She Defines Resilience – One Year Later

We are defined not only by what we do, day to day, but also by how we react and utilize our seemingly random hand of cards in life.  I’ve found over 33 years of life, the mark of character that differentiates those who excel and succeed from those who do not is resilience.  I can point to former students as examples:  The college graduate who grew up with an absent mother and a drug addicted father? Resilience.  The home-care nurse whose parents didn’t value an education past high school?  Resilience.  The successful plumber whose best friend committed suicide his sophomore year of high school?  Resilience.

It seems fitting to give a Webster’s definition of resilience here, however, I think that we all can picture individuals who personify our meaning of the word.   For me, above all, those people are my brother, Matthew, and my sister-in-law Danielle.   This story isn’t about me, or my reaction to this event.  It’s about them and what they have taught the world about resilience and the power of hope.  I hope my intentions come across as I recap their story.

One year ago, January 30th, 2013, Danielle, while finishing up a nursing clinical suffered a massive hemorrhage resulting from a burst aneurysm on the right side of her brain.  She was rushed to the local hospital where she was taken into surgery and given a very bleak prognosis.  The sobbing ER doctor explained to my brother that his wife was probably going to die.  My younger brother, who I’d always joked as being “30 going on 19” now was faced with an incomprehensible, life-altering situation.  He captures his emotion poignantly on a Caring Bridge post about the account of the moment when he told that doctor, as well as the hospital chaplain to F-ing get his wife to Iowa City!  I think those words have defined his attitude on the situation that it does not matter what has plagued us in the past.  He knew she had much more to give this world, so let’s get out of her way so she can fight to give it.

Reflecting during anniversaries of events seems to be a cultural norm and a time to remind ourselves of where we came from and how much further we have to go. A year ago today, we watched in udder horror and shock as Danielle lay motionless, lifeless, with small tubes ushering blood from her brain.  Furthermore, we observed silently as every half an hour, a nurse would shine a light in her eyes and ask for a reaction that never came.  “No change,” became the most chilling words I’ve ever heard.  I didn’t say it at the time, but I went to bed that night believing our precious Danielle was most likely gone.

The next day brought new light, and a miracle.  The overnight nurse said she had never seen anything like it.  When prompted to wiggle her toes, Danielle obliged.  “Thumbs up if you hear me, Danielle?”  And it was the most beautiful thumb I’ve ever seen.  She began her recovery that day and has not stopped since.  In one year, Danielle has gone from “probably going to die” to thriving and living.  Her personality, again, lights up the room as it always had.  She walks with less and less assistance each day and remains poised and confident that she will walk in the Bix 7 this summer.  Every day my brother is there by her side, emotionally and physically.  From the hospital ICU to a rehabilitation center in Ankeny, Iowa.  And now back home, where he’d turn their house upside down if he had to in order to ensure her comfort.

One of Danielle’s doctors said, “When you’ve seen one brain injury, you’ve seen…one brain injury.”  I believe these words are not necessarily a testament to the brain alone but the person in control of it.  Danielle proved that her fate was not finalized and her husband stood by her side believing the same.  These two incredible people inspire me every day to be a better person and to remember that all people fight a battle, in their bodies and their minds.  And I am so thankful for their presence in my life, and the opportunity to learn from them.

Danielle with my daughter, Maria this Christmas.

Danielle with my daughter, Maria this Christmas.

Pattern Power

If you have little kids and you’ve been privy to an episode of Team Umizoomi, then perhaps the title of this post evoked a little jingle in your head. You’re welcome; I’m here all day.

My daughter, although she doesn’t choose Umizoomi over Mickey Mouse as often as I’d like, picked up on patterns relatively quickly after watching this show a couple of times.  She’s 3 years old, and she finds patterns all over the place.  Mostly color and shape patterns, but a string of alternating letters can usually get her attention as well.  These observations of hers made me realize that pattern seeking is something that is innate and our built-in desire for order seeks it out.

High school students search patterns out as well.  For example, I put the numbers 4, 4, 5, 5, 5, 6, 4 so that the custodian knew how many desks should be in each row after it was swept.  It drove students absolutely CRAZY trying to figure out what these numbers meant.  I almost didn’t want to tell them what it really was as I knew they’d be disappointed that it lacked any real mathematical structure.

I’m not as familiar with the elementary and middle school math standards as perhaps I should be, but I’m confident that patterns are almost completely absent from most high school curriculum.  Why are most high school math classes completely devoid of something that is so natural for us?

Dan Meyer tossed out some quotes from David Pimm’s Speaking Mathematically for us to ponder.  This one in particular sheds light on this absence of pattern working in high school mathematics:

Premature symbolization is a common feature of mathematics in schools, and has as much to do with questions of status as with those of need or advantage. (pg. 128)

In other words, we jump to an abstract version of mathematical ideas and see patterns as lacking the “sophistication” that higher-level math is known for.  To be completely honest, this mathematical snobbery is one of the reasons I discounted Visual Patterns at first.  Maybe it was Fawn Nguyen’s charisma that drew me back there, but those patterns have allowed for some pretty powerful interactions in my classroom.   I’ve used them in every class I teach, from remedial mathematics up to college algebra because they are so easy to  differentiate.

I think high school kids can gain a more conceptual understanding of algebraic functions with the use of patterns.  For example, this Nrich task asks students to maximize the area of a pen with a given perimeter.   The students were able to use their pattern-seeking skills to generalize the area of the pen much  more easily than if they had jumped right from the problem context to the abstract formula.  

I also notice that the great high school math textbooks include patterns as a foundation for their algebra curriculum.  For example, Discovering Advanced Algebra begins with recursively defined sequences.  IMP also starts with a unit titled Patterns.   I think these programs highlight what a lot of traditional math curriculums too quickly dismiss:  patterns need to be not only elementary noticings of young math learners but  also valued as an integral part of a rich high school classroom.

Engaging with Engagement

High school students are inherently unpredictable. I’ve been told it’s the condition of their pre-frontal cortex and they can’t help it. I’m sometimes baffled and confused by what intrigues and engages them. If you’ve seen their obsessions with Snapchat, you know what I mean.
Something that always gets teenagers riled up, however, is a statement that challenges their peer group. In fact, I found today, that they’ll engage at a much higher level when presented with data that questions their level of engagement.

After a little guessing and estimating, I revealed this graph resulting from a recent Gallup poll on student engagement during my 9th grade statistics class today:

Gallup Graph

The kids were fired up right away.  Even if students agreed with the representation, it seemed as though every kid wanted to share his or her interpretation of how student engagement changes over time.  They shared their experiences from their formative years of education and respectfully expressed their frustrations for how much more difficult school gets each year.  Surprisingly, the students seemed to place blame for the overall decline in curriculum immersion on themselves.

Until one boy opened up the floodgates with the proclamation, “In elementary school we get to learn by messing around with stuff.  In high school, all we ever do is listen to the teacher talk and do boring worksheets.”  Expecting me to dismiss this kid’s comment for daring to suggest that the burden of student engagement also lies on the teacher, the class was relieved when I asked this student to expand on his thoughts. Almost simultaneously, multiple hands shot up in the air agreeing with this sad truth many of them were thinking and this young man had the courage to say out loud.  A rich, important, respectful discussion ensued about the difference between being busy in class copying, listening, and doing and being engrossed in activities that facilitate learning.

We continued the conversation by critiquing the methodology used to collect the data for this poll and the misleading representation in the graph.  Sorry, Gallup, my 9th graders spotted the flaw in the using in a self-selected study to represent all students right away.  They also debated the validity of broad categories such as “Elementary School” represented only by 5th graders rather than K – 5.

We discovered that the actual Gallup Student Poll is available online.  The students agreed that Friday was probably not a good day to do a survey about school engagement, but we’re really looking forward to collect and analyze the data on their classmates.

Puzzling Perseverance

School mathematics has a bad reputation for being intellectually unattainable and mind-numbingly boring for many students.  Proclaiming the falsity of these beliefs is usually not enough to convince kids (or people in general) of their untruth.  Students need to experience their own success in mathematics and be given the opportunity to engage in curiosity-sparking mathematics.  For me, one of the very best moments in a classroom is when a self-proclaimed math hater fully engages in a challenge and is motivated to work hard to arrive at a solution.

Enter January 2nd and 3rd.  Students are back for a two-day week which they view as punishment and a rude-awakening from a restful winter break.  To boot, the Governor Dayton announced today at about 11 am that all Minnesota schools will close Monday, January 6th due to impending dangerously cold weather.  You can imagine where the motivation level was in school today.

As the CEO of room 114, I decided to make an executive decision and do a puzzle from Nrich (shocking, I know) in my probability and statistics class.  Technically, the students could use the mean or median to help solve the problem, so I wasn’t veering too far off of what I had previously planned.

The Consecutive Seven puzzle starts like this:


Initially, one student began by explaining to me that she took one number from the beginning of the set, one from the middle and one from the end.  Then she figured the other consecutive sums needed to be above and below that number.  (Spoiler alert:  These numbers actually end up being the seven consecutive sums, so I was very interested in her explanation of how she arrived at those particular answers.  )


It’s worth noting that this student’s first words to me at the beginning of the trimester term were, “I hate math and I hate sitting in the front.”  So you can imagine my excitement when she dove in head first into this particular task, happily and correctly.

Adding to my excitement about the class’s progress, another girl (who was equally enthusiastic about math at the beginning of the term) was the first one to arrive at a correct solution.  And although she probably wouldn’t admit it, she was thrilled when I took a picture of her work.  And I am more than thrilled to display it here:

photo 2

If you were wondering about how math-love girl #1 fared in completing the task, she persevered and impressed her skeptical cohorts:

photo 1

This phenomenon fascinates and excites me that students, when confronted with a puzzle, highly engaged and motivated throughout the lesson.  Dan Meyer summarized this idea nicely on his blog recently:

“The “real world” isn’t a guarantee of student engagement. Place your bet, instead, on cultivating a student’s capacity to puzzle and unpuzzle herself. Whether she ends up a poet or a software engineer (and who knows, really) she’ll be well-served by that capacity as an adult and engaged in its pursuit as a child.”

And who knows.  Maybe one of the girls featured above will become a puzzling poet.