Okay, so I’m making lots of connections in the classroom. Not necessarily to the “real” world quite yet, but at least with current topic (radicals) to previous topics.
How? When I wrote the radical symbol, I had several questions – Mr. Thomas, why is that called a radical symbol? Isn’t that the same as the division symbol? (No, the division symbol is an obelus. The other one they meant, when doing long division, is actually two symbols – the parenthesis ) and the vinculum [the bar]) Anyway, I drew a sloppy, lowercase r on the board and it looked the same. “Oh! r for radical!” “No. R for radix – “root” in Latin. ‘Radical’ because it’s a pretty awesome thing.”
Okay, so I still haven’t linked it to anything from the past, just proved my somewhat limited knowledge of trivial, even if not 100% accurate*, math history. What’s inside the radical is the radicand, and as long as we’re dealing with square roots, the radicand cannot be negative. Not in the real number system anyway, but my Algebra I kids aren’t ready for that quite yet. So I say, “in math symbols, how do we say the radicand of x + 3 cannot be negative?” Pretty quickly, to my surprise, a student said “x + 3 >= 0” (greater than or equal to) Super! So I wrote it down.
x + 3 >= 0. “Now solve for x.”
x >= -3. “Now graph the function.”
(graphed.) “What is the domain of the function?”
**Hand raises** “x is greater than or equal to negative three.”
I victoriously pointed the the equation from the “radicand cannot be negative” statement and with a weird little grin on my face, I let the students bask in their glorious connection from chapter 10 on radicals to chapter 5 on inequalities and chapter 8 of LAST YEAR on domain and range. Bam. Today was comic book hero day at school. I didn’t know so I didn’t dress up, but when asked? “I’m Superman. But I’m in public so I have to be Clark Kent.” Actually having 14- and 15- year olds interested in math for just about a whole period? I think it was a justified statement.
So I connected to earlier curriculum successfully, and I taught them some history – that’s 2/3 of my quest. (2/3 incidentally is the same as 0.66… so 0.99… = 1, but I will teach them that another day – maybe) The last third? Connect the history together. An ambitious goal for sure. Here goes…”coss” is “thing” in several romance languages. Algebra is also known as “l’arte della cossa” – The Art of the Thing. Here, Thing is variable. Algebra is the art of variables. Makes sense so far. In the 1520’s, Christoff Rudolff write a book “Die Coss” and it was an algebra book. In it, he introduced the radical symbol we love so dearly. This connects to what I taught just a few weeks before I started this blog – when I taught them about “l’arte della cossa.” Stay tuned, folks. More excitement to follow.
*Most of what I read comes from books which I cite at a later, but not too distant date. Admittedly, some DOES come from wikipedia and while I have tried to cross-check sources for what I tell students, sometimes I have to embellish to get them interested. I will never intentionally lie to them, so if there is anything you ever notice that is not true, or have clarification for, let me know. I will pass this to my students as soon as I can.