Tuesday, January 17, 2012
Talked about reading assignment (due next class period. need password to read) and Pour Favor assignment (due in a week).
Group talked about graphing on the scratch pad on the calculator (me and heather). The group talked about “documents”.
Class discussion on the virutal circular geoboard:
This is a virtual version of what is usually a little board with wood pegs and rubber bands.
What’s good about the vitrual version?: don’t have a limited recource, don’t have to worry about dangers of rubber bands, easier to clear and start new, can color areas in, easy to move ruber bands around quickly (on the geoboard there are layers- you have to remove layers to move the first ruber band), don’t see geoboard from angle like you would when using a real geoboard, not many schools actually have circular geoboards- more often they have squares, often real geoboards are plastic and can break- so you’d have to replace it more often, virtual is free (having the computer is not free though), would need really small vs. really large ruber bands to make different sied triangles (not all triangles can be made with one size ruber bands on the real geoboard), can show work on projector in front of class, easier for students with limited motor skills.
Disadvantages: can’t easily make a circle. You have to go peg to peg- where as in real life you’d just catch the pegs as you move the ruber band around, can’t share work as easily with partner because of shape of computers, get 3D affect on real board that you can’t get on virtual board, real board can help improve motor skills for students who have a hard time.
Mathematical exporation that we did: (learned about arc length- ½ arc length= angle of triangle with all three points on edge of circle)
Easier to draw on paper than to point out on geoboard. It’s ok to work on virtual manipulative then go to paper, then maybe you’ll want to go back to virtual or stay on paper- you’ll see what you like more. This exploration took longer than a lecture. But the exploration helps students learn/ understand more. The answer to your question doesn’t have to be the goal of the question. We were told to find a triangle with the smallest angle possible and find the messure of that angle. We didn’t answer that question, but while we were talking about the different trianlges we looked at the triangle that brought us to talk about the purpose of the lesson. Have to judge when you want the class to open up and talk vs. having the teacher just say “I saw people looking at this triangle, let’s look at it”. When planning activities you have to think of the different ways the lesson could go and decide whether it will be worth if for you to have that lesson. Didn’t actually answer initial question, that bothered me. When we went on “tangents” (which we now know that weren’t real tangents, but where we wanted to look) student was still thinking of the real question because he thoought that was still the real question. Time is always a restraint that we have to take into concideration. There is always more that could be done.
Mathematical fidelity: how faithful is the mathematical technoligy to the mathematics it is trying to represent.