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I've decided to create a concept map of a chapter I covered in a textbook, it's about basic set notation. What I want is suggestions on how to improve the presentation of the map. It seems quite convoluted at the moment, and I feel to anyone apart from me it may be unreadable. I think it may be improved if I addressed the following:

  1. Organisation of concepts — conceptually should you go from general to specific? Should the structure be hierarchical?
  2. Granularity — What is the level of detail one should aim for?
  3. Linkages — as you can see in my map there are concepts lower in the hierarchy that are linked with concepts higher in the hierarchy, with large swooping arrows, is this preferable? or should linkages only be made with local concepts?
  4. Are there other useful tools that may help me visualise knowledge structures?

Any other suggestions are welcome, thank you.

Concept map for basic set notation


EDIT: You need to zoom in with your browser to see the concept map properly, as SE automatically scales it down. If you zoom in the writing will be legible without a problem.

Alternatively, you can view the image directly here.

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  • $\begingroup$ Is this for you, or your students? I guess I don't really understand its purpose (for me, it seems way too detailed for topics I'm comfortable with, and became comfortable with in lieu of such a map). $\endgroup$ – pjs36 Oct 5 '15 at 3:56
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    $\begingroup$ @pjs36 Without speaking to the OP's purpose, there is at least a somewhat rich literature in mathematics education around concept maps. For example, see (occasionally joint) work by JD Novak (google scholar) and AJ Cañas (google scholar). $\endgroup$ – Benjamin Dickman Oct 5 '15 at 4:34
  • $\begingroup$ @BenjaminDickman it's for personal use, to help me understand how various concepts are connected. Thanks for the literature. $\endgroup$ – seeker Oct 5 '15 at 9:48
  • $\begingroup$ @BenjaminDickman The reason why i'm using concept maps is to see where this all fits into my mental mathematical framework. In order to achieve this I intend on making concept maps for chapters, which have a greater level of granularity, and then also creating macro-concept maps, which ties up everything i've learned so far to give a "big-picture" view of everything (i'll be adding to this over time). Do you think this is a good way of improving my understanding of mathematics, and are there any other things you can suggest that may help me improve my understanding? $\endgroup$ – seeker Oct 5 '15 at 14:41
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I found this to be a highly readable concept map. The major problem I see is that it clearly has two main concepts: Sets and The set of Real Numbers. Each one of the concepts has an extensive tree of sub-concepts built from it. Additionally, there are only three connections between these two trees and these are all weaker connections: "can be used...", "is an example of". You could improve this concept map by breaking it into two maps, one for each core concept. (I suspect you combined these because they were combined in the textbook. Realizing that these concepts which are co-taught are only marginally connected is one valuable thing that can come out of making a concept map.)

To address your questions about concept maps in general:

Going from general to specific concepts is a good idea. However, given the highly connected nature of mathematical ideas, you will have lateral connections. Being able to represent lateral connections is advantage that concept maps have over outlines. When possible, arranging your concept map so that the lateral connections are short and don't cross is desirable. Putting the main concept in the center of the page (Radial hierarchy) can help with this.

For reflecting on a concept map, seeing the entire map at once is helpful. Include as much detail as you can while keeping the map to one page or screen.

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