FIRST LOOK: x2 + y2 = z2 “What are some answers?
Looking at this I think of the answers I gave to problem set 1 (lengths of the sides of a triangle, circle equation, numbers that work) and am still thinking about why x, y and z are used. Is it on purpose? Is it simply because x is the most commonly used variable and y and z go with it? Could it be for 3 dimentional space with an x, y and z-axis?
"Students and teachers do not usualy ask questions... rather, they are interested in making sure that their students understand and excecute what is expected of them" (pg. 14) This is math class summed up in one sentance. There are so many things that would be interesting or even fun to explore in a math class but we don't. We are focused on our students being able to add two digit numbers, not caring if they know why or how it works. Obviously time is a huge reason for this, but how much different would students view math if this was the case?? If it wasn't just a list of rules and procedures created to get "right answers"?
SECOND LOOK: x2 + y2 = z2 “What are some questions?
I already thought of some questions above, but now I'm thinking more about what questions I could ask my students about an equation like this: What shape comes to mind when you see this equation? (I could argue for circle or right triangle) How could we solve for one of the variables? What is a story or issue that could be described by this equation? How many solutions are there? Can x, y and z be negatives?
A NEW PERSPECTIVE: I know I'm thinking like my students right now, but all of those examples took the equation and manipulated it. I thought we were just asking about this equation, not about any new ones we could could come up with... Observation #5: Accepting the given! Most of my students wouldn't think twice about accepting what was given to them and not strying away from that for fear of getting the wrong answer. "...the given is a starting point for investigations that modify it." (pg 18)
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