I'm reviewing Michigan's new high school math standards for my department chair, to help make sure that our geometry curriculum is in line with it for our students from Michigan. In general, Michigan is now going to require four years of math through Algebra II for all high school graduates starting with the class of 2011. I'm looking over their geometry standards. It looks fairly reasonable except for one thing: Standard L2: Calculation, Algorithms, and Estimation . . .L2.1: Calculation using real and complex numbers (emphasis mine) Now, I'm no Fields Medalist, but I like to think I know a little bit about math here and there. I honestly cannot think of any reason to teach complex numbers in a high school geometry class as opposed to the algebra classes. Am I missing something here? MathManTim

:huh: I've seen that formula before...in MA 515 Introduction to Complex Analysis. I guess if the students had some familiarity with the exponential function in Algebra I you could pull it off in a sophomore-level Euclidean geometry class. I don't know, though...that still seems like a topic that might best wait until the student has taken Algebra II and some trigonometry. I can definitely see it as part of a Trig-Precalculus program, though. MathManTim

I would agree ... Just giving an example where complex numbers can be used in geometry that is at a level that some HS students might understand.

Once when I was subbing for an 8th grade math class, I was asked to do a lecture on complex numbers. It was just basic addition, but the kids completely freaked out. By the end, they mostly seemed comfortable with it, but nobody believed me that were useful for anything.

My Honors Algebra frosh can't wait to learn about them!!! I'm one of those teachers who won't tell kids that something is impossible if they'll learn to do it in a later course. So when we got to factoring, I told them honestly that THEY couldn't factor the sum of perfect squares, but I could. They of course wanted the secret, and I explained a bit about imaginary numbers. They can't wait to see them as Juniors!

In California, the content standards don't include complex numbers until Algebra 2, which is taken after Geometry. Note that the Wikipedia article says that complex analytic geometry is somtimes covered in advanced high school math classes. Geometry is not an advanced class.

Yes, one could easily make Geometry an advanced class. What is the point of it for the average student?

I'm not saying that by adding complex numbers you make the class advanced. I was just pointing out that geometry can be taught at a very advanced level. If one wanted they could make a rigorous geometry class at the HS level. Complex numbers, at least what is done in HS, are very simple. Adding them to a geometry class really doesn't make it any harder... Just different.

But then you don't require it of all high school graduates without increasing your dropout rate. I agree-- anyone who can do 9th grade algebra with radicals can handle complex numbers. But I think it begs the question: is this the most important thing to teach them? Given that you have them in school for so short a time, is this the best use of the time that the below average kid spends in a math class? We're not worried about the bright kids; they'll opt for the more advanced courses. And a lot of the average kids will as well, with plans for college. But those kids who won't ever see the inside of a classroom again until they meet the teachers of their own kids... is this the best use of their time?

No it isn't. For the average/below average student more time should be spent on the fundamentals of algebra/geometry without the introduction of complex numbers. In reality they should spend more time working on consumer math.

Before I left in 2000 to spend time with my own kids, I taught a consumer math course to our lower level Seniors. (I'm in a college prep Catholic high school, so even our lower level kids have to do well on an entrance exam to get in.) The AP pretty much gave me carte blanche to teach whatever I wanted, and I had so much fun with it! We balanced checkbooks and reconciled checking accounts (and they had to write me a monthly rent check.) We bought insurance, bought a car, compared mortgage rates and bought a house, used scale drawings to figure out where the furniture we bought should go, figured out how much paint and wallpaper we needed, planned a trip to Europe-- and all this was without the use of computers. The other kids were jealous-- they all thought it should be a mandatory course for all seniors! It disappeared in the 6 years I was home.

I taught a consumer math class last year. There were to be three sections this fall. New assistant superintendent decided there won't be any. So, the seniors who have been unsuccessful in math their entire school careers will have to take Geometry or Algebra 2 instead, will fail, and will be given D- instead of F so they can graduate.

No reason was given. The math department and the principal were all for the class. My guess would be that the new assistant superintendent believes that all students should be preparing to go to a four year college right out of high school. This has been a recurring theme in California for several years. Any kind of "remedial" math classes were already officially out. Lowest level math class is Algebra 1 which is actually considered an 8th grade class now in California.

The high pressure emphasis on college prep can really do a disservice to some kids. I am very happy that the district I was just hired in has a very strong vocational education program. Some of those kids will go on to college later too, but it gives good options to all students. I didn't do anything with complex numbers under my differential equations class, and then they were rather horrific because I had forgotten all of my trig. I seem to have a brain defect wherein trigonometric factoids will not stay; they just leak right back out.

The strange thing is that the school I taught at also had a strong vocational program, including automotive, welding, wood shop, ag, nursery, and culinary. It is a real rarity in California. Unfortunately, with California's budget problems, these are all on the table.

If I remember correctly, my department chair said that this philosophy was explicitly stated by the Michigan DOE as justification for those new standards. MathManTim