in which i employ a plant May 11, 2012
Posted by Ashli in Lesson Disclosure, Teaching Thoughts.1 comment so far
One of the fun parts about participating in the online community is meeting members of the online community in person. I had a chance to meet Daniel Schneider, aka Mathy McMatherson, and break some bread while enjoying one of my favorite things: edu-math-chat. And if you are not reading his stuff, you should be. I will be utilizing his Wall of Remediation idea for my Support class kiddos to study for the final in Algebra 1 which covers distinct skills from our SBG setup.
During our chat I was reminded of something I used to do that for some reason I have not been doing the past few years. I thought I would write it out here to help me remember to use it again in the future. I think best when I get a chance to write things down, so this may be a bit free-flowing.
So picture this: you have a lesson planned that will hopefully lead kids through some mathy ideas to a big conclusion. You are concerned, however, that they will not ask the questions you are hoping for and are unsure of your abilities to steer the conversation without obviously grabbing the wheel. This was my state of being for several years (and still is sometimes). On the spur of the moment in class during my 2nd year of teaching I decided to ask I kid I trusted to keep a straight face to ask a specific question if I gave a signal. It wasn’t critical to the question, but it was a nuance I didn’t think the kids were picking up on. I ended up giving the student the signal and they asked the question. This caused a pause in the class and then more back and forth conversations in the group about this point. My plant jumped into the discussion and none of the students thought anything out of the ordinary had happened.
Was I covering for weak group-discussion-leading skills? Maybe. Did the kids see something they wouldn’t have seen otherwise had the question not been asked? Yup. Was it better coming from a student than it was from me? I think so. I believe that students often respond better to the questions/responses of their peers than they do to myself. Peanuts effect and whatnot.
Fast forward a bit. I ended up using plants on occasion. Sometimes for questions, sometimes to say wrong answers I wanted to make sure got covered. I totally got caught in some classes, which I was able to play up enough that the kids found it amusing and the plant was giving off smug ‘chosen one’ vibes. I realized that getting caught could be great. I chose to sometimes give a kid a written question/comment with vocabulary they would never use, but I totally would. Authentic learning environment? Nope. Did kids pay attention, get a laugh, and build not only mathematical understanding but also classroom community? yup.
I once used it freak out students. Used to be my 1st period support kids would see me twice: once for support and once for regular algebra 1. I had a kid ask in support about other math symbols (we were doing inequalities if I remember right). This was a student who expressed dislike of math, but was well-liked by his peers and rather good at math he ‘got’. I wrote out some abstract form of “for all x contained within the reals ….” in symbolic notation. he thought the ‘code’ was pretty cool, so I asked if he could remember what it meant. He repeated it back. Fast-forward to period 2. Regular algebra 1. Same symbols question comes up. I get my plant a quick glance and he is playing it cool. I write up the symbols again, tell the class it’s an advanced math sentence and ask if any of them know what it says. They are, of course, stuck on the upside-down A. My plant raises his hand and TOTALLY plays this up. Squints his eyes a bit, rubs his chin, “well, I think it says …” Beautiful performance. I wanted to applaud. Every other kid in the class is staring at him, his friends are whispering demands for how he knew that. I congratulated him and repeated what he said while pointing at the sentence and then continued with the lesson.
I’m pretty sure he admitted to them later about being a plant, but it definitely got the attention of the class and I started seeing the upside-down A and the triple dots for ‘therefore’ on some papers.
Some notes on the details. I never used the same kid twice. I never made it a regular thing lest they get paranoid about one another. I’ve not done it in years. I think in the National Board year-of-crazy it got lost and I hadn’t even thought about it (which tells you how infrequently I did use it).
I’m much better at helping to direct conversations and making sure that kids are set up properly to make the connections I want these days. That does not, however, mean I am not thinking about how to use the ‘plant’ idea in some of my upcoming lessons.
in which i write a <3 letter April 24, 2012
Posted by Ashli in Uncategorized.add a comment
Twitter & Blog friends are interesting things. They are these people you ‘talk’ to almost every day and whose inner-teacher-workings are out there for the world to see but often you don’t know exactly what they look like.
Let me tell you about this unique tribe of online math educators. We are tech-savvy, aggressive about our own personal development, always ready to give productive feedback, and we hold a strong belief that it is through personal effort in a community setting that we can, and will, become better teachers. No one of us is an expert, but as a group I think we can claim some knowledge in matters mathematical.
We are, at heart, a tribe of experienced novices; teachers new to the profession, teachers who are moving on to higher degrees, to research, and many others. All are welcome to join this tribe, but those who do should prepare for the ‘I wonder what would happen if…’ replies that push ideas to higher levels. They should prepare to engage on a level I have yet to find with consistency at an ‘in person’ professional development. It’s also helpful to be unabashedly excited about education. Being a bit of a geek doesn’t hurt either. Our appreciation for the Queen of Sciences binds us as truly as our love of the classroom buzz. We quest to develop lessons that help kids learn and propel them forward with more questions and a desire to know wrapped in belief that they can do so.
@Cheesemonkeysf is an exemplar of what it means to be in this tribe. Her blog contributions to both the teaching and math spheres show a depth of reflection in her practice far beyond anything I see most ‘new’ teachers doing. Her passion for the profession is evident in the way she engages with the online community–she is always seeking best practices. Cheesemonkeysf’s care for her students and enthusiasm for their successes make me wish I lived closer so that my own students could benefit from that type of energy. I know that her cheer-leading has benefited me many times as I’ve worked up courage before a professional talk or before putting a new lesson into practice. She has done much to help us all be braver teachers.
I can count myself as one of the lucky tribe members who has met Cheesemonkeysf in real life. The dinner, consisting of several members of the tribe who happen to be in the area, was far too short and I think I could have hung out with her for several more hours, if not days, chatting about education and teaching and all those things that make up the job we love the most. There are people in this world you want to be around because of their ability to help you see and actualize your own power. Those are the people we need to be teachers, because what else is youth but that period of time where you begin to understand the effect you can have on this world?
While I don’t think Cheesemonkeysf fully understands her own impact on the tribe she has consistently and delightfully infused with humor, passion, dedication, integrity and, oddly enough, unicorns, I hope that this letter helps you understand what kind of person she is and the type of impact she can have on students.
She’s certainly had an impact on this one.
in which I muse on the fight April 16, 2012
Posted by Ashli in Teaching Philosophy.add a comment
I consume a ridiculous amount of information daily. Most of it related to the things I enjoy (geekery, math, teaching, technology, art), some of it social (Facebook, twitter, tumblr), and some of it relevant to the day (news, weather). Today I came across a new book that I need to buy 20 copies of for my friends and all their kids: Heros for my Daughter.
The selling point for me was this note from the author:
As you’ll see, every hero in this book is a fighter. And as I tell my daughter in the introduction: “No matter what stage of life you’re in, when you want something—no matter how impossible it seems—you need to fight for it. When you believe in something, fight for it. And when you see injustice, fight harder than you’ve ever fought before.”
So what do our students have to fight for? And do they understand that life is just one giant battle, but it’s totally a battle worth fighting when you find those things that Light Your Fire–those things you would do in your free time when you can do anything you choose?
I can arm them for battle, but I’m not sure how to encourage them to take up their own battle cry and charge at Life. I feel all I can do is be joyous in my own life because I do know what Lights my Fire and I do know how to sound my own barbaric yawp at the world. Perhaps that is what it means to be an adult–to take part in a fight worth having.
p.s. My childhood hero was, and still is, Jane Goodall.
in which i listen to conversations not my own March 20, 2012
Posted by Ashli in General, Teaching Thoughts.3 comments
There is always chatter about teaching as a profession and how, in the view of some, teaching isn’t treated like one. “You get the whole summer off!” yells one side. “We work 50+ hours per week the rest of the year!” says the other side. Some worry about Khan Academy taking over teaching while others beg for online classes to get here faster.
I don’t want to discuss that right now. Mostly because it’s lunch and I don’t have the next 20 hours free. Instead, I want to talk about how I hear other teachers talking about teaching by using a real life example.
Recently I was at a committee meeting looking over textbooks my district might be adopting and found myself listening to the conversation a table over a small group was having as they looked through the books. I’m paraphrasing a bit, but the point one of them was making was that they wanted a clear textbook with a listed objective, multiple examples, and practice problems for the kids so that “anyone could come in and teach the lesson.”
…
#headdesk #soapboxup (more…)
in which my mind is blown by polynomial long division January 1, 2012
Posted by Ashli in Planning, Precalculus.5 comments
My love of polynomial long division is already documented, but now I’ve found more reason to love. To give some context, I am working on plans for my Intro to the Calculus Unit for my Precalc kiddos. I do it right at the end of the 1st semester followed by an Introduction to Statistics Unit because I want my Sophomores and Juniors to make an informed decision about whether to take AP Calculus or AP Statistics next year.
The Calc unit is fairly straightforward: here are some of the big ideas, hey lets learn some notations, oh noes division by zero?!, take some deep breaths it’s just a limit stop freaking out type of stuff. After doing some work with the delightful Chris Sangwin, I have chosen to play around with the following piece of information (and hopefully some geogebra modeling) to take polynomial long division to a new level in precalculus:
Given a polynomial P with degree n ≥ 2, the remainer when P is divided by (x – a)² is the equation of the tangent line to P at x = a.
Boo Yah. Go try a few examples–it’s rather fun. I am going to set up the kids w/ the long division and then have them graph the original equation in geogebra along with the remaider equation and then have them write down what they notice. I have yet to come up with anything practical as it’s not all that useful for finding extrema, but I need to think about it some more.
Oh, and please feel free to shoot me down if this is wrong. My working knowledge of Taylor Series is rough at best and that’s where this idea comes about.
in which i present about why i only twitter with math teachers November 19, 2011
Posted by Ashli in Planning, Resources.6 comments
Today I did my first ‘real’ presentation of sorts to a professional math meeting, NWMI. I was asked to talk about twitter and blogging and how I use it to stay connected professionally. The following is an abreviated version of my talk along with promised links for those looking to get into the edutwitterblogosphere. Gesundheit.
I chose prezi as a presentation format. You can find my prezi here. I tried to keep the text minimal and just use the presentation to make points and show a few graphics, so I’m not sure how easy the prezi will be to follow without having seen the actual talk.
the highlights
I stumbled onto blogs in a move of desperation my 3rd year of teaching. I’ve talked about this before, though, so I’m not going to belabor the whole story here. Suffice to stay, I found online professional development that wasn’t about clock hours that I could partake of on my terms. A few summers later I got to go to PCMI and Sam Shah got me into the world of twitter and blogging myself, instead of just lurking. I hadn’t really looking into twitter outside as something I would see occasionally on blogs or mentioned in the news media in a joking context. Sam also gave a presentation on twitter and blogging at PCMI that you should really go read/watch.
Twitter has been an amazing experience me both professionally and on a more personal level. I have people I consider friends (as in, I would let them sleep in my guest room if they needed a place to stay) all around the country and several outside of the country due to twitter. I find this very cool.
the links
During the presentation I showed a variety of links of places to start for new twitter/blog math people.
First off, if you want to really leverage twitter, you will need to go and make an account. Once you have a twitter account, check out this great list of tweeps compiled by @Fouss. You can follow as many people as you like and you can make lists if you only want to read certain things at certain times.
I also recommend checking out the hashtag feature. Hashtags are a way to tag your tweets for a specific channel of conversation. For example, #mathchat is something you can search for and see just tweets about math education. #anyqs is another great channel of people sharing videos/pictures of mathematics in the world. Check out Dan Meyer’s post for a great explanation of this channel.
For blogs, I use WordPress, but there are other sites out there. If you want to find blogs to follow, you can start with the blogroll I have at the right of my page. From there, follow their blogrolls, and so on and so on. There’s really all I did in the beginning and it’s lead to a pretty filled reader that I turn to for inspiration weekly. I’m not as good about blogging as I want to be, but I’ve always felt when I do get a post out there it’s really helped me think about the issues and then any comments I get are just icing on the reflective process I’ve already taken part of.
One other thing I shared out was the Virtual Filing Cabinets people have created. Sam Shah has one of the larger ones I’ve come across. Bowman in Arabia even shares out some sweet Geogebra resources in his. If you just want a place to start reading some quality posts, go check out Riley Lark’s Conference on Core Values from this past summer. The topic was about what is at the center of ones classroom and posts came in from all over.
And if you’re wondering how to join in the conversation, don’t feel like you have to do something like write some amazing blogpost and submit it to a virtual conferences. Just get out there and post on peoples’ blogs. Give feedback. Ask questions. Be respectful. In short, come enjoy being a professional with people who are as dedicated to this profession as you get. It’ll change how you teach in the best ways because there’s nothing like knowing your tweeps have your back, good days, bad days, and all the grey in between.
in which I am invited to fold with others November 13, 2011
Posted by Ashli in Prof. Development.2 comments
some things to know
Back in 1908 Felix Klein did a series of lectures targeted at school teachers with a focus on “elementary mathematics from an advanced standpoint“. Even 100 years ago there was an acknowledged gap between school maths and research maths. The Klein Project is named after Felix and shares his goals of bridging this gap.
goals of the project, as I understand them
How many of us stay in tune with the maths we did in college? My own background is mostly theory. I have pretty distinct memories of taking writtens and orals my senior year, proving most of the underpinnings of calculus in Real Analysis and studying groups and rings in Abstract Algebra. Number Theory along with Combinatorics/Graph Theory were some of my favorite classes. I have forgotten more mathematics than the majority of people will ever know and I suspect a lot of teachers are like that.
In which my folded plans are turned into bad kirigami November 9, 2011
Posted by Ashli in General, Planning, Teaching Thoughts.7 comments
What do you do when a kid cheats? Or worse, steals?
I am away at a conference right now (it’s super cool, but that post will have to wait for the week to be complete), and I made sub plans for 4 days. I had a folder for each class for each day. Seating charts. Annotated keys. I left cocoa for my sub as a thank you.
Tomorrow the kids are taking a midterm. I know it’s more than awkward to have them take a midterm when I’m not around, but they know exactly what the problems are and have spent the past two months working with them. Each day was planned out with review problems like ones they had seen before to practice and a full key to check their work with at the end.
But that’s not the distressing part of this tale.
(more…)
feedback and sbg changes for this year August 17, 2011
Posted by Ashli in Lesson Disclosure, SBG.4 comments
First off, if you’ve not read Working Inside the Black Box: Assessment for Learning the Classroom, I recommend you do so. It was one of the articles we read at PCMI 2011 and probably the one I will re-read the most throughout this year (I re-read things a lot–it helps me think and my memory is a sieve).
spurs
From pg 13: ”A numerical score or a grade does not tell students how to improve their work , so an opportunity to enhance their learning is lost.” I feel that if students are paying attention to what the 0-4 system I use means, the numerical score does give feedback, but it’s not very specific. Sort of like I’ve told them the answer is on that bookshelf over there, but I didn’t say what shelf to look on.
And then you read stuff like this:
Research experiments have established that, while student learning can be advanced by feedback through comments, the giving of numerical scores or grades has a negative effect, in that students ignore comments when marks are also given. (p.13)
…
What’s worse is that I know that is true. I don’t think I’d ever thought it consciously, but I know it. I’ve watched kids get their skill quizzes back, glance at the number and then toss it away. How many of us have spent too much time writing comments on tests that we know our students will never read? But how much of that is our own fault? Why should the kid bother reading comments if they can’t do anything to make it better? (yes, yes, I know there is an answer to that but I don’t think my students do)
One of my goals this year is to make feedback useful. I’m honestly not entirely sure what that is going to look like, but to start I’m changing the format of my skill quizzes and how my kids line up to retake them. (more…)
What’s the Question? July 24, 2011
Posted by Ashli in Lesson Disclosure.8 comments
let’s give them sometin’ to talk about
I am not a fan of quiet classrooms. I like it when students are willing to talk, ask questions, and put their thoughts out there. My room is in table groups of 4 so my students have to face one another and, *gasp*, discuss the math they are working on. Now I’m not trying to say I do good group work because I am not that awesome yet, but I do believe that I do a good job creating a classroom environment where students are willing to talk about the math at hand and ask each other questions.
At PCMI Bill Thill put together an evening of 10 minutes shorts for people to sign up and share something they do in their class that they love. I got to go first and my short was entitled “What’s the Question?”, which is a warm up format I came up with second semester last year that I loved and I think did a lot for creating a classroom environment of discussion. Note: I don’t think this is an activity I ‘borrowed’ from anyone, but if you read the following and know of someone else who does something similar please let me know so I can give credit.
the general set up:
Let’s say you are in my Precalculus class and we’ve been working with trigonometry. At this point you pretty much know what sine and cosine look like, you got right triangle trig down, and you can plunk down a 16 Point Unit Circle down in under 5 minutes (yes, I do make my kids do this). Now as my student you walk into class and see the following on the board:
Here’s how it works. Underneath each of those blue tiles is an answer a la Jeopardy. I pull off the first blue tile to reveal the following:
I give students about 30 seconds to absorb the solution and think of a question that it answers. They are allowed to talk to their group mates, but no cross-table talking. I use a die to randomly pick a table. I write out every question students say under the answer. And try not to offer too much commentary. I do this again for B and C.
