I'm afraid I may have hyped up this post too much, but here it is. I've heard many times people talk how students interpret equal sign as a signal to do something. While I certainly noticed that, I still think it would be unfair to say that the students do not understand the actual meaning of equal sign: the two quantities/objects separated by an equal sign are the same quantity/object. However, this understanding is somewhat fragile, and to me very surprising. This is where my left to right comment came from. It appears to me that the equal sign tells the students that what is on the left hand side of the equal sign is the same as what is on its right, but not the other way around. This was most pronounced in the distributive property of multiplication over addition. They can easily tell me that a(b+c) is the same as ab+ac, but when we start talking about factoring and we have to go from ab+ac=a(b+c) this becomes a great mystery. Even if I write it the usual way a(b+c)=ab+ac, and point out that we have an equal sign therefore going "the other way", that is from right to left, amounts to what we call factoring, it still remains illusive. There are many examples of left to right exclusiveness: (a+b)^2 is easily a^2+2ab+b^2, but not so much the other way; a^2-b^2 can immediately be said to be (a-b)(a+b), but they need to multiply out (a-b)(a+b) -- and often incorrectly. On the other hand if as an answer to some equation you get 5 = x, they will easily tell you that x is 5. Is there something to this or is it just a random peculiarity?
Something I think I forgot to mention that got me upset at the last conference. People will quote things that students say, wrong things, and laugh. Laugh? What exactly is funny?
Also, does anyone have 2 dogs? Mine almost always lie perfectly symmetrically. Do they coordinate? Does one peak at the other to see what a comfy position is for that particular moment?