My Thoughts on #MiFlip15

Today, I attended the MiFlip Conference at Steelcase University in Grand Rapids, MI.

I was going for a variety of reasons. I need people to explain flipped learning to me. I need skeptics to be skeptics. I like to fly-on-the-wall discussions where advocates and skeptics collide. Not because I enjoy confrontation, but because Michigan has some wonderful educators (check out #miched if you want to get a taste) and I figured that this particular collection would be unmasked, open, and willing to both be skeptics and advocates.

I was not disappointed.

First, I want to mention Matt Roberts (@mmcr) from Grand Valley State University who brought this with him as part of his presentation.

Hype-cycle

This is “The Hype Cycle”, which I recognize from a variety of innovations over my relatively short career in education. I’m certainly not trying to talk down the people who are excitedly sharing their experiences and enthusiasm about flipped learning. It’s just that there’s some things that have always made me hesitant about fully advocating flipped learning and Matt helped me make sense of some of them.

I feel like he did a nice job of expressing why he think flipped learning needs to be looked at holistically. He led an awesome session on the realities of learning in a flipped model and understanding what we are asking these students to do… which is, in some cases, something they’ve never been asked to do before. When we lead students through a flipped learning model, we are asking them to take ownership of their learning in ways that might be new to them. They need to self-regulate. They need to recognize their confusion and use that sense of mental discomfort as a motivation to get that issue resolved with the variety of resources the teacher has made available or that the internet as a whole has to offer. This goes even further when we push blended learning to the next level and start (as was so excellently described by Anne Thorp (@athorp) ) expanding the options to include flexibility in assignment contexts, due dates, and formats. There will be an adjustment period if students have only known educational worlds of note-taking, rigid due dates, and common assignments.

That forces us to help the students become comfortable with the learning process. And many of them will need help. The try-fail-improve-try-again model can be a frustrating one for kids who aren’t really accustomed to failing. Besides that, as Matt brought up in his discussion, things like sleep, nutrition, and exercise play a pretty significant role as well. Regular review, making connections and effective practice have to become things that get built into the curriculum. Flipped learning is more holistic than other instructional models because it so often looks at the hour that the class spends together as merely an important part of a larger learning process.

Many students are raised in education looking at the hour that the class spends together as the whole class. Effectively managing that transition is vital to ensuring that students are experiencing the best that flipped learning has to offer.

The teacher looking to embrace the flipped learning model needs to recognize that they are taking on more than simply restructuring their assignments. They are likely redefining learning to students who may not have entered their class expecting that type of experience.

A few additional notes.

  • Thanks to Dan Spencer (@runfardvs) for giving me a one-on-one tutorial on Camtasia. Totally needed it and it totally worked.
  • I appreciate the energy that Anne Thorp brought to the table. (I’m not the only one that is saying that, either, by the way.) Our paths are going to cross a number of times in the future and I am very excited about that.
  • And, in a much less academic way, I’m thankful to Tara Becker-Utess (@t_becker10) for being willing to drive the carpool from Dimondale, MI (about an hour east of Grand Rapids).
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Climbing the Wealth Ladder

So, during my recent internet travels I came across this tasty picture.

Oh! The math we could do with this!

Oh! The math we could do with this!

What questions come to your mind when you see this? I can think of a couple.

Which stack has the second-highest value? Which stack has the lowest-value? (Start with predicting since those are essentially counting by 5s, 10s, and 25s questions.)

Suppose you had three different stacks of dimes and then set them beside three stacks of nickels of equal value. Would there be a consistent height difference? Would the nickels proportionally taller? Would there be no relationship at all?

What questions do you have? What do you think you could do with this? What do you think your students could do with this?

Student blogging has me thinking… (reaching out for help once again.)

I think I want to try student blogging next year in my Algebra II classes. I’ve only ever taught Algebra II once and I didn’t do a particularly wonderful job.

It was the sense-making that really got to me. My students were pretty good at learn procedures and algorithms, but the long-term retention was remarkably low. I have seen several examples of student blogging and feel like if I framed the discussion questions properly and encouraged the students to read each other’s posts, and comment. That could… COULD… open up a different mathematical thinking experience for the students.

If that were used to supplement the number-crunching practice, and the group problem-solving and exploration, that could potentially act as a way to deepen (or at least broaden) the thinking that the students were being asked to do. In addition, the opportunity for the entire internet to read and respond can add an extra-level of interaction. The students wouldn’t have to apply their real name if they didn’t want to. There is a chance for creative anonymity.

All of that being said, if you have your students blog, will you please comment on this so that I can pick your brain on what’s worked, what hasn’t, what to watch out for and what to definitely do! Links to other blog post would be much appreciated. E-mail this post to people you know who do this. I would love a rich, challenging comment section on this one. And trust me, if you don’t help me, I will make my own idea and learn this the hard way!

 

 

Coke vs. Sprite – One Class’ Response to Dan Meyer’s #wcydwt Video

2014-04-03 11.08.14

Almost three years ago, I highlighted the Coke vs. Sprite video that @ddmeyer made. It is a very intriguing question (which glass contains a greater amount of its original pop) without a clear answer.

Today, I let a class give it a go and here’s what they came up with.

First, they chose to model it with integers. Said one student: “I pretended it was a jar with 10,000 marbles.” 2014-04-03 11.07.36

Then they assigned “a dropper-full” to be 100 marbles. So, the first dropper took 100 red marbles and placed them into the jar with the 10,000 green marbles.

Now we assumed the stirring made the mixture homogeneous which meant that there was a consistent 100:1 green-to-red marble ratio in the right jar. So, when we pull another 100 marbles to put back, (with a little bit of rounding) we pull 99 green marbles and a single red marble back into the left jar.

2014-04-03 11.15.25

 

A little number crunching reveals (at least in this model) that there would be 9901 original-colored marbles and 99 other-colored marbles in each jar.

My original assumption matches their investigation. It seems (at least by this model) that at the end of the video, each glass is containing equal amounts of their original soda.

Another teacher Chris Hunter (@ChrisHunter36) also battled with this video and created an excellent read about his experiences. Check them out.

 

Our Geometry Support Site

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So, I’ve talked about Khan Academy before. They make instructional videos for students to watch and learn from.

 

I’ve talked about #flipclass before. In this model, the teacher makes videos for the students to watch and learn from.

 

I like the idea of students having instructional videos to watch and learn from. But, in both Khan Academy (and other related sites) as well as flipped classes, the students are recipients of the videos. We decided that we didn’t want them to simply be recipients. We decided that we wanted them to be producers of the resources, too. So, we decided to just let the students create the math help videos.

Here’s what they did: Today I unveil the @PennGeometry Beta for your review and feedback. Currently, there are videos created from one practice test about triangle similarity. We would like to expand and continually improve.

 

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All of the videos are designed, produced, and completed by our students. Some of my students were sensitive to the boring math video and tried to add their personality to the video. We would love some comments, “likes”, and constructive feedback. Please check it out. Eventually, we want to add our voices to the overall mathematics community to support those in need.

Check it out and let us know what you think. We look forward to hearing from you.

For your students’ sake: Don’t stop being a learner

Yesterday, we designed an Algebra II lesson using 3D modeling to derive the factored formula for difference of cubes. As we began to finish up, Sheila (@mrssheilaorr), the math teacher sitting beside me made a passing reference to being frustrated trying to prove the sum of cubes formula. Me, being a geometry teacher by trade decided to give it a try perhaps hoping to offer a fresh perspective. I mean, I was curious. It looked like this:

2014-02-20 13.26.00

On the surface, it didn’t seem unapproachable. I quickly became frustrated as well. Most frustrating was the mutual feeling that we were so stinkin’ close to cracking the missing piece. Finally, Luann, a math teaching veteran sat down beside us, commented on her consistently getting stuck in the same spot we were stuck and then, as the three of us talked about it, the final piece fell in and it all made sense (it’s always how you group the terms, isn’t it?)

Then this morning, it happened again. Writing a quiz for Calculus, I needed a related rates problem. Getting irritated with the lousy selection of choices online, I decided that I needed to try to create my own. And I wanted to go #3Act and after some preliminary brain storming with John Golden (@mathhombre) (Dan Meyer’s Taco Cart? Nah… rates of walkers not really related…) we found some potential in Ferris Wheel (also by Dan Meyer)! Between my curiosity and my morning got mathy in a hurry.

First I tried to design and solve the problem relating the rotational speed in Act 1 to the height of the red car. That process looked like this:

2014-02-21 20.32.42

Meanwhile Dr. Golden found a video of a double Ferris wheel, which was pretty awesome. Seemed a little it out of my league, so kept plucking away at my original goal.

It clearly wasn’t out of Dr. Golden’s league, as he took to Geogebra and did things I didn’t know Geogebra was capable of. (You’re going to want to check that out.)

So, what is the product of all of this curiosity and random math problem-solving? As I see it, these past 48 hours have done two things: Reminded me of what makes me curious and reminded me what it’s like to be a learner.

I have a feeling my students will be the beneficiaries of both of those products. There’s a certain amount of refreshment that comes from never being too far removed from the stuff that drew us to math in the first place. The problem you want to solve just because you want to see what the answer looks like.

And this curiosity, the pursuit, it feeds itself. In the process of exploring that which you set out to explore, you get a taste of something else that you didn’t know you would be curious about until it fell down in front of you. (For example, Geogebra… have no idea what that program is capable of, which is a shame because it is loaded on all my students’ school-issued laptops…)

And this process breeds enthusiasm. Enthusiasm that comes with us into our classrooms and it spreads. I’m not trying to be cheesy, but much has been said about math functionality in the modern economy, how essential it is in college-readiness and the like with few tangible results. Let’s remember that there are kids who are moved by enthusiasm, who will respond to joy, who will pay attention better simply because the teacher is excited about what they are teaching. It won’t get them all, but neither will trying to convince them of any of the stuff on this poster.

Now, who’s going to teach me how to use Geogebra?

The Anxiety of Open-Ended Lesson Planning

It’s been about three years since I started weaning myself (and my students) off textbook-dependent geometry lesson-planning and toward something better. I’ll admit the lesson planning is more time-consuming (especially at the beginning), but most of the time expenditures are one-time expenses. Once you find your favorite resources, you bookmark them and there they are.

As we pushed away from the textbook, I noticed two things: First, the course became more enjoyable for the students. This had a lot to do with the fact that the classwork took on a noticeably different feel. Like getting a new pair of shoes, the old calluses and weak spots aren’t being irritated (at least not as quickly). Out went the book definitions and “guided practice” problems and in came an exploration though an inductively-reasoned course with more open-ended problems (fewer of them) that seemed to reward students’ efforts more authentically than the constant stream of “1-23 (odds).”

The second thing that I noticed, though, was that I had less of a script already provided. The textbook takes a lot of the guesswork out of sequencing questions and content. When the textbook goes, all that opens up and it fundamentally changes lesson planning. The lesson becomes more of a performance. There’s an order. There’s info that you keep hidden and reveal only when the class is ready. Indeed, to evoke the imagery of Dan Meyer (@ddmeyer) it should follow a similar model to that of a play or movie.

But, see… here’s the thing about the “performance” of the lesson plan. The students have a role to play as well… and they haven’t read your script… and they outnumber you… and there is a ton of diversity among them. So, when you unleash your lesson plan upon them, you have a somewhat limited ability to control where they are going to take it.

Therein lies the anxiety.

If a student puts together a fantastic technique filled with wonderful logical reasoning that arrives at an incorrect answer, you have to handle that on the fly. It helps to be prepared for it and to anticipate it, but the first time you run a problem at a class, anticipating everything a class of students might do with a problem can be a tall order.

Case-in-point:

The candy pieces made a grid. The rectangles were congruent. Let's start there.

The candy pieces made a grid. The rectangles were congruent. Let’s start there.

The Hershey Bar Problem was unleashed for the first time to a group of students. Our department has agreed to have that problem be a common problem among all three geometry teachers and to have the other two teachers observe the delivery and student responses (I love this model, by the way).

The students did a lot of the things we were expecting. But, we also watched as the students took this in a directions that we never saw coming. The student began using the smaller Hershey rectangles as a unit of measure. One of the perplexing qualities of this problem is that the triangles are not similar or congruent. Well, the rectangles are both. So, as we watched, we weren’t sure what conclusions could be drawn, what questions the students might ask, or how strongly the class might gravitate toward this visually satisfying method.

We didn’t want to stop her. We weren’t sure if we could encourage her to continue. We just had to wait and watch. That causes anxiety. It feels like you aren’t in real control of the lesson.

Adding an auxiliary line changes the look of the problem, "How were we supposed to know to do that!"

Adding an auxiliary line changes the look of the problem, “How were we supposed to know to do that!”

In the end, most of what we anticipated ended up happening. The team trying to estimate rectangle grid areas ended up seeking a different method for lack of precision and everything got to where it was supposed to. The experience is valuable. But the anxiety is real.

This student was trying to make sense of the perimeters and areas

This student was trying to make sense of the perimeters and areas

And I suspect that the anxiety has a lot to do with why the textbooks continue to stay close at hand. When the structure leaves, the curriculum opens up. When the curriculum opens up, the task of planning and instructing becomes more stressful and (for a short time) more time-consuming.

If you are reading this and on the cusp of trying to move away from your textbook, please know that this is the right move. Your book is holding you and your students back. You can do this. I won’t say that there is less stress, but with more authentic lessons, there’s more authentic learning.