can you please esnd more information & examples on how to understand bisection method.

And I don’t think I ever learned that name, so I’m glad you told me. Huzzah!

The ‘other method’ your student is comparing Newton’s method to is called the Bisection method. You probably already know this but I thought I would mention it since you didn’t refer to it by name :)

If she has any leanings towards computer programming then it might be fun to gently push her towards ‘discovering’ some fractals that arise from Newton’s method.

http://facstaff.unca.edu/mcmcclur/mathematicaGraphics/Newton/index.html

Cheers,
Mike

That helps. A lot.

Also, I try to go into class being enthusiastic about almost everything we teach. By the end of the year, my kids said to me (when I was teaching them partial fractions and integration), “Mr. Shah, you think EVERYTHING is the most amazing thing ever.” But, in fact, if you take a minute and step back and look at what you’re doing, you can’t end up seeing how cool some of the stuff is that you’re doing.

I tell them, for example, when we’re doing the length of a curve in calculus, that previously, there were only TWO types of curves they knew the length of: a straight line segment and a circle. And what’s amazing is that in class today, they’re going to learn how to find the line of ANY curve, no matter how funky looking. They dig finally seeing it all come together, I think.

I think that one thing I’ve learned in my student teaching and this year is that enthusiasm is infectious. If you have it (or feign it, as I sometimes have to do with the more mundane topics), you’re students will pick it up.

But other thing, for this particular assignment, is that I literally let them do whatever they wanted. The only requirement was that it had to be something they were interested in. This is how it specifically went down…

For homework one night, I asked them to write 1-2 paragraphs describing ANY project at all they would want to do, and I gave some basic examples, but I purposefully spoke vaguely so they wouldn’t be constrained in their thinking. Then I met with them individually to go over what they chose…

One of the students who is teaching the chain rule, for example, wants to become a teacher, and really loved learning the chain rule. It makes sense that she chose her project on teaching the chain rule. The one doing the mechanical model of surface area/volume is super creative and artistic, so we took her embryonic idea ["I want to do something to help other students visualize this"] and made it into something concrete. The one who is doing the rainbows didn’t know what she wanted to do, but she wanted “relevance.” She is a budding poet, so I thought why foist some random applied physics or economics thing on her? So I found this project and presented it to her, thinking that it would appeal to her sensibilities. It did. (I think.) The physics student came up with the idea totally on his own. The Newton’s method project was chosen by my other student from a book of calculus projects that I have, because she loves the “puzzle” of math and the involved proofs and drawing connections. She pegged this project out of the book because it looked the most interesting.

So basically, because I have so much faith in them at this point, have let them go. We’ll see when I get their final projects if they’ve flown or not.

But yeah, I couldn’t do this type of thing with my Algebra II kids, because I don’t have that type of time to guide them, the class size is larger, and also because honestly, many still haven’t come around to becoming converts to the material like my calculus class has.

Was it luck of the draw, or of the class size?