Thursday, April 24, 2014

AP Calc Review (Part 2)

Well, I took all of the accumulated Challenge questions that they wrote and printed them off of PadletThis is a built in feature of Padlet, so it is very easy to do.  I made 15 copies and then had students select groups (of 2 or 3).  Each group had a set (or 2) of the questions.  They worked on the whiteboards or their own notebook paper and proceeded to solve them.  This is where the fun really got going in the classroom as I heard students say "these are hard!" or "so-and-so, why did you have to write this problem?".  Wasn't that the point.  The directions said the questions had to be challenging!!

There were a few mistakes with their answer keys that we found along the way, but then I would hear "that would have been a great choice for a multiple choice wrong answer".  AHA!!!  They are getting it!  Sometimes the author would work the problem and find a mistake before the class did and then we would make corrections to typos they had made.  I enjoyed that the pressure of their peers seeing their work made them really want to take ownership and put their best work out there!  One of the students had to prove that her answer was, in fact, correct and when the students saw that they had not manipulated the answer far enough, there was a big groan.  Several of them were sure they had it correct and when we ALL worked it out on the board, they saw several versions of the correct answer, dependent upon where they stopped in their mathematical manipulations.  It was a thing of beauty....everyone was correct!!  At this level, it has taken all year to teach them that there are several versions of the correct answer, not just one answer (as they are typically taught in so many math classes).  I LOVE THAT!  I have frequently told them that they are master manipulators at this level.

Next year I plan to use this at the end of both semesters for final exam review.  I plan to incorporate this into my other classes as well.  The students love working on each other's problems and having made each one an expert in one section helped each student shine when they got to explain their topic.  So glad I thought of this idea.  Even happier that my friend @KathleenDiver told me about Padlet.

Wednesday, April 23, 2014

AP Calc Review (part 1)

Previous set up:  I had the tech support staff load MathType on the lab computers so students would be able to use it.  I made a list of all the sections we covered in AP Calc this year and created slips with a different section number on them.  In addition, I typed a master student list so they would be able to write down their assigned section and I could keep track of each students assignment.  I wrote the directions for the assignment so students would have a hard copy (I would be happy to send them to you).

The requirements: were that they had to post 3 problems for their topic/section.  One question had to be posted to the "Easy" page, one to the "Medium" page and one to the "Challenge" page.  One of their 3 questions had to be multiple choice with good distractors.  In addition, they were turning in solutions to their 3 problems on paper and solutions for their distractors being appropriate (so 3 ways to get the wrong answers provided and 1 way to get the correct answer).

Days 1 and 2:  I took the students to the computer lab.  The first day, I had to teach them how to create a formula using MathType inside a Word document and then how to snip it and save it so they could retrieve it.  We practiced this together.  Then I showed them how to access Padlet (I had created links on the school web page for my class, so they only had to open the link).  Padlet is so incredibly easy to use!  It did not take much explanation after that.  The beauty of this was both their notes and homework pages are online for them to access, so they had the ability to check what their topic was while on the computer and then start forming their questions.  The few questions that I had to answer were how to use MathType to get particular functions (exponents, infinity symbol, etc.).  I didn't expect they would finish the first day, thus the reason for the second.  Although unintended, there was a week between computer lab days (this had been planned to be consecutive days), but when they went back the 2nd day, they had definitely had enough time to construct the rest of their problems and multiple choices. Almost everyone finished (the couple that didn't came in before or after school or at lunch to do so).

All I had to do was check to see that every student had posted their 3 questions (one multiple choice) and arrange the topics in order by section number (for ease of student use).  The second day in the lab, I simply monitored completion and started arranging the questions in order.  Students got right to work. Often if they got stuck, they would ask each other for help/ideas.

Days 3 and 4:  At the conclusion of Day 2, students were assigned the Easy page for homework. They had to work out everyone's question.  Since they were posted by section number, it made it easy for students to go back and review that section if they got stuck/forgot how to do the problem.  The next day we went over them in class (one problem at a time).  I put them up on the board (using the LCD) and asked each "expert" for the correct answer to their problem.  Sometimes the class was in complete agreement and we moved on, sometimes they needed to know how to arrive at that solution.  At this point, I took the "expert's" work and put it under the document camera to display.  The expert was then able to explain their solution.  We found a few cases of the expert making their own mistake, but we didn't dwell on that, and I pointed out that I NEVER get 100's on the tests that I make and always make sure I check 5 smart students papers before I grade the entire set.  This reminds the students that its okay to make mistakes (we all do).

Here's what I learned (and why I will use it again):  The student's were driven to make good questions.  They enjoyed being the expert and EVERY student got to be an expert on each of the Padlet pages, so each student "got a turn".  They enjoyed working each other's questions.  I heard students say "this was actually fun".  It made it a great way to review every section by using the power of collaboration effectively.  Best part: I believe that this really enlightened the students about "distractors" and how to look for them as they seek the correct answer in the multiple choice questions.  They were able to spot some of the distractors right away and tell me what was wrong with that choice.  I couldn't have planned that part any better!!  Since they all had to create one multiple choice and their own distractors, they all experienced this.

Next up:  the Challenge questions!  I have a different plan for these.  Can't wait to see how they impact the students thinking.

Thursday, April 10, 2014

Fear of Failure

A former student recommended that I read about a topic she had studied in one of her teacher preparation classes.  The topic: Quality of Failure.  I was immediately intrigued and google searched it only to find a couple of fascinating articles Teaching to Fail and The Freedom to Fail. I realize that students have great respect for when I wrestle with a question that they pose or if I find that the math is "not working out in class" and have to pause the class to figure it out.  Some of them even enjoy wrestling with me to arrive at a solution or conclusion about "the magic" that makes the math work.  I love these moments.

The challenge is getting more students on board.  They have grown up in a microwave world and want the instant solutions without a lot of effort or thought, so some of them frequently just sit and wait until "the smarter people" come up with the solution or the rule for the pattern.  I often have to "Ssshhhh" students and remind them not to "spoiler alert" when they want to blurt out the pattern they have spotted.  I remind students to wait for others to process and develop their own hypothesis before sharing "the trick".  What I hope to accomplish next year (and perhaps a little with the few remaining days this year) is to encourage students that failure is how we learn.  I am always telling my students that they don't learn from the problems that they get right, only the wrong ones IF they work them again to get to the correct solution.  I wish I had a dime for the number of times I have seen a student look at only the score on their test and toss it back into the graded pile.  Despite the fact that I encourage them to come in for extra help so they can rework the problems, they don't.  It is disappointing.  I suspect my quality of failure in this respect is still low because I haven't figured out an effective way to get them to rework missed problems or focus on those failures so that they can learn from them.

I hope to incorporate some new strategies next year that will require students to stop and reflect on the problems that they get wrong, and write me an explanation as to why they missed it and then write a new question similar to the missed problem with a solution as well.

I want them to celebrate their failures because it is through those that growth and learning both happen!  Looking forward to failure!!