Abstraction: Generalization

What word would you use to describe the following picture?

Did you say "Fruit?" Classifying all of these objects into a single idea is powerful.  It allows us to conceptualize lots of food into a single category.  When nutritionists advise us to eat "5 fruits daily," we are considering fruit as an abstract concept that we have generalized into a single idea.  Generalization is another way of abstracting information that helps learners think computationally.

Probably the most common method of using abstraction for generalization is through the use of symbols.  Written language itself is just a series of generalized abstractions for sounds that form words.  Lev Vygotsky demonstrated that symbols are both culturally and historically bound.  That means that students learn what an abstracted symbol means by interacting with their surrounding peers and society.  For example, what do you suppose the following symbols mean?

420:12

This symbol may seem odd to you (or not), because you may be used to seeing it in a different manner.  If you were educated in the U.S., you might be more familiar with the following notation instead:

$\frac{420}{12}$

My wife, who grew up and was educated in Chile, learned to represent division using the former symbol and only learned the latter representation when she studied microbiology at a US university.    Symbols, at their core, are just generalized abstractions.  More importantly, they are abstractions that we can use to our advantage. The ability to generalize allows students to take a mess of complex ideas and consider how they can apply them across a series of problems.  We actually already make use of generalized abstractions regularly when conducting scientific investigations.  For example... 

[TODO: provide examples of generalizations used in the different scientific sub-fields]

 SYMBOLS ARE CULTURALLY AND HISTORICALLY BOUND

delta, sigma, parentheses, commas vs. periods (the rest of the world vs. America),