When the Answer is E: He Falls Off the Roof and Breaks His Neck

Our annual state testing season is almost here. The juniors will partake in the Minnesota Comprehensive Assessments in Mathematics a week from Tuesday. Our department decided issuing a practice test to all of our juniors would help re-familiarize them with long lost skills. After distributing copies during our monthly staff meeting, I’m always curious if any teachers in other disciplines look at the practice materials. Much to my delight, the choir director approached me at lunch on Friday, test in hand.

Mr. Warren: Is this test just like the MCAs?
Me: Most likely similar. Why?
Mr. Warren: Ok, well look at this one.


Mr. Warren: I think the answer is E, Xai s going to fall and break his neck.

The conversation went on for another few minutes, with me agreeing  that what’s been called “math education” includes ignoring the context of situations and focusing on a procedure.  In fact, I was curious how many juniors who completed this practice test even noticed that the situation was outrageous.

Since we were running on a 2-hr delay schedule Friday, I thought it would be the perfect opportunity to present the problem to my algebra class. They are mostly juniors who have been continually frustrated with a mathematics curriculum that doesn’t make any sense in the real world.

Me: Read through this problem. Does it make sense?

Student: ok, it looks like 32.

I didn’t expect any of them to apply any trigonometry, so I thought we needed to approach the problem differently.  In fact, I wasn’t even concerned about the angle measure.  I wanted them to look at the scenario itself.

Me: Imagine this scenario. We’ve done a lot of estimating in here. We need to envision a 20-foot ladder, three feet away from a house. Does this seem reasonable?

Unfortunately, it did seem reasonable to most of them. I needed another approach.

Me: ok, how could we simulate this in classroom-scaled size?

Student: Get a ruler.

Me: Perfect. How close does it need to be to the wall?

Students: (a chorus of answers)

After exploring multiple methods of calculating exactly how far, we arrived at 1.8 inches.  With as much drama as possible, I set the ruler against the wall, exactly 1.8 inches away.

Me:  Does this look like a ladder that any of you would want to stand on? (of course, a few did).  Keep in mind, this is a TWENTY foot ladder, not a 12 inch ruler.

Student:  Yea, I don’t think anyone is climbing up that ladder and coming down in one piece.

Another Student:  What if they had a spotter?

A spotter!  Now we’re talking.  To be honest, I have no idea if a spotter could hold a 20-foot ladder so that it could be placed three feet from the wall.  But now I’m interested to find out!

I know Mathalicious investigated a similar scenario using a claim from Governor Janet Napolitano.

In my mind, these are the questions that should be circulating Facebook and aggravating parents.  This is the kind of math that should rile up Glenn Beck and company.  Our state of Minnesota opted not to adopt the Common Core State Standards in Mathematics, but requiring this kind of math instead is what is actually dumbing down the curriculum.  It assumes that the real world doesn’t apply, only rote procedure does.  “Just figure out the answer, don’t question the situation,” is what kids read and do over and over when problems like this are solved without real context.  A richer classroom experience for both teachers and students comes when we ask students to assess the reasonableness of situations, create new scenarios that are more appropriate, and solve the new problems they develop.  The CCSS Standards for Mathematical Practice tell students that it’s vital that they “construct viable arguments and critique the reasoning of others.”  I don’t think “critique the reasoning of others” should be reserved for only reasoning created in the classroom.  I’d like my students to critique the reasoning of the creator of these types of problems and others like it that have been deemed a necessary component of high school math success.

Thank you, Mr. Warren for igniting the exciting conversation in my classroom.


Class Commences – an hour I won’t soon forget

Recently, Michael Pershan unearthed a Shell Centre gem straight from the 80’s (literally).  This collection of materials is fantastic, and hopefully demonstrates to both students and teachers that engaging in rich tasks and high-level thinking is timeless.

I decided to give the function unit a shot in my Algebra 2 class today.  Some background on this group of students:  there are 38 juniors and seniors, last hour of the day, in a class geared toward lower-level students.   So far though, the only thing that’s been “lower” in this class is the number of empty desks I have.   I handed out this task, gave minimal directions and let them go for a few minutes on their own:


from:  Shell Centre for Mathematical Education, University of Nottingham, 1985

from: Shell Centre for Mathematical Education, University of Nottingham, 1985

It was so interesting to watch the different ways each of them started.  Some began with 7, since that was the first you saw when reading the graph from left to right.  Others insisted to work from 1 to 7, identifying the corresponding people along the way.  A few worked the other way around, from the people to the graph.

I walked around to make sure each student was able to get started and that those who thought they had determined a solution also supported their claims.  Then, I wrote the numbers 1 – 7 on the dry-erase board, stepped back, and let these kids amaze me.
One student volunteered an answer, and then handed the marker off to another.  I intervened only briefly to make sure that every student had an opportunity to contribute if he or she wanted.  Once 7 names were completed, I knew a couple of them were out of place.  I sat and said nothing, and this entire class showed me what they are capable of.  Here was a class full of students labeled mathematical underachievers completely nailing SMP #3.  Their arguments were viable, their critiques constructive, their discussion productive.  It bothered a few of them that I wouldn’t let them know if/when they were correct.   But most of them are starting to understand that my main focus here is not the correct answer, but the incredibly rich and interesting process they used on their journey to finding it.  They came up with multiple ways to support their answers and noticed tiny details about the people that supported their findings.  For example, did you notice that Alice is wearing heels? According to my students, that is perhaps why she appears slightly taller than Errol.

I had a heart-to-heart with this group when we were done about how proud I was at how they conducted themselves throughout this task.  I’m really thoroughly looking forward to a fantastic trimester with this special group of kids.  Their work on this task gives both of us the confidence that they can tackle something more difficult next time, and they are capable of mastering high-level mathematics this trimester.

Curiosity Driven Mathematics

In my very first years of teaching, I used to have students ask me, in that age-old, cliche teenage fashion, “When are we ever going to use this?”  I vividly remember my response being, “Maybe never.  But there are plenty of other things we do in life, like play video games, that have no real-world application. That doesn’t seem to bother us too much.”

In fact, if every moment of our lives needed to apply to the bigger picture, the REAL-world, when would we do anything for pure enjoyment? or challenge?  or even spite?  I know kids are capable of this because some of them spend hours upon hours a day engaging not only with a video game but also collaborating with other people through their game system.

And furthermore, where do we think this resentment for learning math really comes from?  I have a guess…probably adults who have realized that through the course of their lives, being able to solve a polynomial equation algebraically is not all that useful! News flash, math teachers:  Our secret is out! 

There are many kids across all levels of achievement that will not engage in the learning process simply because the state mandates it or the teacher swears by its real-world relevance.  Students (and arguably people in general) are motivated by immediate consequences and results and cannot easily connect that the algebra they are learning today will be the key to success in the future.  They do not care that if they don’t nail down lines, they’ll never have a prayer understanding quadratics.  If they are bored to death by linear functions, I can’t imagine that they have even an inkling of desire to comprehend the inner workings of a parabola.  

What does resonate with learners is the satisfaction of completing a difficult task, puzzling through a complicated scenario, or engaging in something for pure enjoyment.  Kids are naturally problem-solving balls of curiosity.   There are ways to provoke curiosity and interest while simultaneously engaging in rich mathematics.  I think many teachers assume that in mathematics, especially Algebra, curiosity and deep understanding need to be mutually exclusive, and I’m positive that mindset is dead wrong.  For example, show this card trick to any group of kids, and you’d be hard-pressed to find a group who isn’t trying to figure out how it works.  I also think you’d be hard-pressed to find the real-world relevance to a card trick.  It’s still no less amazing, as well as algebraic.  



The fabulous life of Megan Schmidt

I read an article recently that asked when being “busy” became the new black.

When we ask students how they are, we always get the same answer: tired. Teachers, on the other hand can always be counted on to tell you how BUSY they are. Sometimes, you’ll even be lucky enough to get a teacher to tell you, “busy, but good.” As if to say, “I want to be polite, but get the heck out of my room so I can get something done!”

I once asked myself, if I had extra hours in the day, would I use them to be more productive with what I have on my plate? Or would I find new projects to fill up the time? If I’m being honest with myself, I’d have to say it would be the latter.

My day begins at about 5:25 am after about 45 alarm snoozes. I unglue the two beagles that have suctioned themselves to my arms and feet during the night. My husband and I leave to drop our daughter off at Montessori at 6:15. I want to take this moment to acknowledge how blessed I am to work at the same school as my husband. Getting to drop our daughter off together is a priceless bonus. I’m always drawn to the different building sets and usually sit down and play with her before we head off to our own school.

We try to arrive a little before 7am which doesn’t always happen.  Our school day starts at 7:25am so those 25 minutes can be pretty frantic.  Lunch goes into the fridge in the math office on my way to my room.  Then I walk into my classroom and wonder why I left it such a mess the afternoon before.  I then organize my paper stacks to give my desk some semblance of order.  I then need to run upstairs to grab copies, say hello to the office professionals up there, and hit the bathroom (very important).

We run a 5 period, trimester schedule, which makes each of our classes 68 minutes.  First hour is math recovery, which is about 20 kids that have failed a previous math course.  Their abilities are all over the place and their motivation to do mathematics is as well.  It’s a challenge to engage them sometimes, but they’ve gotten to know Andrew Stadel pretty well.  As Mr. Stadel talked about in his recent post, I too have acquired some puzzles over the course of the last 9 years and let this class work with them during the last 20 or so minutes of class.

Second hour is college algebra so I’ve got 7 minutes to run to the bathroom (I know but I drink a lot of soda).  This class is amazingly exhausting.  I’ve been just blown away by the mental power in that room.  When I give them a problem, those kids go AT IT.  I swear that the brain sweat is palpable.

Third hour is my prep period.  I have a million things going on during this 68 minutes since I am also the head of our department.  I never feel like I get enough done, but is there any teacher that feels like they are caught up ever?

We then have a 28-minute “study hall” time where kids can study, meet with clubs, go to the media center, make up assessments, etcetera.  Most students use the time to sit and chill out.  I don’t blame them; high school demands a lot.

At about 11:30, 4th hour officially begins.  This is an advanced probability and statistics course, and it has been fun to challenge these kids with real world scenarios.   These kids are naturally curious, and we often spend an entire class period discussing a problem and all of the statistics that come into play.  I end that class period wishing I taught it more than once a day.

It’s now 12:41.  Yep, the day starts at 7:25 and some of the kids don’t eat until 12:41.  Brutal.  I run to the bathroom, suck down my kale salad, and laugh with my co-workers.  One great thing about my department is lunch usually brings about hilariousness for one reason or another.   I really enjoy that comradery and I’m very lucky to be part of a department that enjoys one another.

1:17 is the beginning of 5th hour, so I will of course need to run to the bathroom one last time.  This class is college algebra again.  This is the last hour of the day, so the kids are a little more energetic but no less mathematically clever.

The bell rings at 2:25 for the day.  Unless I have a meeting after school, I leave between 2:50 and 3:30.  I want to get my T25 workout done before I pick up my daughter from her school.  (T25 is a great workout program from Beachbody.  Best workout I’ve ever done.)

Once my daughter is home, we usually build with Legos, play a game, or make a fort.  Bedtime routine starts at 6:00 so it’s not long before we are watching her allotted half-hour of TV and then reading books.  (I try to suggest Team Umizoomi everyday, but their mighty math powers are usually trumped by Minnie and her Bowtique.)

She’s asleep by about 7:30pm and we won the kid sleeping lottery, so unless it is an extreme circumstance, we don’t hear from her until we wake her in the morning.  Now it’s time to catch up on blogs, lesson plans, working through problems, or adding student feedback.  Since mathematics has also become a personal passion of mine, working on these things at night is enjoyable as well as productive.

I enjoy most of my days because I have a pretty positive outlook on being a teacher.  I have a strong belief that what I do makes a difference and that belief is what drives my passion for teaching.  When you show kids that you believe in them, there is a tremendous benefit to both you AND them.  Each day, I try to spread that to my students.  If they know that I believe in them first, they are more likely to believe in themselves and achieve more mathematically.

Ever-loving Evernote – #ExploreMTBoS 6

When I started discovering the math teacher amusement park that is the MathTwitterBlogosphere, I quickly found myself so excited about what I had discovered and so overwhelmed about what I had discovered.

My first instinct was to bookmark, bookmark, bookmark.  I made bookmark icons on my ipad, bookmarks on my web browsers and bookmarks on my desktop.  I had bookmarks inside bookmarks inside bookmarks. The problem:  I couldn’t find resources when I got ready to use them and I now had more bookmarks on my ipad than I had actual apps.

Then an angel appeared in the form of Kate Nowak at a Global Math Department session last spring.  Kate suggested Evernote as a method of organizing all of the resources I had found.  I had a few things in Evernote and had used it very infrequently as a medium for holding a few PDF files or interesting articles.  Kate Nowak uttered the words I was waiting to hear when deciding how to organize my mountain of resources:  Tagging and Searchable PDFs.

Many of you might be thinking “there are plenty of sky drives that are searchable.”  (Maybe you are now wondering what a sky drive is.)  Anyway, none of the online storage platforms have been as versatile, flexible, and easy to use.  I’ve tried Adobe Reader, Dropbox, Google Drive, iCloud, the works.  Evernote surpasses them all.

A bonus:  Evernote and Adonit joined forces and created Jot Script, a one-of-a-kind stylus for note-taking.  Now, I can handwrite notes into Evernote and they are searchable as well! It’s like Christmas and my birthday!

Vegan Teacher Crazy about Cheeseburgers

A year and a half ago, I made the best dietary decision of my life and decided to try a vegan diet for 30 days.  Fast forward to now, I love the vegan lifestyle and I’d never go back to a diet filled with animal products.  I know too much.  But that’s a story for another post.

A couple of weeks ago, I logged into Robert Kaplinsky’s presentation on Global Math Department.  He started off with a visual, which is usually good to draw listeners into the presentation.  However, this visual was a cheeseburger.  And he went through more and more visuals, and the cheeseburgers kept getting bigger and bigger until finally I’m face to screen with 100×100 cheeseburger from In N’ Out burger.  I try very hard not to be one of those ‘enlightened and superior’ vegans who constantly judge the dietary choices of others, but these burger pictures were not how I envisioned spending my Tuesday evening.  His methodology had my attention however.

After explaining his problem solving process and distributing his problem solving template, he threw this photo into the mix and asked,

“How much would that 100×100 cost?

Now I was hooked and needed to figure out how much that 100 x 100 cost.  I didn’t care if it was a cheeseburger or a truckload of kale.  The wizardry of Robert Kaplinsky drew this vegan teacher into the problem solving process and made me care how much this monstrosity of a cheeseburger cost.  Brilliant.

Then Robert Kaplinsky threw down the dynamite:

That’s right.  The actual receipt of this 100×100 cheeseburger.  A boatload of kudos to Mr. Kaplinsky for presenting something that was simple, with some great mathematics to go with it.

I’m glad this weeks ExploreMTBos mission was LISTEN and learn.  This was a great presentation, a great lesson, and a great resource.  I’m glad I took the time to listen to Robert Kaplinsky’s presentation, even if it wasn’t so appetizing on the outside.

Olympians, Tweagles, & Friends in my Phone

I started tweeting in 2008, around the Beijing Olympics. It was cool that actual Olympians would respond to my tweets.  When Summer Sanders responded to one of my tweets, I about fainted. Twitter was new, they probably didn’t know any better.  

I followed a few celebrities. I found some of their off-color honesty hilarious and sad at the same time.  In the meantime, my hilarious brother managed to rack up tens of thousands of twitter followers. (@sucittam if you are looking to add some hilariousness to your timeline). Here’s one of his tweets being featured on Ellen:

He opened my eyes to the idea that following actual REAL people is more entertaining and fulfilling. He was absolutely right.

I went through a phase where I followed a bunch of people who tweet as their beagle.  I’m pretty sure I was the first one to use the term Tweagles, although I have no proof of that. 

Then in January 2013, my indifferent view of people on twitter changed forever. My 29-yr old sister in-law, Danielle, suffered a massive brain aneurysm and it wasn’t certain she would recover.  She was in the ICU at the University of Iowa for almost 6 weeks, and while my brother stayed by her side every day, his twitter followers rallied support that went viral. All of these people, most of which he’d never met, wanted to reach out to help. Benefits were organized, gifts were donated, and memorabilia was auctioned all to benefit Danielle whose recover was slow, but steady. 

Rex Huppke (@RexHuppke) wrote a beautiful article illustrating that the people we interact with on twitter are not just cyber-acquaintances.  Danny Zucker makes the best point:

 “We’re willing to accept the concept that cyberbullying is real, and it is. But if you can accept the idea that the negative is real, then you have to accept the idea that the positive is real. If strangers can hurt you, they can be friends as well.”

And just like that I leaped head first into the T of the MBToS. I realized that people like Fawn Nguyen, Andrew Stadel, Kate Nowak, and Christopher Danielson were real teachers just like I was.  They had great blogs, and they were on twitter too. And if I wanted to get a real benefit from all of the resources I had found online, I needed to start posting feedback of how I incorporated them into my classroom.  And then tell the creator of the activity about how it went. Through this I’ve really been able to experience the genuine human behind all of these @ symbols. These are not only great teachers who don’t just shine on their own. They want to freely share what they’ve done so that others can shine just as brightly.