Monday, June 6, 2011

Fantastic Peter Nimble

I’ve been looking forward to Peter Nimble since the moment I came across Jonathan Auxier’s website, The Scop.   The site is simple, the sketches are fun and that might be the best “about me’ section I’ve ever come across.   So to hear Jonathan was publishing his first middle-grade this fall, literally made me giddy.  Then I found that this particular middle grade novel is set in a quazi-Victorian age, starring a blind-orphan-thief.

Here’s what I need: books that I can look a kid in the eye and say, “Trust me, you’re going to love this.”  So that while they’re developing their reading (and thinking) strategies, they’ll fall in love with literature and see the relevancy for the skills.   I’m looking for books that create “the circulation effect” (I pass off a book and by the time it’s returned two months later, I’ve seen it on 15 different desks).   I’m quite confident that Peter Nimble and his Fantastic Eyes will be one of those books. 

First and foremost, Peter Nimble has an absolutely mesmerizing flow to it.   It’s got all the fun of disenfranchised Dickens mixed with Phantom Tollbooth absurdity.  Jonathan Auxier seamlessly blends these two very diverse attributes, strapping his readers to his back as he takes them along for a breakneck ride through complete obscurity.  One minute you’re meeting his traveling companion, an enchanted horse-cat-knight; the next minute you’re giggling over a reference to 18th century burgling proverb.  And that’s what makes this novel so much fun.

Auxier immerses you in this wonderfully substantial tale while relentlessly sprinkling in bits of humor at every turn.  To really buy into fantasy, there needs to be in a believable world.  In a lot of the high-fantasy for middle-graders that I’ve read, this tends to get a bit descriptive.  Not that it’s a bad thing, most of the time it’s completely essential to the story.  But for inexperienced readers who haven’t built the stamina to stick it out, such description can slow the story down to abandonment.  Auxier does much of his world-building through an astute sense for humor.  Thieving terminology and old sayings build Peter’s culture.   This enables the author to spend less time creating the world and more time pushing Peter through it.  And the reader can pick the rest up along the way.

By omitting the overly descriptive elements of fantasy, we’re left with a story that moves at a truly exceptional pace.  Take my knees for example.  I had an hour to kill before heading home for dinner.  I made my way over to the beach with Peter Nimble in tow.  Before I knew it three hours had passed, my legs were cooked, and I was late for family dinner. 


The chapter structure and pace just work sensationally.   Some end in total cliffhangers, others are satisfying bookends; all without ever feeling predictable or formulaic.   Sometimes a section was wrapped up nicely when I assumed it would stretch out, while other times I thought I knew how a chapter would end only to be left with a dropped jaw and a yearning to find out where we’re going next.  And all of this happens from the moment we set foot into Peter’s tale. 

Right from the introduction it’s clear that we’re in the hands of a storyteller.  It doesn’t feel like the characters or the narrator know something that you don’t.  The information we learn in the beginning later becomes pertinent but it never comes off overly mysterious.   There’s nothing wrong with employing those strategies at a story’s onset but doing so risks losing that audience that isn’t quite ready to pick out the questions they’ll need to keep in their heads for a few hundred pages.  



Another major component of Peter Nimble’s flow is the manner in which we meet new characters and explore new settings.  The story’s landscapes constantly shift without inundating the reader with detail.  We grow accustomed to Peter’s new surroundings with him.  Seeing as how Peter is blind, both he and the reader are exposed to the setting by moving through it.    Characters too, flow in and out without coming off hollow or hurried. 

But the essential thread that ties this novel together is Jonathan Auxier’s outstanding narration.  I’m always telling my students, “You can’t talk to your reader unless you really mean it.”  And when they ask me what that means, I tell them, “I don’t know.  But go read Adam Gidwitz or Lemony Snicket.” 

Bad narration is intolerable and insulting to the reader, which makes discovering quality narrators that much more satiating.  Auxier guides us through Peter’s story without ever tipping his hand or pandering to his readers, unless he’s doing so intentionally, in which case, it’s pretty damn funny.  He’s constantly dropping bits of humor that range from explicit to embedded to ludicrously sarcastic.  And we haven’t even touched the most impressive part…

Our main character is blind.  The disability drives the story without ever becoming preachy or asking the reader for sympathy.  It’s refreshing to have a main character whose handicap is the source of his success (without him having to learn some character trait by coming to terms with the disability).  In fact, frequently, the disability becomes the butt of many a pun.  Good.  We certainly want to teach our kids to treat everybody, able or handicapped, with respect.  It’s nice to see Peter isn’t discluded from good-natured humor at his expense, like so often is the case when disabilities appear in children’s literature.

Peter Nimble and his Fantastic Eyes is sure to be hit with middle grade boys and girls alike.  At times it’s utterly absurd; others, rich and poignant, but it always remains sensationally obscure.  And if nothing else, it’s that current of obscurity running throughout the novel that will charge its readers and keep them chuckling until the last page.

It’s my job to get emerging readers the skills they need to be proficient with text.  But what good is a skill set if you can’t find a relevancy in it?  I say I have just as much a responsibility to help my readers find both.  Many times, it requires some salesmanship.  And, a salesman is only as good as his product.  It’s the caliber of story that is simply… Fantastic.  


Okay, I can't end without mentioning how every bit of this book drips with style.  The cover is gorgeous, the chapter titles are some of the best I've ever heard, and as I was finishing it up on the way to our field trip today a student leaned in to check out the illustration at the top of the chapter.  That attention to detail clearly shows the amount of respect both the author and the publisher have for their readers.      

Sunday, April 17, 2011

Video Station: How to Clone Yourself


Perspective and Mood from mlewis@cohassetk12.org on Vimeo.

Thanks to Salman Kahn for the excellent inspiration he shared with the world via TED Talks. Of course it makes sense to video record lessons. I was enamored with the idea that students watch lessons at home to provide for workshop time in class with teachers.

The Classroom 



The writing block's split into two sessions.  Groups are meeting with me two of the days to plan out some non-fiction writing.  On the first, they meet with me to go over the goals, then they have a follow-up group planning session.   The next day, they're group goal is an extension of the previous day's work and in the second block, I'm able to follow up, check in, extend, or answer questions.

While I'm meeting with those groups, I'm simultaneously teaching an extension lesson to 5 students on the back computers.  In the second block, those students post the activity to our writing wiki.  Another group worked on a reflection discussing the importance of a writer's notebook, to be video taped in the following block.  The final group watched a TED Talk, audio recorded a discussion about it before writing a reflection in their daybook.



The Other Shoe


The kids loved it.  They seemed to enjoy the different stations, were able to work independently, enabling me to focus on the small groups.  Their products were high quality and the kids stayed focused for the majority of the week.

About mid-week, as everybody worked away, over the loud speaker in the school, "If anybody is streaming video in the building, could you please turn them off, it's interfering with Galileo Testing." (Galileo tests are standardized tests to predict how our students will perform on the standardized tests).

One of the girls looked at me and asked if we should go apologize.  My response, "We will happily honor their request but do you feel we have anything to apologize for?"

When I went to check on the group filming their Writer's Notebook tour, the camera was put away in its case but they were still sharing... They thought the call about streaming video applied to their recording as well.

We've got some work to do here.  I just hope there are other classrooms that can use it!



Monday, February 28, 2011

A Book-Banning Discussion


I walk into the staff meeting after a particularly stressful day to see a teacher with a copy of a Common Sense book review.  To give you some history, the Common Sense organization has been criticized in the past for some overly conservative views on media.  Just upon seeing this review made my blood pressure sky-rocket.  I automatically assumed that this teacher was gearing up for a good-ole-fashioned book banning.  And, working in a district that loves to ban, (birthdays, food, the internet) I took this symbolic review personally. 

I then made some snap comments that I later regretted, as I realized the motivations of this teacher were solely based on assumption.  The next day, I first apologized for leaving the conversation at, “It’s a good thing it’s not up to you to censor.” 

Now, after discussing the matter more, I did find out that this teacher does, in fact, believe that no fourth or fifth grader should be reading the book The Hunger Games.  There’s no question, it’s a controversial subject matter.  24 kids from 12-18 are placed into an outdoor area, the winner is the last one alive.  I believe that many- not all, students of this age stand to benefit tremendously from the message of the book.  In fact, the author geared her work towards middle-grade readers because she feels that by the time kids read books that deal with situational ethics and war, it’s usually too late.  They don’t begin to grapple with these heavy concepts until they’re 15 or 16 and in a matter of a couple years, can enlist in the military. 

Over the next few weeks, other teachers began to take notice of the book; reading it and agreeing that it should not be for our age group.  The discussion then popped up on a Facebook page, where I again, reacting on emotion, reinforced that it isn’t their decision to make. 

After reading the chapter on “Seeing” my approach completely altered (not that I have any issues downloading, just the opposite, I was having issues advocating rather than inquiring.  The timing was perfect, as we were in the heat of the argument.  I told my colleague that I needed to shift my approach, and I began to inquire into her motivation.  I assured her that it wasn’t a set up first because after coming off brash, I would be skeptical. 

I rephrased what I thought I was hearing from her, “So, I understand that you don’t believe any of our students should be exposed to this material.  Where do you see us moving to as a school community?”  That question was met with a considerable amount of posturing, “It’s labeled a teen read, no student under 13 should be exposed to it before that age…  developmentally students our age… etc. 

Concentration on moving to the bystander role, I tried to suspend my belief that age is an arbitrary number.  And when I retorted, I expressed that I would in no way ask of her to promote material she didn’t feel comfortable with and then further inquired about why she felt it was her responsibility to limit the topics I feel comfortable working with my students on. 

It was then that she crystallized her intent.  She was merely expressing her views and that she would never seek to dictate my own choices for my students.

Now, I don’t buy that at all but that’s beside the point.  I think that once I came at the issue from a more measured and inquisitive standpoint, she realized she had been just as polarizing. 

There is no question in my mind that once I employed the Kantor 4 player model, the conversation became productive.  At times I expressed why I wanted to move in the direction of my beliefs.  At times I followed and listened, agreeing that parents have every right to oversee what their kids read.   And at times, I opposed stating the examples of the powerfully deep conversations I’ve had with students regarding the subject matter in the book.  But most importantly, throughout the conversation I was able to suspend my position in order to facilitate a productive conversation. 

This morning in the hallway before school, I was met with a smile and, “Hey, great discussion!”  What could be better?

Based on all the previous discussion I had with my students who have read The Hunger Games, I knew they ascertained the deeper meaning of the violence depicted with in the book.  But, the discussion with my colleague gave me a wonderful new idea…

So I pulled the group of students who read the book and put it out to them.  “Some people don’t believe a student your age should be reading this book, why do you think that is?  How do you feel about that stance?  Why do you believe kids your age should be allowed to read Hunger Games?”  All of their responses confirmed every bit of what I assumed to be true.  In three years of working with that text, that was by far the most interesting discussion I’ve had yet.  

Monday, February 21, 2011

Read Your Heart Out Day 2011

A RYHOD DAY MESSAGE




I don't have a single picture from the day.  It blew by so quickly, I didn't have a second to even catch my breath long enough to grab the camera.


RYHOD


New England winters can be long and dreary, especially with the feet of snow on the ground this year.  Instead of letting the weather suck the energy out of our school, winter is the perfect vehicle for an all-out, no-holds-barred, winner-take-all Read-a-Thon.  Yep, Read-a-thon.  We're stuck inside, daylight's in short supply, why capitalize on this opportunity and get everyone jazzed about literacy?  


And, at Deer Hill School, we go all out.  The thon kicked off with an all-school  Are You Smarter Than A Book Character?, a take off on the game show, Are You Smarter Than A Fifth Grader? Mrs. Clark and Mrs. Parrell, put all of their charisma on display while the battled off over general knowledge against, Harry Potter, Percy Jackson, Poseidon, and Greg Heffley, and many other popular characters.  


This year we've added a very special event to the Read-a-Thon family.  Our first ever school-wide Read Your Heart Out Day celebration.  Valentine's Day is so close to February Vacation, what better way to transition than with an entire day devoted to the love of reading?  


Nothing, if you ask me. 


Students come to school in comfortable attire, bring sleeping bags, pillows, their independent reading and a collection of their favorite picture story books.  In the morning, parents are invited to bring the newspaper, a magazine, or the book they're reading to join in the celebration.  Younger siblings are welcome as students volunteer to read their favorite books to them.  


The Evolution:


RYHOD began as a self-contained activity in my classroom.  Over the past few years, it's caught on and taken flight throughout the building.  This year it was celebrated school wide.  As we began planning it in the fourth grade, teachers suggested a classroom rotation.  This spawned the creation of themes.  It added a whole other dimension to the day.  Ms. Mosher's classroom was set up like Hollywood Blvd, complete with red carpet and walk of "book character" fame. 


Mrs. Corkhum's room erected a temporary tent city where every student could find a quiet nook for reading.  There was the beach with Playa de Parrell, Ms. O'Hara's Red Sox theme to remind us that spring is just around the corner and, of course, Mrs. Clark's recreation of Disney World.  


My class had just finished up a major writing unit that we were putting together in ebook format.  It was the perfect merging of literacy and technology, a great premier for RYHOD.  


That got me thinking.  What about video of teachers reading at home?  Wouldn't that be cool for the kids to see where their teachers read?  We had it, technology and literacy.


The Theme: 


It was a little last minute but there were a few teachers who were happy to help out.  My good friend and mentor, Dr. Susannah Richards, was kind enough to lend her colleagues and undergraduates to the cause.  I was even able to pester some writers into participating. (A very heartfelt thank you to Barbara O'Connor, Gareth Hinds, Audrey Vernick, and Jonathan Auxier).  


The kids were floored.  The loved the videos of their teachers and that would have been good enough.  The best part about the reaction to the authors; you would have thought they were movie stars or athletes.  I do a "Book News" Wednesday at snack each week and it's seemed to have payed off.  The students recognized the authors and their cultural status in the classroom matched that of any celebrity.  It was exciting to be a part of.  


With dropped jaws, all the kids asked how and, that itself, turned into a nice little mini-lesson: What is the responsible way to go about pestering people for favors?  I explained to them that I asked Barbara O'Connor only because she was visiting the school after vacation.  I asked Gareth Hinds because we've met on several occasions.  


Jonathan's story was a little different.  We had only recently connected through Twitter, but his first book is due out this fall.  I went out on a limb and asked for a favor from a relative stranger.  The reason being; I thought we could be helpful and generate some buzz around the book.  Oh, it worked.  The day before I showed the video, I showed the students Jonathan's website, The Scop, (they loved the "dress Jonathan up" feature in the about me.  Then, Bam!, I hit them with the delightful video he put together for us.  One student responded, "His book has to be good," referring to his comical nature.  


The final part to the lesson was where I showed the students Chris Barton's comment on a previous post.  I explained to them that just because somebody left a comment, it doesn't give me the right to ask for their time.  Author's are extremely busy folks and it's not very respectful to solicit favors from people you don't know very well.  


However, I do that exact thing to Audrey Vernick.  Audrey was kind enough to leave a comment and I hit her up.  I had to.  I have this lovely little girl my classroom who plays tackle football on an all-boy-except-her team and I thought The Effa Manley would resonate with her in particular, especially because her turning-point narrative was about how she discovered a lot about herself through playing football.  Sorry Audrey!


How Wonderful It Was


It was really wonderful, that's how wonderful it was.  The day flew by so quickly I didn't pick up my camera once.  Which I always have attached to me.  So you know I must have been having a blast.  It was a RYHOD for the ages.  Thank you to everybody who kindly lent their their time, it was truly a success.  


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Monday, February 7, 2011

If you're going to take a book out of the hands of a reader...

Greg’s mom came to me this summer with a common dilemma.  Greg, a very bright kid, hates to read. 

My solution: better books. 

My M.O.- stack a pile of my favorites in front of him, read the first chapters until he finds something he likes. 

The result: Greg reads. 

It doesn’t take a whole lot. 

So, they kept me on as a tutor this school year.  The proposition: sit with Greg once a week while he does his spelling worksheets.  Apparently, not getting into a huge fight over homework is worth every penny to have me there. 

Once a month, Greg has a book report on a different genre.  I set up the books.  Greg knocks them down. 

That brings us to the problem... 

I had just finished A Tale Dark and Grimm by Adam Gidwitz, and as anyone who has read it knows, it… is… awesome.  Especially, for a highly capable but reluctant 4th grade reader.  Humor, blood and gore, what’s not to love?  Well, Greg ate it up. 

Unfortunately: not the month’s genre.  That would be biography. 
Solution: You Never Heard of Sandy Kofax? By Jonah Winter, Illustrated by Andre Carrilho, an outstanding picture book biography eloquently told and exquisitely illustrated.  Greg and his dad, both huge baseball fans, were psyched. 

The book report: not rocket science; one page, half summary, half reaction.  Perfect right?  Keep the “love of reading” flow, while still adhering to his assigned reading.  Greg can certainly gain an understanding of Kofax’s tremendous determination while still having time to read the book he’s into. 

Well, at least that’s what I thought. 

Greg’s teacher, however, took the Kofax book out of his hands. 
Her problem: it’s too short. 

It’s too short? I wonder if his teacher even took the time to open the book up.

I definitely disagree. You Never Heard of Sandy Kofax? tells the Kofax story through meticulously crafted prose.  And I have a feeling, not too many people who are reading this post would disagree that you can garner just as much of a person’s essence from 32 pages as you could from a 100 page book (Especially if all you’re required to do is write a ½ page summary, ½ page reflection).  And the author included a glossary and source notes!

The teacher's solution:  
She hands him John F. Kennedy: America’s 35th President by Barry Denenberg.  I have nothing against Mr. Denenberg, his Dear America series brings wonderful excitement to non-fiction.  My issue is that the book this teacher handed this student was published when I was in fourth grade (1988).  Now, I know- there’s not too much new to the JFK story.

Here’s what is new.  Today’s juvenile non-fiction treats the reader with much more respect that was expected in 1988. 



As you can see, many pages are a sea of text.  Well written, yes.  Overly engaging, not for me.  I’ve been hearing that kids don’t read enough non-fiction since the day I began teaching.  I certainly understand why.  For a long, long time too much of what we handed our students doesn’t bring the subject to life.



If you look at the final page, notice how this book ends.  There’s not even an about the author.  From further research, I know Mr. Denenberg has done his homework but there’s nothing to inform the reader of this.

So.  Greg’s mom smiles after I finish ranting and calls over to him, “Hey, Greg, what did you think of the JFK biography?”

Greg: “Didn’t read it.”

That’s when his mom tells me not to worry about it.  His dad would help him “ad-lib” the assignment.  Not good enough for me.  It was my recommendation that got Greg into this mess.

My solution:  And the timing couldn’t have been more perfect....


I was just at my favorite independent bookstore, Wellesley Booksmith, and I remember glancing over at the biography section to see this beautiful JFK biography.  I call up Margaret for the name, and drive on over.  It’s snowing (shocker) but that doesn’t stop me.  I have a point to make. 


An hour later I show back up to the house with Kennedy Through the Lens: A look at how Photography and Television Revealed and Shaped an Extraordinary Leader.   Doesn’t the title alone do it for you?


Martin Sandler has done a few of these photo-biographies but this book is pure extraordinary!  The organization of the book is remarkable.  It tells the JFK story relating each piece of his life and of his presidency with a remarkable photograph.  Each page highlights a different aspect of the JFK presidency and Sandler does it justice in one page, summing up the importance of the photograph. Civil rights- Wallace blockading the door; Kennedy’s untimely assassination- LBJ being sworn in.  A one page synopsis encapsulating the mood and importance of each photograph.  The format is engaging, the text isn't overwhelming, and overall, it makes the book not feel as long as it is.  







But my favorite quality of this book, the added information.  Sandler treats his young readers with the utmost respect throughout the story and it fits that he’s included places of historic significance to JFK, further juvenile reading and even prevalent web-resources. 


And just as any adult would expect, just as any teacher requires from their students, Sandler includes not only a list of his source material but even the sources of the photographs. 


It’s the final endpage that leaves makes the most impactful statement.  A inspirational quote from Kennedy…

From the speech he was on his way to deliver in Dallas.  Classy.



Oh, and is Martin Sandler a trusted source?  Here’s his about the author: 


As for Greg?  After I previewed the book with the family, I left one explicit instruction: show your teacher and donate this book to your classroom library. 

How did it turn out?  Even though Greg only had a few days to complete the assignment he got his A. 

As for the donation?  Greg promised me he would… just as soon as he finishes it from cover to cover. 

Honestly, if you're going to take a book out of the hands of a reader, just make sure to replace it with that of the same quality.  









Saturday, February 5, 2011

The Time My Favorite Teacher Gave Up On Me...

The other day I told a group of students the story of an experience in fifth grade that I vividly recall to this day.

I was showing my class this following "prime time watch" as a review of prime and composite numbers.  As we  quickly scrolled through the factors I asked a student what I believed to be an obvious, simple question, "What is 7x1?" Trying not to put students who struggle on the spot yet still getting them involved in our rare whole-class lessons, I thought this would be a no-brainer.  

12 was her answer.  It's not that I was totally shocked but rather a little disheartened that this connection was still not obvious, as we've spent the majority of the year working with multiplication. 

So, I tried to give the quick "array demonstration" for 7x1 with the chance for redemption on 6x1.  The answer... 8.  

Clearly something's not working out.  


I have a group of 7 students who severely struggle with math.  So much so that they usually end up being pulled out of the group any time we're working with new concepts.  Generally speaking this happens everyday at one point or another.  I try to do my due diligence in planning activities, math games, creative problems, etc. that allow them to interact with peer models. But, when it comes to the curriculum, the appropriate pace for this group would slow everybody else to a tedious crawl and that certainly wouldn't be fair either. 

Yesterday during the pull-out I could tell moral was low so I recounted the following story:

Mr. Crowley (go ahead Black Sabbath fans) was an energetic, first-year teacher whom I adored.  It was about the 5th day of working with algebra and I was lost. Lost, lost. I wasn't the strongest math student but I wasn't quite used to the failure I had been experiencing this week and I remember feeling pretty devastated.  Okay, so he had given me a few days to struggle, I'm sure hoping that I would come around.  Finally, he pulled out the manipulatives, sat down with me and only me, and proceeded to walk me through the basic explanation from the first day yet again.  

The conversation went a little something like this:
Him: "Okay, so take these two white pawns and put them on the left side of the diagram."
Me: "Okay."
Him: "Now, we're going to say that these two white ones are half the weight of the red one (insert real life examples) and place it on the right."
Me: "Okay."
Him: "Now, if we take 2 red pawns and place them on the right, how many white pawns does it equal?"
Me: "Two."
Him: "Let's go back to the original problem, how many white pawns does it take to equal 1 red?"
Me: "One."
Him: "Look at the diagram again.  How are you getting your answer?"
Me: "One white pawn equals one red pawn.  There both pawns, they're just different colors."

And it went on and on from there. Frustration to the point of tears (probably from both of us at that point) until finally, he said to me, "You're not ready for this," and gave me some multiplication work from the previous unit that I was particularly good at.

He gave us both some cooling off time before coming back over.  "Mike, don't worry.  You'll get it at some point.  For now, just do something you're good at, get that confidence back up."

I don't remember when I finally did understand algebra but by the time I hit freshman year, I got straight As in that class.  I worked hard at it, stayed after with my teacher, etc.  By that time my brian was ready for it.  It was still challenging but I was ready and I wanted it.  

If algebra had been a state standard, would I have been proficient in it? Nope.  If NCLB happened during my tenure in middle school, would I have got those questions wrong on the 5th grade test? Probably.  Could examples like the above contributed to our school not making our AYP? Who knows?

The one thing we both came to realize during that experience was that forcing a round peg though a square hole wasn't healthy for either of us.  Reflecting on that experience, I realize my own students shouldn't be made to feel like failures day in and day out.  It may not happen everyday, but it's been happening too often.  My eye has been too focused on our test scores.  

So beginning with this unit, we're pared down our curriculum to hopefully meet their needs.  I pull them out and separate them even though I hate it.  Because, at the end of the day I feel more of an allegiance to their future attitudes more so than I feel to my schools standardized test performance.  I wasn't a healthy math teacher for the majority of this year.  Stressed out and frustrated with having to circle so many wrong answers on assessments.  

Even though my district is the one signing my paycheck, I realized that as hard as I'm trying to do right by my school and its numbers, proceeding along the current path is just failing everybody.  And I feel like I'm in a position where I have to choose, fail my school or fail these kids whose parents have entrusted me to do right by everyone.  

I ran across this article: Why things just don't add up for some students.  (Thank you @briankotts & @thehomeworkdog) which inspired this post.  

I realize, I have to give these students something different.  Their time must be focused, not on cramming in the standards, but in strengthening the connections between concept and symbols in even the most basic mathematical situations.  Something inherently below 4th grade expectations.  

I know it's going to take even more planning to keep the standards in mind while lessening my student's load but I want to be my student's Mr. Crowley.  WWMCD?

And the funniest thing, after telling the story and illustrating the example on the board, every one of those struggling students picked up on that problem.  hmmmm....