The idea of mastery of a topic, or ‘fluency’ is an area in the education business where there are some interesting problems (related to epistemology) as well as a place where the fundamental shortcomings of standardized test are most obvious. The blog post I am citing below relates this idea to learning vocabulary in English, but this is an idea (fluency…or mastery) which is well understood in plenty of arenas besides school classrooms.

In language, merely learning how to pronounce, spell, and simply define a word is considered ‘knowing it’…obviously it really isn’t, and the following quote showcases a bit of this…

What Do You Know When You “Know” a Word?
http://blog.eyeoneducation.com/2011/04/19/what-do-you-know-when-you-know-a-word.aspx

When you know a word, you know how it can change. Think about the knowledge that you possess that allows you to change the words below from their positive to negative meanings. We’ll do the first two for you.

• legal : illegal
• possible : impossible
• relevant :
• appear :
• divisible :
• reliable :

Would it ever occur to you to say something like “You can’t do that—that’s dispossible”? Or “That’s unlegal”? Of course not—to a native speaker of English, that sounds incredibly wrong. Yet, you probably can’t explain why you know that the negative form of “reliable” is “unreliable” and not “disreliable” or “inreliable.” You produce the word “unreliable” because that’s the form that you’ve heard repeatedly. You’ve come to know it intuitively.

Do you remember memorizing lists of this kind of stuff as a child? (“Let’s see: the opposite of appear is disappear, but the opposite of possible is impossible. How can I remember that?”) Of course not—you learned this information naturally as you were acquiring English. And these examples only represent the tip of the iceberg: The body of knowledge that you have about word derivations is immense!

When native speakers truly "know" a word, they have acquired a complex body of knowledge including knowing how the word can change.

In some ways this is yet another way to look at critical learning skills, Bloom’s Taxonomy (or any other hierarchy of understanding), and to understand that learning lists of facts has some value (in a decreasing manner these days, with online access becoming more and more ubiquitous). While this has been the core of many classes, there is a growing need for educators to think more about fluency (i.e. deeper understanding and use of new information).

There are some reasonable analogs to this in the study of music… For instance, when learning a new chord, on the guitar, it isn’t just that you need to (1) know the name, (2) know how to ‘finger’ it… there are innumerable other aspects of musical knowledge involved in mastering this small musical object.

On the guitar, there is a need to understand every note in this group of notes, to know how to derive it, to know of all (at least most) of the cognate chords (the same, or similar chord, using different fingerings, different places on the fretboard, and differing arrangements of the notes themselves). Then there is the need to understand how this particle of music interacts inside musical compositions… This implies that you must know where to use this chord (versus any others)…

This point isn’t about learning a new word, or a guitar chord…almost any tangible skill or specific area of knowledge has similar rules… For instance, just memorizing some Trigonometry identities has little or no real value (other than the ability to pass some introductory quizzes)…this area of mathematics become incredibly powerful once you start to see how to use these relationships to describe and to solve real problems…

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