Comments | hauntmeister: The challenges of chapter 5

hauntmeister

The challenges of chapter 5

Nov 26, 2009 08:24

The 5th chapter of Glencoe's Algebra 2 is a jumble of related topics, which are all critical to this class. My challenge here is to make the students understand the connections between all the topics, rather than learning them as a rote collection of isolated mechanical symbol manipulations ( Read more... )

Comments 4

magid November 26 2009, 13:57:39 UTC

I assume complex numbers meandered in via the discriminant.

And I've always found parabolas in y = a(x-h)^2 + k form to fit better with looking at all the rest of the conics, rather than quadratics as a stand alone (In my head, that is.).

hauntmeister November 26 2009, 14:50:36 UTC

It would be great to introduce the equation along with the rest of the conics, but we don't get to that until chapter 10 ... which will probably be in May! Annoying city pacing guide ...

frobzwiththingz November 26 2009, 18:16:06 UTC

I get theatrically exasperated in class whenever a student punches "-5^2" into the calculator and dutifully reports that the square of negative 5 is negative 25.

Only allow them to use RPN calculators. :-)

jcgbigler November 26 2009, 23:11:28 UTC

Give them graph paper and ban the use of calculators.

Seriously.

Practically speaking, algebra 1 is all about finding exact solutions to linear equations. Algebra 2 is all about turning non-linear equations into linear equations or sets of linear equations so you can solve them--i.e., reducing more complicated equations to Algebra 1 problems. Most kids never realize this. (I'm not even convinced that most math teachers realize it!)

Years of MCAS training have taught kids to mechanically perform a set of steps, and write down the result of the last step, calling it "the answer". They're drilled in how to recognize which set of steps goes with which kind of question, and how to execute the steps and fill in the correct circle. Most of them have no idea what they're doing or why it works, and they're well past the point of wanting to know or even thinking it's possible for them to know. They simply declare, "This is the right answer because I typed the equation into my calculator and this is what it said." If you replaced the ( ... )