17 July 2009

Thinking Maps


    Dr. D. Hyerle grouped under Thinking Maps syntagm a set of eight metacognitive visual tools rooted in the eight cognitive skills: defining in context, describing attributes, comparing and contrasting, classification, part-whole spatial reasoning, sequencing, cause and effect reasoning, and reasoning by analogy [1]. He used the tools to create a easy to use language for learning and information representation, the eight graphic primitives can be used in an infinite of ways. There are several diagrams which summarize what the eight Maps are about:

Thinking Maps [8] Thinking Maps [9]

    Benefits associated with the use of Thinking Maps can be found in [3], [11] and [2] together with modes of employment.

Circle Maps

    Circle Maps are used to place concepts into a context with the help of two concentric circles, the smaller one containing the context, while in the outer circle are placed the associated concepts, acting like properties or association bag. Concepts are usually clustered without creating explicit relations between them, more complex Circle Maps being created using multiple concentric circles, a target diagram according to [12], or by partitioning the outer circle, creating thus different spheres of meaning.

    Given its geometrical properties (e.g. centricity, equidistance, regularity), the circle is a perfect tool for representations, though it doesn’t have to be used as a leitmotif; triangles, squares, rectangles or any other regular polygons can be used for the same purpose, especially when additional intrinsic characteristic are highlighted, for example trinity, square of opposition, n-tuplicity, etc.

    Circle Maps can be pretty simplistic, in simplicity residing their beauty and use; overall Circle Maps are a perfect tool to introduce concepts, especially in primary school. Their importance should not be underestimated, they can have strong representational power especially when used in combination with other representational patterns.

Bubble Maps

    Bubble Maps focus on direct associations between a concept and its descriptors, also called adjectives, qualities, attributes or characteristics [11]. Such representations are integrant part of many types of Maps that represent associations explicitly (e.g. Mind Maps, Concept Maps). Extensively, a Bubble Map could be used for the same representations as Circle Maps, allowing thus explicit associations between a concept and its attributes, same it can include other part of speech, concepts or fragments of text. For greater effect, Bubble Maps could be combined with Circle Maps, especially when needed to highlight different boundaries.

Double Bubble Maps

    Double Bubble Maps are used for comparing and contrasting the descriptors of two concepts. Another popular tools used for the same purpose are the Venn diagrams, which mixes some of the characteristics of Circle Maps and Double Bubble Maps, though they are sometimes more complex to use and, in plus, they allow the comparison of multiple concepts. Are few the situations in which more than two concepts need to be compared, how should such a Map be called?! Maybe Multi-Bubble Maps…

Flow Map

    Most probably many people are already familiar with flowcharts or flow diagrams, one of the process diagrams used to model the flow of processes (systems), and sometimes considered synonym to them. Hyerle’s Flow Map seems to be slightly different than the flow diagrams used to model processes, and even if both maps are based on sequencing and ordering principle, the later seems to be more complex and use more representational elements, containing symbols for decision, delays, predefined subprocesses or data input/output. Hyerle’s Flow Map resumes only at presenting information in sequencing and ordering manner, being capable of represent for example a linear causality sequence or the points on a scale (e.g. past, present, near future, future or very cold, cold, warm, very warm). I consider scales, also named continuums by [12], a pattern of its own, used to represent a set of ordered concepts, including timelines, transition between two states, scales of values, ordered sets, etc. It is possible to represent together two or more scales/continuums within the same system of coordinates, each scale on an axis of its own. Such a system is called a crossed continuum by [12] and conceptual space by [13].

Multi-Flow Maps

    A Multi-Flow Map is obtained by combining more than one Flow Maps, creating parallel or intersected sequences. Therefore they are useful to represent causes and effects diagrams, more like the well-known Fishbone diagram, the distinction residing in the fact that the multi-flow Maps not necessarily follow a hierarchical structure, multiple effects being possible. In addition the Fishbone diagram has a “methodology” of its own, the causes being identified starting from an observed effect.

    It’s interesting that [10] makes distinction between Multiple Causes Maps and Multiple Effects, which could be taken as particular Multi-Flow Maps.

Brace Maps and Tree Maps

    Brace Maps are the only type of Maps I often saw used in manuals or other type of books, usually for detailing the parts of concepts allowing thus to analyze the parts of a concept and the concept itself. Brace Maps are used also for the classification and grouping of concepts, in Hyerle’s system usually represented using Tree Maps.

    I often used Brace Maps in Mathematical definitions, when the definitions need to be split in parallel threads (left braces), or demonstrations, when multiple threads flow into the final result (right). Even the use is slightly different the principle is somehow similar.

Bridge Maps

    Bridge Maps are used for highlighting analogies between concepts into an inversed Vee-like diagram, which can be repeated for each additional analogy added to the chain, with the comparison concepts on top and the relating factors below. Bridge Maps can be used not only for simple analogies, but also for metaphors.     I expect that in case are needed to be compared multiple related factor types for the same concepts, then it will be created one Bridge Map for each factor type. For such scenarios a simple table could be a better choice, in which the compared concepts form the headers, while the related factors are the actual records. Even more, the concept representing the concept type can be added too, forming a matrix. An example of such matrix can be found in a previous posting on Web’s evolution.     Even if the use of Bridge Maps expresses directly the intent of representing analogies, I find tables or matrixes much simpler to use and non-redundant.

New Patterns, Old Patterns

    The patterns encompassed in Thinking Maps are not new, many of them have been used a few centuries ago, as can be seen from the below examples. In the first figure can be seen the Buenting clover leaf map, woodcut made in 1581 in Megdeburg; it can be regarded as a combination between Circle Map and Bubble Map. In the second figure from Athanasius Kircher’s Oedipus Aegyptiacus can be seen a wonderful complex diagram of the names of God, a combination of a partitioned target diagram (multi-concentric Circle Maps) and Tree Maps. In the third figure, a simple I Chin diagram based on Pa Gua trigrams, a partitioned Circle Map making use of symbols, the same theme being present also in the fourth diagram, which evolves the I Ching model to a representation of the DNA world.

Buenting clover leaf map Athanasius Kircher’s Oedipus Aegyptiacus
Buenting clover leaf map [6] Athanasius Kircher’s Oedipus Aegyptiacus [14]

I Ching DNA/RMA Mandala
I Ching [4] DNA/RNA Mandala [5]


[1] Hyerle, D. (2008). Thinking Maps®: A Visual Language for Learning. In: Thinking Maps®: A Visual Language for Learning, ISBN: 978-1-84800-149-7. [Online] Available from: http://www.springerlink.com/content/x57121720731381j/ (Accessed: 23 June 2009)
[2] A. Costa, P. Wolfe, H. Gardner, D. Goldman. The Networking Brain and Mind. [Online] Available from: http://www.mapthemind.com/pdf/visual_tools/visual_tools_CH2_20_35.pdf (Accessed: 7 July 2009)
[3] Learning Prep School. Thinking Maps. [Online] Available from: http://www.learningprep.org/thinkingmaps.htm (Accessed: 7 July 2009)
[4] Zen’s Sekai I. (2007). I Ching. [Online] Available from: http://zensekai.wordpress.com/2007/04/05/i-ching/ (Accessed: 8 July 2009)
[5] The Abysmal. (2006). DNA Codon Mandala. [Online] Available from: http://theabysmal.wordpress.com/2006/07/15/dna-codon-mandala/ (Accessed: 8 July 2009)
[6] Learn NC. Buenting clover leaf map. [Online] Available from: http://www.learnnc.org/lp/multimedia/6981
[7] L. Sachar. Multiple Mapping: Holes. [Online] Available from: http://www.learningprep.org/images/thinkingmaps_album/student_work_images/mult_mapping_holes_louis.JPG (Accessed: 12 July 2009)
[8] Seattle Schools. Thinking Maps. [Online] Available from: http://www.seattleschools.org/area/arts/visualarts/thi_map.html (Accessed: 13 July 2009)
[9] SaskEd. Unit Five: Social Development. [Online] Available from: http://www.sasked.gov.sk.ca/docs/native30/nover5.html (Accessed: 13 July 2009)
[10] Somers Central School District. ????. Graphic Organizers that Support Specific Thinking Skills. [Online] Available from: http://www.somers.k12.ny.us/intranet/skills/thinkmaps.html (Accessed: 14 July 2009)
[11] Hyerle. D. (2000) Thinking Maps® for Reading Minds. In: A Field Guide to Using Visual Tools. Association for Supervision & Curriculum Deve. ISBN: 978-0871203670. [Online] Available from: http://www.mapthemind.com/PDF/visual_tools/visual_tools_CH6_100_123.pdf (Accessed: 14 July 2009)
[12] G. Petty. (2009). ISBN: 978-1-4085-0452-9. Evidence Based Teaching: A Practical Approach. 2nd Ed. [Online] Available from: http://bookshop.blackwell.co.uk/extracts/evidence_based_teaching.pdf (Accessed: 16 July 2009)
[13] Gaerdenfors, P. (2000). Conceptual Spaces: The Geometry of Thought. Massachusetts Institute of Technology. ISBN: 0-262-07199-1.
[14] Cramer, F (2005) Computations of Totality. In: Words Made Flesh – Code, Culture, Imagination. Piet Zwart Institute. [Online] Available from: http://pzwart.wdka.hro.nl/mdr/research/fcramer/wordsmadeflesh/03-chapter_2/ (Accessed: 16 July 2009)

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