# [TMC15] Day 2 Reflections

3D Printers, from Heather Kohn, had me excited about 3D printers. I thought about writing a grant for one last year but never did. I think I want to now. Creole (sp?) takes a PDF and makes it into a 3D object. (Talk to John Stevens, too!)

In the Activity-Based Teaching (my morning session), we talked more about spiraling curriculum and the benefits. We also did a cool activity where he asked us all to remember 20 words and regurgitate them as best as possible. This typically makes a parabola, which can unload tons of questions from there, not only about math, but about studying and real-world applications, such as telling someone a list of objects to be sold, etc. I was comforted when Alex & Mary admitted that it is difficult for more higher-level math courses to do activity based teaching. However, Alex says he does this with his “Precalculus” class (the Canadian equivalent of it for his district).

During lunch, Julie, Sam, & Tina talked about the blogger initiation for this year and I got excited about the possibilities. The main idea they want to work around is having 2 strands: 1) for bloggers/tweeters who are brand new and 2) for bloggers who aren’t, but could use encouragement. They’re also talking about having mentors & mentees and grouping people, which I think would be HUGE for both the mentor and the mentee. I really want to mentor 3 or so teachers from across the country who want to “test out” blogging and tweeting but aren’t sure what to do. That would be fulfilling as well as motivating to get more involved in the community myself!

Christopher Danielson shared, at the keynote, how we need to find our favorite thing and do that, both in our classrooms and online, so our students & other teachers (and by extension other students) can benefit from what we love. He shared that what he loves is ambiguity (at it’s root) which is why he wrote the book “Which One Doesn’t Belong?” After hearing his talk on it, I’m definitely going to use the website that Mary Bourassa created: Which One Doesn’t Belong.  However, Christopher did explain that, while it’s great for everyone to get excited about ambiguity (or debate, as I’m going to use it to that end some), I still need to think about what I love and why I love it. I need to do some reflection on that later.

In the afternoon sessions, first I attended Meg Craig’s “Function Transformations without Tears”. I not only got some cool worksheets out of it (more posted on the TMC wiki), but she provided a neat, new approach to function transformations. In the past I had always done an exploration, which took way, way too long since it’s Precalculus and they should have seen much of this already. The new idea is to “move the origin (whether or not it’s on the function” and graph the parent function using the new origin. It gets a little tricky when talking about what I used to call “stretching”, but Jed explained how he sticks to the vocabulary “Input” and “output” and Jim kept going back to the question “what do you plug in to get the origin?” (Which, I just realized, doesn’t work if the function doesn’t go through the origin… but it’ll be a good starting point). I’m also going to use “h,k” notation and move the k to the other side so it’s actually physically next to the y! I also want to consider using the “Window Pane” method for graphing sin & cos, as well as look deeper into figuring out whether I can also divide both sides to get the other factor closer to the y for consistency. Would it be weird for me to ask my student to turn this:

$y=a(b(x-h))^2+k$

into this:

$y-x=a(b(x-h))^2$

or even into this:

$\frac{y-x}{a}=(b(x-h))^2$

or possibly/ultimately into this (if $c=1/b$):

$\frac{y-x}{a}=(\frac{(x-h)}{c})^2$

This will take more thinking.

Perhaps it would be better to instead define $z=1/a$ and have students do this:

$z(y-x) = (b(x-h))^2$

That not only makes it obvious what is affecting the input vs output, but it’s also consistent, so there’s no memorizing “oh yeah, inside the function means opposite of the other thing…”. I’m excited about this! Of course this applies to any function where we’re applying a transformation.

$z(y-x)=f(b(x-h))$

The final session was on SBG and I got into some great discussions with Anna Hester, Nathan Kraft, and others concerning when to grade (formative vs summative assessment), how much to grade (size of scope of standards), and how to connect standards (leave it alone & talk about it, or grade it somehow…). Great discussions and lots of food for thought.