# Category Archives: Uncategorized

## Activity Builder Reflections

We’re now about 9 months into the Desmos Activity Builder Era (9 AAB – after activity-builder). It’s an exciting time to be a math teacher, and I have learned a great deal from peeling apart activities and conversing with my #MTBoS friends (run to teacher.desmos.com to start peeling on your own – we’ll wait…). In the last few weeks, I have used Activities multiple times with my 9th graders.  To assess the “success” of these activities, I want to go back to 2 questions I posed in my previous post on classroom design considerations, specifically:

• What path do I want them (students) to take to get there?
• How does this improve upon my usual delivery?

AN INTRODUCTION TO ARITHMETIC SERIES (click here to check out the activity)

My unit or arithmetic sequences and series often became buried near the end of the year, at the mercy of “do we have time for this” and featuring weird notation and formulas which confused the kids. I never felt quite satisfied by what I was doing here.  I ripped apart my approach this year, hoping to leverage what students knew about linear functions to develop an experience which made sense. After a draft activity which still left me cold, awesome advice by Bowen Kerins and Nathan Kraft inspired some positive edits.

In the activity, students first consider seats in a theater, which leads to a review of linear function ideas. Vocabulary for arithmetic sequences is introduced, followed by a formal function for finding terms in a sequence. It’s this last piece, moving to a general rule, which worried me the most.  Was this too fast?  Was I beating kids over the head with a formula they weren’t ready for? Would the notation scare them off?

The path – having students move from a context, to prediction, to generalization, to application – was navigated cleanly by most of my students.  The important role of the common difference in building equations was evident in the conversations, and many were able to complete my final application challenge.  The next day, students were able to quickly generate functions which represent arithmetic sequences, and with less notational confusion than the past.  It certainly wasn’t all a smooth ride, but the improvement, and lack of tooth-pulling, made this a vast improvement over my previous delivery.

DID IT HIT THE HOOP? (check out the activity)

Dan Meyer’s “Did It Hit the Hoop” 3-act Activity probably sits on the Mount Rushmore of math goodness, and Dan’s recent share of an Activity Builder makes it all the more easy to engage your classes with this premise. In class, we are working through polynomial operations, with factoring looming large on the horizon.  My 9th graders have little experience with anything non-linear, so this seemed a perfect time to toss them into the deep end of the pool.  The students worked in partnerships, and kept track of their shot predictions with dry-erase markers on their desks. Conversations regarding parabola behavior were abundant, and I kept mental notes to work their ideas into our formal conversations the next day.  What I appreciate most about this activity is that students explore quadratic functions, but don’t need to know a lick about them to have fun with it – nor do we scare them off by demanding high-level language or intimidating equations right away.

The next day, we explored parabolas more before factoring, and developed links between standard form of a quadratic and its factored form. Specifically, what information does one form provide which the other doesn’t, and why do we care?  The path here feels less intimidating, and we always have the chance to circle back to Dan’s shots if we need to re-center discussion.  And while the jury is out on whether this improves my unit as a whole, not one person has complained about “why”…yet.

MORE ACTIVITY BUILDER GOODNESS

Last night, the Global Math Department hosted a well-attended webinar featuring Shelley Carranza, who is the newest Desmos Teaching Faculty member (congrats Shelley!).  It was an exciting night of sharing – if you missed it, you can replay the session on the Bigmarker GMD site.

## How Do We Assess Efficiency? Or Do We?

A problem on a recent assessment I gave to my 9th graders caused me to reflect upon the role of efficiency in mathematical problem solving. In particular, how much value is there in asking students to be efficient with their approaches, if all paths lead to a similar solution?  And should / could we assess efficiency?

The scene: this particular 9th grade class took algebra 1 in 7th grade, then geometry in 8th.  As such, I find I need to embed some algebra refreshing through the semester to dust off cobwebs and set expectations for honors high school work. For this assessment, we reviewed linear functions from soup to nuts. My observation is that these students often have had slope-intercept form burned into their memory, but that the link between this and standard form is weak or non-existant.  Eventually, the link between standard form and slope ( -A/B ) is developed in class, and we extend this to understanding to think about parallel and perpendicular lines.  It’s often refreshing to see the class see something new in the standard form structure which they hadn’t considered before.

The problem: on the unit quiz, I gave a problem which asked students to find the equation of a line parallel to a given line, passing through a point.  Both problem and solution are given in standard form.  Here is an example of student work (actually, it’s my re-creation of their work)….

So, what’s wrong with the solution?  Nothing, nothing at all.

Everything here answers the problem as stated, and there are no errors in the work. But am I worried that a student took 5 minutes to complete a problem which takes 30 seconds if standard dorm structure is understood?…just a little bit.  Sharing this work with the class, many agreed that the only required “work” here is the answer…maybe just a “plug in the point” line.

My twitter friends provided some awesome feedback….

Yep, we would all prefer efficiency (maybe except Jason). Thinking that I am headed towards an important math practice here:

#### CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

It may be unreasonable for me to expect absolute efficiency after one assessment, but let’s see what happens if I ask a similar question down the road.

Confession, I really had no idea what #CThenC was before this tweet.  Some digging found the “Contemplate then Calculate” framework from Amy Lucenta and Grace Kelemanik, which at first glance seems perfect for encoruaging the appreciation for structure I was looking for here.  Thanks for the share Andrew!

Yes, yes!  Love this idea.  The beauty of sticking to standard form in the originial problem is that it avoids all of the fraction messiness of finding the y-intercept, which is really not germane to the problem anyway. Enjoy having students share out their methods and make them their own.

What do you do to encrouage efficiency in mathematical reasoning?  Share your ideas or war stories.

## 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: http://regionals.nctm.org/.  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.”

Wow!

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.

After 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):

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…

I 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.

USING 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.

The 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.

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.