Monthly Archives: June 2012

Take-Aways From Kansas City

Last week, I had the opportunity to participate in the Advanced Placement Statistics reading in Kansas City  Over 600 educators convened to grade over 900,000 questions.  Heading into the week, I wasn’t quite sure what I was getting myself into, but the Facebook groups dedicated to both readers and us newbies (“acorns”) were extremely helpful and generated buzz for the week.  Also, the e-mails from Chief Reader Alan Rossman were helpful in getting us new folk acclimated.  So, what is a week as an AP reader like?

  • You’ll do a LOT of grading.  I spent 4 days straight grading the same hypothesis test over and over.  On other days, I graded the investiagtional task question.  By my count, I graded a little short of 2,000 papers.
  • The training and supports are outstanding.  My partner, Cora, was fantasitc and my table partners kept me from going bonkers by Saturday.
  • The organization requiredto move 150,000 test booklets efficiently around a conventional hall leaves me speechless.

But more than anything else, I meet dozens of people who share my same strange excitement over teaching Statistics.  To one colleague, I described the experience as hanging out with the “Stats all-star team”.  Everywhere you turned, there was an educator whose materials and ideas you had used and shared, and the opportunity to touch base with so many of them was fantastic.  (aside: I think an opening exercise for all stats classes should be to utilize an activity authored by Floyd Bullard.  Then, after the activity, have your students describe what they believe Floyd looks like.  Then, sit back as you show them what Floyd really looks like.)

My take-away from the week applies not only to Stats, but to all teachers I coach and classes I encounter.  Specifically, how can we utilize vetted performance tasks (like AP Stats questions) in classrooms as formative assessments?  Jason Molesky has done a fantastic job with this through his “Frappys” on the iconic stats website Stats Monkey.  The group of teachers I hung out with during the week are interested in using these problems and sharing papers and ideas online.  But why not do this in more classes?  What sort of problems are we giving in Geometry and Algebra which require students to reflect upon multiple standards?  How often do we ask students to peer-assess their work, and train them to look at external rubrics?

The best stats teachers I know utilize past free-response problems throughout the course, and use student work to forward instruction.  Wouldn’t it be great to have these resources for non-AP courses?  My dream here would be to work with a group of teachers to build a bank of tasks for Algebra I, Geometry and Algebra II, with rubrics to share.  I know many states have “free response” questions already, and we work with students in my home district to prepare for those.  But many of them are so clear-cut, so watered down in their expectation, that they are un-usuable as instructional tools.  Seeing so many alternate and valid approaches to problems at last week’s reading speaks to the quality of the questions being asked.  If you have any thoughts on written performance tasks, or want to work together on writing, shoot me a message here. 

Thanks to all of my new friends from the reading for making the grade-fest an event I will look forward to next year, and to Brian, Andy, John, Nick and Dave for the great conversations!

 
Royals game

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Conic Sections Project – Part Deux

The conics project has produced the most hits of any post on the mathcoachblog to date (including over 25 from the Netherlands….I can’t explain it, but it’s pretty cool).  A few comments and e-mails to me requested a rubric for the project.  To be honest, I don’t have an uber-detailed rubric for this project beyond the file I share below…

http://dl.dropbox.com/u/68005919/Conic%20Sectins%20Drawing%20Rubric.doc

Kevin and I discussed some ideas and modifications to grading for this project, and I give you all these suggestions:

First, as a mentioned before, the peer grade can be achieved by giving all students 5 sticky stars. Have them discuss guidelines for choosing the best works beforehand, then allot their stars and stick them to their favorites. Also, you will notice that I am a bit of a stickler for having students leave their names off their works. This is intended to eliminate some bias from having students select their buddies. Also, if possible, have different sections of students grade other sections of student works.

Next, I would alter the requirement of having students provide all equations they used. Realistically, I never looked at all of the equations anyway. An interesting compromise would be to have students select 3 equations, and provide an explanation for the transformations and stretches needed, and how they play into the overall theme. This would be an improvement over a laundry list.

Channeling Creativity in Algebra 2

UPDATE – I recently posted more info about this project, with a rubric and more examples, at this post.

One of my favorite math projects takes place during our unit on conic sections in Algebra II.  In the project, students are challenged to manipulate equations of conics and graph them using software to make pictures.  I started with this project 12 years ago when a colleague, who has since retired, introduced me to his ideas.  Back then, we used a DOS program which could only graph in black, cyan and magenta.  We were happy if we saw a tree made from a hyperbola and a parabola leaf line.

The project grew new wings with a program called Math Toolkit, which allowed for finer graphing and the ability to save work.  Later, we started using Print Screen to grab the graphs and move them into MS Paint.  The projects grew more intricate, and many kids took off with their creativity.

This year, the Desmos online calculator brought the project to a new level.  Students this year could work on their equations at home, save work, and work with their teacher during time allotted in class.  Thanks to Kevin for working with his class to share their creations.

First up is Kristin.  Her project moves from Desmos to Paint.  Then un-needed pieces are removed, and the final product emerges.

Conic 1

Conic 2

Conic 3

Next up is Matt.  Here are his graphs after the axes and grid were removed….

Conic 4

Any ideas what the finished product will be?

Did you guess yet?

OK, so you just want to see it…ok….

Conic 5

What I love most about this project is when students discover how the conics behave, and experiment with them without fear.  In the next example, Connor wanted to tilt his ellipses and researched on his own how to make that work using trig functions (did I mention that these kids haven’t had trig yet?).

Connor1

Connor 2

Connor 3

In some years, I have had students peer-assess their work by creating an art gallery of their work.  Giving each student 5 star stickers, I had students select their favorites.  Contact me if you would like any of the instructions or rubrics I have used for this project in the past.  Thanks again to Kevin and his Algebra II class!