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LIMITS OF TERNARY PROPOSITIONS IN CONCEPT MAPS

(Italiano sotto)

I will report in this post a collection of "normal sentences" that are hardly transformable in simple ternary propositions, as required by concept mapping, and I will propose "quasi-solutions" for them. These examples want demonstrate that "not good concept maps" and difficulties in costructing valid propositions and hierarquies are not always related to a lack of deep understanding by the learner in the logic and in the relations among concepts of a certain domain, but it can be inherent to the technical issue of concept mapping, also for expert c-mappers.

Anybody is welcomed to do the same by proposing sentences and/or solutions.

This research is aimed at both: a) explaining the rejection of concept mapping by adults as partially due to the insufficient complexity of ternary propositional structure of concept maps, compared to the complexity of relations that adults manage in their natural language, and b) to show how these limits can be (partially) overcame by approaching further the language of concept mapping to the natural language, by enriching the variety of types of admitted linking phrases and words, by admitting exceptions to some syntax rules of each language, reducing to the essential minimum the rules that are accepted by the concept mapping community. As an example, nouns and pronouns are not advised in linking phrases, whereas some authors want force single words in links. If we want the students to construct accurate and unambiguous propositions, then the rules and conventions that aren't strictly and explicitly related to Ausubel's background of concept mapping should be released. For the same theoretical reasons I am convinced that the basic core of concept mapping is the most privileged code to interface with the processes that accompain meaningful learning in every field, as described by Ausubel's, therefore it would be a nonsense to search for or select among other forms of knowledge representation downstreaming the specificity of each knowledge domain, if the main task is not the representative, but the metacognitive one and of giving the teacher a tool for learning mediation.

1. Example due to Meena Kharatmal ( http://okeanos.wordpress.com/2007/06/13/representing-biological-statement-into-logical-form/ ):

"Plastides are found in plant cells only"

if plastides concept is the more inclusive in the cmap, a proposition can be easily made from this sentence:

[ Plastides] are exclusively found in [plant Cells]

However we have to notice that it is impossible to find a single word that make the same relation (linking phrase) explicit.

The real problem stands out when 'plant cells ' concept is more inclusive than ' plastides ' concept, in the cmap:

We have some unacceptable solutions:

1A. [Plant cells] can consist of [Plastides]; this is logically wrong as a proposition, because it implies that plastides could be found elsewhere, whereas the intial sentence excludes this possibility.

1B. [Plant cells] contain [plastides]; this proposition is incorrect because it implies that all plant cell cell should contain plastides, and this could be false in some istances. Moreover it has the same inaccuracy of 1A.

Better solutions can be:

1 C. [plant cells] are the only that (can) have [plastides] ( only and can partially "save" the logic of the sentence).

Drawbacks : the linking words can have ( or even have) introduce extra information not deducible from the original sentence, i.e. that "not all (or all) plant cells have plastides". From "Plastides are found in plant cells only", we don't know anything whether all plant cells contain plastides or not. Independently by our biological extra-knowledge that root cells haven't plastides, we are in trouble if we want maintain the same level of ambiguity (or lack of knowledge) in the cmap proposition as in the original sentence.

I T A L I A N O

Limiti delle proposizioni ternary in concept maps

This post will report cases of texts quite ordinary, however, prove difficult parts of attempts to transform into simple propositions ternary, as required in the concept mapping. Proporrrò addition of the "quasi-solutions" to these sentences. These examples are intended to show that concept maps "not good" and the difficulty in constructing sentences and hierarchies are not always valid due to the lack of deep understanding of the logic and relationships between the concepts of a topic by the learner, but may result technical difficulties inherent in the concept mapping itself, also found by experts in this technique.

All are welcome to propose other words "stubborn" and / or additional solutions.

This research is aimed at both: a) explain the rejection of the concept maps by adults as they should - in part - to the low complexity of the structure of ternary propositional concept maps, compared to the complexity of relationships that adults handle natural language, and b) show how these limitations might (partly) be overcome by further approaching the language of concept maps in natural language, enriching the variety of types phrases or words bond eligible, admitting some exceptions to the syntax rules in different languages, minimizing the essential rules accepted by the community concept maps. For example, nouns and pronouns in sentences are not recommended bond, while some authors would force individual words in sentences bond. If we want students construct sentences more accurate and unambiguous, we give up those rules and conventions that are not strictly and explicitly by the descendants of the theory of Ausubel backgroung. For the same reasons I am convinced that the core theoretical basis of the concept mapping is the most privileged code to interface with the processes that accompany the meaningful learning in each field, as described by Ausubel's theory. Therefore it would be pointless research or selection between different forms of knowledge representation furthering the characteristics of each domain of knowledge, if the primary purpose is not representative, but that metacognitive and provide a tool for mediation of the teacher ' learning.

1. "The plastids are found only in plant cells"

(translated by a proposal for Meena Kahratmal in http://okeanos.wordpress.com/2007/06/13/representing-biological-statement-into -logical-form / )

If the map of the plastid is more overarching concept of the plant cell, it poses problems:

[Plastids] are found exclusively in the [plant cells].

But we should note that you can not find a simple, single word, spelling out the same report (sentence link).

The real problem is created if, in the drawing of the map to Plant Cell must be a more inclusive concept of Plastids. We then

some unacceptable solutions:

1A. [Plant cells] may contain [Plastids] , which is not correct, because it leaves open the possibility that the plastid can be contained elsewhere, they are prohibited from saying something original.

1B. [ plant cells] contain [Plastids] , that is not correct, since it is understood narrowly ( all plant cells contain plastids), information that can not be obtained so logically from the original. It also has the same inaccuracy of 1A.

solutions proposed (Proposed solutions)

1C. [Plant cells] are the only ones that may contain (or contain) [plastids] (words only and can "save" the logic of the statement).

Disadvantages: the word link may contain (or contain ) introduce extra information is not deductible from the original sentence, that "not all (or all) plant cells have plastids. From the phrase "The plastids are found only in plant cells "we can not determine whether all plant cells contain plastids or if this is true for some. Regardless of our biological knowledge of the fact that the cells of the roots, for example, do not contain plastids, we are in difficulty in making bond in the same sentence ambiguity (or lack of knowledge) of the original sentence.

2. The report (ie combination) of (a) two concepts is related to a third concept

Example 1: scopolamine combined with morphine was used for the anesthetic effect called "twilight sleep" (serum of truth ")

Solution 1A: Create a unique concept of [morphine-scopolamine combination]

Disadvantage: If the scopolamine has an independent role in the map, somewhere will be necessary to repeat this concept.

Solution 1B: Y structure with sentence link "combined injury" or simply "give" -> [combination anesthetic ...]

Disadvantage: If scopolamine is part of the context of the map, but this is not true for morphine, we introduce two concepts that the same level are on two completely different plans, with a jarring because there are no visible links that lead to morphine, and scopolamine is well integrated in the map with incoming and outgoing.

Solution 1C: If a combination of the two concepts is not part of the context of the map, it is combined in the phrase link: [scopolamine] - is combined with morphine to give -> [anesthetic ... ]

Problem: The phrase becomes a binding fragment of text. Are not always one of the two concepts has a marginal role in the map.

Solution 1D bond branched sentence: [scopolamine] can be combined to give the {-> [anesthetic]} -> [morphine]. With the use of combination Ctrl-Shift, CmapTools to create branched structures to link phrases.

Disadvantage: can be read incorrectly (one branch). That is binding on the reading, contrary to the normal link phrases that are not or should not have a preferential order of reading level.

3. A building containing two or more concepts is related to a separate building containing two or more concepts.

Example 2: ergotism is a syndrome of mass poisoning from the consumption of rye "horned", that is affected by a fungus that releases toxins that different produce vasoconstriction, gangrene and burns (shingles), neurological symptoms such as hallucinations, manic behavior, muscle spasms (St. Vitus' dance), which often end in death.

The complete ignorance of the cause of these disorders has caused real massacre of entire villages in the Middle Ages, but in the last century, when the case was now established and well known to millers. The people wondered why his community had been chosen to be hit by this disaster, especially when neighboring countries were spared. The search for the guilty of witchcraft often ended with the additive old innocent, poor and marginalized, who survived thanks to knowledge of the healing properties of herbs, but did not have enough money to buy flour contaminated. When these poor women were thus spared from the poisons of ergot, for this became exposed to ruthless convicted of witchcraft. ¹

The link does not refer explicitly pointed to a single concept, but complete the event, which includes a relationship between two concepts.

Try to represent as a map, the last sentence in italics (and possibly also the context).

Example 4. A changed the role of B to C to D

are four concepts A, B, C, D

(eg Tobacco changed the role of opium in Chinese society, from a medicinal herb (That Was swallowed pellets or as drunk as infusion) forbidden to an addictive drug to be smoked)

putting the proposition "to change the role of B", the logical point of view it is closed but from the standpoint of the meaning does not say anything.

fact, the reader wants to know how was the role of A before and as it became later.

One possibility is to illustrate these roles before and after, read on to Λ

B was used as the first C, then B is transformed into [D]

Disadvantage: not stated that you understand the role of A in causing the change from C to D.

other solution:

The change in the role of B-event is a concept that arises in time halfway between the old and the new role role C D

there is a solution triangular

[B used for C] suffered [role,] produced a new [role B with D];

the concept of event [role,] 'receive' the proposition [A] results -> , [role,]

Problem: I do not think proper to insert a generic concept, decontextualized (change of role), in the midst of a chain of events clearly set in context.

other solution:

[A] changed the role of [B as C] (and receding along) [A] produced the role of [B as D]

Disadvantage: Requires an inference, however, to understand the sequencing between the old and the new role that has been broken here.

The fact that you can not find a fully satisfactory solution to this recurring type of texts (not only in scientific language), can only be seen as a limitation of the language of maps.

in oral and written language of children, mainly including minimum sentences, is rarely observed this type of constructs, while it is frequent in adult language. For this reason, in my opinion, it often happens that students and adults receive concept maps as something that forces you to do stunts in order to follow the rules too restrictive, all texts to encode or thoughts that are already clear.

To exit this divergence of views between the educator and the learner offers maps that the end of these wonders, should the logical structures of the text to be recognized in their complexity, so you can make an immediate appeal to a sample of possible alternative technical solutions, without losing confidence in the concept map and its ability to facilitate metacognitive reflection.

The existence of the limit of ternary clauses based on simple relationships can lead There are two possible consequences:

1. limit the scope of the concept maps and opt for other forms of representation depending on the type of text;

2. allow greater flexibility and extension to the repertoire of syntactic forms and also eligible hybrid forms of organization patterns within graphics have a structure, however, the prevailing concept map.

I think the second solution is more reasonable for two reasons:

a) for logical reasons. Unless you want to reduce the application of concept maps in elementary and primary school texts, it is not possible to distinguish clearly between text types and a priori that not entail or imply relationships more complex than ternary. The practice of concept maps shows that these are feasible and produced for more complex texts, where there are objective difficulties in setting the strategic importance of complex relationships, difficulties that may be independent from the actual understanding of those relationships.

b) for pedagogical reasons. The first solution is valid if the maps are seen solely as a tool of knowledge representation. If instead we see in the maps also an educational tool for the construction of knowledge, we are aware of the opportunity represented by having access to a general metacognitive approach in the educational relationship, rather that different techniques of representation that the student should master to represent various forms of knowledge already gained. The student will learn, however, different forms of representation, graphics, symbols, icons, etc.. in various specific disciplines.

The critical point is, in fact, whether or not to recognize the usefulness of concept mapping in the phase where it is still building learning in a meaningful way, and it can be of maximum effectiveness of the mediator ' teacher, not just in the next step in which this practice can become almost superfluous (as is often seen by teachers and pupils).

What happens in middle phase of learning?

focal questions are identified, he should acknowledge and concepts with various processes of nominalization, unification and generalization, we compare various options for curing and ordering in pairs or small groups of concepts, one begins to think of predicates that condense the links between these concepts with a high degree of ownership. If you do all this within a text or a knowledge domain is sufficiently complex, and you can do it without writing or typing a single word, it means that you are in any case:

1. studying

2. adopting a meaningful learning methodology

3. doing concept mapping

If at this point you still want to go forward and represent - to yourself first - the structuring of own ideas, and you must choose a form of representation, one has before one option: building a concept map, using all the rules necessary, think, change over time by experts not to construct a standard graph-language, but to fit as much as possible to how the mind to construct, assimilate and represent concepts and links , with less constraints as possible outsourcing this task, metacognition and cognitive distance. Included in this process become understandable Novak maps that do not meet the standard of Novak, the propositions made up of three concepts and two ties, a few sentences bond formed by a simple preposition and other measures "natural" much less complex than the "tricks" that (probably) make us lose Just time. Are all these concept maps equally understandable (as a means of communication) with respect to the maps more orthodox, and are sufficiently effective as forms of presentation of the knowledge domain. Concept maps are full because they arise from a process of representation and organization internal knowledge and constitute a natural continuation. And if the role of education you should enter on this line can not choose more than the concept map. If you leave the process of learning to deal with issues and production techniques that are based on static knowledge and background, how to represent a web, design a hypertext list a tree, outline a decision tree and so on. Then you choose the 'organizer that best suits your needs. Anyway, for the teaching profession, I consider important and indispensable tool concept map. At the point of looking for ways out quick and easy to hitch idiots.

point that connects with a beret we are looking for solutions adapted to store logical-syntactic criteria base (and benefits) of concept maps in the presence of a native language that puts the verb at the end and prepositions to the name stuck.

Conlon's generalization is not useful for this purpose predominantly educational graphic organizers as regards the knowledge and the learning mode in the theory of meaningful, having a direct link with concept maps.

a free text summary from "Napoleon's Buttons", P. Le Couter, J. Burreson, Longanesi