On Roman Numerals

During the last few weeks, Robert and I spent a few minutes each day on learning Roman Numerals. At first, I didn’t treat it seriously. I presented it mostly as an interesting fact. Just a curiosity. But as Robert was changing Arabic numbers into Roman and vice versa, I noticed that in the process, Robert could deepen his understanding of values of numbers and their relations. Presenting 3 as III which translates into 1+1+1, 30 as XXX (10+10+10), and 8 as VII (5+1+1) helped Robert to look at the numbers from different perspective.
He built new numbers using a few symbols I, V, X, L, and C by adding them (as in 86 – LXXXVI), subtracting (as in 90 -XC), or doing both.
Those translations from one system to another were supposed to help Robert understand the values of numbers.
Of course, we spent much more time over the last 10 years to understand decimal system – to switch from words to digits, to expanded notations, and back. We compared numbers to each other, ordered them from the least to the greatest and from the greatest to the least. We rounded the numbers believing that ability to, for instance, round 321 to 300 and 371 to 400 was a sign that Robert understood the value of numbers.
A few months ago, I wrote a long and rather convoluted post about different approaches to teaching Robert to round and estimate.
https://krymarh.wordpress.com/2012/12/11/take-it-to-your-brain/
All the methods, however, were based on algorithms. They were supposed to lead to a better understanding of values of numbers, but I wonder if they did.
With Roman Numerals, ciphering 263 as CCLXIII offered a simpler (someone might say. “More primitive.”) way to grasp the connections among the values of symbols representing numbers.
I have to clarify, however, that I did not expect Robert to master Roman Numerals. I did not expect Robert to even memorize the values of L or C. We always ciphered and deciphered together using the symbols as a code. Because after all,it was just a curiosity.

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