Notational Load

I define notational load as the cognitive load imposed on a learner by the notation in which a concept is expressed, rather than by the concept itself.

As examples of notational load, consider:

• Roman numerals vs. Arabic numerals: Arithmetic operations such as long division are much easier to teach, learn, and apply using Arabic numerals than Roman numerals. Indeed, the Romans’ numeric notation is often given as the main reason why the Romans contributed almost nothing to mathematics per se, whereas the Arabs made great advances in mathematics.
• Chinese writing vs. Korean writing: The use of Chinese ideograms for Korean writing restricted literacy to Korean elites until the invention of the Korean-specific Hangul writing system, which made it possible for “a bright Korean-speaking student to become literate in one day, and a slow student in ten.” Smilarly, the Cherokee-specific writing system produced a similar jump in literacy rates within the Cherokee-speaking population of the early 1800's.
• The musical staff vs. neumes: Guido d’Arrezo’s invention of sight-singing, including the musical staff and solmization, is credited with reducing the training time of Church singers from ten years to “one, or at most two” – thus reducing the cost of music education by between 80% and 90% without sacrificing quality.

The development of other notational systems, such as calculus, the Periodic Table, and Feynman diagrams, have similarly contributed to significant increases in the efficiency of education.

Perhaps of even greater importance, the development of new notations has often led to new discoveries that were literally “inconceivable” using the previous notations, because notations invariably constrain, in addition to reflecting, patterns of thought. Examples include the Arabs’ use of their numerals in developing algebra and algorithms (the names of which reflect their Arabic roots), Mendeleev’s prediction of new elements based on “holes” in his Periodic Table, and Feynman’s use of his own diagrams in making major contributions to quantum mechanics.

Cognitive load theory recognizes three kinds of cognitive loads (from an educational perspective): intrinsic load (inherent to the subject being studied), extraneous load (irrelevant to the subject being studied), and germane load (which is extraneous to the current lesson in isolation, but which reduces of the overall load of the lesson-sequence as a whole).

Notational load seems to me to be an entirely extraneous load. In opposition to this position, one could argue that the mastery of a given domain’s traditional notation is required for communication with other professionals within that domain, and that this “communication conformity requirement” makes mastery of a domain’s traditional notation intrinsic. For example, without the ability to read traditional music notation, musicians cannot read the works of other composers.

Or…can they? Using modern music notation software programs, musicians can convert any given piece of written music to alternative, non-traditional notations such as guitar tab. Many of these programs support a “plug-in” architecture that enables the developers of alternative notations to retroactively upgrade the software to support new notations The potential availability of such notation-translation software, in any given domain, and the ease of distributing it over the Internet, significantly reduces the communication conformity requirement, supporting the claim that notational load is extraneous.

Changes in notation are not easy to effect in any domain, especially among tightly inter-connected professionals. However, a dramatic increase in learning efficiency may make it possible for non-professionals to rapidly gain knowledge previously restricted to a domain’s professionals. For example, more people in the USA now read Guitar Hero’s scrolling tablature than read traditional music notation, and are, as a result, learning more about music than they otherwise would.