. J., Krajcik, J. S., & Soloway, E. (1996). Making dynamic modeling accessible to pre-college science students. Interactive Learning Environments, 4(3), 233–257.


Blumenfeld, P. C., Soloway, E., Marx, R. W., Krajcik, J. S., Guzdial, M., & Palinscar, A. (1991). Motivating project-based learning: Sustaining the doing, supporting the learning. Educational Psychologist, 26(3 & 4), 369–398.
* Jonassen, D. (1991). Objectivism versus constructivism: Do we need a new philosophical paradigm? Educational Technology Research & Development, 39(3), 5–14.


Clements, D. (1989). Computers in elementary mathematics education. Englewood Cliffs, NJ: Prentice Hall.
* Jonassen, D. H. (1996). Computers in the classroom: Mindtools for critical thinking. Upper Saddle River, NJ: Prentice Hall.


diSessa, A. A. (1989). Computational media as a foundation for new learning cultures. Technical Report G5. Berkeley: University of California.
* Joolingen van, Dr. W.R. and King, S. and Jong de, Prof. dr. T. (1997) The SimQuest authoring system for simulation-based discovery learning. In: B. du Boulay & R. Mizoguchi (Eds.), Artificial intelligence and education: Knowledge and media in learning systems. IOS Press, Amsterdam, pp. 79-86. [http://doc.utwente.nl/27531/1/K27531__.PDF PDF]


diSessa, A. A. (2000). Changing minds: Computers, learning, and literacy. Cambridge, MA: MIT Press.
* Maier, F.H. and A. Grössler (2000), “What are we talking about? – A taxonomy of computer simulations to support learning”, System Dynamics Review, 16, 135-148.


diSessa, A. A., Abelson, H., & Ploger, D. (1991). An overview of Boxer. Journal of Mathematical Behavior, 10, 3–15.
* Norman, D. A. (1993). Things that make us smart: Defending human attributes in the age of the machine. Reading, MA: Addison–Wesley.


Edwards, L. D. (1995). Microworlds as representations. In A. A. diSessa, C. Hoyles, R. Noss, & L. D. Edwards (Eds.), Computers and exploratory learning (pp. 127–154). New York: Springer.
* Ogborn, J. (1999). Modeling clay for thinking and learning. In W. Feurzeig & N. Roberts (Eds.), Modeling and simulation in science and mathematics education (pp. 5–37). New York: Springer- Verlag.


Feurzeig, W., & Roberts, N. (1999). Introduction. In W. Feurzeig & N. Roberts (Eds.), Modeling and simulation in science and mathematics education (pp. xv–xviii). New York: Springer-Verlag.
* Olive, J. (1998). Opportunities to explore and integrate mathematics with “The Geometer’s Sketchpad.” In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 395–418). Mahwah, NJ: Lawrence Erlbaum Associates.


Forrester, J.W. (1989). The beginning of system dynamics. International meeting of the System Dynamics Society, Stuttgart, Germany [online]. Available: http://sysdyn.mit.edu/sdep/papers/D-4165-1.pdf.
* Papert, S. (1980). Computer-based microworlds as incubators for powerful ideas. In R. Taylor (Ed.), The computer in the school: Tutor, tool, tutee (pp. 203–210). New York: Teacher’s College Press.


Harel, I., & Papert, S. (1991). Software design as a learning environment. In I. Harel & S. Papert (Eds.), Constructionism (pp. 41–84). Norwood, NJ: Ablex.
* Resnick, M. (1991). Overcoming the centralized mindset: Towards an understanding of emergent phenomena. In I. Harel & S. Papert (Eds.), Constructionism (pp. 204–214). Norwood, NJ: Ablex.


Horwitz, P., & Christie, M. A. (2000). Computer-based manipulatives for teaching scientific reasoning: An example. In M. J. Jacobson & R. B. Kozma (Eds.), Learning the sciences of the 21st century: Research, design, and implementing advanced technology learning environments (pp. 163–191). Mahwah, NJ: Lawrence Erlbaum Associates.
* Resnick, M. (1999). Decentralized modeling and decentralized thinking. In W. Feurzeig & N. Roberts (Eds.), Modeling and simulation in science and mathematics education (pp. 114–137). New York: Springer-Verlag.


Horwitz, P., & Christie, M. A. (2002, April). Hypermodels: Embedding curriculum and assessment in computer-based manipulatives. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.
* Richmond, B., & Peterson, S. (1996). STELLA: An introduction to systems thinking. Hanover, NJ: High Performance Systems.


Jackson, S., Stratford, S. J., Krajcik, J. S., & Soloway, E. (1996). Making dynamic modeling accessible to pre-college science students. Interactive Learning Environments, 4(3), 233–257.
* Rieber, L. P. (1996) Microworlds, in Jonassen, David, H. (ed.) Handbook of research on educational communications and technology. Handbook of Research for Educational Communications and Technology. Second edition. Simon and Schuster, 583-603 ISBN 0-02-864663-0
 
Jonassen, D. (1991). Objectivism versus constructivism: Do we need
a new philosophical paradigm? Educational Technology Research & Development, 39(3), 5–14.
 
Jonassen, D. H. (1996). Computers in the classroom: Mindtools for critical thinking. Upper Saddle River, NJ: Prentice Hall.
 
Norman, D. A. (1993). Things that make us smart: Defending human attributes in the age of the machine. Reading, MA: Addison–Wesley.
 
Ogborn, J. (1999). Modeling clay for thinking and learning. In W. Feurzeig & N. Roberts (Eds.), Modeling and simulation in science and mathematics education (pp. 5–37). New York: Springer- Verlag.
 
Olive, J. (1998). Opportunities to explore and integrate mathematics with “The Geometer’s Sketchpad.” In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 395–418). Mahwah, NJ: Lawrence Erlbaum Associates.
 
Papert, S. (1980). Computer-based microworlds as incubators for powerful ideas. In R. Taylor (Ed.), The computer in the school: Tutor, tool, tutee (pp. 203–210). New York: Teacher’s College Press.
 
Resnick, M. (1991). Overcoming the centralized mindset: Towards an understanding of emergent phenomena. In I. Harel & S. Papert (Eds.), Constructionism (pp. 204–214). Norwood, NJ: Ablex.


Resnick, M. (1999). Decentralized modeling and decentralized thinking. In W. Feurzeig & N. Roberts (Eds.), Modeling and simulation in science and mathematics education (pp. 114–137). New York: Springer-Verlag.
* Rieber, L. P. (1996b). Seriously considering play: Designing interactive learning environments based on the blending of microworlds, simulations, and games. Educational Technology Research & Development, 44(2), 43–58.


Richmond, B., & Peterson, S. (1996). STELLA: An introduction to systems thinking. Hanover, NJ: High Performance Systems.
* Roschelle, J., Kaput, J., & Stroup, W. (2000). SimCalc: Accelerating student engagement with the mathematics of change. In M. J. Jacobson & R. B. Kozma (Eds.), Learning the sciences of the 21st century: Research, design, and implementing advanced technology learning environments (pp. 47–75). Mahwah, NJ: Lawrence Erlbaum Associates.


Rieber, L. P. (1996). Seriously considering play: Designing interactive learning environments based on the blending of microworlds, simulations, and games. Educational Technology Research & Development, 44(2), 43–58.
* Romme, A. Georges (2002). Microworlds for Management Education and Learning, Tilburg University, Faculty of Economics & Business Administration, [http://www.unice.fr/sg/resources/articles/romme_2002_microworlds-management-ed-learning.pdf PDF].
 
* Rieber, L. P. (1996) Microworlds, in Jonassen, David, H. (ed.) Handbook of research on educational communications and technology. Handbook of Research for Educational Communications and Technology. Second edition. Simon and Schuster, 583-603 ISBN 0-02-864663-0


Roschelle, J., Kaput, J., & Stroup, W. (2000). SimCalc: Accelerating student engagement with the mathematics of change. In M. J. Jacobson & R. B. Kozma (Eds.), Learning the sciences of the 21st century: Research, design, and implementing advanced technology learning environments (pp. 47–75). Mahwah, NJ: Lawrence Erlbaum Associates.
* Salomon, G., Perkins, D. N., & Globerson, T. (1991). Partners in cognition: Extending human intelligence with intelligent technologies. Educational Researcher, 20(3), 2–9.


Salomon, G., Perkins, D. N., & Globerson, T. (1991). Partners in cognition: Extending human intelligence with intelligent technologies. Educational Researcher, 20(3), 2–9.
* Spitulnik, M. W., Krajcik, J. S., & Soloway, E. (1999). Construction of models to promote scientific understanding. In W. Feurzeig & N. Roberts (Eds.), Modeling and simulation in science and mathematics education (pp. 70–94). New York: Springer-Verlag.


Spitulnik, M. W., Krajcik, J. S., & Soloway, E. (1999). Construction of models to promote scientific understanding. In W. Feurzeig & N. Roberts (Eds.), Modeling and simulation in science and mathematics education (pp. 70–94). New York: Springer-Verlag.
* White, B. Y. (1992). A microworld-based approach to science education. In E. Scanlon & T. O'Shea (Eds.), New directions in educational technology (pp. 227-242). New York: Springer-Verlag.


White, B. Y. (1992). A microworld-based approach to science education. In E. Scanlon & T. O\u2019Shea (Eds.), New directions in educational technology (pp. 227\u2013242). New York: Springer-Verlag.
* White, B. Y. (1993). ThinkerTools: Causal models, conceptual change, and science education. Cognition and Instruction, 10(1), 1–100.


White, B. Y. (1993). ThinkerTools: Causal models, conceptual change, and science education. Cognition and Instruction, 10(1), 1–100.
* Wilensky, U., & Stroup,W. (2002, April). Participatory simulations: Envisioning the networked classroom as a way to support systems learning for all. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.


White, B. Y., & Frederiksen, J. R. (2000). Technological tools and instructional approaches for making scientific inquiry accessible to all. In M. J. Jacobson & R. B. Kozma (Eds.), Innovations in science
* Wilson, B. (1995). "Metaphors for instruction: Why we talk about learning environments", ''Educational Technology'', 35(5), 25-30 [http://carbon.ucdenver.edu/~bwilson/wils95 HTML Reprint]
and mathematics education: Advanced designs for technologies of learning (pp. 321–359). Mahwah, NJ: Lawrence Erlbaum Associates.


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Wilensky, U., & Stroup,W. (2002, April). Participatory simulations: Envisioning the networked classroom as a way to support systems learning for all. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.
[[Category:Edutech families]]
[[Category: Simulation environments]]
[[Category: Technology education]]

Latest revision as of 11:40, 23 May 2019

This article is in a large part a synthesis of Rieber 1996

Introduction

Microworlds are a kind of educational technology used in constructionist instructional designs.

See also:

Brent Wilson (1995) implicitly classifies microworlds as a kind of learning environment, which is an "idea" expressed as follows:

Like the classroom metaphor, thinking of instruction as an environment gives emphasis to the "place" or "space" where learning occurs. At a minimum, a learning environment contains:

  • the learner;
  • a setting or "space" wherein the learner acts--using tools and devices, collecting and interpreting information, interacting perhaps with others, etc. This metaphor holds considerable potential because instructional designers like to think that effective instruction requires a degree of student initiative and choice. An environment wherein students are given room to explore, and determine goals and learning activities seems an attractive concept. Students who are given generous access to information resources-- books, print and video materials, etc.--and tools--word-processing programs, e-mail, search tools, etc.--are likely to learn something if they are also given proper support and guidance. Under this conception, learning is fostered and supported, but not controlled or dictated in any strict fashion.

Microworlds emerged in the 1980's together with pedagogical constructivism as defined by Wilson (1995) as:

  • a place where learners may work together and support each other
  • as they use a variety of tools and information resources
  • in their pursuit of learning goals and problem-solving activities.

Microwords continue to be developped in various forms. On major current debate focusses on the question of how much structure or scenarization is required in effective learning designs. See also Scaffolding and pedagogical scenario, discovery learning vs. guided discovery learning.

Definitions

  • Microworlds are small playground of the mind (Clements, 1989, p. 86 cited by Rieber, 1996:587),
  • Microworlds are tiny worlds inside which a student can explore alternatives, test hypotheses, and discover facts that are true about that world. (Larry Latour).
  • A microworld implements a constructivist instructional design model that lets the learner "play" within an artificial or real (e.g. a Sandbox) environment and learn by building things. The purpose is to give students the resources to build and refine their own knowledge.
  • “A microworld is a type of computational document aimed at embedding important ideas in a form that students can readily explore. The best microworlds have an easy-to-understand set of operations that students can use to engage tasks of value to them, and in doing so, they come to understanding powerful underlying principles. You might come to understand ecology, for example, by building your own little creatures that compete with and are dependent on each other.” (diSessa, 2000, p.47)

History

In 1980, Papert made popular concepts developped around the programming language Logo whose design was influenced by a particular constructionist vision of education. Logo included "turtle geometry", a drawing pen in the form of a turtle that children could move and draw around on the screen or the floor. The turtle is an "object to think with", i.e. a cognitive tool. Since Logo many other environments in the same spirit have been built, but the scope of modern micro-worlds goes much beyound programming environments for children.

Papert (1980) gave a first formal definition of a microworld as a:“...subset of reality or a constructed reality whose structure matches that of a given cognitive mechanism so as to provide an environment where the latter can operate effectively. The concept leads to the project of inventing microworlds so structured as to allow a human learner to exercise particular powerful ideas or intellectual skills.”(p. 204)

For Papert, a microworld is based to a large degree on the way in which an individual is able to use a technological tool for the kinds of thinking and cognitive exploration that would not be possible without the technology.

But Papert knew that a learner needs support structures: “...The use of the microworld provides a model of a learning theory in which active learning consists of exploration by the learner of a microworld sufficiently bounded and transparent for constructive exploration and yet sufficiently rich for significant discovery.”(p. 208)

While it demonstrates the importance Papert placed on exploration and discovery learning, it also shows the need for a teacher or a microworld designer to identify boundaries for learning. Papert has maybe underestimated the difficulty of designing such boundaries, especially identifying where the boundaries lie for a particular child in a particular domain, but he certainly recognized the need for guidance, both in the microworld itself and in the teacher’s assistance to a child using it. As Papert (1980) writes,“...The construction of a network of microworlds provides a vision of education planning that is in important respects “opposite” to the concept of “curriculum.” This does not mean that no teaching is necessary or that there are no “behavioral objectives.” But the relationship of the teacher to learner is very different: the teacher introduces the learner to the microworld in which discoveries will be made, rather than to the discovery itself.”(p. 209)

Initially LOGO-like environments, were confined to the computer and the individual users. More recent developments (e.g. in MIT's Lifelong Kindergarten group) concern a wide range of constructionist learning objects such as:

Features of microworlds

A microworld would consist of (Edwards, 1995)
  • A set of computational objects that model the mathematical or physical properties of the microworld’s domain
  • Links to multiple representations of the underlying properties of the model
  • The ability to combine objects or operations in complex ways, similar to the idea of combining words and sentences in a language
  • A set of activities or challenges that are inherent or preprogrammed in the microworld; the student is challenged to solve problems, reach a goal, etc.
So microworlds
  • allow more and younger people to understand highly significant and applicable concepts and principles underlying all complex systems.
  • are objects to think with to extend our intellectual capabilities. the Logo turtle is an example: the turtle becomes a way for the child to grapple with mathematical ideas usually considered too difficult or abstract. A prime role served by the turtle is the way it “concretizes” abstract ideas.
  • are central to some forms of exploratory learning.
  • have the idea of debugging: errors in problem-solving tasks become a rich source of information, without which a correct solution could not be found.
A software can be considered as a microworld...or not

Whether or not the software can be considered a microworld depends on this interrelationship when the software is actually used. Student have to:

  • understand a simple aspect of the domain very quickly (Rieber, 1996b);
  • explore the domain further with the microworld (Rieber, 1996b);
  • be able to manipulate the objects and features of the microworld “with the purpose of inducing or discovering their properties and the functioning of the system as a whole” (Edwards, 1995, p. 144).
  • be able to interpret the feedback generated by the software based on their actions and modify the microworld to achieve their goal (i.e., debugging).
  • “use the objects and operations in the microworld either to create new entities or to solve specific problems or challenges (or both)” (Edwards, 1995, p. 144).

Therefore, a microworld must be defined at the interface between an individual user in a social context and a software tool possessing the following five functional attributes:

  • domain specific;
  • provides a doorway to the domain for the user by offering a simple example of the domain that is immediately understandable by the user;
  • leads to activity that can be intrinsically motivating to the user—the user wants to participate and persist at the task for some time;
  • leads to immersive activity best characterized by words such as play, inquiry, and invention; and
  • situated in a constructivist philosophy of learning (demands a very able teacher serving a dual role: teacher-asfacilitator and teacher-as-learner).
Simulations are not necessarily microworlds

Microworlds have two important characteristics that may not be present in a simulation (Rieber, 1996).

  1. a microworld presents the learner with the "simplest case" of the domain, even though the learner would usually be given the means to reshape the microworld to explore increasingly more sophisticated and complex ideas.
  2. a microworld must match the learner's cognitive and affective state. Learners immediately know what to do with a microworld - little or no training is necessary to begin using it (imagine first "training" a child how to use a sandbox).

the student is encouraged to think about it as a "real" world, and not simply as a simulation of another world. (http://www.umcs.maine.edu/~larry/microworlds/microworld.html)

Alternative names and/or specialized kinds (see Rieber, 1996, p. 583)

Theorical basis for learning in a microworld

Representations assist problem solving activities in 3 ways:

  1. the right representation reduces the cognitive load and allows students to use their precious working memory for higher-order tasks.
  2. representations clarify the problem space for students, such as by organizing the problem and the search path.
  3. a good representation reveals immediate implications.

Microworlds offer the means of maximizing all 3 benefits of representations, when used in the context of an appropriate science teaching pedagogy, such as one based on the scientific method of hypothesis generating and hypothesis testing. For example, in the ThinkerTools microworld, students directly interact with a dynamic object while having the discrete forces they impart on the object horizontally or vertically displayed on a simple, yet effective datacross. Students can also manipulate various parameters in the microworld, such as gravity and friction. ThinkerTools ably creates a problem space in which numeric, qualitative, and visual representations consistently work together.

Furthermore, Perkins and Unger (1994) suggest that microworlds afford the integration of structuremapping frameworks based on analogies and metaphors. Similarly, a microworld can be designed so as to provide a representation that purposefully directs a student to focus on the most salient relationships of the phenomena being studied. Of course, such benefits do not come without certain costs or risks. For example, if the users do not correctly understand the mapping structure of the analogy, then the benefits will be lost and the students may potentially form misconceptions. Just providing a microworld to students, without the pedagogical underpinnings, should not be expected to lead to learning. The role of the teacher and the resulting classroom practice is crucial here. Microworlds rely on a culture of learning in which students are expected to inquire, test, and justify their understanding. “Students needs to be actively engaged in the construction and assessment of their understandings by working thoughtfully in challenging and reflective problem contexts” (p. 27). As Perkins and Unger (1994) point out, microworld designers have to articulate adequately the components and relationships among components of the domain to be learned. Next they have to construct an illustrative world exemplifying that targeted domain. Finally, the illustrative world should provide natural or familiar referents that, when placed in correspondence with one another and mapped to the target domain, yield a better understanding of the domain. (p. 30)

Constructionism: microworld research evolves

Constructionism is strongly rooted in student-generated projects. Projects offer a way critically to relate motivation and thinking and can be defined as “relatively long-term, problemfocused, and meaningful units of instruction that integrate concepts from a number of disciplines or fields of study” (Blumenfeld et al., 1991, p. 370). Projects have 2 essential components: a driving question or problem and activities that result in one or more artifacts (Blumenfeld et al., 1991). Artifacts are “sharable and critiquable externalizations of students’ cognitive work in classrooms” and “proceed through intermediate phases and are continuously subject to revision and improvement” (Blumenfeld et al., 1991, pp. 370–371).

It is important that the driving question not be overly constrained by the teacher. Instead, students need much room to create and use their own approaches to designing and developing the project. Projects, as external artifacts, are public representations of the students’ solution. The artifacts, developed over time, reflect their understanding of the problem over time aswell. In contrast, traditional school tasks have no driving question and, thus, no authentic purpose to motivate the student to draw or rally the difficult cognitive processes necessary for complex problem- solving.

In an early constructionnism research, Harel and Papert (1991) strongly suggest that what made a difference was not Logo or any particular group of strategies but, rather, that a “total learning environment” (p. 70) was created that permitted a culture of design work to flourish. They particularly point to the affective influences of this environment. These students developed a different “relationship with fractions” (p. 71), that is, they came to like fractions and saw the relevancy of this mathematics to their everyday lives. Many reported “seeing fractions everywhere.” Harel and Papert resist any tendency to report the success as being “caused” by Logo. Instead, “learning how to program and using Logo enabled these students to become more involved in thinking about fractions knowledge” (p. 73). They point to Logo’s allowing such constructions about fractions to take place.

But, successful project-based learning is not a panacea. Success is based on many critical assumptions or characteristics and failure in any one can thwart the experience. Examples include an appreciation of the complex interrelationship between learning and motivation, an emphasis on student-driven questions or problems, and the commitment of the teacher and his/her willingness to organize the classroom to allow the complexities of project-based learning to occur and be supported (Blumenfeld et al., 1991). Fortunately, the recent and continuing development of rich technological tools directly support both teachers and students in the creation and sharing of artifacts.

Students must be sufficiently motivated over a long period to gain the benefits of project-based learning: Among the factors that contribute to this motivation are “whether students find the project to be interesting and valuable, whether they perceive that they have the competence to engage in and complete the project, and whether they focus on learning rather than on outcomes and grades” (Blumenfeld et al. 1991, p. 375).

The teacher’s role is critical in all this:

  • create opportunities for project-based learning,
  • support and guide student learning through scaffolding and modeling,
  • encourage and help students manage learning and metacognitive processes,
  • help students assess their own learning and provide feedback.

Whether teachers will be able to meet these demands depends in large part on

  • their own understanding of the content embedded in projects,
  • their ability to teach and recognition of student difficulty in learning the content (i.e., pedagogical awarenesses),
  • their willingness to assume a constructivist culture in their classrooms.

Examples of microworlds

Many microworlds have become available since 1980:

See also

Repositories
  • MathTools at Math Form. This is a large library (not just for microworlds)

References

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