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keywords, four inter-sections and a meta-concept
amount of4 knowledge
12x1=12 elements
(12x2)+(12x(1+1))=48 elements
(6x3)+(6x(3+1))=42 elements
(4x3)+(4x1)+(4x4)=32 elements
knowledge transfer
E-learning 0%
E-learning 50%
E-learning 43%
E-learning 37%
knowledge of the learner5
list of doctrines
list of isolated rela-tions and methods
set of concepts
meta-knowledge (essence)
applied knowledge
repeating the doc-trines (facts)
accomplishing tasks
managing processes
creating solutions (seeing what nobody has seen)
knowledge media and authors
several authors
HANDBOOK
single author
TEXTBOOK
team of authors led by a master
BOOK
The knower at the lowest knowledge level may see isolated dots only, which correspond to isolated facts or doctrines presented as facts. This we call the dimensionless (0-D) knowledge. At the second level the knower sees two dots at the same time and can connect them by a di-rected relation, such as causal relations or logical ‘if… then’ rules. Along these relations methods can be devised, i.e. we can learn how to get from one point to another. As two dots determine a line this we call the one-dimensional (1-D) knowledge. It can be expected that the next level should be called two-dimensional (2-D) knowledge and be described by three dots. If one sees three dots the simple relations from the previous level will prove poor for provid-ing satisfactory explanation. Thus we describe this knowledge level with three sets in inter-section. This does not mean, of course, that on this level the knower cannot handle e.g. causal relations (any two from the three dots may be connected by an arrow); this means that here we can have a richer picture of less rigid relations, such as intersections. The highest level of knowledge presented here is the three-dimensional (3-D) knowledge corresponding to four dots. We know little so far about the 3-D knowledge but there are several details observed. The fourth point is qualitatively different from the previous three; it somehow throws light to the previous three through their interrelations (this is why there are fewer elements at this level than at the previous one). There is no much sense to try to describe higher knowledge levels – very few of us can imagine pictures of more than three dimensions.
In the present paper only the knowledge of the educator is used as a point of reference but in application we also must take into the account that the learner can only perceive teaching de-livered one level higher than her/his existing knowledge (meaning that the delivered teaching cannot be higher than that; it can always be lower – but why would we do that?)
1 A particular topic is described by keywords and their relationships.
2 Another proof for the capacity limit of STM – there can be no more elements than 7±2. (Miller, 1956)
3 The four intersections in two-dimensional thinking do not mean the same as in the three-dimensional thinking. In two-dimensional thinking the ‘fourth’ intersection is only a special case; thus it is said to be ‘3+1’. At the same time in the three-dimensional thinking it is something new, often the representation of or a shortcut to the essence.
4 Assuming 12 weeks in a semester.
5 The new knowledge that a talented student may achieve.
2
We shall now examine somewhat more closely how much of knowledge at different levels can be transmitted in one semester. Th