November 22, 2015

What's Coming Up Next?

When Christopher Danielson spoke this summer about finding what you love and doing more of that, I wasn't really sure what my thing was. I mean, I love teaching and I made a commitment to spend more of my time in the classroom, which means presenting at fewer conferences this year and avoiding my department head whenever she talks about wanting to be done being department head (she only gets to teach two classes and spends the rest of the day in meetings - yuck!). But this fall I figured out what it is I love doing, and I must love it because I signed up to do it so many times things got a bit overwhelming for a while there.

I love organizing.

Not just my desk (which I do like to keep organized, my system incorporates three accordion file folders this year). Not just my file cabinet or computer files (which are both sorted by course and then by unit). But big things, like events. There was a week recently where I was working on the Explore/Blogging Initiative in December/January, a PCMI conference in December, two NCTM MTBoS booths in November and TMC in July. For anyone who had to interact with me that week, sorry you didn't get my full attention. And major kudos to Ashli for listening to me whine about how four things that were occurring in four different months all somehow needed my attention simultaneously and why do I do this to myself?! (I have the best best friend.) But secretly? I loved it. I love the spreadsheets and the mental decision trees, the excitement of things coming together. I love helping other people accomplish their vision. I love problem solving as we hit snags, and sometimes stumbling across even better ideas as we plan.

So, what are these things that I'm organizing?

Explore MTBoS Mentoring Program
There's just about a week left to sign up to mentor or be mentored! We want to spread the word about this community but sometimes large scale initiatives aren't the right mechanism. Sometimes people really need tailored help. Maybe they read blogs but don't know how to use Twitter. Maybe they are on Twitter but don't know how to connect to the 'right' people. Maybe they are comfortable lurking but not so sure when it's okay to jump in. In those cases the generic instructions aren't sufficient. If you feel comfortable blogging and tweeting with other math teachers, we really need your help as a mentor! If you want to get started blogging and tweeting with other math teachers, get yourself a mentor! Sign up (by clicking the title above or images below) by December 1st and we'll get you all paired up for a month of exploration in December.


Explore MTBoS Blogging Initiation
We hope you'll join us in making a new years resolution to blog more. To help you carry out that resolution we will be posting weekly prompts in two strands - one geared toward new bloggers and one geared toward seasoned bloggers. I'm excited for the plans we've worked up!

MTBoS Booth at NCTM Regionals
You're probably thinking, hey Tina! December is pretty busy for most people, why would you want people exploring then? And I'll say, hey reader! Thanks for reading! We chose December because the NCTM regional conferences (plus a variety of state conferences) just finished up and we wanted all of the people we invited to check out the MTBoS to have a mentor.

After we closed down the booth in Boston in April, Justin and I took notes on what future organizers would need to know, split the supplies into a couple boxes and got ready to pass the torch. Megan was the first to try her hand at exhibiting. She and Carl each wrote about that experience. Robert's chance followed shortly after and his exhibition concluded just a couple days ago. The supplies are headed off to San Francisco but the conversations don't have to wait until the next conference - because that's the beauty of the MTBoS - conversation is available for your perusal and contribution 24/7.

PCMI December PD Weekend
This event has definitely been the most work to organize. It's new - so new that the website is still in development and I have yet to decide if it's a conference or professional development opportunity or whatever other phrase surfaces as I type yet another email trying to figure this thing out. No matter what we call it, it's gonna be awesome! It's too late to join this event, but there are two more planned (in Salt Lake City and Chicago) for this school year, and as long as I don't screw things up too badly this year the plan is to really ramp up next school year and offer a lot of mini-PCMI experiences all over the country. One of the benefits of organizing events is that I get to make sure my friends know about it - two of my colleagues from school and several twitter friends applied before we reached capacity. I sent approximately 15,000 emails in the past couple months preparing for this but I'm confident it's gonna be worth the effort I put in. I'm so excited for the chance to do math, talk about education, hang out with awesome people and spread the amazing culture of PCMI.

Twitter Math Camp
Speaker proposals will be open soon. We're looking at last year's survey results and thinking up new ideas and generally getting excited! Mostly I'm excited about how much sun there is in summer. I love New England but waking up in the dark and leaving school at sunset is really depressing. Thoughts of summer fun with all of you counteract that!

So that's what I've been up to. What do you love? How have you been doing more of that?

November 15, 2015

Sine and Cosine Waves with Activity Builder

My PreCalc students have been studying the graphs and equations of sine and cosine for a month (an interrupted month but a month nonetheless). Tuesday they will have one final day to review before their test on Thursday (we run an alternating day block schedule). Some students are completely ready. They can identify transformations, graph complex equations, and write equations from both graphs and descriptions. They can apply their knowledge to a novel context (we did a Ferris wheel project). Other students still have to think about what the graph of y=sin(x) looks like. This is the widest range of students I've ever had in an Honors PreCalculus course so I'm really appreciative that Desmos made the activity builder just in time for this class! It's a great way for me to differentiate.

Last week while working on the Ferris wheel project when I had some students who had no idea how to write an equation given their more complicated graph, I sent them to Rachel's activity builder Curve Fitting w/ Sine and Cosine that went back to the basics of equation writing. They wrote the equation for a graph with amplitude not equal to one, then I referred them back to their Ferris wheel to identify the amplitude and put it into their equation. It was great because it was self checking and students experienced some success working simpler problems when they were frustrated with the complex problem I'd posed.

Tuesday I want to create a similar situation - so I built a couple different activities.

Graphing Basic Trig Equations
This starts all the way back with y=sin(x) so my students who are lost can start back at the beginning and practice the whole unit all over again. When we sketch a graph, students plot the important points and then fill in the curve. I recreated this activity on Desmos by having students drag points on a grid. Then they can check their work by un-hiding the curve.

Sine and Cosine Graphs with Multiple Transformations
Students will describe, graph and write equations for functions with multiple transformations. This one is aligned with what will be on the test.

I would love feedback on these activities! (Especially if you can provide it before 7:24 am on Tuesday.) I'll let you know how they go after that.

November 13, 2015

Last Block

We run an A/B day block schedule. Our kids who are behind in math get double block math. A few years ago I had some students who had math last block every day. Then last year I had a great schedule where I had one group last block A days and a different group last block B days. It meant that on the alternating days I saw them second or third block. And they're really different kids at different times. This year I have my contained math class last block every day. I was not excited when I saw that schedule, but it wasn't until today that I realized exactly why it's so hard - I have them after every other class.

Reasons I've cited before:

  • some kids medications are wearing off by the end of the day
  • some kids have expended all their energy focusing in other classes and don't have anything left for me 
  • some kids (less my ninth graders) will leave school last block if they don't want to attend, but they're less likely to skip a class in the middle of the day
These reasons are all true, but today I realized that the biggest issue is not about the time, it's about all the things that have happened between 7:30 and 12:30. 

One kid walked into my class and immediately put her head down. 
One kid walked into my class and was talking rapidly in a high pitched voice. 
One kid walked into my class and touched another student, I told him to stop and then he did it again on his way back to his seat. I sent the affronting student in the hall and asked the other student to not yell because I was going to take care of it. That student threw his paper and pencil on the ground and pulled his sweatshirt up over his head and hid inside it. 
Two kids started class ready to complete the first task. 

Yes, I have a special group of kids. All the more reason for them not to have math after all their other classes. 

Because the girl who put her head down starts her day cheerful but her mood changes based on her interactions with peers. 
Because when I asked the boy talking in a high pitch voice to stop he said he'd had a hard day but he'd try to stay in control.
Because when I talked to the student in the hall he told me that he was really mad. He didn't want to talk about it. He didn't think he could come into the class without getting in trouble.
Because the student who was sitting in his seat until that other kid tapped his neck? If he'd been having an okay day he would have joked with his friend, or yelled at him and then moved on. But he was out of patience for the day.
Because I don't have quite as much patience as I would have earlier in the day.
Because one of those two kids who started class ready fell asleep repeatedly during class. He apologized at the end of class explaining that he'd had physical training in JROTC. He also shuts down and falls asleep in stressful situations - and class today wasn't exactly calm.
One student had a good day today.

Does every day start like this? Of course not. Usually only a couple of them start the class off already frustrated. But every single one of them has a substantial learning disability in math. Almost all of them have other challenges (that's typical for kids with substantial learning disabilities). Asking me to teach them math (a challenging task to begin with) after they have already faced the challenges of an entire day of navigating ninth grade is unfair.

So next time someone (including me) complains about teaching last block, I'm going to remind them (myself) that it's not really that they're fidgety and ready to get out of there by the end of the day, it's because they've already faced all the challenges of the day. Because school is really hard for a lot of our students for many more reasons than we ever remember. Because we're not our best selves as teachers after a full day either. But the schedule is already set for the year, so we have to deal with what we've got and allow students to take a minute to let the rest of the day go before we jump on them demanding they get started with our class. Maybe our do now activity should be deep breathing. I might just try that on Monday. At the very least it would prepare me to bounce between all the different emotions and experiences of my students.

November 12, 2015

Bar Models in Algebra

At ATMNE a couple weeks ago I attended Kate Marin's session "Bar Modeling: A Model for All" and remembered this sheet (below) I had used in years past which was perfect for our current unit of equations in one variable. I've seen bar modeling before but attending Kate's session reminded me of some important ideas. One is the banter that should be involved in solving any problem but particularly a problem in context. She modeled the back and forth between teacher and students of asking who the problem is about, what the problem is about and drawing a model as they tell her pieces of information. I gave students some of the banter questions in the handout and also did it with the class for the first problem. Kate also told us that the model doesn't replace the equation, the model is an aid in writing the equation. The equation is still part of the goal. However, there are many possible equations, encourage students to share as many as they can to validate everyone's way of seeing the problem (we used 72-48=3B, 3B+48=72, 72=3B+48, B+B+B+48=72...). And finally she reminded us that the final goal isn't a number, it's an answer in context, so the answer should be in a complete sentence. I modified my sheet to make it clear that every problem needs an equation and a sentence. My kids with large handwriting didn't have enough space to work but they could always draw the model and solve the equation on separate paper and record just the equation and sentence on the handout.

You might notice that none of the problems have a question. Last year some students noticed at one point, but this year no one even remarked on it! A couple times I had to encourage students to find all the missing information (the price of the sandwich as well as the fries or the amount spent on books rather than the amount left) but generally students want to fill in everything they can on their model.

I did not require students to draw a model, but I refused to discuss an incorrect equation with them until they had a model. Kids would tell me "I don't know how to do fractions or percents" but when I told them to draw a bar, and then draw 4/5, they could do that without assistance. The percents took a bit more banter, one conversation went like this:
What do you know?
"There's a 20% discount"
What does 20% mean?
"I told you I can't do percents."
What percent do you have if you have everything?
So what does 20% mean?
"20 out of 100. No way! I'm not drawing that!"
I agree, let's not.
"20, 40, 60, 80..." 
No joke, I said nothing leading and he started counting by 20 under his breath! He trailed off so I said yes! that! and he drew his bar model. Who can't do percents? Not this kid!

I'm not going to tell you how long we spent on this because you'll think less of me or my students (who are in 9th grade) or both(!) but suffice it to say, there was a lot of struggle, most of it in the form of learned helplessness. When I stood over them and said "Draw a model. Read me the info. Write it down. Read it again. Label. And again." they did great. Then I'd walk away and come back and find an answer without a sentence. "What does that mean? What does x represent? Read the problem. Read it again. Write down exactly what you just said." Basically my job in this class is to refocus their attention on the task and refuse to do things for them while convincing them I believe they can do it. For other 9th grade classes this might be a breeze. For plenty of middle school classes too I'm sure. But if you have kids who need spaced repetition this isn't too painful of a way to mix in some fractions and percents while doing Algebra. It reinforced rules of solving equations that some of my students are still shaky on: 5x means five x's and we divide by five in 5x=80 because we need to split that 80 up among the 5 boxes. Oh! I'm so glad that finally clicked for you kid, missing half of the introduction to solving equations wasn't helpful but we got you there eventually!

This is what happens when I see a kid working quietly and independently and don't go check on him:

Didn't anyone teach you that math makes sense? There are -2 stickers? Where? There aren't even any gift bags in the equation. I'm sorry that you learned that math is a magical land where you put numbers and operations together to get a mystery number, I'll work on undoing that belief.
(I cut this problem from the sheet above because the bar model isn't super helpful nor is there a particularly interesting equation to write, so I cut it for some extra space to write on the other problems. Forgot to fix the numbering, sorry!)

Interestingly though, this student did expect the problem he wrote to make sense. It looks like he solved it by saying 40 (collars) - 20 (left) = 20 (who knows what unit) but then realized this didn't make sense, so he fixed it. This is the only problem he wrote a sentence for, and the only one where his equation matches the context. I also love all the student problems that don't have questions!

November 9, 2015

Update: Math Practice Standard Portfolios

In August I had an idea that students could build a portfolio of examples of the standards of mathematical practices. Our first quarter ended on Friday so I gave students the second version I drafted in August. I'd planned to do it earlier, but... it's been a busy quarter. So on the last day of the quarter I told students to clean their binders, choose four examples of good work and describe how they exhibit the math practices on the sheet.

Note! If you tell ninth graders to "clean up" their binders they will hear "clean out" and recycle everything. Even if you have clear instructions on the board about what is okay to recycle and what they need to keep. Organize is a much better word. Lesson learned.

I wanted to give students some examples of what to write. For PreCalc I gave them an example of evidence and I asked which practice it could apply to (multiple! Persevering and using tools are the two I was thinking of). Then I set them loose and they did well. Yay for honors juniors and seniors.

For Algebra I gave them some more specific examples. They still struggled. I walked around reading specific quotes to them "I can discover patterns." - "Can you find a paper in your binder where you found a pattern?" or having them find a paper they were proud of and asking them which practice it applies to (by reading them one at a time). This was kind of painful so in my contained class for students with substantial learning disabilities I took it one step further and we did the whole thing as a class. I read the practice, I read the student friendly quotes, I told them to find an example in their binders of that particular thing. I checked with everyone that they filled in the title and evidence, repeat three more times. For this class I just picked four practices that I knew would be easy to find examples based on the work we had done this quarter so they didn't have as many options. Maybe if I provide some support at the end of second quarter they'll be able to use their exemplars from first semester to work more independently second semester? Seems possible!

I ended up with some great reflection from my PreCalc students. Plus it was interesting to look back at all the work we had accomplished in all my classes and see what students chose as examples of their best work! I would definitely recommend trying this activity with all your classes. If I was doing this again I might try asking students to reflect a few times on what they had done in class that day before jumping directly to reflecting over the whole quarter. I meant to do this, but again with the busy quarter. Luckily there's still most of the year left!

The unit circle is a great example of precision! Several students used their unit circle projects for repeated reasoning.

I had students submit the work sample but this student is correct, not all math practices are visible. Ditto for kids who used tools (like the calculator example above).

Perseverance and growth mindset!

This was pne of the few cases where I needed to read the sample work, this student's explanations got more precise and concise as she figured out which information was important to record.

Using the same work sample for multiple practices was fine with me. In fact, I bet they could have found all four examples they needed this quarter in some projects!