Custom Polygraph from Desmos

It’s been a while since I’ve blogged about a math-specific activity.  But today, I spent the better part of 5 hours creating a Polygraph Activity with scatter plots on Desmos, and it was a ton of crazy math fun.  Here is the link if you’d like to use it. 

It’s kind of like the game Guess Who, but with mathematical concepts like parabolas, quadrilaterals, and systems of equations.  It’s relatively easy to make one of these activities, but incredibly complex and time-consuming to create a good one.

Christopher confirmed my inclination:

https://twitter.com/Trianglemancsd/status/626896794782408705

Bob and Michael had some helpful thoughts:

Here’s what I came up with for my scatter plots:

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polyscatter

 

I had my husband field test it for me.  He used language like “mostly linear” when eliminating graphs but then seemed to focus on how many points are in each quadrant.  I took out the axes to see if that solves the problem but I’m worried that might make the graphs indistinguishable to students.

polyscatter

 

What I learned:

  • The Math:  By first experimenting on StatKey (thanks @rockychat3), I was able to determine the effect on the line of best fit when maneuvering points.
  • The Logistics:  The only window available is -5 to 5.  I had to edit most of my graphs to fit in that space.  Also, intermediate saving is not currently available so ensuring your graph inputs are ready to go is helpful.
  • The People: I’m never short of completely humbled when I reach out for help with something on twitter.  Thank you everyone for your input.

 

We Admitted We Were Powerless

I wrote this blog post about a week ago when preparing for my presentation at Twitter Math Camp.  I don’t have any resources to post to the TMC Wiki page.  All I have is this glimpse into my humanity as a teacher and an account of how I release myself from the burden of powerlessness.

On March 31, 2012, I made the choice to put down my drink for the last time and join Alcoholics Anonymous.  This decision had a profound impact on not only my personal relationships and my health, but also on my role as a teacher and my relationships with students.

If you’re at all familiar with the 12 steps, you know that step 1 is the only one that mentions our substance of choice.  (Step 1:  We admitted we are powerless over [insert substance here] and our lives had become unmanageable.)

Many of the other steps involve an appeal to a power greater than ourselves.  Many unfortunately dismiss or reject the real, profound, positive change that can result from a 12-step experience because of this mention of a higher power.  The incorrect assumption that this refers to only a religious deity robs many of even exploring the impact the 12 steps can have on their lives.

BUT, since my goal here isn’t to convince you of AA’s ambiguous, non-definition of “God” as you understand Him, I thought it was more productive to talk about how I have applied this work with the 12 steps to my work with students, administrators, and other teachers.  Also, my goal is to look at how these same ideas can be applied to your teaching, sans 12-step meetings.  I’m here to share my experience, strength, and hope, and consider that the real power you have in your classroom is through accepting your powerlessness over it.

I shared a survey a few weeks back.  One of the questions was What do you feel powerless over in your job as an educator?
Because survey answers presented in Wordle form are visually interesting, see if you can pick out some of the common themes here:

wordle

 

Most of us can clearly identify what we are powerless over, but how do we actually rid ourselves of the resentment we have toward that powerlessness?  How do we really accept it and focus our energy on something we do have the power to positively change?   For example, we are powerless over the brown-nosing, pompous, know-it-all teacher at the other end of the school.  We know we cannot control that they say outlandish things at staff meetings and toot their own horn whenever their mouths are moving.  Regardless, even the mention of their name sends us into an anxiety-laced, physical reaction, complete with a roll of the eyes.  Wouldn’t we like to be free of the anger that accompanies our interactions with this individual?  Because no matter where you go, what school, level, grade, or subject you teach, that person will be there in one form or another.

For me, I’ll call this person…Bert (not his real name).  We started teaching at the same time.  We had a…miscommunication of sorts.  The details don’t matter.  What does is that all of my future interactions with Bert were strained, anxiety provoking, and negative.  If I was to be completely honest with myself, I needed to make an amends with him.

Whether you get to this point through 12-step work or through your own examination of conscience, the only thing in your control is your actions and your reaction to others.  I’m completely powerless over what happened with Bert in the past.  I felt he had wronged me.  I continued to hold a grudge.  And I remained angry and hurt.

It was a Tuesday, really early, 6:30 am. I was sure I’d be the only one needing to talk to Bert.  Hi Bert.  Over the last seven years, I have not been very friendly.  Perhaps you’ve noticed.  I’ve had expectations for you that were unfair because you did not know about them. I’m very sorry I’ve treated you in a way that was unkind.  

You could tell he was surprised, but relieved.  He told me thank you, that my words meant a lot and that he was very glad I took the time to clear the air.  I felt fantastic.  Like, floating on air, free as a bird, happiest person on the planet AMAZING.  The physical reaction I had to the mention of him – gone.  My annoyance when he’d speak up at meetings – vanished.  I no longer required myself to carry around the burden of being bothered by his actions, which I couldn’t control in the first place.  By turning the table to my contribution to the breakdown in communication, I was able to release the effect that his contribution had on me.

This empowered me to use this release of resentment in so many other areas of my teaching.

I was absolutely humbled by the humanity and authenticity that was shared at my session.  In the spirit of anonymity, I am not going to share any of that here.  I know that when we share our humanity with each other, our students, our fellow colleagues, and our “friends in our phones,” we then allow learning to happen.

Everyday Endeavors

You’ve seen the semi-colon.  Maybe you’ve been intrigued; maybe you’ve rolled your eyes.  Regardless, we can’t bring humanity to an issue we aren’t willing to shed light on.   It’s illusive and  easily camouflaged by jokes and smiles.  It masquerades as “moodiness”  or “sensitivity,” when in reality, this disease is a killer.

I was diagnosed with chronic depression when I was 23, but like alcoholism, it wasn’t something I was going to be “cured” of.  At 25, I sought relief by striking my legs with the blunt end of a toothbrush.  The bruises were easy to hide, but the emotional trauma was not.  At 29, pregnant with my daughter, I confined myself to my bedroom for most of the summer in order to avoid contact with the 3-dimensional world.  I chose my depression medication over breastfeeding my baby because the hopelessness that accompanied the medication withdrawal was too much to handle.  The fear of reliving that summer prevents me from even contemplating the thought of having another child.

This week is Mental Illness Awareness week, and it’s vital that we take the social stigma off of depression and other mental health issues.   It’s for us to recognize and reach out to those who need help.  For us to see the Robin Williams’ in our lives who cover up feelings of worthlessness with telling of jokes. Because if we have everyone laughing, no one will see us crying, right?  Which students of ours are holding a pencil in their hand on Monday, but are contemplating a bullet in their head on Friday?  How many of our fellow educator colleagues live in fear of the mental illness labels and don’t seek professional help?

I am a regular [relatively speaking] 30-something math teacher in a Minneapolis suburb, and I suffer from chronic depression.  Eleven years ago, I sought help, and at the age of 34, I can manage my condition in a healthy way.  I still trip over my feelings of hopelessness.  But I now have the tools I need to rise higher after falling.  If you’re struggling, please know you aren’t alone.  If you know someone who struggles, reach out to them.  They will probably push you away.  They will probably push you away again. And again. And again.  But every time you give your hand to someone with depression, they are given the opportunity to reach for it, rather than reaching for something destructive.

The Comfort of a Canine

Despite the summer sun and the endless stream of Netflix, last week was a tough week.  And when the going gets tough, the tough get…their dog.  Those two little 13-inch, tri-color bundles of joy always know how to de-stress me, without saying a word.  So, indulge me for a moment, while I get sentimental and highlight some of the dogs of the Math-Twitter-Blogosphere and other comforting canines that have enriched our lives.

russo

This is Smudge, Susan Russo’s precious mutt. As you can see, he’s attempting to master all of the ballet positions.

illana

Here’s Affie, Ilana Horn’s dog, who stuck his tongue in the electric socket before this picture, apparently.

Both of Max Ray-Riek’s dogs are cover stars.  Recognize them from Powerful Problem Solving??

megdog

I didn’t think anyone integrated dog love into their lessons more than me until I met Meg Craig at Twitter Math Camp last year.  Her Corgi is such a fun part of much of her mathy-ness.

Elizabeth Statmore and her husband serve as a guardian family for Topper.  Look at that face!

Weezer, Kaja, and Frankie, Laurie Worthington’s lovies each have their own special treat bowls.

Sadie Estrella tells me that Sasha and Shotsy keep their yard mongoose free.

b&Y

My brother and sister-in-laws dogs, Booger and Yoshi, are loving companions through a challenging few years.

Molly is my parents’ dog, and i remember picking her up from the farm when she was only 8 pounds.

nataliedog

Natalie Perez’s beagle mix, Bella,  has a howl that scares away bears from their yard.

herbiestella

My two little beagle creatures, Herbie and Stella, whose unconditional affection warms my heart every single day.

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Here we are, every single morn

There is something so beautifully personal about the way we share our love for our furry friends.  Many of you know that part of my classroom display is my Dog Wall.  Just recently, I started seeing Facebook statuses of former students.  This dog wall allows me to connect with those students one more time and let them know that their pet has been more than just a photo on a removable wall.  I am able to let them know that the unconditional love their dog had for them will always grace my classroom wall and be part of the happiness that fills my room each day.

Continuing the Conversation on Race

On April 17, 2015, Saint Francis High School, nestled in rural Anoka County, with a student population made up of over 90% white students, was rededicated for the day and renamed Frederick Douglass High School.  Students spent the day engaging in conversations about white privilege, appreciating African and Native American performances, and learning how racism is deeply embedded in our historical foundation.  This was an enormous undertaking by Tim McLean, and his commitment to this project was nothing short of inspiring.

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Unfortunately, since Frederick Douglass Day was a pre-planned event, many students elected to stay home that day and excluded themselves from any meaningful conversations (or difficult) conversations addressing race and racism.  Despite the absence of a portion of the student population, just as the “one-and-done” model of professional development does not lead to lasting change, neither does the “one-day discussion” about racism lead to a deep commitment to equity in education.

And why does this matter in a district where less than 2% of the student population is Black? Because of horrific hate crimes happening in places where racism, subtle and overt, is allowed to flourish.  The most recent in Charleston, South Carolina makes it clear that this is today’s issue, and that racism didn’t end with the Civil Rights Act.  What’s disheartening about a mass shooting a thousand miles away (besides the loss of life) is the numbness our students feel as this happens over and over again.  Additionally, there is a problematic dismissal of these incidents as isolated insanity from a troubled madman rather than an acknowledgement that they are a manifestation of continuing patterns of oppression.

Charleston’s proud display of a flag of treason over their statehouse sends the message to our students that in America, we still cling to a past steeped in hate and white supremacy.  The dress code in the St. Francis high school student handbook makes specific reference to the Confederate flag as a “symbolic representation of intolerance.”  St. Francis is no stranger to racial controversy, especially involving the Confederate flag.  And it is vital that we as teachers, administrators, school board members, educational assistants, office professionals, custodians, parents, and coaches make talking about racial equality a priority.   Because every day we are silent and say, “I teach math/english/art/computers…” we send the message that we accept symbols of hatred in our country.   We can no longer make “essential standards” a priority before we make equity essential.

Some good resources for educators:

 

Bingo Lingo

This time of year, the standards used to measure the success of a lesson may look different than they do at other times of the year.  For example, some teachers might consider “Students not using worksheets to have paper airplane throwing contest” to consistute a lesson well executed.  To a certain extent, I am joking, but there’s a thread of reality there.   Think back to a time when your excitement for a future event prevented you from doing anything productive.  Now imagine leading a room full of 32 people with that same excitement and handing them a manual for their new scanner/copier.  You get the idea.

I can usually distinguish between my being pleased with a lesson based on lowered expectations and my being pleased with a lesson because of a high level of learning and collaboration.  Today was the latter, with my 9th grade probability and statistics class again.

I found this on Don Steward’s website.  If you have seen his blog and are not fascinated, or at least intrigued, we cannot be friends.  He comes up with some amazingly simple, yet elegant classroom problems.

Picture1  Picture2 Picture3

 

We started this yesterday.  They are in groups of 4; the oldest student in the group got to choose first and so on.  Then they played three “games” using a pair of dice and a whiteboard with their numbers on it.  Today, they worked on figuring out why the “6,7” card was the best and determining how to rearrange the numbers  on the cards to make them all equally likely to win.

I’ve had this glossy paper in my room forever, so I decided to have them make a mini-poster with their solution and some reasoning.  Here are my two favorites:

0521151413a-1 0521151415a-1

Making Math Talks a Habit

How many dots are there?  

One of the best experiences about being a teacher is the opportunity to bear witness to student sense-making.  I enjoy hearing learners help one another develop different ways of approaching problems because I know this is a skill that will transcend mathematics class into when-are-we-ever-going-to-use-this land.

I was first introduced to the idea of a Math Talk when I was taking Jo Boaler’s online course How to Learn Math.  This one is simple enough that anyone able to count can do it.  Seriously, take a second and give this one a go:

How many dots are on the card?  How did you determine your answer?  

How many dots are on the card?  How did you determine your answer?

The answer of ten is hopefully quite obvious to your students.  But it’s the incredible number of ways in which they determined that answer that blows me away.  Is it two rows of 3 and two rows of 2?  Or is it 4 diagonals of 1, 2, 3, and 4?  Maybe 5 in the top 2 rows and 5 in the bottom 2 rows?  Perhaps 5 pairs of vertical dots catches their eye?  THESE ARE JUST DOTS, PEOPLE!  All of this awesome thinking over dots arranged strategically on a piece of paper.  But these dots opened the door to my getting my students to explain their thinking to one another.

Fast forward to MCTM this past weekend.  I was reminded of the power of the Math Talk at a session hosted by Christy Pettis and Terry Wyberg.  I knew Fawn Nguyen had some wonderful examples on her website, so I jumped in.

The results have been lovely.

Monday:  Which is greater 79×25 or 75×29?

Tuesday: Visual Pattern #10

How would you have determined that there were 85 puppies in step 43?

How would you have determined that there were 85 puppies in step 43?

Wednesday:  Which is greater 12/17 or 5/8?

There were many lovely responses to all of these questions in each of my classes. But the one that stands out as my favorite was Caytlin in my 5th period Algebra 2 class.  For Wednesday’s problem, Caytlin says that it’s easier to compare the reciprocals of those fractions, so she flipped them over to compare 17/12 and 8/5.  When converted into a mixed number, 1 and 5/12 is smaller than 1 and 3/5.  The opposite would be true for the reciprocals of the numbers.  Therefore, 12/17 is larger than 5/8 since its reciprocal is smaller.

Honestly, isn’t that golden!?  What I love about math talks is that students are asked to make sense of the problem themselves.  They aren’t shown an example or taught a rule.  They develop their own method and then help their classmates by sharing it.  There have been a lot of good experiences in my classroom this year, and math talks rank up there near the top.

(For additional information on math talks, I recommend the book Making Number Talks Matter by Cathy Humphreys and Ruth Parker)

Secret Teacher Problems

I came clean recently about my addiction to alcohol, and this past Tuesday, March 31st, I celebrated 3 years of sobriety.  As problems have arisen (a broken thumb is a fine example), I know that no problem is so big that alcohol won’t make much worse.  Trust me, I’ve tried alcohol as the solution more times than I can remember.  It failed ten times out of ten.

Rewind about 4 years, and you’ll see a teacher who’s put together on the outside, but falling apart within.  I kept beer hidden in the garage, wine stashed in the basement, and vodka in my purse.  All because of fear.  Fear that people would discover the unhappy person that loomed underneath my smile.  After a drink (or five), I could keep up that smile that I believed others wanted to see.  I had a happy marriage, a beautiful daughter, a great job, and financial security.  There wasn’t a reason to not be smiling, so instead, I drank.  And then I constantly lived in fear that my secret would be discovered and that i wasn’t truly as happy as I outwardly appeared.

As teachers, we are all control freaks. Every. Single. One of us.  I’m even exhibiting controlling behavior with my insistence of putting on a happy face outwardly.  It’s a more subtle type of control, but it keeps others at bay from what’s going on beneath the surface.  It’s similar to those who use humor to deflect serious conversation.  If we keep people laughing, we deflect their attention from the pain that lurks beneath the surface.

Yes, the degree at which we exhibit control varies from teacher to teacher, but can you think of anything more terrifying than a chaotic classroom? I know I’ve been awakened from that nightmare more than once.

Even if you’ve had no brush with addiction I’d venture to guess that the Serenity Prayer is something familiar to you:

God, grant me the serenity to accept the things I cannot change, the courage to change the things I can, and the wisdom to know the difference.

Putting any religious context  aside, this prayer has powerful implications to the classroom . what is it in my classroom that I have the power to change? Do I have the necessary courage to face the challenges head on? Can I discern the difference between what is teachable and what is not?

More important recently, am I able to take what I preach in my classroom and apply it to my personal life? Do I have the courage to say “no, I cannot,” but more importantly be at peace with a decision to step away?

Because as control freaks, it’s one thing to say no and quite another to accept that decision. Relating this back to the Serenity Prayer, I’m very good at trying to change the things I can. I’d also say I do a decent job at knowing the difference between what I can change and what I cannot. It’s the serenity to accept what cannot be changed that gets me every time.

What a Difference 12 Kids Make

from map.mathshell.org

We’ve entered Spring Trimester and the volatile Minnesota weather is cooperating thus far.  If there’s a silver lining to last year’s Spring suckfest, the lack of warmer weather put off the end-of-the-year slide until closer to May.  I’m not sure we’ll have the same luxury this year.

I teach the same level of Algebra 2 that I did last year but my class sizes are a more manageable 22-24 rather than the monstrosity of 36 I had last year.  I know class size isn’t high on Hattie’s list of influences on student achievement, but providing formative evaluation (something VERY influential, according to Hattie) is much more doable with 20-something rather than 30+.

I’ve left the desks in pods because I’m convinced students interact and collaborate mathematically more often when they have multiple classmates within conversation distance.  I want to switch their groups periodically, if only I could get them to sit in their assigned seat!

One of my go-to resources is the Mathematics Assessment Project. Their lessons are robust, and provide good opportunities for students to have great conversations around the mathematics.  This lesson on investments is no exception.  The main activity is a card sort where students match a principal and interest rate of an investment with a formula, graph, table, and description.  But the everything from the pre-assessment to the closing slide makes students think and share.

Here are the openers of the main lesson:

from map.mathshell.org

from map.mathshell.org

from map.mathshell.org

from map.mathshell.org

My assumption, not being familiar with this group of kids, was that they’d go right for the obvious – Investment 3 is the odd one out because it has a 10% interest rate and the others have a 5% interest rate.  I underestimated them.  They came up with very creative, thoughtful reasons why each investment could be considered the odd one out.  I really like these questions because all three can be correct, and students have an opportunity to defend multiple answers.

The card sort was also spectacular.  I was able to have great conversations with each group about their thinking. (Yes, that’s much easier to do with 24 rather than 36).  What a difference 12 kids makes.  There is so much to this lesson to love.  If you have a unit on exponential functions, give it a try.  I’d love to hear how it went in your classroom.

Emotional Baggage Around My Wrist

This blog post is more personal therapy than it is educational reflection, but I hope that others dealing with similar strife can relate and find solidarity.

Two weeks ago, I was in a car accident on the way to school on a clear, dry, sunny Monday morning.  I was heading north on a county highway when a car pulled out from my right to head south.  My SUV slammed into him at about 50 miles per hour deploying all of my airbags and sending my car into oncoming traffic.  When my car came to a stop on the opposite side of the road, I was relieved that my Sync system was dialing 911 on my behalf.  Who knows where my cell phone was at that point.  Fifteen minutes later, a police officer arrived.  The driver of the other car was issued a citation for distracted driving and my mangled Escape was hauled away.

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My Ford Escape immediately following the accident.

The pain that remained in my hand kept intensifying as the morning went on, so instead of waiting for a doctor appointment to get myself checked out, I headed for the ER.  Sure enough, my left thumb was fractured.  The airbag that saved my face instead broke my thumb when I gripped the wheel, bracing for impact.

I was angry.  Thumbs are important.  Two working thumbs are a lot more productive than one.  I didn’t cause this accident, yet I’m the one left with a broken hand, smashed car, and sore neck. To add more gas to my resentment-fueled fire, the Doogie Howser-esque orthopedic surgeon informed me that my busted digit would require pins to heal properly.

This past week, I’ve thankfully moved past anger but haven’t seemed to be able to rise above the emotional grip this hand cast has had on my day-to-day functioning.  I couldn’t imagine that having difficulty taking the cap off of a dry-erase marker would have such a strong emotional impact.

This week we began a new trimester, so I struggled with the decision to take a few days off of work so I could wrap my brain around this injury and release myself from the emotional handcuff surrounding my thumb.  Our culture accepts physical injury, but the unseen toll on our mental well-being is what really needs the most care.

The part of the first step in Alcoholics Anonymous is accepting powerlessness over alcohol.  While this is true for addictions in general, that thinking is also applicable here.  I am powerless over my broken thumb, the 6-week casting period and my physical disabilities resulting.  My emotional interpretation of the event, however, is completely in my control, and I’m determined to make the best of it and be a better person because of it.  Life is full of lessons, and this one is teaching me humility.  I am determined to be humble enough to accept it.