Note: Today’s post uses each of the Standards of Mathematical Practice, or SMP.
I threw a temper tantrum, dear reader.
Back in 1997, I learned about base 2 notation. Mr. Konrad Dzwonkiewicz, taught MST’s introductory computer science class, where we learned the Pascal programming language, introduced us to the language of 1s and 0s that make up all our work with computers. (SMP 7: Look for and make use of structure)
Through Mathematics in Civilization, I’ve learned that in every single major civilization from antiquity onward, the development of a number system preceded any written language. In this sense, then, learning mathematics can be considered studying the roots of our language system, English. (SMP 8: Look for and express regularity in repeated reasoning)
We consider the alphabet as being the building blocks of our language. But I’m quickly learning that math holds many pre-language building blocks that our kids need. (SMP 2: Reason abstractly and quantitatively)
That doesn’t mean teaching toward this idea is easy. In fact, I straight-up threw a temper tantrum when I hit a tough spot (and I’m still in Chapter 1, sooo it’s probably going to get crazier). What did this grown-up temper tantrum look like? Welp, I scribbled and tore the paper like many of our young mathematicians would in a similar situation. I’m not perfect.
But just like we encourage our students to make sense of problems and persevere in solving them (SMP 1), I carried on. And if you’re thinking, as I did, that familiarity with the duodecimal system (a counting system based on using the digits 0-9, then T and E to represent 10 and 11) is a silly obscure skill, consider that our time system is based on 12 and, to a greater extent, the Babylonian Base 60 notation.
Speaking of the Babylonians, after I regrouped, I looked more closely at my work, and corrected my errors (SMP 3: Construct viable arguments and critique the reasoning of others and SMP 6: Attend to precision). And then I got caught up in the aforementioned Babylonian Base-60 math. This time, I was able to control my rage, but not my confusion.
Those trumpet-and-rewind marks on the righthand page are the symbols (SMP 4: Model with mathematics) used by the Sumerians and Babylonians because they were the only two symbols that could clearly be etched into tablets (The symbols look remarkably like the iconography used in The Crying of Lot 49 (There’s a ton of ELA standards and social studies crossover here; I’m not going to list out all the standards for this cross-curricular extension).
Looking at my work, I was able to convert from base 10 (our decimal system) into base 60 for numbers that were smaller than 100. Anything beyond that was largely out of my control. But I remembered Chip Brock telling me that even if we can’t complete a problem, we should write out the solution so we can perhaps gain additional insight. I tried that, but it still didn’t provide any clues.
You can see my highlighted bits remind me that I need to sally back online and find some videos that explained things more clearly. (SMP 5: Use appropriate tools strategically)
I returned to Khan Academy because of their ease of searchability, but there wasn’t much available. I found this and it’s quite nice and has a lovely, lush green background.
Worth noting: This video never explicitly tells me **how to do the problem I was working on,** but it does give me a broader understanding of the context of the problem I’m working on, which provides additional entry points for students (me) who have shut down. (SMP 1)
More later, once I muster up the energy to view aforementioned video.