I really question the merit of a system of teaching that damages a child's self esteem.
This student is a high school girl whose confidence is being shaken by her inability to understand algebra they way it is presented in her text book and by her teacher. I am getting through to her because she easily sees the concepts and is starting to see it's not hard once you get the basic idea.
I hear her go "ohh" and "ahh" and "I get it!" and I know I'm am succeeding at making her understand. The two main concepts we are going to cover is no fun get back to one; knowing what one is; having an understanding of one and hero zero followed closely by the concept of the rectangle. More basic math concepts here.
This screencast and post is a little incomplete because I am a little pressed for time when I work with her and I don't have time to stop and take pictures because currently it detracts from the lesson. The first session I failed to snap even one picture and here I barely got any either...if you have read many posts or spent any time on my website the themes should be familiar by now.
completing the square now so it makes much more sense when it's presented to her later, and by later I mean in her next chapter. Here you see her contemplating the concept, she understand the factors and is seeing what I mean by dividing by two and multiplying the result to complete the square. She can SEE it.
The symbols themselves cause minor panics at the moment. x2 + 8x + ____
x2 + 8x + 16
still seems a little scary but now she's finding it easy.
She also SEEs that the factors can be written
(x + 4)2
and it makes sense, and so does this:
x2 + 8x + 16 = (x + 4)2
more so because we just did a lesson on exponents and economy of symbol.
“Teaching is the greatest act of optimism.” ~Colleen Wilcox