Signed Numbers

My last semester in college, while I was student teaching, I had a class that emphasized different key topics in the field of Deaf Education.  One such topic was vocabulary development.  We all already knew that students who are deaf/hard of hearing have a lower vocabulary than their same-age hearing peers for a variety of reasons not least of which being their limited access to "incidental learning" that comes from listening to other people's conversations/tv/radio, etc.  In our class, we talked about ways to introduce new vocabulary in order to give students a more connected understanding of the new word in its five distinct forms. Picture Description/definition ASL sign (if applicable) English word (in print) Fingerspelling of English word I try to be conscious of this as I teach.  It's very difficult sometimes, and many of the math terms to not have standard ASL signs, so it is more difficult for the students to attach meaning and use the new term through f...

Highlight of the Day: Context: AP Calc class, talking through some multiple choice (no calculator) problems from a practice test. Problem: what is  ; Me (typical first question): So....what should we do? Student: Substitute the 2 in for t to find the answer Me: Why would we want to do that? Student: Well, f(x) is the integral there, which means it's really the anti-derivative of the function. We want the derivative of that anti-derivative, which basically means we want the stuff inside the integral. So if you just substitute 2 in, you'll get the answer. Me: You basically just explained the first part of the Fundamental Theorem of Calculus that you struggled with when we first talked about it. Woohoo! Granted, I know his explanation skips the step where t in the integrand becomes x after you take the derivative, but the conceptual understanding of the relationship between derivatives and integrals is there. Made my day.

Hello friends. This is what I've been doing this afternoon. It's a Geometer's Sketchpad file that I hope to use with my calc class when we talk about volumes of revolution. I tried to upload it using Javasketch for those of you that don't have GSP, but found out that JavaSketch doesn't support function plots, or pretty much anything I used to create the sketch. Typical. Anyway, I'm looking for feedback. Play with the sketch, press the buttons, see what you think. Ideally, I'd like this to be along the lines of a Dan Meyer "What Can You Do With This" type activity, but I don't think I'm there yet. It's not finished, mainly because I don't quite know how to create functions for the last 1.5 pictures. Any help is appreciated! Thanks, friends. ** UPDATE ** A new version is posted here . Thanks to iTeach in the comments section ( @PersidaB on twitter) for coming up with cubic regressions for the lasat 2 pictures. I didn't th...

I stole Mr. Sweeney's catapult project and tweaked it (more like, added to it) for Calculus class. It was fun! We not only calculated the equation of the parabolic motion of the projectile, but at the end we talked about how fast it was going using the limit definition of the derivative at different points during its flight. It was a really great discovery point of how the velocity is zero at the maximum height. We were also able to then talk about why that "makes sense". The next goal was for my calculus student to help my Algebra 2 students with the project while I was at a conference...stay tuned to hear how that went! (I started writing this post 1 1/2 weeks ago...and the other one has been started, too...just waiting for some TIME to finish up!)

Wednesday I gave a test in Calculus. It was covering limits at a point, at infinity, one-sided limits, continuity, etc., even some free fall questions leading into our next unit on differentiation. The day before the test, I was nervous that the test was not going to go well. Review, things that should have been easy, was like pulling teeth. I was starting to doubt myself and my teaching. During the test, I was looking through some stuff in my classroom and I happened upon my limits test from when I was in high school. I got a B+, and there was a calculator and no-calculator portion. I instantly thought, "Arg! I should've made a no-calculator portion!" Instead of dwelling on that, though, I just looked it over and found my mistakes...very interesting ones. Since the class finished the test with time to spare, I decided to show my test, and look at my mistakes. Looking at the problems I answered incorrectly, I asked the student to decide where I went wrong and what the ...

Calc class today: Limits review...he was actually on it! Material that I thought was going way over his head last week was processed and we had some really good conversations about different types of problems. Great questions were asked, showing that he's actually thinking about what he's doing and why, too. (There are, of course, still some trouble areas like knowing when to factor/rationalize and what numbers will "help" in the simplification process, but it's a process, right?). Then, we did some free fall problems, applying limits and previewing derivatives. It was so great to actually apply what we've been talking about to a real situation and make it mean something. Here's the problem we spent time looking at, and some of the humor that came out of it... A construction worker is working on a building that is 1000 feet tall. (side note, we took a tangent to see how many stories that would be, because 1000 ft is just an strange number to envis...