August 24, 2014

Goal Setting

My brain is still in summer mode but I've managed a few moments of clarity where I've reflected on my summer experiences and past years to make a plan for this year. I've come up with four goals, two that I am setting for students and two that I am setting for myself.

Student goals:

Develop (or strengthen) a growth mindset

Catch phrase: YET

Message: You can learn everything I ask of you (and more!) if you do the work. You don't need to be told how to do every step, you are capable of thinking.

Monitoring: I am required to give four interim assessments throughout the year as predictors for the state test. Along with each of those I will have students complete a growth mindset survey.
Question: How do I convince students to answer with their true belief rather than what they think I want to hear (it's specifically named a survey not quiz and is ungraded, right now I have a question for name but I'm not attached to including it)
Hope: Taking a growth mindset survey before taking a test that they aren't necessarily prepared for might encourage students to see difficult problems on the test as challenges to look forward to accomplishing.

I have a (draft?) of my survey as a google form and figured out how to get the spreadsheet to score it for me! Make a copy of the form to save to your own drive. I don't think the spreadsheet and form will be linked if you copy both of them so don't do anything with my spreadsheet yet. You'll need some data to see how this works, so take the survey. Then go back to your editable form and select "view responses." Insert a new sheet in this spreadsheet and then copy the first two rows of my sheet 2 into your sheet 2. It should score your responses automatically. Once kids fill out the form their responses will be in the first sheet only. To score them, highlight cells A-Q in row 2 of sheet 2 and use the autofill dragging feature (drag the square in the right corner of selected cells down until you've highlighted as many rows as were filled in sheet 1). If that's totally unclear leave a comment or send me a tweet (@crstn85) and I'll try to help you figure this out. I wish forms were as easy to share as other things!


Catch phrase: You are responsible for your own understanding.

Message: We provide resources to help you learn. It's important that you figure out how you learn (this is especially important since I teach many students with learning disabilities). Use group space and alone time wisely. Find your math soul mate(s) and use them wisely. Take the initiative (to ask a question, to do extra practice, to take a break).

Monitoring: In my Algebra 1 classes I will use a modified form of the stamp charts we used last year. (I'll share my new notebook setup once we've tested it and determined if there are major bugs.) The chart hits on many of the elements of responsibility and will communicate both to the students and the teachers what areas of weakness are. Perhaps in my PreCalc class I will use participation quizzes.

Teacher Goals:

Build in review

After attend Kathryn's Math Maintenance session at TMC14 I realized that I need structure in order to successfully build in review. If it's not a routine then it never happens. I'm taking her Math Maintenance routine and using it for homework. Each night there will be several problems on the topic from that day. In addition, there will be one problem on the review topic of the week and one problem that is sort of bootcamp for an upcoming topic. I love the idea of taking an open response question and spreading it across the week. It's also an easy place to put multiple choice practice (state test, SAT etc.). As an added incentive, I'll count the week's worth of review problems as sufficient to retake a test/quiz on that topic. In discussing this with my new colleague he mentioned that teachers at his previous school put problems that many students had struggled with on a recent assessment on the homework. I love this idea!

Balanced Units

There are some units that include many skills that are easy to separate, those units see many quizzes. There are other units where I've found great tasks, lots of great tasks, and I want to do all of them. Part way through second semester last year I realized that my gradebook was becoming very uneven and I decided that I needed to be planning more medium picture. I have the big picture of which units happen in what order, and I plan the day to day, but I wasn't taking time to look at the unit to see if it was balanced in investigation vs. practice vs. assessment. This year I'm going to decide on skills and tasks before I start each unit. I will make a document with this list to go into the unit folder and then write comments there after completing any lesson that went particularly well or poorly and at the end of the unit. Ideally I will get my colleagues to comment on these documents as well so we can have a comprehensive unit overview to refer to next year. (Idea for the shared doc that people reflect in comes from a PCMI presentation.)

I'd love for the monitoring on my teacher goals to come from you. Ask me sometime to share my progress?

What are your goals for the school year?

August 5, 2014

TMC: Nix the Tricks

I got to give a presentation on Nix the Tricks for the first time at Twitter Math Camp. I was pleased how well attended the session was and feel the need to apologize to all those people for being my "first period class." Thank you for your enthusiasm, patience, understanding and feedback. Second period is going to go much better but I'm hopeful that the guinea pigs still gained something from the experience.

We started the session with groups discussing the following problems:

They didn't know it at the time, but these were all problems that I chose from Math Mistakes with Michael's assistance because we felt the mistakes students made were a consequence of tricks they had learned. Here's a place where I need your help - I would love to have lots of examples of how students solve these problems. Having a single mistake to hold up and say, "I hypothesize this kid made this mistake for this reason." and then conclude, "Therefore no one should use tricks ever." is not good logic. But having a pile of mistakes that correlate to a variety of tricks? That would be more convincing. (I should also read those articles that I saved on research about understanding, as that's even better logic. Time has been at a real premium the past few months...) Feel free to check out the slides which match problem to mistake to trick. (Next time I plan to include more info on how to nix the tricks, not just why tricks are bad.)

We then got into some great conversations about long division, the multiple methods for teaching it and the necessity for teaching the standard algorithm in preparation for polynomial division. I love listening to people talk about areas of math I don't teach and seeing how it relates to what I know. I guess I'm not the only one:


These conversations are the aspect of Nix the Tricks that I've loved the most. People coming together to think deeply about how to teach something students find challenging. Because people don't invent tricks for things kids can do easily; tricks are in place because someone thought the understanding was too hard (for the kids or to teach). I'm wondering how to get that conversation going in a room full of teachers who don't know each other and who teach different things. There were many participants interested in this conversation but not everyone. To differentiate I could have each group pick one of the 8 problems from the beginning and decide how they would teach a lesson around that problem for understanding? But I'll have already talked about the related mistakes and tricks and how to avoid them. Although that sounds ambitious for an hour, perhaps I'll only have skimmed how to avoid them and it would make sense for people to dig deeper...

I leave you with some questions:
1) Can you give one, some or all of the 8 questions above to one, some or all of your kids (at home or in school) and then share their mistakes with me? I'll even give you a form to make it easy to share out. Also, if you know of anyone who already has this type of data I'd love to see it!

2) I don't want a Nix the Tricks presentation to be about me telling people how to teach, but instead to get people thinking and interested in engaging on the site. How can I get teachers to talk to each other in small groups about nixing tricks? Is this the best way to get people interested in having continued conversation on the topic?

August 4, 2014

TMC: PreCalc Session

I was lucky enough to spend my mornings at Twitter Math Camp facilitating the PreCalculus session with Jim Doherty. We had a wonderful crew of teachers who were all eager to jump in and share and work together to create some awesome tasks.

Each day Jim and I planned some sort of opening activity. We folded conics on patty paper, identified creatures using a dichotomous key (and discussed how dichotomous keys apply in PreCalc) and did a rational card sort. All three activities are on the wiki.

We started the discussion by sharing the topics in our courses as everyone's interpretation of PreCalc is different, plus we had a few participants from outside the US who have an entirely different scope and sequence. Once we had a set of topics we considered what essential skills we'd like students to focus on in Algebra 2, and what essential PreCalc skills are necessary for Calculus.

Our Brainstorm

The three highlighted phrases are the three topics we focused on. We split into groups to tackle the tasks. I know my group had some excellent insights and a lot of enthusiasm. It was wonderful to have three days to think about a single topic. I rarely have time for such depth on my own, but to have it with a group of teachers who were equally passionate about students making connections and understanding was amazing. We had the time to try things that didn't work (deriving the equation of an ellipse from the geometric definition is tedious and not a good use of kids time in our cases) and explore ideas that we weren't sure about. We didn't finish what we had hoped to, but we made progress and I think the energy of this conversation will carry me through to continue tinkering with it. Everything we did accomplish is posted on the wiki.

The Wiki

If you have any questions on how people intended to use the materials linked please ask, we want the information to be useful for everyone whether they were present or not. Greg did a nice job of recapping our presentations.

I can't wait to try out the trig and conic tasks (my course doesn't include vectors). I'll try to remember to share my experiences and adaptations, I hope you will too!

August 3, 2014

TMWYK: Productive Struggle

A couple days ago a tweet rolled by on my feed that I wanted to respond to, that is really important to respond to, but was too big for me to begin communicating in tweet sized bits.

But then yesterday I was hanging out with a seventh grader (my soon to be foster placement) and I did some things that supported her productive struggle that connect to the classroom.

We were checking out the shelf of puzzles and games trying to decide what to do when she spotted the Rubiks cube. She'd never seen one before and picked it up. I told her to mix it up and suggested spinning in more than one direction (explicit instruction on how this thing works). She asked if I'd solved it and I confessed that I only knew how to completely solve it by following instructions (acknowledgement that this is a challenging task). This was plenty to pique her interest. Once I saw her eyes switch to focus mode I stepped away, said "I'll let you play" and picked up my yarn. While I watched her puzzle I realized that crocheting is an excellent equivalent to Greg's Ukulele, I could watch her without her feeling the pressure of being watched because I was also doing something. She could talk to me but I didn't feel the need to constantly engage her in conversation because my hands were busy. She did talk while she puzzled; she said "This is hard!" every couple minutes for 15 minutes. Nothing else, and her eyes quickly returned to focus on the puzzle. And this is the hardest part for a teacher - how do you respond? It's tempting to jump in and provide help. But she didn't want help, she was expressing her thought process "My brain is working right now and I'm surprised how much my brain is working while spinning cubes!" I sometimes smiled, sometimes said "Yes." and other times said "Yup! But it looks like you're making progress." (growth mindset is helpful here). After 15 minutes she looked up and said "Wouldn't it be crazy if someone just did [mimed rapid spinning of the parts] and solved it?" To which I responded "There are people who can do that! They've worked really hard and learned how to solve it quickly. Have you ever seen a video of that?" She grabbed her phone and I wondered if seeing someone successfully complete the task would be motivating or frustrating, then I realized there must be "how to" videos online and I didn't want her to ruin the experience by stumbling upon one of those. I told her to search "Rubiks Cube Competition" so that they wouldn't appear in her search. The look of intense focus reappeared as she watched a video. She expressed shock, "15 seconds! It was too fast for me to even see what he did!" She watched a few more, then sat back in awe. I explained that some people could look at the cube, see the positions of all the blocks and then figure out in their head how to solve it, but that they had to practice a lot to get there. This prompted another 15 minutes of playing. At some point I gave her the hint of focusing on just one color to start with (strategy of looking at a simpler case) and she would occasionally share how many blue pieces she had grouped together. After another 15 minutes she put it down and said she was done. I went over and showed her a technique - thinking back I wish I'd asked if she wanted to know before telling (but 30 minutes of restraint was all I could handle!) - I showed her how to move some pieces out of the way to get a block in without messing up the current progress. She was impressed and excited and spent another few minutes trying to replicate the technique before deciding she was really done. And I let her be done.

So how does this apply to my classroom?
I pose a problem and provide a bit of information.
Then I step back and let kids explore.
I'm available so they can ask for help, but not hovering.
I use growth mindset language as much as possible (the focus is the process not the answer).
I value kids ideas and questions.
I provide assistance when they are stuck: if a kid is just struggling (no longer productively) or has quit they need a teacher. The tricky part is deciding exactly what kind of assistance you can provide so the kid can continue working.

The last thing I did, letting her stop, is really hard to do in a classroom. There's a goal for today and a pacing guide and all those outside pressures that make it challenging to let kids proceed at their own pace. One thing my co-teacher and I are planning to do is provide a puzzle table where kids can go if they need a break from the class activity. I also let kids go to the bathroom or get a drink of water whenever they want. Knowing yourself well enough to know when you need to step away and clear your head is an essential skill. In the classroom, I'd ask a kid to re-engage after a short break, but that's also the difference between working on a task carefully chosen for your students and picking up a Rubik's cube!

Wondering what the TMWYK in the title stands for? That would be Talking Math With Your Kids, the awesome idea, blog and book of Christopher Danielson.

July 13, 2014

Parametric Functions

It's summer! I can't wait to share all the awesome things I've been up to at PCMI, but first I'm going back to my final unit in PreCalculus which I never got a chance to share. Last year we did an exploration of polar functions but ran out of time to look into parametrics. This year when I asked the calculus teacher what her preference was she said to focus on parametric instead. I chatted with several people on twitter, someone (@dandersod I believe) showed me how to graph parametrics on Desmos and my colleague* shared her awesome materials with me. Put it all together and I got this:

Kids finish a test and the instructions on the board say:
1. Pick up the assignment papers
2. Sign out an iPad
3. Work silently (other people are testing!)

On the desks where I've spread out the assignment papers I write Introduction above the first page (in dry erase marker because I have dry erase desks) and Choose One above the remaining three pages. Most students finish the introduction (about half an hour) so I assign as homework completing that page and making a first attempt at the other assignment. The following class we discuss the intro, why parametrics exist and then they spend the rest of the period working on the context they chose. I like projects where there are similar options because students can still have conversations (they all have to graph and calculate) but each of them has to do their own work.

Parametric Intro

It was important to begin graphing by hand so students had an understanding of how parametrics work. Some students were concerned that the t value wasn't showing up on the graph and tried to include it in some rather creative ways. I've edited the instructions slightly (should've thought to post the original to ask for feedback on the adjustments...) so hopefully that will be a less prevalent error. Other students picked strange values for the second set of equations, ah radians. Two thoughts: 1) I'm glad I was able to incorporate a trig function since we hadn't used them much since first semester 2) I love graphing utilities - I was able to say, "Okay, you're not really sure what this graph was supposed to look like, that's fine. Graph it on Desmos and see what happens!" My box of helpful hints on how to type things into Desmos wasn't as visible in the first version, many kids skipped those steps. They were also unclear on what to type exactly as written and what to substitute with other information. Turns out (-4+3t, 1+2t) graphs just as well as f(t)=-4+3t, g(t)=1+2t and (f(t), g(t)), but I like the way we found to use Desmos as it shows that each value of t gives an (x,y) coordinate a bit clearer.

Choose One:

These activities are designed to be done on Desmos as well. Some students didn't appreciate when I wouldn't help them with technical issues until they got out the intro sheet and put it side by side with their iPad. But, they were able to correct their own issues that way so it was worth the eye rolling. They also struggled with graphing the obstacle/hoop. In response to those questions I asked them, "Where is the obstacle/hoop?" And continued asking variations on that question until they told me "At x=__" At which point I responded, "So type x=__ on the next line." Then I pointed to the next line of instructions (how to restrict the range) and walked away.

Great things:
These context based questions require students to continuously switch among equations, graph and description. They have to know what t represents and what it means to land as well as solve quadratics and estimate values on a graph.
A student asked me if the equation took gravity into account. What an awesome question! I was proud that I remembered my physics to point out the -16t^2 (this is feet based physics, I remember 9.8 for meters even more clearly).
In my opinion this assignment shows why parametrics are useful - you can know horizontal distance, vertical distance and time using one set of equations. I failed to successfully convince my students that this was amazing. They obediently wrote that down and that the parameter allows them to restrict the function. But neither of these facts were impressive to them. Thoughts on how to convince students that parametrics are useful and different?

*Colleague O'Malley - I've yet to convince her to jump into our awesome online math community but she does recognize its power and occasionally asks me to ask twitter questions on her behalf. She found the equations and contexts in McDougal Littell Algebra 2 and then wrote up projects for TI. I only had to modify a bit so we could use Desmos. She very generously allowed me to share with all of you!