Scenes From Summer, and What's Next

For these past eight weeks, I have thought very little about the teaching and learning of math. I spent about eight hours getting settled into my new classroom (still a ton left to do) and I have kept up with google reader (leave that thing alone for a week and it's out of control, am I right?). That is all.

But I have been doing some very important things. Like working on my flip-flop tan.

And a  family vacation in Colorado. We un-plugged for a week of hiking and relaxing. It could not have been more perfect!

And a six-day getaway, just me and the Hubs. This Kansas girl loves me some California.

As I prep for another year, I will be drawing from this inspiration:

1.  This quote from Rational Expressions' letter to a new(er) teacher, advising new teachers to toss a large part of their curriculum each year:

"Put it like this: you get smarter as you keep on at this job. If you use old materials, you're using the stuff that the stupider version of you made."

I like to think that I am always trying something new, but I will admit that way too much of my curriculum dates pre-2009 (the year that I became a parent and spare time became a distant memory). I started reading/blogging in 2010, so I am way smarter now. :) One of my goals this year is to toss lessons/units that are "just okay" to see what the smarter version of myself will do instead.

2.  Common Core conference.  I will be attending a 3-day conference with a focus on planning for implementation. I am hoping for some inspiration and direction. And fun times with my colleagues are certain to get me in the back-to-school spirit.

3.  Made4Math. This is right down my alley! I heart crafts. I have a few things up my sleeve that I hope to be rolling out in the next few weeks.

4.  Twitter Math Camp. I am sad that I won't be attending. Maybe next time. I hope there is a next time! For this year, I will be jealously waiting to hear all about it. So let's hear it, bloggers!

Happy Endings (Mostly)

Last day of school. The end is always bittersweet. I hate good-byes and generally dislike the ending of things, but I am looking forward to time at home with my 2-year-old and resting up for a fresh start next year. I have a list of things to do over the summer, both work and fun. I love how this year is ending. Mostly.

This activity went better than I hoped:  Try to write an equivalent for the numbers 1-100 using four 4's and any mathematical procedure. Autograph your solution. It was nice to see students work on this when they were otherwise ready to be done with thinking. I really loved seeing factorials and other creative solutions as they showed up.

I always get especially attached to my seniors in physics and calculus. A group of students in my physics class did a skit as part of their senior class variety show. There was Humpty Dumpty falling off of a wall, and calculations for force and final velocity. Oh, and a senior boy dressed as me, singing to the class and offering to have everyone over for meatloaf. I am not sure that the crowd understood our inside jokes, but it warmed my heart. Here they are, don't they look like a fun group?

There was a class t-shirt. "Life doesn't come with an answer book". I love to say that. It used to be true, before Google. Now I have to insert the word "always".

My algebra students worked pretty diligently on their final projects. Speaking of final projects, today I am more in love with blogging than ever. I posted about this project just a few days ago, and received some wonderful comments. Thanks to others being kind enough to read and thoughtful enough to comment, I now know how to make the project better for next time. Thank you, blogosphere! I hope that I can return the favor.

And, one not-so-happy ending . . . One of my favorite colleagues has officially announced that she is leaving. I will move to her room next year, trading my cinderblock walls for a lovely corner window. The view is street side parking and a railroad track, but I am looking forward to seeing sunshine and the first snowflakes falling next winter . . .

. . . Still, I would be much happier if she was staying! We have been through a lot together these last seven years:  Tornado recovery, a trailer classroom, celebrity sightings, and learning (the hard way) that the top shelf in the closet won’t hold a full set of textbooks. Together we conquered our state's math assessment. We shared the victory of watching our most struggling students succeed. Working with her made me a better teacher. I am going to miss you, friend in the middle. We all will.

PIeces (Final) Project

Students at our school can opt out of second semester final exams by doing well on state assessments. Most of my students fall into that category. Given the choice to take finals or get out of school two days early, you can imagine what most high school students will choose. With no exams, trying to convince students to review at the end of the year is next to impossible.

A few years ago, I switched to a final project instead:  Create a picture using parent functions (and/or conics) and their transformations along with restricted domains or ranges. I like how it encompasses so many things we have learned this year. Review, without looking at all like a painful study guide.

Leading up to this project, I do a week-long mini-unit reviewing all the different types of graphs we've studied this year -- linear, absolute value, quadratic, exponential, rational, polynomial, and conics. We work on their transformations, and then add in restricted domains and ranges. We sketch simple piecewise functions using known functions, and then more complex ones using a graphing calculator.

At the end of the unit, they do this outline of Texas using a graphing calculator.  (I wish I knew where this came from. Someone gave it to me and it became the inspiration for this project).

Now students are primed to make their own picture.

Here are the project requirements, rubric, and final product sheet.

Some questions/discussions that come naturally out of this activity:  How do I make the vertex of x^2 hit the point (5, 2)? How do I make x^2 skinnier? How to I find where this straight line intersects this parabola?  How do I restrict this domain/range to get half of the ellipse?  And (yikes!) how do I write the equation for this straight line?

Here are a few student samples from a previous year. I loved the penguin!

I've received a few projects already this year that are okay. Students are looking for ways to keep it as simple as possible and still meet all the requirements. I am not disappointed, really. They are doing exactly what I have asked them to do. For next time, I think I will edit the project a bit to require that more variety in graph selection be used.

Over all, it isn't a bad way to end the year. I like that students are still working on math up to the last day. They are being creative and I hear mathy conversations taking place. And I am not pulling my hair out trying to convince anybody to review for an exam they aren't going to take. 

Zero Effort Videos (not just for flipping)

I've gone back and forth on my thoughts about flipping the class, but that is not the point of this post. Flipped classroom aside, I think there are some really good reasons to record direct instruction:

1. For students who are absent.
2. For students to review.
3. To store up a bank of videos for future use.

So, I've spent this entire year recording all of my direct instruction . . . LIVE*.

Live videos are not perfect. They contain mistakes, interruptions, announcements over the intercom, and (my personal favorite) fire alarms (followed by my voice, "Nooooooo!", it happened). I have definitely had to let go of my perfectionist tendencies to put them out there.

Obviously, live videos are not useful for flipping. Unless, like me, you teach the same courses every year and are willing to delay the flip for a year while you make recordings. Then BAM, there you go.

On the up side, live videos have some great benefits. I can pause and check for understanding and then address misconceptions as part of the video. Student questions and answers naturally become part of the video as well. After class, I can make them available to absent students with a couple of clicks. I can also save what I have written as a pdf and make that available, too.

I am mostly happy with the results (minus the noticeable raw-ness of the videos). The process could not be easier. Not counting the practice needed to become proficient with the equipment I am using, I have spent zero extra time creating videos. I just hit the record button whenever I say something in front of the class.

I wanted to know how many of my students were using the videos or pdfs, so I gave a quick survey:

28% said they had never used either, indicating that they didn't have internet access (computers are readily available at school, so not exactly a good excuse), or that they simply preferred getting help from me or another student in class.

The remaining 72% had used one or the other or both. Many said that they appreciated these resources and found them to be very helpful. The majority sited one or the other as the primary method they used to catch up after being absent from class.

I am encouraged by these numbers, and I plan to continue to live record in the future. Technology has provided me with a low effort, high result means for communicating with my students. I am still on the fence about the flip.

*The mechanics:  To create my live videos I use a smart slate, a blue snowball microphone, a mac mini, and projector. The result is a Khan Academy-ish screen cast where you hear the teacher talking and watch the writing magically appear. I am sure there are other means to accomplish the same thing. In fact, these tools are not necessarily my first choice. They are standard (except for the microphone) in all the classrooms at my school, so I am just using what is available. The smart slate takes a lot of practice. I have also used an interwrite pad and felt it was a bit more user-friendly.

Confession Time

I've had a lot of positive response to the "spoon pencil" strategy I've been using this year. (Thanks, Sam!)

I waited 8 weeks into the year before posting, just to make sure it was working well. This was the result at the end of the first quarter, and I couldn't wait to share the genius of it all.

But, I've been feeling a little guilty.  I think I need to confess the truth of my "genius" plan.

It doesn't work.

At the end of the second quarter, I replaced about half of the spoons and doubled the tape.

And here it is now, with four weeks left in the year:

On the positive side, my knife erasers fared much better. Five of the eight originals remain.

And the green fork pens?  Seven out of eight originals are still intact.

Still, I have enjoyed an entire year of not hearing "Mrs. Gruen, I forgot a pencil", or "Mrs. Gruen, do you have a BIG eraser?", or similar distress calls.

For next year, I have decided to step up my game with indestructible spoons:

If this doesn't work, I am attaching pencils to bricks.

I am not even kidding.

Visualizing Volumes

My calculus class is working on volumes of revolution. I have found that success with this particular topic is related to a student's ability to visualize in three dimensions. I always have a few who struggle with that.

Fast forward to last week. I was shopping, and I found these on clearance:

For decorative use only. I am such a rule-breaker.

I traced out the shape of the region I wanted to rotate.

Cut it out. Open it up. Voila!

You have to hold it a certain way or it will sort of fall apart, but I thought it was a nice visual and tactile representation of a volume of rotation.

This one fell apart when I opened it up. I learned that you have to make sure some of the original glue is left intact when you cut out your shape. I tried running a bead of glue along one side, but then it wouldn't open very well.

Another drawback is that the semi-circular shape of the original pieces is somewhat limiting. I am sure these must be made in other shapes? I am going to raid a party store before we get to this topic again next year.

Still, my students were really intrigued to see what would happen as we cut and unfolded each one.

This one turned out really nice:

Happy rotating!

April Fools!

This morning before school, two of the sweetest girls walk into my classroom to tell me they saw two boys (one of whom is my nephew) messing with my car. I knew there was some sort of late April Fools joke in the works, so I took the bait and hustled out to the parking lot to catch them in the act. Nothing. My car looks fine, so I return to my classroom to find that my nice comfy chair has been replaced with a bucket.

Well played, nephew and his friend. Well played.

The use of two innocent girls as accomplices was particularly brilliant.

As soon as I think of a very good prank, I am totally going to get even.