## Saturday, November 30, 2013

The $2 White Board I know that lots of other teachers use white boards regularly. Over break I went to Lowe's and got two 4'x8' sheets of wall board cut down into six boards each (free cutting when you tell them you're a teacher!). I'm going to cut up some fleece to be erasers, and I've got the$2 white boards!  I bought 4 boards from Amazon several weeks ago (for $17 each!), and they have revolutionized my calculus class, so I'm looking forward to introducing these to Math 9. In class, students get up to get boards on their own, and love to figure things out on them. Freedom to Explore Students feel more free to try things out and to make/correct errors when they are using whiteboards. And, who doesn’t love a bright purple marker? The only issues: comparing work later and having records to use for future problem solving. Enter the smartphone camera! Photos Almost all of my students have fancy phones, so I’ve started asking them to take photos of their work before they erase, and to title it in their phone memory. Now students have been zooming in on their photos on phone cameras to remember what they did and to compare their work. They can e-mail photos to me or to each other. One student got a classroom sized whiteboard for her birthday from her retired-math-professor grandmother. She regularly works on assignments at home on her board, takes photos of them, and then sends them to me, both for advice to get unstuck and to turn in her work. ### What Draws me to Blogs A late response to @k8nowak's request for why we blog. I have a hard time actually writing blogs, hence this coming in about a month after she asked the question. Hook 1. What hooked you on reading the blogs? Was it a particular post or person? Was it an initiative by the nice MTBoS folks? A colleague in your building got you into it? Desperation? Blogs, not Twitter, got me into the #MTBoS. In the summer of 2008, I was a backyard BBQ at a co-worker's house. I met a friend of theirs, Ben Blum-Smith, http://researchinpractice.wordpress.com/, a fellow math tutor visiting from NYC. At that point, I was mostly doing private tutoring and only teaching Calculus at my school. After a long conversation about the merits of tutoring, he gave me his business card. I went to check out his website, and found his blog. I'm not sure that I fully understood what a "blog" was, but gosh, he wrote about things that I had been thinking about for years! And, he linked to other people writing about interesting topics. I binge-read everything that Sam Shah, samjshah.com, had written. I saw the blog-rolls on people's pages, and realized that many more people were writing about things that I found fascinating! Over the next several years, I would periodically binge-read on a weekend day. At some point, I set up a Google Reader Coming Back 2. What keeps you coming back? What's the biggest thing you get out of reading and/or commenting? At this point, I feel like fellow bloggers are my friends, supportive, insightful, intelligent and driven friends. After attending TMC13, I actually know some of these people, and their words and passion help me to stay inspired, even when the going gets rough. The gift culture is astounding...so much amazing stuff is available! I have a hard time understanding why other teachers don't also jump in! This fall, as I have been blogging a bit more myself, I have been trying to push myself to comment on posts since I know how much I love it when folks comment on my posts. Writing 3. If you write, why do you write? What's the biggest thing you get out of it? For years, I had been feeling like I really ought to write myself. But writing for me is like pulling teeth. To be honest, a tiny portion of my decision to major in math in college was to avoid writing as many papers! I respond very well to deadlines, and for the most part, there are not deadlines around blogging. In the summer of 2012, the New Blogger Initiative gave me the push to actually start this blog. I dutifully completed each assignment (usually hours before the next one would be announced). Once I get past the, "I don't want to write" whiners in my head, I'm actually not a bad writer, and a part of me enjoys it. So, having the deadlines really helped! For the Explore the MTBoS Challenge, I didn't hold myself to the same strictness around deadlines, and I have participated much less. I have tons of blog ideas in my head, and briefly outlined on my computer, but something often stops me from taking the time to really sit down and write. Perhaps I'll write a blog post about that! NCTM Presentation 4. If you chose to enter a room where I was going to talk about blogging for an hour (or however long you could stand it), what would you hope to be hearing from me? MTBoS cheerleading and/or tourism? How-to's? Stories? I would want to hear how your blogging has changed over the years, your story generally. I would want some quotes from folks who use blogs well, and then some guided time to explore things on my own. Maybe a short lesson on Feedly or something else to help me to organize all of this stuff! Overall, though, I would want to hear your story and the stories or other bloggers. ### Proving Radical Simplification Training them to beg for proof I wrote a post a couple of weeks ago about proving things in my calculus class. I aim to create the same ethic of proof in my Math 9 class. Some of them have definitely bought into the need to prove everything we use, but since it's a bit more mixed class, some of them wish that I would just give them formulas. Just before vacation, we were working on the Pythagorean Theorem (I'll put up another post soon on how we proved this without any algebra using "I Notice, I Wonder" thank you @maxmathforum!). I gave a quiz last week on the Pythagorean Theorem, and the kids totally rocked it, better than any other quiz so far this year. How it fits in All of this is part of the unit that is leading up the grand programming project TI-83 Programming Project. We are working toward the distance formula next week, then midpoint. We have already discussed slope of parallel and perpendicular lines. The investigation So, the next couple of days after break are devoted to simplifying radicals (i.e. $\sqrt{40}$$2\sqrt{10}$). Before break, students worked through the Discovering Algebra investigation to see this visually: The activity guided them to see than $\sqrt{40}$ = $2\sqrt{10}$. This process works great to be able to "see" the what we are doing. Next, I want to guide them to the more traditional method of simplifying roots (i.e. $\sqrt{40}$ = $\sqrt{4}\sqrt{10}$ = $2\sqrt{10}$ ). Also, this visual method only works for roots that are sums of perfect squares. The proof So, last night I was thinking about how to connect the visual activity to a more classical simplifying strategy. I don't really know quite yet--maybe the visual one is just to get students thinking about how it's possible to write roots in multiple ways, and then we go into a more classical approach. My students don't yet know about fractional exponents, and I'd like to be able to prove this without them. Several of you (including @adkpiper, in person) suggested that I just square both sides of the equation above to show that it's true. How simple! It's great to have a community of folks who will play with the problems that I get stuck on, no matter how simple they actually are. So elegant and totally appropriate for ninth graders without a great grasp on proof or complicated exponent rules. ## Sunday, November 24, 2013 ### My blogging intentions...made public My sweet boyfriend Hollis (www.holliseaster.com/blog/) is helping me to write this blog post because I am scared that the water is too cold and don't want to jump in. I've been having a hard time getting into a blogging groove. I really want to share more of my thoughts here, but it's like I get blocked when I start thinking of what to actually write. I keep putting it off thinking that the Big Idea will eventually arrive, but then I feel guilty about postponing other work, and I move on to other tasks. It's odd...either I can't think of anything to write about, so I don't write, or I think of ten different posts, and don't write any of them, because "you can't post ten things on your blog in one day." Of course, there are ways around this. If I binge-write, I'm sure I can schedule things to come out at different times. I think I'm just trying to come up with excuses to myself to not write, but I want to write. It feels good to share my ideas, but it's scary too! So I'm setting myself a public challenge. It's Thanksgiving break this week, which means I won't have as many distractions. So: at some point before Thanksgiving (Thursday of this week) I will write a blog post and publish it, and it will be about at least one of the following: • Calculus class and photographing the whiteboards for comparison among groups • Math 9 and my continued frustrations, documenting my efforts • Legos for linear programming • The stations for simplifying radicals that I designed with Hollis • MTBoS challenge blog posts, even though they're late • Something else that feels relevant before Thursday So, check back soon for my next post! ## Monday, November 11, 2013 ### Muting myself: A study in silent teaching I've been frustrated with the lack of focus and attention in my Math 9 class recently. About a third of the students have diagnosed ADHD, and it's wreaking havoc on our productivity. I mostly try to not spend much time with a teacher directed class, but there are some things that I still need to get across. For example, sometimes I need to give directions for an investigation or facilitate summarizing our findings as a class. Silencing Myself A lot of students have been talking while I'm talking or will talk over each other. So, today I thought it might be interesting to try to lead a discussion about the warm up during which I would not speak. I knew that they had discussed their solutions and come to consensus on most of the problems at tables. So, I pulled out a name stick and called on (by pointing at them) a student to answer the first question. Our warm up was a review of quadrilateral classification and labeling. Then I asked (written on the board) "what is the most specific shape name for each figure?" Again, I pointed to students after I pulled their name sticks. I'm realizing that I shouldn't use the random method for calling on students unless I give students a chance to think or discuss at their tables first as it puts some students uncomfortably on the spot. Facilitated Debate on the Board We ended up having some good debate about the third problem. Some said it was a rhombus b/c the sides looked congruent. But others argued that we couldn't make that jump since they weren't labeled. Others forgot what the arrows meant. I facilitated this whole discussion without speaking. I wrote what students shared on the board, and kept pointing to more students to join the conversation. When I thought we had come to consensus, I asked for a thumbs up or down and waited for every student. I even had them work through their investigation without speaking. I wrote directions on the board and pointed to a student to read them. Results Overall, they were much less off-task. I think that for students with attention issues, having fewer stimuli (not hearing my voice as well as seeing my writing) helped them to focus their attention. At the end of class I asked them to write me a sentence or two about how they thought it went. Some of them didn't like that they were teaching each other (but I love that, honestly!). Some appreciated the organization. Some thought it helped them to "solve our own problems." One said "everyone was quieter and more productive." Another said "I wish we had spoken directions." "At first I didn't like it, but I think should it again because I had to stay engaged to know what was going on. We were also quieter, which was nice." Overall, it was a good experiment, and a good technique to have in my back pocket! ## Sunday, November 10, 2013 ### "Don't Ruin the Punchline": Proof in Calculus Class This is my fifth year calculus, and by far my best. I have a gloriously small class of six motivated students. It's the first year that I have the privilege of teaching students whom I previously taught (I had most of them three years ago in Math 9). Setting the Stage From Day 1 I have created an ethic of "we don't use things we can't prove." I encourage them to use their intuition and estimation to make conjectures about new ideas, but I don't give them formulas to plug and chug on. I do my best to eliminate or limit lecture and instead give them guided explorations to work through. In the last several weeks, they have proven: the power rule, the product rule, the quotient rule, and derivatives of sine and cosine. Begging for Proofs (yes, really!) What's so amazing this year is that students are begging to prove more things. When I mentioned that I might go through the proof on the board for the quotient rule one student said, "what, do you not trust us to figure it out ourselves?" is a gloriously sassy voice! Another student has been e-mailing me photos from home as she figures long proofs on her whiteboard in her bedroom. When she was home sick for a day she asked, "is there anything else I can prove, this is a fun game?" Often some students will figure out how to prove something before others do. I've started to say "don't ruin the punchline," as if we're talking about a joke. If someone finds out what to add and subtract to prove something, they may give small hints if their classmates ask, but they must keep in mind the joy that they had with finding it on their own. ## Sunday, October 27, 2013 ### Twitter--young but getting wiser #MTBoS Challenge 2 In the past couple of weeks I've been challenging myself to actually participate in some of the conversations going on on Twitter. Historically, I would read them and think they were interesting, but not necessarily toss in my two cents. The MTBos (Math Twitter Blog o Sphere)...mostly blogs for me in the past...has offered me so much. I feel ready to start giving back and being more active. On Saturday afternoon of TMC13 (Twitter Math Camp), David Wees @davidwees and Justin Lanier @j_lanier schooled me on why I might want to dive into the Twitter World to participate in the MTBoS. "It's like a dinner party with tons of people that you admire," David said. "You can ask people about their cool ideas directly. It's the best faculty lounge there is." I have Facebook (though I don't really love it...I mostly just feel jealous and lazy when I read it) and I wasn't sure why I would want to add another platform like that to my life. After TMC13, though, I couldn't imagine not being about to continue the conversations that I had had with folks there. Although I still feel very young in the MTBoS world, last night as I read some posts from new folks, I was realizing how much I've learned from this community, how much I have grown in the last several years as a teacher: -Instituted Standards Based Grading in my ninth grade -Convinced my entire department (and got the admin team to consider it school-wide) to use SBG -Felt supported and in good company as I think about new ideas -Know a ton more acronyms :-) -Inspired to start thinking about Interactive Student Notebooks -Huge files full of lesson and method ideas If the MTBoS were a foreign language, I would be conversational, not quite proficient and still striving for fluent. I love that there is always more to learn, always new ideas and concepts to explore. Through Twitter I hope to challenge my fears of writing and jump more fully into the conversations. Last night, my partner, @adkpiper, and I explored how replying to tweets affects who gets to see them. He even wrote a blog post about it: http://www.holliseaster.com/p/why-are-tweets-missing/ ## Saturday, October 26, 2013 ### TI-83 Programming Project for Coordinate Geometry At TMC13 I got the courage to present during the My Favorites session on Sunday morning. For the first Explore the MTBoS Challenge (a bit late, I know) I am going to write about the project that I presented then: a computer programming challenge using the TI calculator. [Please note: I did not create this totally on my own, Hollis Easter @adkpiper helped quite a bit.] Full disclosure: I am not a programmer. I know very little about computer programming. That does not stop me from assigning this project. (I would like to learn more about programming at some point, but it hasn't risen high enough on my lists yet.) The setting: Ninth grade math. My school teaches an integrated curriculum, so the course includes units from traditional Algebra 1, Geometry and a bit of Algebra 2. My units are as follows-- • Linear models (basic algebra review, linear models from points/slopes, linear regression, systems of linear equations, systems of inequalities) • Coordinate geometry proof (Pythagorean, using distance, midpoint and slope to prove types of triangles and quads, transformations) • Trigonometry (intro to basic right triangle trig, special triangles, simplifying rads, intro to radians) • Geometry (congruency, similarity, parallel line conjectures, traditional proof) • Exponential models (exponent rules, modeling using changing rates, comparison to linear) The coordinate geometry unit is where this project falls. I love starting geometry on the coordinate plane. We have spent a great deal of time graphing in the first unit, and for the most part students are comfortable graphing lines. By starting geometry as "what happens when several of these lines intersect?" makes a really nice transition. We look at what we need to know in order to determine whether or not lines are perpendicular. We do a bunch of proofs of the Pythagorean Theorem. We extend to distance and midpoint formulas. We draw tons of quadrilaterals and categorize them based on first the characteristics of their sides and then the qualities of their diagonals. In essence, students know how to classify quadrilaterals. In comes the project! On the first day, I really hype up the idea of programming. I ask students to name the top careers in terms of job satisfaction. A lot of kids come up with doctors, lawyers and other jobs that their parents have. Sometimes one or two will mention something about software or programming. I then share the stats about programmers being some of the most satisfied employees. Many students are not exposed to much in the way of computer programming in their high school years, so this project gives kids a taste and helps them to know if it's a field that they may want to explore in the future. I hand out a sheet that walks students through the parts of an algorithm and gives explicit directions for what to enter into the calculator [from the Core Plus curriculum]. I go very slowly together with the whole class. If students want to work ahead, or start writing other programs, that's fine, but if they have questions, they have to wait until I get to that point. So, we all have success with entering a program into the calculator. Next I ask them if they can think about how to write code for the midpoint and slope equations. Most of them are quick to figure that out and write a couple more small programs. Then I hand out the project requirements. Assignment: Write a program that when four coordinate pairs are input, the calculator outputs the correct quadrilateral classification. In addition to writing the program, they need to include code notes for each line and a justification of why their process is the best method. They also need to hand in three examples worked by hand that agree with the calculator outputs. I don't do much more in class. For the next couple of weeks I don't assign much other homework...we do most of our practice in class. I'm available outside of class for help with debugging, but I rarely know how. I mostly just send students to YouTube to watch videos or give them CS texts that I have around. I suggest If, then, else loops or ask them about syntax, but I don't necessarily know how to fix the issues, and I think that's good for them to see. Another key to this project working so well is that I give two options. Students can do the programming project, or they can write a grant proposal to the Mathematical Association of America in support of an exhibit on Escher. For that project they need to research his work (we have also just finished studying geometric transformations), create their own art piece, write a compelling grant proposal, research some other artists who use transformations, and explain it all in terms of mathematical language. So, it's also a rigorous project, and appeals to most students who don't seem inspired by the programming. There is quite a bit of lore about this project at my school at this point. We are very small (80 students in grades 7-12). This is my fourth year teaching Math 9, so all of the upper classmen at my school have been through this unit. So, students are also welcome to ask older students to help with the debugging. ## Thursday, August 29, 2013 ### Tabletop Twitter Today was the first day of class with my Math 9 class. I have been agonizing over what to do to open the year with them. The last three years, I have started the first day with the question: Why do we learn math? We go from individual brainstrorming to partners to groups to whole class. Since the content starts to get fairly abstract this year, I want kids to start to add to their reasons for learning math (not just to cook and balance the checkbooks, but also about modelling, making sense of the world and making good arguments, etc). The activity has gone really well each year--so well in fact that as I've shared it in the department other teachers have started using it as well. Sounds like a great thing, until you realize that most of these ninth graders did the "Why do we learn math?" activity in both seventh and eighth grades. But it's such a good question to get them thinking about! What could I do? I don't remember where I read about "Silent Conversations" as a classroom participation tool--possibly on a blog or in the NCTM magazine. Please comment if you know who coined the term! The idea is that each student has a colored marker, there are several pieces of butcher paper around with questions or prompts on them and students have conversations about the topic just through writing to each other. I've wanted to do it for awhile, but hadn't found a good topic yet. As a new Twitter user, I'm still learning about #'s and @'s, but I assumed that many of the students use Twitter. So, I framed our Silent Conversations as Twitter conversations. I encouraged #s and @s and let them go wild responding to each other. I had students write their name on a piece of butcher paper with their color so that I could track who wrote what, and I reminded them that nothing on social media is anonymous, so this wouldn't be either. They moved around the room in groups of 4. I set a timer for 3 mins and had them rotate each time it went off. We had four prompts: -Why do we learn math? -What makes a good teacher? -What will make class a good learning environment? -How to be a good math student. At the end of the activity I had students take photos of the poster they started with. Each of those four students are to summarize the content. They can do their summary in any format they want (paragraph, mind map, wordle, prezi...). One student asked if she could summarize it with Twitter and take screen shots. Another asked if he could make a clay sculpture. I gave them both emphatic yes's, and I'm looking forward to seeing what comes in tomorrow! The students were super engaged through the whole activity and left feeling really excited about the class. When a student teacher came by she said, "oh, is this Tabletop Twitter?" So, I guess it's a thing! ## Wednesday, July 31, 2013 ### How I Organize this Vast World Before going to TMC, the workshop that I was most looking forward to was on how other people organize the vast stream of information coming in. And that was before I started to use Twitter. Yikes! Tina (@crstn85) and Anna (@Borschtwithanna) both had some great ideas with their DropBox and EverNote solutions. I'm fortunate that I've used some of these tools already, so the learning curve isn't quite as steep as it is for some other folks. My task now is to figure out HOW I will use these tools and incorporate them into a smooth work flow that helps to alleviate the overwhelm. Even if I can't read everything and research everything and learn everything all at the same time, at least I can find ways to store some of the most interesting things so that I can find them when I'm ready to investigate them later. There are so many options for organizing, which is amazing, but also overwhelming in its own right. I think I've gotten it narrowed down to about eight apps/programs that I'm considering using/patching together in some way. I want a system that flows for me, is not too complicated, and does not try to force an app or program to do something that it is not really designed for (like, you could use EverNote for everything, but it doesn't do everything well, sort of like trying to use inductive reasoning for every proof). Here are the tools that are likely in my toolkit: Gmail I have been using it for seven years, is super easy for me to just archive everything that comes through my box. I work at a Google school, so my school e-mail has the same interface and I can toggle between them. I have kept a "reading/watching" tag in gmail that I use to store things that I want to read or watch in the future. I'm hoping to convert that to Pocket and not use Gmail for that purpose anymore. Gmail is good at email and at storing correspondence in a searchable way; I want to use it for that Evernote I have dabbled in Evernote over the past year or so. I know that it's super powerful in its search capabilities and will work to store all different types of media. I'm planning to use a web clipper to store things that I read that I want to access later (lesson ideas, really inspiring posts, etc). I also plan to use Evernote to keep track of lists of future ideas that I have, not things that have active action items, but future ideas (like: explore formative assessment, read a book about symbolic logic, play with Blockly, etc), sort of like a list of things to play with when I have time. Evernote is good at collecting web content and thoughts that I can access when I need them; I want to use it for that. Pocket When I come across content that I want to read later (through Twitter or Feedly or e-mails or Facebook) I'll store it here. Pocket can send full articles (with cabinets and tags selected) to Evernote, so items that I want to save after reading are easy to file. Pocket is good at saving things to read later; I want to use if for that. Twitter I'm still learning about this medium as I've been using it for less than a week. My sense is that I will use it to find content, to interact with people in real time in a public space, and I'll use it to participate more fully in the MTBoS. So far I have starred tweets that seem clever to me. I don't want to use the star system to store things that I want to read later as I want it all in one place (Pocket). I don't know yet exactly what Twitter is good at, but I want to use it for that. :-) 11/10/13 Update: I find that I use Twitter to crowdsource ideas and to share the small day to day things that happen in my classroom. Remember the Milk My boyfriend introduced me to this incredible task management software about a year ago. I use it on my phone, iPad and on the computer. I pay the$25/year to have automatic syncing; it's the only app that I pay for.  I loosely use David Allen's Getting Things Done philosophy to keep lists of things that I need/want to do.  I recently made a "Global Math Department" list to keep track of all of the ideas that I'm having of things that I want to explore.  Since many of these are not actionable yet (I don't know what the next thing that I'll do on them is), I think it would probably be better to store these lists of ideas in EverNote.  We'll see.  RTM is good at helping me remember to do things and to prioritize what I need to do; I want to use it for that.

Dropbox
Just signed up for an account.  After Tina presented her system, I think that this would be the best way for me to collect both my personal and my school files all in one place that's accessible from anywhere.  It will take a bit of work to organize everything, but I think it will be worth it.  Dropbox is good at storing files; I want to use it for that.

Feedly
Started using when gReader quit on us.  I don't love it, but it seems to do the job alright.  I'm considering checking out the Newsify app as some folks seem to like that for other devices.  I hope to not use starring too much in Feedly as I'll feel fractured between different systems.  If I want to read something later, it should go in Pocket.  If I want to keep something because I think I'll use it later, I should clip it into EverNote.  Unfortunately you have to pay for Feedly to send directly to Evernote.  I send to Pocket and then to EverNote as a work-around.  Feedly is good at aggregating blog content; I want to use it for that.

This past week I spent four days with the most inspiring, innovative, welcoming, joyful, intelligent, hard working group of teachers (well, people in general) ever.  I had the distinct privilege of attending Twitter Math Camp '13, a gathering of about 115 math teachers who use Twitter and blogs to connect, collaborate and support each other.

I have been reading math teacher blogs for about four years.  I met a friend (Ben Blum Smith http://researchinpractice.wordpress.com/) of a math teacher co-worker at a picnic who gave me his business card, with his blog listed.  I saw that many of his posts included links to other bloggers.  I read several of Sam Shah's posts and quickly thought, "wow, this world has some good stuff to offer!"  So, I set up a Google Reader and started some hard-core lurking.

In recent years I keep hearing people say "the action is all on Twitter."  I'm a late adopter in general...I got my first smart phone less than a year ago, I waited until 2009 to get Facebook, etc.  I like to wait until an app has a ton of reviews before I consider trying it out.  I also have quite a few friends (and I often feel this way too) who try hard to have less technology in their life.  I have mostly stopped using Facebook recently as I don't want the time suck of browsing things without fully engaging and I don't like having so much screen time.

And then in walks this whole MTBoS (Math Twitter Blog 'o Sphere).  I arrived at Twitter Math Camp with a handle (the word for your name on Twitter) created, but having never tweeted and not yet following anyone.  I figured that if I enjoyed the gathering, then I would consider trying it out.  By Friday morning, I was tweeting and trying to find how to follow this glorious community.

Much of what the general public dislikes about Twitter does not seem to be how people are using it in the MTBoS.  The medium and the community allows me to connect with several hundred like-minded, helpful, passionate, intelligent math teachers.  Wow!  I work at an incredibly small school (80 kids in grades 7-12, one full time math teacher, two part time math teachers), so finding this world where I can share ideas with a Global Math Department is so liberating and fascinating!

I would like to write more about all of the sessions that I participated in at TMC13, both so that I can remember what I learned, and also to share with other folks.  At the moment, that is feeling somewhat overwhelming, so I decided to just write about why I feel so much joy in joining this splendid community.