Very “perplex” ;-)

Good, very good. Just a suggestion: why don’t you put a video for simulate how to do class. What are the real sessions that you do with your students?

Can you record some kind of session? For example, how do you explain the equations? What are the question do you ask? What are the question that do you expect students ask you?

Sorry for my bad english

@RandomDude: I know that. I used several times, but I miss something more “complete”. Something like what happens next? After 3-act presentation, what follows? What are your objectives (related to procedures, knowledge, actitude, …)? What is your schredule? I suppose that you don’t use *always* 3-act activities for teaching whole leson.

I would be very glad if we have a “demo” about Dan Meyer’s sessions ;-)

Thanks,

“Perplexity” from a urinal, have to love the odd places where Math sneaks up on you.

@ Jenni: Would you then, after the exercise has been completed and the extension has been addressed, lecture a bit and have more typical problems for students to practice on in the following days? Would you model math that they’ll need for tests/SAT/ACT/etc and then give independent work relating to the perplexity activity?

I am not sure what Dan’s reply will be, but this is how I would address these points. First, the only real need to address “typical” problems is for teaching to the test. If you explore the perplexity correctly, the math should be presented such that there comes a time when a statement or equation emerges that is a perfect example of “typical.” The math you model are dictated by how you choose to guide student inquiry. When students come up with a list of questions- hopefully your reason for having students watch a video or view a picture is listed. If not, you can pose your question in relation to theirs. I think Dan stated it this way: Those are all great questions and I hope we can answer them all but I need you to help me with this question first.

Standardized testing has real world consequences but we have to not let that define how we introduce mathematics to our students. Showing students perplexity or engaging them in this way does not shut down your options, it just opens more. You, as their teacher, have every opportunity to guide students through the content and make explicit the math behind the tasks. There is nothing more powerful in the mathematics classroom than being able to reference to a great task you worked on in class when a “typical” problem comes up. You will find that there are less students who ask’ “How do i do this?” and state “This is just like ___, this is how we find our answer.”

+1 to Jenni’s comment.

In teaching exponent rules, I honestly have tried to think of models to help students remember that (a^b)^c = a^(bc) or a^(-1) = 1/a. I consider exponent rules one of the “boring bits” of the mathematical world. There are other topics like it.

I tried to have an tournament among my students in applying exponent rules to see if that would act as a motivator. It worked temporarily, just as Dan predicted in the video. No matter how many times I give a reassessment in class, some people seem to not be learning it as I would like. I’m just not sure that there is an alternative to direct instruction of these things.

For things like exponent rules, students are expected to act like a computer programmer and be meticulous in how they work through the problems. Because exponents are just symbols to my students, sometimes they make up their own rules (as any teacher probably knows).

Numerical exponents have meaning, but what about the abstract, variable counterparts?

In your ideal world, would you teach exponent rules, especially with abstract bases? If you would, where do they fit? If not, then how do you help students take the derivative of (x+4)^3 later in calculus?

Thanks for the keynote.
‘Today’s Tantalizer’ is what I will call mine.

Thank you all so much for your responses. It continues to amaze me that I can so readily learn from your experiences and your perspectives… I only hope to return the favor one day. (Uh, patience is one of those finite resources, right? Crap.)

Dan, I am very grateful you took the time to respond. I am sure to have more questions as I attempt to improve my teaching practices, but for now, you and others have addressed my initial questions. I would be so star-struck if I were to run into you at a conference, but I do hope to see you present live sometime as I have been very impressed with the videos I have seen. Thanks again!

I particularly liked what Bob Lochel said about finding the epitomic math problem from a unit, and I think this is a great place to start for me. As I see it, ideally I would organize my units around such a problem and radiate outward from there, fleshing out the beginning (within a perplexity framework) and end (an assessment of some kind) and filling in the rest using Bryan Anderson’s notion about guiding student inquiry. (Whew, I’m already exhausted with the possibilities of paths a topic could diverge and evolve into – graph theory anyone?) The tough part for me is finding that cohesion and fluidity, but that just might come with experience (uh… and trial and error. Sorry kids!) After all, SOMEONE at sometime had to encounter a problem where this topic was necessary and/or useful, right? Right??