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

April 4, 2014

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.



I teach math (and film-making, and troubleshooting iOS, and…)

April 3, 2014


At #macul14, Erica Hamilton (@ericarhamilton) gave a wonderfully practical talk about how going 1:1 fundamentally changes the job of teaching.

For the last 6 years, I’ve been teaching in a 1:1 laptop program, although, to be fair, the number of students who have iOS or Android devices sends that ratio a lot closer to 2:1. With all that different technology in use, the instructional videos that our students just completed has been one big case study that supported practically everything that (soon-to-be) Dr. Hamilton discussed in Grand Rapids.

To summarize what I took from her discussion, teaching has always required a firm understanding of the content, the curriculum, the community, and few other things. Adding a 1:1 structure to the classroom doesn’t remove any of those classical understandings from the teacher, but also adds a variety of new knowledge bases that the teacher needs to draw on. The teacher now needs to understand software (and how to troubleshoot it), hardware (especially wonderful in BYOD schools), the network infrastructure (why are these computers so SLOW!?), and have some reasonable understanding of the tech background of the students in your classrooms.

In our project, I wanted my students to be able to record the video and publish it online, so I could collect and embed the videos in a central location for people to use as needed. As a math teacher, that’s a heck of a lot of non-mathy stuff that I need to know how to do. I needed to be able to use YouTube and Vimeo (and help troubleshoot error messages). I needed to introduce a few students to Dropbox when the mobile devices wouldn’t transfer the video to the computer (which was sometimes necessary). I needed to know how to create a website to host the resources (I chose Weebly). I needed to know how to embed the videos. And I needed to know how to support the students through these processes. (Side note: I was surprised how many of my high schoolers had never uploaded a video to YouTube.)

I’m a math teacher, right?

In addition to all of that, I wanted the students to be able to make high-quality videos. That means, I need to teach a bit about film making. Lighting, sound, how to stabilize the camera so it isn’t shaking, editing software so that you can edit out mistakes, and the delicate art of peer-review. These are things that students need to be taught or else you’ll get videos that give you motion sickness, writing you can’t read, and commentary that you can’t understand.

I’m a math teacher, right?

And here’s the kicker: if I don’t have all of that knowledge, I really can’t run that project. That awesome opportunity for my students REQUIRED that of me.

This… THIS… is why integrating instructional technology is so intimidating. This is why education is slow to adopt new things.

There was a time when I needed to know math and my students. Now, I need to know so incredibly much more. The wonderful work that Erica Hamilton is doing is helping to put words and structures to the complexity that comes with every step into new instructional technology. Every step a teacher takes, though it might just look like a small step, brings with a complex set of new knowledge that is essential to making the process work.

We’d be wise to understand that when we introduce a new piece of technology (especially a technology that will be simultaneously used by both teacher and students), we aren’t asking teachers to simply teach one new thing. We are asking teachers to learn a whole lot of (potentially) brand new stuff all at the same time.


Our Geometry Support Site

March 31, 2014

Website Snip2


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.


Website Snip


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.


The Power of Network: The Wedding Cake Problem

March 25, 2014

I have another wonderful story about the power of the wider math community to support its own. Earlier in March I presented at MACUL 2014 in Grand Rapids, MI. During that presentation, I led the group through an experience with the Wedding Cake Problem, which ended up being a wonderfully energetic interaction.

Sitting in that meeting was a gentleman named Jeff who teaches at a school in Michigan. He wrote me an email some time later that included a message and the following photos:

“I’m planning on using the cake problem this week as review in my Trigonometry class, as well as later in the year with my Geometry students. Well, here are a few improvements, well, really just pictures. See attached.
Pans are 5″, 7″ and 9″. I think I’m just going to give my class the actual pans without the pictures.”








Now, these photos change the dynamic a bit, don’t they? Let’s do pros and cons… What do you like better about giving the problem with these pictures? What do you prefer about the original problem?

I would love some feedback (especially if you have tried either one with your class).


The Power of Network: Triangle Similarity

March 19, 2014

I want to share a story that shows the power of an effective PLN.

In a previous post, “proof and consequences: circular reasoning“, I begged for help solving a problem with students struggling to see their own logical crisis that was leading to predictable and consistent problems.

Several people reached out to me with suggestions. Thanks for that. I would like to highlight one specific suggestion that I tried to today and it worked just exactly as the designer predicted.

The suggestion was made by @nerdypoo.

From the comment:

“(i drew an example of this on the train home from work where i drew two isosceles triangles — the first had congruent legs 2 & 2 and the second had congruent legs 3 & 3, so scale factor of 1.5, but the first triangle was an isosceles right triangle and the second had an angle of a bit more than 90. i can send a jpeg if you want!)”

I loved this idea. And yes… I did. I did want that .jpg.

So, here’s a portion of what she sent back.

Dutch Triangle Idea Original

Today, I tried it in class. I began by putting up this image…

Dutch Triangle Idea Starter

… and asking the students to vote on whether the triangles were similar, not similar, or we don’t know. Overwhelmingly most students voted that they were similar. The thoughts they articulated were mainly that they could find the legnth of the missing side (which they claimed to be 3 cm long) and then could use SSS to show a consistent scale factor.

Then I showed them this image and asked them to vote again.
Dutch Triangle Idea

A lot of votes changed. Many changed from “similar” to “not similar”. A few others changed from “similar” to “don’t know”. An additional piece of information revealed an assumption. The assumption was that finding a consistent scale factor in two pairs implied the third. Perhaps an assumption that the angles were congruent.

It was essential that I made sure the students knew that I wasn’t changing the situation from the first question to the second. I was simply revealing information that was hidden. Those angles were never congruent. They simply didn’t know that, but most them assumed they were. But every person who voted that the first two sets of triangles were similar were making an assumption, an assumption that they didn’t recognize before. An assumption that shouldn’t be made because sometimes it’s incorrect.


A forum for real PD and authentic learning

March 17, 2014

It’s time we talked about Twitter. Actually, I’ll let my professional colleague Shauna Hedgepeth do it for me…


That person is not a salesman. She’s a teacher. Like me and like you. Question: When was the last time you heard a teacher so excited about a professional development?

Twitter is something that most district-provided, one-size-fits-all, canned professional development packages aren’t: individualized and timely. Through Twitter, an educator has the ability to reach out to people… a lot of people. A lot of people who teach what you teach. A lot of people who see what you see. That’s a lot of brainstorming…

… oh and It’s free.

I understand that Twitter has a reputation of being a sounding board for famous people’s monotonous daily blah-blah, but, well I’ll quote educator Rushton Hurley:

“If you’re Twitter feed is full of people telling you they just ate a sandwich. That’s YOUR fault. Follow people who say interesting things!”

Perfect. Twitter is what you make of it. I’m increasingly finding my professional development needs, ideas, and improvements are coming from ideas that I’ve shared on Twitter or stolen from people who have willing offered them on Twitter.

We are in an unprecedented time of connectivity and teachers don’t have to feel isolated anymore. It’s no longer a time when educators have to feel burden to come up with unique solutions to the problems that every educator faces. There’s a conversation going on right now and, well, I’ll let George Couros close this post (oh, by the way, I read this quote on Twitter.).

“Isolation is a choice educators make. If you’re isolated, you are CHOOSING not to connect.”


Reflecting on #macul14

March 15, 2014

So many great things went on these past few days in Grand Rapids, MI. When I consider that the last time I was along the Lake Michigan coast, I was in Ludington to see Dan Meyer, I’d say West Michigan has treated me and my students pretty well.

For those of you who aren’t familiar MACUL is Michigan Association of Computer Users and Learning. They are an organization dedicated to supporting Michigan teachers in the pursuit of making education better through the effective use of instructional technology. This was their annual conference.

The best thing about this particular experience is that there was a little of everything from academic talks like Erica Hamilton’s (@ericarhamilton) talk about Teacher Integrated Knowledge, to incredibly practical, I-could-totally-do-this-tomorrow talks like Bree Davey’s (@studiobree) talk on student blogging. There was the inspirational talks of Rushton Hurley (@rushtonh) to the intensely technical and energetic Leslie Fisher (@lesliefisher) teaching use the finer points of how to use iStuff to take pictures that don’t suck. It’s a lot to take in. Here are some summaries of my favorite sessions:

Erica Hamilton – Teacher Integrated Knowledge – Erica (soon-to-be Dr. Hamilton) did a fantastic job of detailing the how teaching becomes more complex in the 1:1 format. She spoke about the different types of knowledge that a teacher naturally has to draw from in the process of doing his/her job. (Content knowledge, curriculum knowledge, pedagogical knowledge, environmental knowledge, etc.) Switching to a 1:1 format add a few others that aren’t there (at least not nearly with the intensity) otherwise, which can make reinventing teaching to maximize 1:1 seem really, really intimidating because if you are, for example, going to ask your students to go out and make short videos, you might need to teach them what to consider to make a video effective (Lighting, stabilizing the camera, speaking clearly, editing tools, etc.). That isn’t part of most curricula. 1:1 puts teachers face-to-face with having to acquire those kinds of knowledge. My favorite idea that Erica kept coming back to: “It all comes back to what do you want students to learn? What do you need to teach to do it? What tools are available?” Excellent, excellent talk.

Ben Rimes and friends – #MichEd PLN – #MichEd is a PLN dedicated to connecting educators in Michigan with the goal of spreading ideas. This is a dedicated group of educators with a podcast and a weekly twitter chat. They are dedicated to the idea that we all need to grow and all we should have to do is ask the experts around us for help. We all have something to ask and to offer. It seems this panel discussion was best summed up by George Couros the next morning when he said “Isolation is a choice teachers make. If you’re isolated, you’re choosing not to connect.” Speaking of connecting, it was fantastic to get to meet these folks face to face for the first time.

Tara Becker-Utess – Flip Class Model – This was an important talk for me to go to because I was always a little bit uncomfortable with the flipped class model. Tara (whom I am proud to know personally these past 10 years) didn’t quite draw into the realm of the full believers (for reasons I can explain more if your curious), but she did a very nice job of explaining the philosophy behind flipping. I was relieved to find that I was able to identify with a ton of the spirit. Tara made some fantastic points, especially the absolute need for teachers who flip to plan very, very well for their time in class. “If you were used to using 20-30 minutes to lecture, you just got 20-30 minutes to plan rich activities for your students. That is usually a shock to people who are flipping for the first time.” (Those are probably more paraphrased thoughts than actual quotes, to be fair.)

I also had the privilege of presenting a one-hour session. If you are curious what it was about (or if you attended and want to revisit) I invite you to check out the “MACUL 2014 Presentation” link at the top right of my blog to get the details. Thank you for your kindness, warmth and enthusiasm during my session. It definitely did not go unnoticed.


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