Visualizing Complex Numbers

In my continued quest to spread an understanding of complex numbers I put together this little dance sequence with my Summer School Algebra 2 students. I used the function f(x)=(x-1)^2+1 determine the dance sequence. This function has two complex roots (1+i) and (1-i). I had students stand at 1+i, i, -1+i, 1, -1, 1-i, -i, and -1-i, then we went through the three steps of the function. These were "minus 1", "squared", and "plus 1". The most important visual here is to get a sense of what squaring does to the complex plane. This includes some expansion of the numbers with distance greater than 1 and a wrapping of plane on top of itself. Watch the video and let me know what you think?

Classroom Projects

So late one night last year, I had a strong desire to change the way I teach. In many ways I see myself as very traditional. Some people tell me not so much, but I think at least philosophically I am very much in the land of I have knowledge; their minds are empty; must put my knowledge in their heads. Despite this I definitely see myself as a constructivist. A bad word to many I am sure (I know the spell check doesn't like it).

So about a year later, I am doing something with my late night ponderings. In my 8th grade Algebra 2 class, we are doing a unit on quadratics with an introduction to complex numbers thrown in for good measure. I have done a few teaching to the whole class days, but mostly we have days for the kids to work on a variety of projects. Some examples you ask? Why sure

* Hardy-Weinberg Equations from Biology
* Understanding how complex numbers increase the range of quadratic functions
* Deriving the quadratic formula
* How do the a, b, c in ax^2+bx+c=y affect the graph of the function
* Real-life applications of parabolas

There are more, but you probably get the drift. Each student will have to make a "presentation" of some kind. Not every kid can make an oral presentation to the class, we don't have the time. I am hoping that technology will come to my rescue, and some kids will make little videos that I can assign for homework. Students will have to critique each other's work. These are teaching problems I haven't worked out before, but I am enjoying it so far...