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Residuals from the Past Month

It’s been a busy month of October. I don’t have a new lesson or resource to share this time – instead, here are some things which have been rattling around my brain.

Last night at the weekly Global Math Department online meet, NCTM President-Elect Matt Larson shared new and “in the works” resources for members, and a revised vision for PD in the coming years.  In the past few months, I have been fortunate to speak personally with both Matt and current President Diane Briars, and I am happy to hear that NCTM not only values the work of the Math-Twitter-Blog O-Sphere, but are now beginning to take lessons from the successes of ourline community and bring it to the national organization.

With regional conferences starting this week, I am most excited to see a new website NCTM has established to encourage ongoing dialogue:  I won’t be able to make any of the regionals, but will be checking in from afar on this new site. I’m already enjoying the sharing from presenters, and the sense of ongoing discussion.

I re-arranged my bedroom furniture this summer, and I’m not sure I like it better.

This afternoon, I took one of my daily walks through the neighborhood, with the Bill Simmons podcast as my companion. His guest was Judd Apatow, and the conversation turned towards the negative aspects of celebrity.  Judd mentioned Eddie Murphy who started as observational comic, then became hugely famous, as someone whose work was altered by the seclusion of celebrity status. No longer able to make the every-day connection to his audience, the observational aspect of Eddie’s career withered away, and was replaced by other things.  Judd Apatow, sensing a need to re-visit his comedic roots for inspiration, dusted himself off to do stand-up and has caught his comedic second wind.

Is there a lesson here for teachers who leave the classroom to become administrators? How long does it take for separation from the classroom to take root – and can (and should) it be re-visited now and again?

Sometimes I wonder why nobody has been arrested yet for assaulting one of the Impractical Jokers

I have 3 quite different preps this semester, and I am professionally miserable because of it.  With block scheduling here, teachers have 3 courses each semester.  Now and then, 3 preps is not a big deal.  But I teach each course with someone different (or a different group) from the department, and I rarely share prep with any of them.  I’m also the only member of my department to have 3 preps, and this is the second semester in a row this has happened.  OK…I’m getting real close to my whining quota here, but I don’t think I am doing a good job right now.  Instead of having laser-focus on my courses, I find myself all over the place.  This is not helping my students and I am worried.

Some of my AP students report that they will go trick-or-treating next week.  For me, high school age is when you are out of the candy loop.  Am I right?

My Math Club kids are the most enthusiastic bunch I have “coached” in recent memory.  And the weekly Math Madness contests have been great for getting kids to talk about problem solving approaches.  I don’t usually enjoy doing math for competition’s sake, but we have been holding weekly de-briefs after each contest and the conversations have been informal, spirited and genuine.  I’m lucky to work with such a great group of kids!

Today is “Back to the Future” day – October 21, 2015.  The day Marty McFly visited the future on the big screen.  And I passed a DeLorean on the way home from work (no lie, this really happened!)

My new local hero is a colleague of mine at my school who teachers Anatomy and Physiology, Chris Baker.  In addition to being an awesome role model for kids, and someone passionate about his craft, he has jumped deeper into the Twitter pool and has embraced 20% time as part of his classroom culture.  Consider giving him a follow – he’s a good egg!


Making It Stick…With Beanbags

The book Making It Stick – the Science of Succesful Learning has caused me to consider how I approach practice and assessment in my math classroom. The section “Mix Up Your Practice”, in particular, provides ideas for considering why spaced practice, rather than massed practice, should be considered in all courses.

But it was an anecdote which began the chapter on spaced practice which led to an interesting experiment for stats class.  The author presents a scenario where eight-year-olds practiced tossing bean bags at a bucket.  One group practiced by tossing from 3 feet away; in the other group, tosses were made at two buckets located two feet and four feet away.  Later, all students were tested on their ability to toss at a three-foot bucket.  Surprisingly, “the kids who did best by far were those who’d practiced on two and four-foot buckets, but never on three foot buckets.”


Let’s do it.

My colleague and I teach the same course, but on different floors of the building during different periods. Each class was given bean bags to toss, but with different practice targets to attempt to reach.

  • In my class, lines were taped on the floor 10 and 20 feet from the toss line.
  • For Mr. Kurek’s class, one target was placed 15 feet from the toss line.

Photo Oct 05, 9 33 54 AMAfter every student had a chance to practice (and some juggling of beanbags was demonstrated by the goofy….), I picked up my tape lines, and placed a new, single line 15 feet from the toss line.  Each student then took two tosses at the target, and distances were recorded (in cms).

We then analyzed the data, and compared the two groups (the green lines are the means):

bean bags

I love when a plan comes together!  The students, who did not know they were part of a secret experiment, were surprised by the results – and this led to a fun class discussion of mixed practice.  Here, the mixed practice group was associated with better performance on the tossing task. Totally a “wow” moment for the class, and a teachable moment on experimental design.

A Sneak Preview of My 2015-2016 Classroom

Today is the last day of summer vacation. In the past week, boxes have been unpacked, t-shirts and class decorations have been hung, and my awesome school custodians have provided me with even more whiteboard space – all the better for getting students up and moving


But beyond the physical layout for this year, here are some ideas I’ll focus on this coming year, many provided by my friends in the Math-Twitter-Blog-O-Sphere, the #mtbos for short.

GREETING STUDENTS WITH HIGH FIVES – Intertwined with all of the mathy goodness of Twitter Math Camp this past July was a simple and powerful device for student engagement from my friend Glenn Waddell – the High Five.

Each day last year, Glenn met his students at the door to give them a high five – a simple, caring gesture to establish a positive tone for class.  I often meet students at the door before class or linger in the hallway for informal chat, but I love the tradition and rapport Glenn establishes here and hope to emulate it.

ESTABLISH SEMI-REGULAR RANDOM GROUPINGS – this gem comes from Alex Overwijk, who is the king of Vertical Non-Permanent Surfaces and Visible Random Groupings. This year, I plan to randomly change my seating chart once each week, or at the start of a new unit – whichever seems to make the most sense at the time.  Traditionally, I’ll assign groups on my own and change them once or twice in a semester.  With some classes, I’ll allow students to choose their own groups.  But I have found that these practices often foster group-think, where a group will together develop the same bad habits through their work together.  I want more interaction, more sharing of ideas, especially in cases where students otherwise would not have encountered each other. I’m planning to assign each student a playing card on the first day, and set the new groups by dealing cards on the desks on days when it’s time to change.  I also confess here that a static seating chart was a huge crutch for me, as I would print out student names for me to glance down at when I needed.  Which leads into another goal for the new year…

better jobI MUST LEARN NAMES DAMMIT! – I confess this could be one of my weakest areas as a teacher. I could make all kinds of excuses for it, but it comes down to this – I drop the ball when it comes to learning and recalling my students’ names. We start school next Tuesday with a 4-day school week, and my goal is to know all names as they walk in the door by the first Friday.  I have already gone through my class rosters (which conveniently provide photos). How awesome would it be to know student names before they even walk in the door?

And beyond my current students, I am brushing up on names from students I taught last year. I’ve missed out on these connections for too long, and it’s my fault – time to work harder at it.

IMPROVING MY HOMEWORK PRACTICES – I don’t grade homework anymore, and in many cases have changed the nature of assignments. I’ve settled into the philosophy that I would rather have students think about a handful of meaningful, discussable problems rather than complete a laundry list. This year, I am looking to include more articles and video clips for students to observe and discuss in lieu of traditional assignments.

To go over homework, I often employ random methods to share works on my document camera, with mixed success. I’m finding that since I don’t directly look at assignments anymore, the completion is spotty at all levels. I may need to go back to a few minutes of checking and informal greeting at the start of a period to improve assignment fidelity.

grabUSING REFLECTOR TO ENCOURAGE PARTICIPATION – It can’t be the new school year without a new tech tool to try out. This year, I am looking forward to using the Reflector 2 program from the folks at Squirrels. This inexpensive software, loaded onto my laptop, allows me to relfect the screen from my ipad or iphone onto the laptop. I’m hoping this will allow me to be more hands-free for presentations, and hand over the ipad to students to take control – using Desmos or Deoceri to create works and share in front of the class. Also, I’m wondering what a class would look like where students could reflect their own phones onto the screen and share works. Day 1 of class could feature a “load test” – what happens when many, many students all try to reflect their graphs at the same time?

Now, out to the craft store to buy some last-minute stuff!

Twitter Math Camp – A Scalable Model for PD?

I’m finally gettick myself back to “real life” after about 3 weeks on the road, with stops at the Jersey shore, San Diego and Las Vegas. Sandwiched in the middle is the annual professional awesomeness of Twitter Math Camp. Now in its 4th year, TMC has evolved from a small group of online colleagues interested in discussing Exeter problems do a full-blown 4-day conference. Participants take part in the same morning session for each of the 3 days, a structure designed for digging deeper, encouraging conversation beyond the conference time, and developing ideas. In the afternoon, Keynotes by Ilana Horn, Chris Danielson and Fawn Nguyen inspire the crowd before afternoon sessions, which feel similar in structure to traditional conferences.  But with only 225 participants, the difference lies in the intimacy. Conversations easily move to meals and informal evening gatherings. The opportunity to extend the conversation with a speaker after the session hours is welcomed and embraced.

Compare this to the NCTM and ISTE conference models, even down to the regional and state-level conferences (full disclosure: I am programming co-chair of the upcoming Pennsylvania state conference, so I may wind up unintentionally yet, maybe I kinda-sorta mean it bashing myself here….let’s see).  There is a menu of sessions, some keynotes designed to draw folks in, and some planned sessions to wrangle folks together.  And vendors. Lots of vendors. No vendors at TMC…just straight-up PD, with the exception of sessions on Desmos and from folks at Mathalicious which begin to blur the lines between PD and self-promotion, but the mission is certinly not designed to support product. So, how is the TMC model different than the large-scale conferences? Here’s my non-exhaustive list:

  • Morning “themed” sessions at TMC encourage reflection through the week. Participants are expected to stick with their morning sessions and see it through.
  • The size of the conference provides laser-focus on math PD. No getting lost in the sea of 10,000 people in the convention hall.  The speaker you just saw in the last session may be sitting next to you learning along-side in the next session. Deeper conversation takes place at all hours.
  • Participants are encouraged to share out their experiences after the conference. Conversations continue via twitter, blogs and facebook long after the conference ends.
  • Teachers who cannot attend can participate and are welcomed into conversation. Global Math Department this week will feature a menu of speakers from TMC designed to summarize sessions and provide resources for those who missed the conference.  Presenters are encouraged to share resources for all on the conference wiki, and twitter conversations link teachers to teachers.

tmcThe morning session on Desmos I helped facilitate may have been the most powerful PD experience in my career. This is mostly due to the positive, team approach with enthusiasic colleagues who I admire greatly. Glenn Waddell from Reno and I have shared Stats ideas through twitter often, and see each other only now and then at conferences – his blog is a fountain of classroom resources.  Jed Butler has definitely become one of my go-to guys in the last year; his creativity and ability to build something new and meaningful quickly astounds me – check out the Desmos Bank he has developed, and share your works. And I was most excited to work with Michael Fenton. If you have never seen Michael’s Ignite talk – Technology and the Curious Mind – run there now….it’s only 5 minutes…we’ll wait for you… and visit the Reason and Wonder blog to get your feet wet with Desmos challenges. In the months leading up to TMC, we “met” a number of times via Google hangout to discuss what we wanted from our morning session – how do we structure the session for a large, diverse groups of learners. What themes do we want to develop through the conversations? How do we encourage learning to continue after the the conference has ended?  The team facilitation model has encouraged me to think this way as I consider other conference talks – hopefully starting with an ISTE session next summer with Jed.

What’s the future of the traditional “set and get” conference, in a connected world?  It seems that NCTM is starting to feel heat to change its model, as Matt Larson (President-elect of NCTM) attended TMC for a day with the NCTM executive director to soak in the experience, and presented a session in which NCTM’s Professional Learning Strategic Plan was outlined.  Some highlights:

  • NCTM will establish smaller, regional conferences based upon a theme, and replicate.  This sounded a lot to me like the Future Ready regional summit concept which is making the rounds this year – promoting a common message in more intimate gatherings,
  • Teams of professionals will be encouraged to attend and participate. How this works out financially is up in the air.
  • Reflective practice will become a bigger part of the NCTM message. This could mean promoting conversation after a conference through message boards (eh), allowing comments to published articles (I’d like to see this) or twitter/facebook/social media.

But in terms of PD, this exciting announcement leads me to believe NCTM is on the right track:

There are some promising developments here, though a problem of scalability will remain sticky.  TMC works because of its size and the zeal of its participants, and there is no desire to get much bigger. The math teacher twitter community is still small enough that conversations with colleagues from across the country are manageable.  What would happen is even 10% of the math teacher workforce became actively engaged?  It would be a great problem to have – but what gets lost?

Regional, focused conferences also sound great, but also present missed opportunity.  This year’s California TMC was amazing for me, as I had the chance to interact with west-coast math folks who I rarely see (or whom I have never met). Matt Vaudrey, Fawn Ngyuen, John Stevens, Michael Fenton, Peg Cagle….ok…..I’m stopping here….too many names to list. What connections are missed by regionalizing? Does it matter?

There’s a lot here to think about…check out the TMC wiki, find that 1 thing which fits in your classroom, and share it out.  The future of PD seems bright, but how do we manage it? I welcome your thoughts.

I Really LOVE These Math Tools, But…..

While the meat and potatoes of my recent ISTE session dealt with classroom use of the Desmos graphing calculator, a number of conversations with attendees after the session, both in person and via e-mail, moved in a different direction.  Specifically, the teachers I spoke with want to know where free apps fit in a handheld graphing calculator world?.  Some Q&A here….I’m hoping other will share their experiences and ideas.

Q: I’m not a 1-1 school.  How does this fit in my school?

Even though I work (and live) in a “nice” suburban district with decent financial support, I struggle to get technology working in my classroom.  A teacher across the hall from me has a cart, but the laptops there are slower than Cecil turtle and generally the educational payoff is not worth the technology aggravation.  We have a few computer labs available to use, but a lab scenario is often not what I am seeking for in my lessons.

cell phone

But all of my students have cell phones, and by the end of the first week with me we have used them a number of ways to explore and communicate.  Desmos works remarkably well on a cell phone, kids pick it up immediately, and many have it on throughout class time to use.  While the app is nice, our wifi is quite good so we prefer using the web version. For stats class, Stat Key was a welcome online addition, and allowed for many class investigations.

Q: But don’t your kids end up texting in class?

Yep, kids are generally weasels, when provided the opportunity.  But I recall my own 8th grade math class, where I passed notes constantly.  I’m relieved that none of my teachers told me I had lost paper and pencil privledges over my middle-school note-transit system.

I’m constantly reviewing my classroom management style, and make revisions based on readings and discussions.  I’m confident that handheld devices aren’t going anyplace soon, so I have two options: utilize the technology or bury my head deeper in the sand.  Sure, there are moments where I resort to silly tactics to focus my high schoolers – cell phones face down, corner of the desk, or away altogether.  But making sure students understand responsible use of technology should be build into our classroom mission; I’ll do my part to prepare them for these eventualities.

Q: Do you mandate your students purchase graphing calculators?

This question has many tentacles for me.  I teach honors freshmen, so my suggestion has usually been to consider purchasing a device, learn how to use it well in our courses, and this will put them in a good place for AP Calculus.  Also, I teach AP Statistics, where a graphing calculator is an indispensible tool and I do expect them to have one. (Yes, there are some great individual sites and apps for statistics. But the TI products are still ideal for what we do in AP Stats).  I also have a class set of Nspires, which helps with our non-AP students.

So, the short answer here is a conditional “yes”, but it is becoming much more difficult for me to stand in front of parents at Back to School night and justify the purchase, especially after I discuss the many tools we use in my class.  I also understand that while I am comfortable with many new, free tools, many of my colleagues are not.  I need to consider where I reside in my department’s tech eco-system.

I’m expecting that my answer to this question will shift to a definitive “no” in the next few years.  Until then, some creative solutions, like graphing calculator loan-out programs, may be a way to go.

Q: What about standardized tests?

In AP Stats, students are expected to bring a device to use to the exam, and know how to use it.  So, there is responsibility on my end to ensure that my students have meaningful problems and practice.  There has been chatter of AP eventually moving to an online administration, but I didn’t hear anything concrete about this at last month’s AP reading.  SAT and ACT exams still expect students to bring their own approved calculator devices.  With many of the recent bad press there has been over exam exposure and cheating, I have trouble seeing a scenario anytime soon where any communication devices would be allowed.  Put another notch in the “I still need my students to have a graphing calculator” column.

But if you take a look at some online versions of state and national assessments, you’ll see students provided tools within the test.  And there are some exciting things happening regarding ipads and other non-traditional devices. Texas recently approved the Desmos test-mode app for use on state assessments, where the first attempts at implentation occured recently. Cathy Yenca chronicles her experiences with this on her blog, and you can read more about implentation issues on the Hooked on Innovation blog.

It’s an exciting time to be a math teacher, but also one where some technology growing pains will occur.  Looking forward to hearing what other schools and districts are thinking.

Put(t)ing Rational Numbers in Order

Many of my friends and followers have caught onto one of my guilty pleasures: my wierd fascination with The Price is Right (read about Price is Right and counting principles in this old post).  Here’s how a pricing game made for a fun review activity, and also made my life flash before my eyes (read to the end for that).

Here in Pennsylvania, we use the PA Core Standards.  For Algebra 1, here is a standard under “Anchor 1”:

A1. Compare and/or order any real numbers.  Note: Rational and irrational may be mixed.

Seems innocent enough.  Here is a sample “open-ended” task used to assess understanding on our state’s Keystone Algebra 1 exam:

image001 (1)

Exciting….now let me go over here and watch the paint dry….

But during the NCTM conference, a lightning bolt hit. I was checking out a putting game at one of the booths, and I suppose rational numbers were on my brain….Hey – Golf + ordering rationals = feels like Hole in One to me!

In the Price is Right Hole in One game, contestants place groceries in order from least to greatest by price.  The number of items they can order until they are incorrect determines where they putt from. After a quick trip to the sporting goods store to find a putting cup, and some time with a Google Doc, we’re all set!

To start, I created a Google Slides presentation with 6 games.  Each game has 6 numbers for students to put in order:

During the game, all students in the class had about 2 minutes to place the numbers in order.  They, we randomly drew our “contestant”, who came to the board to fill in the 6 boxes on the board.


Next, we went through the numbers from left to right, and determined how far the contestant had gone in successful ordering.

puttOn the floor, 6 lines were taped.  Line 1 was on the other side of the room, and the lines were closer and closer to the hole. If a student had 4 numbers correctly ordered, they were allowed to putt from line 4.  Two students were able to order all of the numbers and tried their putt from about 2 feet away.

Those who made their putts earned candy to share with their group.  In about 20 minutes, we got through 4 games – not bad for ending a Friday on a fun note.

But be careful! My last “contestant” – one of my less cooperative students and a sometimes hot-head – was able to putt from line 6 with the help of his group.  After missing the first putt, I reminded him that the game is really Hole in One – OR TWO, and had a second chance. Lining up the putt…he took it easy…and missed again.  This is when he raised the putter up and, for a brief second, it looked like the putter could end up flying in my direction.

“Sean, just pick up the ball and put it in the hole….here’s some candy…”

Introducing Discovery Hour with Codebreaking

Our school has been on a semester block schedule for over 20 years, with some tweaks made to accomodate building size, AP courses and electives. But this year brought a major schedule change, and an opportunity to think about how we use time to engage students. After periods 1 and 2 (each 75 minutes), all students move into something called HATS period. The acronym stands for Hatters Achieving Targeted Success, and during the period students have a lunch period, along with assigned time with teachers. It’s a great mid-day block for students to touch base with activities and clubs, seek help, make up work, and our RTII team has utilized the time to meet formally with students and facilitate individual help sessions.

I saw an opportunity to engage students in meaningful activities during this time, and have started Hatters Discovery Hour – modeled after the Genius Hour concept many elementary and middle schools offer. My thought is that so many of our teachers have awesome ideas to share which don’t quite fit class time. Also, it’s an opportunity for students to experience teachers they may not cross paths with during their high school career. Let’s build more connections!

The past 2 months have seen some fascinating offerings.  Our No Place for Hate Team has used Discovery Hour to facilitate open discussions on race relations.  Meanwhile, a science teacher shared his experiences working as an EMT in a medical diagnosis session. Juggling was the fun focus of one session, and Discovery Hours on memory systems, photography and meditation are in the works.


For my Discovery Hour session, I shared many of my collected activities on codebreaking. With Oscar season just passed and some simmering interest in the Imitation Game, it was a perfect time to talk about the role of codebreaking through history. Even better, my principal and district curriculum director (and my former boss) were on hand to join in the fun:

I was ambitious, trying to fit 4 codebreaking challenges into the hour. In the end, we had just enough time to keep things moving and hold some fun discussions in these 4 areas. Scroll below to download the handouts.

CRYPTOGRAMS – We started with a basic letter-to-letter cipher. I used a long quote from Bill Gates, which almost turned out to be too long – as I felt a time crunch hitting early. But longer quotes allow more entry points, and I couldn’t pull my principla away from the challenge!

CAESAR SHIFTS – Here we used an online applet to explore shifts, and this provided an entry point for modular arithmetic, which few of the students had encountered before.

HILL CIPHER – By now we had established that the first two coding procedures did not seem too secure. I have shared Hill Cipher with students in my classes before during matrix units, and again a cryptography website was helpful in providing some easy codebreaking trials. When I have done these in class, I often develop problems which get around the modular arithmetic issue (it takes longer to discuss than I often have time for) but we were able to squeeze in a 5-minute mod primer.  See below for other Hill Cipher problems I have used.

THE ENIGMA – The cherry on the sundae, and where many students were stunned by the complexity. This online Enigma simulator is one of my favorites – I love the visual of the wiring. So many good questions concerning inverses, how codebooks were traded and how the British broke the code. I left enough time to show Numberphile’s Enigma video, which capped off the hour nicely.

Looking forward to sharing more of what I know in later Discovery Hour sessions, and thrilled so many of my colleagues are buying into the idea.