The chapter starts with a discussion of the NCTM professional teaching standards. It emphasizes moving classrooms more towards a constructivist, group oriented environment. The standard is divided into standards for teaching mathematics, standards for evaluating teaching, standards for professional development, and standards for support of teachers. Finally, the end of the first section talks about teaching and learning principles.
Next the chapter talks about selecting activities and problems, with an example of using a mira tool to explore absolute value problems. This leads to several pages on the use of manipulatives in the classroom.
The next section is on classroom discourse - student/teacher roles, the value of good questioning skills (using open questions as opposed to closed), and cooperative learning.
The last section is on the learning environment, with a discussion of seating, bulletin boards, etc. Finally, the talk about using reflection again to improve your teaching.
I chose to look into the quadratic formula, because I'm going to be covering it in my class in a couple of days.
In my textbook they have a derivation of the quadratic formula, some examples of how to use it, and a brief discussion of the meaning of the discriminant. It's a nice coverage of the key points of the topic, but hardly inspirational - and I'm not sure it constitutes a real activity.
I did a google on "quadratic formula", and found a pretty nice website at http://www.purplemath.com/modules/quadform.htm. It covers pretty much the same information as the textbook, but it is a little more informal in tone and a little more in depth in the exhttp://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activitiesamples and in hints on how to use the formula. It also has quite a few really nice graphs. This seems like a pretty good website and I'm glad I found it. I could create an activity by having the students go there to do research.
I found another webpage on the quadratic formula at http://mathworld.wolfram.com/QuadraticEquation.html . It is a lot more technical and is aimed at a more advanced audience. It gives an alternate form of the formula that I didn't know existed, so that's pretty cool. I don't think I would bother with this webpage in my Algebra I class though.
I found another site with a lesson plan for programming the quadratic formula into a TI-83 calculator. This activity looks pretty tempting if I can find time for it, because we do have TI-82 calculators in the class and maybe I can have the students write a little program to do the formula for them.
I found an interactive website lesson at http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_quad_formula.xml that looked pretty interesting. The students can actually enter their answers and check them and stuff. It looked pretty neat. In fact, the greater website is huge, and could be used as a textbook all by itself.
I think for my lesson I will go with "none of the above" for my key activity. Rather, I'm thinking about putting together a "real life" example based on ballistic trajectory and a free fall simulator used by Nasa called "The Vomit Comet." Still, I certainly found some interesting sites with this search.
I googled "Geoboard" because I didn't know what they are, and I found this cool virtual geoboard website at http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities. I had no idea what they could be used for until I googled some geoboard lessons which focus on using the geoboard to visualize areas and perimeters of two dimensional figures and stuff. I even found a lesson for doing Pythagorean theorem - not that I loved it. I also found a cool website at http://www.picciotto.org/math-ed/annotated-map.html#manipulatives with some good discussions about using manipulatives in the classroom.