I call them squares. They called them arrays. What do they mean? So I was in C++, and we had third graders come today to play our programs. Whilst the others just drilled them with problems, my game was subtract a square. It was fun watching them discover that numbers like "9" were bad positions (I never explicitly referred to squaring, I just had them multiply the number by itself.) I decided to draw something like this on the board, to show the geometric connection:

The teacher called their attention that I had drawn "arrays" on the board, and they were still used in High School. I didn't bring it up, but I was wondering what they meant by "arrays".


*

*Is it an another name for square?

*Is it a multiplication method?

*Do they mean multidimensional arrays, as in programming? (If so, third grade has sure advanced since I was in school!)

*Something else?


These were USA/Pennsylvania third graders, if that helps.
Note: I know various meanings of "array", but I am wondering what they could possibly mean in this context, with a third grade teacher explaining to their students.
 A: Even though programmers know that the term can be applied when placing data in one, two, or multiple dimensions, I believe that "array", if used in elementary school, gets used specifically to refer to a two-dimensional arrangement of things. 
I certainly remember a similar experience growing up: after being exposed to the idea of arrays being two-dimensional arrangements, I was initially confused when, while learning about programming, I was introduced to the notion of arrays (initially) as one-dimensional.
A: You are correct. The photos that you posted are examples of multidimensional arrays. It makes sense as well since the definition of an array is an arrangement of objects that can be constructed in rows and columns. 
A: Programmers in particular will call them arrays as that has been the term in all the languages I have worked with.  This does not bring attention to the fact that all your examples have exactly two dimensions and the dimensions are the same.  Arrays can have any number of dimensions and each dimension may be a different size.  As figures, I think squares is a better term.
A: The rectangular arrangement of the square boxes is meant by the term "array". 
The German word for this would be back translated to "field", like in grainfield. 
The geometric relation might be visible from the Japanese character for field: 田
If you look in an English dictionary on the origin of words (etymology), you get:

From Middle English arrayen, from Anglo-Norman arayer (compare Old
  French arayer, areer (“to put in order”)), from Medieval Latin arrēdō
  (“to put in order, arrange, array”), from Medieval Latin *rēdum
  (“preparation, order”), from Frankish *reida (“preparation, order”) or
  Gothic  (garaids, “ready, prepared”), from
  Proto-Germanic *raidaz, *raidiz (“ready”), from Proto-Indo-European
  *reydʰ- (“to put in order, ease, make comfortable”). Cognate with Old High German gireiti (“preparation”), Old Frisian rēde (“ready”), Old
  English ġerǣde (“preparation, equipment”).

(Source)
The term is also used for an arrangement of antennas (antenna array).

(Source)
