The Escalator Problem – It’s not perfect… yet.

One of the things we try to tell teachers is that they shouldn’t let the fact that a homemade resource has an imperfection force them to not make it or post it. We say this to teachers that are interested in attempting to flip their classes all the time. If you can think of a way to support your kids when they are away from you, then do it. Imperfections be darned.

Really, there is only one way to get better at providing homemade resources to your students, and that is just to practice, practice, practice. This is a great model to show your students, as well. The learning process is one that rests on attempts and feedback. The feedback on a perfect try tends to be quite boring. The feedback on a high-quality, but imperfect try tends to be a heck of a lot more interesting.

2guys - success

The message here is not to make mistakes on purpose because it makes like interesting, but rather that we shouldn’t wait for our contribution to be perfect to make it. Active contributors form the foundation for effective collaboration.

There is a lot of value, too, even in an imperfect video or picture, even an imperfect one. The students just respond differently when there is a story, or better yet, the image or voice (or both) of their instructor in the footage.

In my own practice, there is definitely a ceiling to the quality with which I can create material. I just don’t have skill or the tools to make things perfectly.

But, let’s not let that get in the way of a good idea…

So, if I showed you this…

… which is a video of this…

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… could you answer this?

What’s your guess?

If you wanted to check your guess, what kind of math would you do?

I have a video answer, too, if you wanna check your work.

Great Conversations and Important Lessons – Reflections on #MACUL15

Chance to Surprise you

#MACUL15 is over and yet it feels like it’s just begun. The conference ended after Two Guys (@2GuysShow) finished their closing keynote, but there were a lot of conversations that were just beginning at that same point. Some excellent conversations among some excellent educators. These conversations aren’t ending because the conference is. These conversations are just getting started.

Just like everyone else, I’m having my own conversations that I’m looking to keep going. And these conversations seem to have a few recurring themes.

The young people in our classes are capable of so, so much.

Often, the reason we are disappointed with our students’ performance isn’t because our expectations are too high, but instead because they are too low. Improved curriculum, classroom management, and updated assignments can play significant play roles in helping students achieve and #macul15 offered lots of chances to discuss this. Have you seen The Literacy Shed? Explore it and consider what it might do for our struggling writers. Videos with no dialogue that the students can watch, discuss, and then write the story for. Sometimes they just need help finding the words. There’s a math version, too.

But there’s more to it than that. Many of the presenters that I heard communicated a consistent message: Releasing the incredible potential inside of every kid requires meaningful relationships with caring adults. The kids need to know that they matter. That the community is richer because they are a part of it and weaker when they are missing. That each individual contribution has value because it reflects a perspective that is unique. Many kids have parents and coaches who fill those roles. Many do not. The teacher can be that caring adult. In the world of education, where so much is out of the teacher’s control, each teacher can control one thing: That they value each student in their class. As Amber Fante (@AmberFante) said, “When you believe, you teach differently… the underdog can become the hero.” If you haven’t watched her Lightning Session, you probably should.

There are few things as powerful as connecting our classroom to the outside world. 

Our students are getting more and more used to a world without walls. There’s a reason for that: Being connected to that world is really friggin’ cool. I met the two teachers in the picture below (who refer to themselves as Two Sassy Apples). They were honored on stage before Friday’s keynote. They wanted their second graders to be able to be there and see it. So… Facetime.

Sassy Apples Facetime2

It was such a wonderful moment. The students cheered and laughed through the phone. They shhhhhhh’ed at each other vigorously while the MC was introducing their teachers. I know this, of course, because I got the honor of holding the phone so the kids could watch. (It happened to be hat day in their class. They loved that I was wearing a hat, too.)

Sassy Apples Facetime

Consider what those kids are learning from experiences like these? Those students are learning that their classroom’s walls are really only there to keep them out of the wind and rain. Those walls don’t have to be barriers to things that were previously too expensive, too distant, or logistically impossible to bring to them. The awesome and exciting things that are outside those walls can totally come into their classroom. We have the tools to go and get them.

If you want to teach effectively with technology, real student growth MUST be the primary focus. And real student growth is a messy process. It takes mistakes, retries, feedback, patience. The timeline is indefinite.

2guys - success

And while we’re on the subject, the same is true for teachers updating their practice. Brooke Mulartrick (@brookem1015) did a great job of modeling a differentiated learning process in her session by creating experiences like these in her half-day Wednesday session. Something to challenge people at all levels. A chance to collaborate and get instruction. And a chance to contribute to a single product that serves both as feedback to the teacher and learner, but also a reference that the learners can take with them going forward. Just an excellent design.

Learning is learning. And learners are learners. Given similar conditions, adult learners look a lot like young learners. See?

These are adults on Thursday exploring Dan Meyer’s (@ddmeyer) Magic Octagon:

MACUL Octagon

And these are my students this past fall exploring The Magic Octagon in class:

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Those of us who primarily teach adults shouldn’t prepare for differentiation any differently than teachers who teach young people.

Couros Quote

With all learners, it’s less about the final goal and more about the process of learning.

And finally, anyone who says that secondary math teachers aren’t flexible, curious, or interested in learning new things? I would encourage you to reconsider. There are a lot of us who want to get better. You see why I’m not that concerned about the future of math education? We turn out quite nicely when given the opportunity to discuss it.

MACUL Selfie

And then I went to check out my #miched colleague Zach Cresswell’s (@z_cress) math session…

Zcress Full

Thanks for everything #macul15. Let’s keep these conversation going and see where they’ll take us.

A toolbox that is truly full

When I think of a math activity that really flexes it’s muscles, I’m reminded of the activities that could reasonably be solved multiple different ways with no method being preferable on the surface. These are tricky to create (or to find and steal). They are also somewhat taxing on your students (especially if they aren’t used to this kind of problem-solving). It requires a more intense, higher-order level of thinking.

photo credit: Jo Fothergill - Used under Creative Commons

photo credit: Jo Fothergill – Used under Creative Commons

Many schools are reaching the stage where students are carrying around smart devices. Increasingly schools are issuing them (we are up to 4 districts in our country that are now 1:1). Also, in many districts, students can be trusted to bring smart phones in with them. With all of these devices available, it seems like we could integrate a new set of tools into our tool box for consideration. We should design activities that allow the students some control over what mathematical techniques they choose to employ. But increasingly, it’s making more sense to also allow the students some control over what tech tools they are making use of.

That is a nerve-racking idea for some, especially since as soon as students start dabbling in technology that the teacher is unfamiliar with, they become their own tech support. There is a very real (and perfectly understandable) anxiety over students using technology pieces that the teachers aren’t familiar with. But we could flip that on it’s head.

First, we could model some of the tech pieces that we are familiar with.

Consider an activity where in the students use a Google Form to poll their classmates, then enter the data into a Desmos sheet to do the analysis. The formative assessment of the analysis could be done on Socrative or Google Forms.

I mean, this is a standard math task: Gather some data, represent it visually, analyze, and produce a product to submit to your teacher. What makes this different it two-fold: First, some of the more annoying parts are going to be relieved by the technology (namely recording the data, plotting the points, and drawing/calculating the best fit line… those are also the parts that create barriers to our students with special needs). Second, you are giving the students meaningful experience using their technology for something that makes their school work easier and more productive. (Imagine that… both easier and more productive… both…)

One of the goals of an activity like this is the students gaining an appreciation of the roles of each of those different technology pieces, in the same way as we give them specific prescribed practice with the math skills to gain comfort. But it should stay there in either case. At some point, the students need to build in a working understanding of each of the tools in their tool box – math, tech, or otherwise. (I was even vulnerable to whining… the right kind… used at the right time. Proper tool for the proper job.)

Then, when we unleash our students to solve a problem by any means necessary, with a proper foundation underneath them, we run a much lower risk of them choosing something completely off-the-wall. Students might replace our technology with choices of their own, but if they know that we have a standby that will work, then often the replacement is something they find more useful… and it might be something we’ve never seen before… and they might be able to teach us how to use it.

And never underestimate the power of allowing a student to be the expert in the room once in a while.

Full disclosure: The data that I plugged into the Google form came from here. Many thanks to who is named as the owner on the site.

Should we test them? or not test them? (Hint: Those are the wrong questions…)

This time of year in Michigan, standardized testing is on everyone’s mind. This year is a little more frantic than others, I’m afraid. Michigan’s Department of Education is piloting the online version of a new state test. In my role, I’ve spent a lot of time contributing to support all over the state trying to help concerned educators prepare themselves and their students for this transition.

Besides that, every Michigan HS Junior is given a chance to take a college entrance exam. Since the inception of this practice, this exam had always been the ACT. Then, just after the new year, news broke (somewhat out of nowhere) that Michigan was going to switch to giving the SAT.

Now, each of these tests has a whole machine surrounding it. There are practice tests, prep sessions, special activities put in place to prepare for both the look and feel of the testing items as well as for the content. In many ways, “teaching-to-the-test” has become a foregone conclusion. This is especially true in districts who are working very, very hard to improve the test scores for evaluative or punitive reasons. (More on this later.)

All of this fervor can really make a guy wonder whether or not this testing is worth all the hassle. Are we doing good things to education by instituting all of this testing? Are frequent assessments the right way to go?

And I think those are the wrong questions.

Consider a person who is hyper-interested in his or her weight. Like dangerously so. This person steps on the scale several times a day. And makes aggressive changes for the sake of gaining or losing 10 or 20 lbs very, very quickly. On what can we blame this problem?

Lots of things, I suspect. This person may have a background with some experiences that need to be reconciled. This person may have anxiety issues that need to be resolved. This person may be in a personal or professional relationship that puts unrealistic pressure on his or her appearance. This person may spend too much time focusing on and associating with other people who have similar habits. There is a culture that he or she has become a part of that feeds into this point-of-view.

The scale that he or she steps isn’t the problem (provided the scale is accurate). The scale is the tool that provides the information. The information is then getting abuse by the recipient. The solution to this problem is NOT to dispose of the scale. The abusive recipient is still going to seek for information and they will find it in perceived tightness of clothes, or calories consumed or duration of a workout.

What we need to adjust is the response to the information.

Right now, we are asking our schools to step on the scale too frequently, and making too much of the number we get.

Look, changes in policy and curricula often show effects slowly. And we should look for slow, sustained improvement. This is evidence of a cultural change that is becoming a new standard. Just like the dieter who is looking to lose 50 pounds. A two-year journey losing a three or four pounds per month doesn’t make for an exciting, story. It doens’t get you on NBC Shows, but it’s healthy. It’s sustainable. It is evidence that a real change has taken place.

It is with this in mind that I will assert that the tests aren’t the problem with our educational testing culture. While I suspect that we are testing too much. If the person from the analogy has a scale in every room, then it might be useful to reduce that number to one, but it would be wrong to blame the tests. They are giving us information. And we in the educational community aren’t handling the influx of information very well.

So, I have some thoughts about this.

What if we only formally and decisively tested students every other year? When it comes to state tests that determine school ratings, funding, oversight, and evaluation, how about we get on an every other year plan. We aren’t looking for quick-hitting solutions. We are looking for culture changes. The most effective instructional and curricular changes take time to go from implementation to fruitful improvement anyway. So, if the 2013 testing cycle revealed content weaknesses in a certain area, then you have 24 months to implement an update to your system that will improve it. Then in 2015, we’ll see how it’s going.

Taking a standardized test well is NOT a meaningful life skill with which to send students away from school. I’ve heard this one from a variety of different angles. The “they’ll-need-it-to-get-through-college” argument, to the “managing-test-anxiety” argument, to the “we-need-our-scores-to-jump-30-percentage-points-in-3-months” argument. This has been the most troubling development I’ve seen. This goes beyond “teaching-to-the-test”. This is downright teaching test-taking strategies as though the skill of taking a test has any application. It doesn’t. Students need to take tests well because we choose to test them. When we change our focus, we change this skill set. It is completely dependent on our choice. EVERY SINGLE other skill we want students to leave school with are determined by appealing to some outside need. Critical thinking, basic math skills, reading, obedience, playing well with others, healthy eating, tolerance for diversity, etc. These are things that you can EASILY give reasons for students leaving school with these skills in their hip pockets. So, why are we spending one second teaching standardized teaching strategies?

I’ve never seen a school or educational department include students (or even suggest it) in the process of collecting or analyzing the formal and decisive testing data. Why not? When it is becoming more and more evident that there are huge gains to be made by putting students in a position to self-monitor and to train them to be competent in doing so, why are we allowing this opportunity to pass us by. (I don’t think our decision-makers trust young people as much as you and I do.) Perhaps while we are training them to be effective self-monitors, we see minutes that they could be spending practice math problems ticking away. It’s too bad that we have begun to operate on such a short-sighted view of efficiency.

Look folks, I’m not any more excited about this hyper-evaluative testing culture than anyone else, but I think that we need to take a step back from our repulsion and really look at what the problem is so that we can really solve it.

Algebra, Geometry, Desmos, and the number line…

Number lines are wonderful tools. Simple, elegant, and useful to everything from beginning to count, to categorizing number groups, to helping students make sense of irrational numbers.

So, naturally my mind started racing when my daughter handed me this.

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I think she intended for me to throw it away, but, sticking to the old adage “One man’s trash is another man opportunity to integrate several pieces of instructional tech to create a delicious opportunity for young people to learn mathematics” (Paraphrased), I decided that this was just to powerful a tool to chuck.

So, I thought 3-Act. The problem is, unless I’m extremely resourceful, I don’t have enough for an Act III here, so I switched to a different number line.

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And trimmed it.

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There we go!

Okay, so let’s start estimating the locations of some missing values. To give it a bit of context, I placed the number line scrap on a grid on Desmos.


Then, to collect the data, I created a Google Form for the students to enter their estimated coordinates at points 100 and at 55 in the missing portions of the number line.

Once you get all of the student data entered, you can simply copy the x and y columns in the Google Sheet…

Desmos Forms

… and paste it into a new line in your Desmos graph.


Then, the second part of the lesson becomes the teacher facilitating a conversation about the different ways we could either hone down our estimates, or calculate EXACTLY where the 100 point would be. (The two ideas I had were modeling the number line as a linear function or as a hypotenuse of a right triangle. Both scream for proportional reasoning, which my experience suggests is a useful activity anytime it can be fit into the curriculum.)

Then, once they feel like they’ve come up with answer they like a bunch, you can reveal to them the answer.

You may also choose to re-paste their estimate points so they can see how well they did as a group.


I like activities like this because it provides ample opportunity for focused guessing, collaboration, and a variety of solution processes. It also asks a pretty simple question at the beginning, which helps to include everyone, regardless of level.

It just seems the longer I’m involved in math education, the more and more functional uses I’m seeing for the number line.

Not to reinvent the wheel, or anything…

photo credit: Crispin Semmens - Used under Creative Commons

photo credit: Crispin Semmens – Used under Creative Commons

Now that I’ve taken a few steps forward into this world of instructional technology, I’ve been able to step back and reflect a bit.

I find myself often getting opportunities to explore new apps, devices, technologies, etc. (Most recently was this ball called “Sphero” which connected to a device via bluetooth and turns the device into a remote to move the ball around on the floor… pretty solid design and challenging to use. Anyway…)

All these devices/apps/tools seem to fit into two very broad categories: stuff that helps us do stuff we already do better and stuff that allows us to do stuff we previously couldn’t do (or at least couldn’t realistically do).

and while I feel like those are important distinctions, they tend to both get brushed aside as “reinventing the wheel”.

And it makes sense. Teachers are resourceful people. They are pretty good at recognizing what they need and finding solutions to make it happen. Teachers generally don’t spent time reusing tools/processes that don’t work or don’t provide value (based on the values that teacher has).

So, it seems like anytime we introduce a new technology piece to a teacher, we are comparing that teacher’s existing processes and practices to either…

A. something that gives them a different (hopefully better) way to do something they already do or

B. something that give the teacher the ability to do something they don’t currently do.

Either way, we are asking that teacher to update their practice. And if they don’t already have a need (or a desire) to do that, then they are likely to perceive this as “reinventing the wheel.”

And they aren’t really wrong.

This is where those of us to are inclined to consistently seek innovation need to recognize the value of creating “intellectual need.” This idea was first introduced to me by Dan Meyer being applied introducing new processes and tools to math students, but I think there are pretty solid parallels to sharing new technologies or processes to teachers. The idea is that as long as the learners have tools or processes that work fairly well for them, they won’t value learning new tools or processes.

To get around this with students, teachers can introduce a new problem-type or content to create a need for a new tool or process. You can administrate the need.

With teachers, it’s not quite as simple as that. Teachers have the ability to shield themselves in a lot of different ways from the changing conditions. Teachers are flexible. In this case, the task of creating need for a new tool isn’t administrative.

The task is inspirational.

Teachers need to see the potential for the new tools. They need have the new processes modeled. They need to see the vision of where this could take them and their students.

We need to be out of the business of process-sharing and into the business of idea-building. What would you like to do that you can’t do now? What do you do now that you wish worked better? Let me show you some cool classroom action that got me excited.

It’s can’t be about the tools. It needs to be about the vision for the classroom.

“Folks, this isn’t a session on Google Drive. It’s a session on collaboration and accessibility.”

“This isn’t a training on Desmos. It’s a training on helping make higher-order math thinking easier for your students to engage.”

“This isn’t a PD on the TI-Nspire. This is a PD on how to make statistical and graphical analysis a community activity.”

If they already have a wheel, they don’t need a new one. But perhaps with this or that new tool or process (whatever it is), that wheel that’s already been invented can take the students farther than they’ve ever gone before.