Hello, reader! If you intend to post a link to this blog on Twitter, be aware that for utterly mysterious reasons, Twitter thinks this blog is spam, and will prevent you from linking to it. Here's a workaround: change the .com in the address to .ca. I call it the "Maple Leaf Loophole." And thanks for sharing!

Wednesday, August 31, 2011

Pre School Year Jitters

I don't think I've ever posted at this point in the school year before. To recap, I'm coming up on year seven of this delightful and terrifying profession.

I appreciate that I get the opportunity to totally start over every year. And I don't even have to go to the trouble to press RESET and pay a new quarter.

Today I looked around my classroom and realized it is TOTALLY TRICKED OUT. Smartboard. Document camera. TI Navigator. (Really, Nowak, you have no excuses. None.) Gigantic Darth Vader poster. (Fun Miss Nowak fact: my childhood dog was an all-black ChouChou/shephard mix, with a black tongue. Named Darth Vader. We just called him Darth. He was great.)

I have things to complain about. My Regents classes that are supposed to be a healthy mix of accelerated and not kids are pretty much totally NOT. Out of 54 Geometry kids, I have one 9th grader. ONE. Out of 42 Trig kids, I have four 10th graders. FOUR. I don't know if this is some kind of conspiracy or scheduling fluke or what, but this year is not going to be a walk in the park from the classroom management or instructional perspective. NOT. But they're in my computer scheduling thingie and I can see their names and pictures. And I love them a little already. And I can't bring myself to object although I realize Guidance is probably trying to see how far they can push me. Now, when I can only speculate about them. By reputation. Much like they're looking at my name on their schedule, and making predictions about me, by reputation. She's hard. She's easy. She's a bitch. She's awesome. Just make her laugh. Just be yourself. You're doomed. There is hope.

I posed an inservice class to my department that was basically "us hanging out and working collaboratively on difficult math with maybe food" and they were totally on board. I wrote up a proposal and sent it in. That class is going to be amazing if it gets approved. And maybe if it works and I'm a little bit lucky it will change the way we teach and change the nature of what the children learn.

Since something like 90% of our faculty are new in the last five years, our new-ish principal wants to open discussions of just about everything, including scheduling and grading. We talked about it in small cross-discipline faculty groups this morning, and that experience surprisingly did not leave me in abject despair. I gingerly broached my lunatic-academic-fringe stance on grading and they did not treat me as if I were radioactive.


You're doomed!

There is hope!

Wednesday, August 24, 2011

Tuesday, August 23, 2011

Linear Equations Review Lesson for Algebra 2

So, I just spent two days making one lesson for one class! Yeah, this does not bode well for this year. This pays serious homage to the PCMI problem sets by Bowen Kerins and Darryl Yong, who I already know are way funnier than I will ever be.

The goals for the lesson are the students remembering and being able to... (NB, they should already "know" all this from their previous Algebra 1 and Geometry courses)
  • Explain the meaning of all the terms in slope-intercept form
  • Write equations of horizontal and vertical lines and know how their slopes work
  • Sketch the graph of a line given various kinds of information about the line
  • Interpret point-slope form
  • Write the equation of a line in point-slope form given its slope and a point on it
  • Find the slope of a line given two points on the line, or its graph, or its equation in either form
  • Know how slopes of parallel and perpendicular lines work
Open questions
  • Is this too ambitious and going to scare the bejeezus out of the poor summer-addled adolescent brains?
  • How am I going to assess who knows what as the students are working?
  • What's the best way to organize the kidlets so that they might benefit from some cooperation? I'm thinking groups of three or four with minimal guidance about how they "should" work together.
  • Aside from the lame jokes in the marginal notes, how can I bring more joy into this exercise?
  • Are there better ways to ask any of these questions that make them more tangible?

As always, I welcome your thoughts. 

So...I had the first version here? But because of's helpful versioning, it's no longer available. The latest version is posted here.

Monday, August 15, 2011

New Blogs You Should Read

The authors in this list have one thing in common - I have met them all in person! I know, weird, right? So I feel utterly qualified to endorse them as smart, interesting, nice people. I will try to tell you something about them that is compelling and not readily apparent. Their blogs are relatively new, but all shaping up nicely. Check it out:

Tina (not sure if she wants her last name used) was at PCMI '11. She is SMIZZ-ART, yo, and one of those earnest, wholesome, authentic people who you suspect might not own a television and might spend her weekends hiking and canning seasonal produce. She could also fit in your pocket.

Bill Thill is one of the most thoughtful educators I have ever met. He will push back against all your assumptions and you can count on him to ask the most laser-like, insightful questions. Seriously, your bullshit is not safe within 50 yards of him. Also does a mean Chloe Sevigny impression.

Allison Krasnow, in the first conversation I had with her, gave me a brilliant way to manage homework to make it much more useful as a self-checking tool for the kiddos, but no more work for me. She's warm, genuine, and wears very cool earrings. Her new blog has four posts so far and I want to hug every one of them.

I met Paul Salomon at a School of Math session where we worked on a super-fun problem together. Paul teaches at Saint Ann's School, where they have no grades and the loosest of a math curriculum a.k.a. heaven. He writes a lot about the way math should be taught but he has a bit of authority in this arena, as he gets to teach math the way it should be taught. He's also a demon on Twitter and has been stirring the pot lately on the "how much paper/pencil computation is too much" front.

Chris Luzniak has really just dipped his toe into blogging about teaching math and running his school's speech and debate team, and I am hoping he sticks with it and starts writing some more. But this pattern fits with his persona - he mostly keeps is own counsel when it comes to teaching math and how to do it, but when he does weigh in, it knocks you over, and you wonder just what is going on in there the rest of the time. A real tour de force.

Friday, August 12, 2011

Good Problems: Follow That Diagonal

This is a sweet little problem because it is simple to state and understand. It seems like anybody should be able to make progress investigating it, but it won't be obvious to your smartypants kids.

Draw a 9 by 3 rectangle on a square grid. Draw one diagonal. How many squares does the diagonal pass through? Draw some non-similar rectangles with one diagonal. How many squares does the diagonal pass through? Develop a rule to determine the number of squares a diagonal passes through for any rectangle of any size. 

I think I'm going to keep it in my back pocket for a day when I need to kill half a period. It might be nice for the first day of school if you like that sort of thing. I don't think I've seen it before. It was sent to me by Øistein Gjøvik - he has a post about it that includes access to a Geogebra file. (One benefit of blogging I would have never predicted: a cool Norwegian sends awesome math problems to my inbox.)

I have been on a bit of a Sketchpad bender since we used it at PCMI, so here's a sketch I made.

I am torn about giving guidance about posting solutions in the comments. I have one way to think about it that works, but I'm sure there are more and I really want to hear them. On the other hand, I don't want to spoil anyone's fun. So maybe if you want to work on it, resist looking at comments?

Another thing I'd like to hear about is, do you see this fitting into a curriculum? Or is it just a nice problem that doesn't have a home in a unit of study?

Monday, August 1, 2011

Summer Learning, PCMI Edition: Odds and Ends

This is a series of posts that are reflections from the Park City Mathematics Institute Secondary School Teachers Program.

This is a catch-all for things I want to remember and post that aren't big enough for their own post.

In a 5-minute short, Cal Armstrong presented his use of Livescribe smart pens. I had a little "holy cow" moment during his presentation, because I've long dreamed of kids' recording their problem-solving process, but there's only one smartboard in the room, and writing with a mouse is hard. Enter the Livescribe pen which records both your writing as you write, and audio along with it. And they are only like $100 a pop. I could ask kids to record a livescribe of them solving a problem as their reassessment, or record a tutoring session of them teaching it to someone else. We could put them on blackboard and build up a little library of these, or upload them to voicethread for feedback.

Google Forms for Recording Small-Group Discussion
I am pretty good at incorporating small-group or partner discussion, but I don't often have an efficient way for groups to share their thinking. One technique I noticed frequently deployed at PCMI was to give groups a link to a google form, so that each group could send in a summary of their discussion or response to a prompt. We aren't a 1:1 school, but it would be sufficient for each group to have one laptop for this purpose, and I'm pretty sure I could secure 5-6 laptops to keep in my room. Then again, I am supposed to have a TI-navigator system next year, so maybe I could just use it for this purpose.

Other Kinds of Tasks
Do you ever get stuck in a problem-writing rut? I do. Throughout, I was keeping track of all the tasks I saw that were something other than "find the missing value:"
  • write an equivalent expression
  • give an example
  • show that two expressions are equivalent
  • interpret expressions/equations in writing
  • interpret a graph in writing
Metacognition: See How I Think
We spent a few days talking about what is metacognition, and ways for students to "do" metacognition. We participated in an exercise that I think could be adapted for students to use. In a group of three, students take on three roles: problem solver, listener, notetaker. The listener is NOT HELPING solve the problem, just asking the problem-solver to clarify their process and state it out loud. Meanwhile, the notetaker is writing down any evidence of metacognition or "thinking about thinking" that she hears. I think this could be very beneficial in helping students see how the same thought processes (making use of structure, considering extreme cases, organizing data, etc) cut across mathematical content, but I wonder at designing it in such a way that they can see the point. I need to spend some more time thinking about this.

The Vampire Animations
I worked on a lesson as part of our working group, and I don't think I'm supposed to disclose all the inner-workings of the lesson because it may be reviewed for publication as part of a larger project, but I do want to share this super-fun simulation we made. If you can use it, steal away.

Here is a "question" video of an infection spreading up to 64 victims:

And here is an "answer" video up to 512 victims:

Arts and Crafts
Finally, what is camp without crafts?

Summer Learning, PCMI Edition: Formative Assessment

This is a series of posts that are reflections from the Park City Mathematics Institute Secondary School Teachers Program.

Our middle session every day was called Reflecting on Practice, and it was basically a mini ed-school class. The focus this year was on formative assessment or assessment for learning. These types of classes are not usually my favorite (make a fake assignment! watch a video of someone teaching! talk about your feelings!), but in this case they were exceptionally well planned and executed so I didn't have much time to feel sorry for myself.

Biggest takeaway - there needs to be deliberate feedback, not attached to a numerical grade, built in to classes. Because when there's a number there, kids don't pay attention to anything else. (On the flip side, in the absence of a grade you run into kids not taking the work seriously, so giving feedback on their marginal efforts feels like a waste of time.) At least some of the time, the attitude toward assessment should be less "judgment day" than "a conversation about learning and understanding." I was influenced especially by two articles we read: Classroom Assessment: Minute by Minute, Day by Day and Working Inside the Black Box: Assessment for Learning in the Classroom (which does not appear to be available online.)

These simple ideas lead me to rethink the whole process for "level 1" quizzes - the kids' first stab at a concept on an SBG quiz. I spent way too much time re-designing what a quiz paper should look like:

That's super-helpful for you, right? Sorry. After I try this in class I'll have more to say about it with a nicely-typed up version. But the idea is, there's half a page for the student to do his work, and predict his score. The bottom half of the page is set up for structured teacher, self, and peer feedback. I want the message for level 1 to be "I want to help you figure out what you still don't understand" instead of "Fear my red pen!"

I asked the cherubs to weigh in on Facebook and got mixed responses.

So anyway, the idea for a process will look like this for Level 1 questions:
  • Students take the quiz, and predict a score.
  • I collect the quizzes and write feedback in sentence form, like "right idea but computational errors" or "a more careful and accurate diagram would be helpful"
  • Next day, students give feedback to each other. One idea, so that they are working to understand and not to just get the right thing on the paper without understanding, is to not let them use pens or pencils, but communicate with mini-whiteboards. While they are doing this, I can be assessing/rewarding/publicizing helpful dialog that I hear.
  • Then, students have an opportunity to re-work the problem, or possibly a new but similar problem.
  • Then...what, grade the quality of their feedback to each other? Or never grade this part of the process? I am thinking that if I want the focus to be on the learning and not a numerical grade, I can't give a grade to this part ever.
Obviously there are questions here that will take time to sort out. But this seems like a step in the right direction.