Saturday, November 30, 2013

Cheap White Boards

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!


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.

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,, 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,, 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 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.

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. ).  Before break, students worked through the Discovering Algebra investigation to see this visually:

The activity guided them to see than = .  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. = = ).  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 ( 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.

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.