After reading Maggie's article in the Math Chronicle (3 is not 'Three'.....the art of Digit Dancing) I am convinced more than ever about how important it is for students to explore their thinking (dig deep for understanding) and then to explore and experiment with ways to represent their thinking. I've done this often with representing data, but rarely with some of the basic symbols that we take for granted as being part of everyone's math culture.
On another note, I really like the admonition to 'Never Just Accept' - to understand you need to dig deeper........what a great way to start giving up being the keeper of the keys as well as designing and scaffolding lessons that support thinking and risk taking.
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I agree. In fact, I think it would be really interesting to give an open response writing activity in the fall to find out what they know about that little equal sign, then of course share and discuss. :-) I also liked the idea of actually using a balance scale!! The Everyday Math program does a great job of moving the equal sign around in an algorithm. They also use the concept of a "name collection box" to elicit multiple ways to name a specific number. Both are really helpful.
When my students were exposed to the concept that there were 8 ways to show a fact family in multiplication and division, with half of the ways giving the answer first and then the equal sign and then the fact....
4x3=12 12=4x3 several of them thought "it was against the rules" because of what they had been taught previously. We had to do lots of practice with it. It was really easy to see who didn't understand because they would have the numbers in random order! Now I am thinking the real problem is probably their misunderstanding of the = sign.
By the way, is there a key on the keyboard for division?
Hi Judi.
Never Just Accept reminds me of an adage that was a mantra in many of my grad classes at USM.... "Question your assumptions!"
We take so much for granted... especially by thinking that our students understand everything we are saying to them!
CindyN
Hi Loco.
On a Mac?
Hold the Option Key, then type a forward slash (/) and you get: ÷
On a PC? I would go into Word, go to Insert/Symbol... choose the Symbol font, and look for the sign there.
BTW: I tried that now on my PC... copied and tried to paste it into a FireFox field... it did not translate, so maybe you can only do this in a .doc or .docx file. I am still using Word 2000 though...
Cindy
Another PC idea...
Go into Start/Programs/Accessories/Tools/Character Map
Change the font to Symbol; I bet you'll find all the math signs and symbols in there.
CindyN
You make a great point Judi. As a special education teacher, this seems imperitive for my students to really retain and "own" their learning. I am always looking for new and exciting ways to promote these experiences consistently in the environment in which I teach.
When we were in our small discussion groups talking about "balance" all I could visualize was the balance scale that I use so rarely. This class has really helped me become child like as I use the C rods and manipulate my ideas.
Lisa
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