## The Virtuous Variety of Variables

Reflection on an assigned reading: “What Are These Things Called Variables?”, Wagner (October 1983)

I enjoyed Wagner’s article on variables. His favorite algebra story where a student could increment a numeral easily to find the next consecutive integer but did not see the similarity when using a variable was enlightening. Although I suggest that the instruction in the story missed an opportunity in between the student stating “add 1” to 17 to get 18 , the teacher saying “Good” and then immediately jumping to x to represent “any” unknown integer and asking the student “how can we write the next consecutive integer after x?” and the student answers, “y.” The opportunity is to connect the variable to the earlier numeral explicitly using the same logic and structure (if 17+1 = 18 as you stated, and x=17, how could I represent 18, the next consecutive integer, using x? or similar), and repeat this with differing numerals as often as needed until the light bulbs go on.

I also remember struggling with algebra and variables back in the day, especially the definition for absolute value.

What I liked most about this article were the references to: 1) “the advent of computers and their impact on symbology, especially recursive notation for indexing” and whether the research they referred to revealed anything about any impact on student learning of literal symbols, and 2) the “Valuable Discovery” ad stating that “it includes software (cassette and diskette) programs” referring to the Radio Shack TRS-80 and the Apple II, respectively, but not explicitly. My high school had a state of the art lab with both “Trash 80’s” and Apples, as they were called back then. The TRS-80 used a processor clocked at 1.77 MHz as opposed to today’s 2.2 GHz machines. The basic model originally shipped with 4 kB of RAM, and later 16 kB, as opposed to the 2 GB standard in most computers today. Its data storage unit was a cassette tape player. I learned to program in BASIC on the TRS-80 – can you say “spaghetti code?”