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You learn only some things by receiving information from others, orally or in words or pictures. You learn most things by constructing knowledge.

Why do we continue to act as if the universe were constructed from nouns linked by verbs, when we know it is really constructed from verbs linked by nouns?
--  Steve Grand, Edge 2002

How is your knowledge constrained by the tool you use for gaining that knowledge?

How do you know what you know until you read what you write?

How do you represent a set of concepts and their relationships?

Mental Maps

aka cognitive maps, concept maps,
mind maps, thinking maps, frames of reference

Excuse me, but what do you see in your head while you're thinking? That's not something we're used to talking about. Of course, we know how to organize things in the "real" world. For instance, we can fit blocks through holes or rearrange the living room furniture.

What about larger spaces, such as Buffalo? How do you find your way around? I'll bet that your mental map of Buffalo is different from mine, which looks south and is centered around the mile-long street between my house and my classrooms.

What about ideas?

How do you organize historical events?
How do you visualize the sides of an argument?
How do you remember the points in a lecture?

More to the point, how are you going to visualize the webs you make? You're designing an information system, or information space, as it is often called. If you can visualize it as connected objects (whether "pages" or "ideas"), you can communicate to colleagues and customers by drawing boxes for the objects and lines for the connections. Boxes and lines. Nodes and links.

A large proportion of all Webs' problems have roots in the initial, informal, subjective phase of conceptualizing how the web should be organized.

A large proportion of all organizations' problems have roots in the initial, informal, subjective phrase of conceptualizing how its information should be organized.

A conclusion is the place where you got tired of thinking.

Mappaemundi - world maps

After naming things, the human mind wants to put the things in some kind of spatial relationship: a map.

Atlapedia Online - full color physical and political maps as well as key country facts and stats

Scholars on the importance of maps 

David TurnbullMaps are national knowledge spaces.

Richard SmithFor encapsulating a worldview there is nothing quite like a world map. As with other forms of cartography, mappaemundi -- whether medieval or modern, Asian or Western -- tell us about values and attitudes, aims and aspirations, hopes and fears; but they express them on a particularly grand, indeed global, scale.

J. B. HarleyBoth in the selectivity of their content and in their signs and styles of representation, maps are a way of conceiving, articulating and structuring the human world.

David HarveyCommand over space is a fundamental and all-pervasive source of social power.

source: Richard J. Smith, Maps, Myths, and Multiple Realities

Mind Maps

What about the maps inside our heads?

In 1991, George Johnson published In the Palaces of Memory. This excerpt from the Preface explains:

Whenever you read a book or have a conversation, the experience causes physical changes in your brain. In a matter of seconds, new circuits are formed, memories that can change forever the way you think about the world. I find that idea so remarkable that for the last three years it has been difficult for me to maintain much of an interest in anything else. How is it that memory leaves its mark so that we are able to carry around the past inside our heads? ...

The art of building memory palaces has become a historical curiosity. But in a way, we are unconsciously building structures like this all the time. What Ricci taught as a deliberate mnemonic device comes close to describing what the brain does automatically. As we move through the world, experience is converted into memories. Neuron by neuron we snap together mental structures, constantly evolving palaces of memory that we carry with us until we die.

Unlike Ricci's palaces, ours are invisible to introspection, but slowly scientists and philosophers are deciphering the blueprints of these worlds inside our heads.

Or, as Richard Smith says about ink-on-paper maps in Maps, Myths, and Multiple Realities:

Cartographers construct the world, they do not reproduce it. Places are where they are, but maps represent them where the mapmakers want them (or need them, or think them) to be. Every map, then, has an author, a subject and a theme (or themes). No map is a neutral document. All reflect efforts of one kind or another to impose oneself (or one's culture) on physical space. A map is an interpretation that needs, in turn, to be interpreted.

In 1995, the library at Hong Kong University of Science and Technology had an exhibit called "China In Maps: 16th - 19th Century". The gallery, still available, has dozens of mappaemundi -- world maps.

why use them?

Concept maps are visualizations of our mental models or belief systems. We use them to interpret, frame, simplify, and make sense of complex problems. We build mental models from our experiences and then use them to interpret new events.

As a decision-maker, you will have a limited capacity for processing information. When dealing with complex problems like innovation, you rarely process all the information that would be relevant. Your mental models help you select information and decide what actions are appropriate, depending, of course, on the socio-political context and on your ability to influence decisions in your organization.

Your personal mental map won't look like anyone else's. Thus, organizations have developed some conventional maps. Two people or the members of a decision-making group can adapt their personal maps to one of the conventional maps so that they can compare and discuss them.

What is a concept map?

A purposeful arrangement of nodes and links.

parts

nodes
links

attributes

shape
size
color
position

If concept mapping is a new idea to you, you can find some background at the Concept Mapping Workshop developed by Douglas McCabe at Hong Kong Polytechnic University. His concept mapping page has other resources worth your while, especially those at the University of Twente's Concept Mapping Homepage

The Theory Underlying Concept Maps and How To Construct Them
Joseph D. Novak, Cornell University

A concept map is never finished.

How are these parts organized?

If you hand in a ten-page term paper essay, neither you nor I have to give much thought to orientation and navigation. One staple; ten page numbers. Maybe instead of the staple you slide the text into a slick blue plastic sheet with a white strip to grasp it on the left. Should the pages come flying out, the ten numbers will let me quickly reassemble them. I read top to bottom, left to right. You can count on it. I might follow a reference to the Works Cited. I might flip back from page 8 to check something on page 3.

How else do we navigate? Some of you may have had occasion to look for a recipe in a printed and bound cookbook. As long as there was a table of contents, you could find your way around pretty well. If there was an index of ingredients used, even better.

Navigation in hypertext is a little different. It's harder because each writer (author? designer? developer? builder?) gets to make up his or her own navigation and orientation system to replace the staple and the linear 1, 2, 3 page order. You can pretty much count on the top / bottom left / right as everyone's default behavior. But you've had your eye bounce around enough Web pages. The way you integrate text and graphics opens up a world of page-reading possibilities. People are more than willing to abandon the linear text if you reward them with attractive, accessible content. Even better, let them interact with it. Let it behave.

What about nodes?

On the concept map below of a generic Medaille course disclosure, the blue oval shapes represent the four course objectives. Their relative sizes reveal the teacher's idea about the relative importance and their relative position make me think that it's the second objective on the list that is the most important. The squares can show, in chronological order, the written (red), tests (gold), and oral (green) assignments. I made all the squares the same size because they all count the same 10%. What other relationships of shape, size, color, and position do you see?

What about links?

The map above has only nodes, no link. Why bother with links? Because if the nodes are like the nouns in a sentence, if the attributes are like the adjectives, then links are like the verbs. And verbs are where the action is. The teacher can use lines to link the tests with specific objectives and help the students integrate the parts of the course. Those lines can also be thick or thin, solid or dotted, colored and overlapped. In context, reading those visual cues can help.

This line-drawing exercise process might enlighten all of us. Let's say I had a version of the above concept map specifically for this course.

before the course, I draw the lines between the squares (assignments) and ovals (objectives) representing what I intend to teach

after the course, I draw the lines -- thick, thin, broken, solid -- between the squares and ovals according to what I think I ended up teaching

after the course, on a separate map, you draw the lines according to what you think you learned

finally, we compare our concept maps of the course

Hypothesis | Grades tend to be higher when the students' and teachers' concept maps are more similar.