## Watch Students Watch The Answer To Their Math Problem

Sadie Estrella’s class worked on Pixel Pattern and then watched the answer.

I’ll try not to be ideological here about photos and videos in modeling tasks. If you have another way to achieve the same cathartic reaction we find 38 seconds into the video, drop me a note in the comments. I’ll take it.

Previously

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

### 20 Comments

1. #### Barry Lewis

December 12, 2012 - 8:05 pm -

This is the crackle that turns finding answers into satisfying work and makes asking good questions harder to resist. Yes, make proficient critical thinking skills the name of the game, but it’s the collateral benefit of becoming passionate questioners that will allow us to do remarkable things.

2. #### Jen

December 13, 2012 - 4:21 am -

I’d still love to have seen it through — that is, did they get it?! Or was it just exciting to watch and by the time they found out if it was red or green were they over it, in the afterglow?

3. #### Sadie Estrella

December 13, 2012 - 7:07 pm -

My question to you is: Did they get what? Did they understand that all of the blocks were growing in a linear pattern? Were they able to calculate the slope given a set of points? Did they understand what the y-intercept=2 for the length meant? did they understand the relationship between the slope of the red blocks, green blocks, blue blocks and total blocks? There are so many standards connected to this activity that I am not sure what you mean by “it”?

The thing about learning that people forget is that it does not happen in 1 day, 2 days, 1 lesson or even 1 week. so when my class started on this activity they had been practicing calculating slopes, y-intercepts, equations, graphs, discussing relationships among all of the above and much more in depth topics that you can find present in this pixel pattern activity. I used this activity as a combination of practice, assessment and introduction into the use behind math equations (to predict outcomes in the future based on data). The part of the video I shared is the reaction to an activity that got students so engaged that they were discussing this video/assignment in ALL OTHER CONTENT AREA CLASSES! This video did NOT capture the immense amount of learning, strategy building, connection making and all the other added in topics. If you need to see that then book yourself a 1 week trip to Hana, Maui because there is NO WAY I can capture that on video. But what IT did do was show kids that math is real, we use it for something, that math is not just some memorized formulas and procedural steps we perform to get an answer that means nothing. We instead used, as ancient mathematicians used, math as a tool to help answer perplexing questions found in life. Whether it be “real-world” or pure math (as seen here).

So did they “get it”? I’m not sure but I do know that they will remember calculating the slopes, y-intercepts and discussing the relationships because of the video that lead to this reaction that will forever be embedded in their educational experience. Learning does not happen when a student is able to repeat back an equation, definition or rule they learned through some test but instead:

“He who takes his teachings and applies them increases his knowledge”
E lawe i ke a`o a mÃ¤lama, a e `oi mau ka na`auao
QED

4. #### a different eric

December 15, 2012 - 12:57 pm -

One of my kids said this after the lesson, “This is when I love math the most! When I can use it in real life!”

I kind of laughed at the idea that he thought of this was using math in “real life”.

I win.

5. #### Jen

December 17, 2012 - 2:55 pm -

I totally understand your point about how learning happens and about how it builds on previous experience etc. I also pointed out that this was a teensy clip. I wondered if there were many students who could explain which one “won,” for instance, to those that didn’t know.

My point was that the cathartic moment, as it was referred to, was similar to one that I might hear in the car if my kids were watching two rain drops race down the window. They’d be yelling and excited to see who won. That’s what I saw in the video.

I honestly (and not sarcastically) think teachers should always be interested in is the consolidation, the taking the time to draw the conclusions, the learning from the moment. I’m not surprised at the reaction from an activity like that. But, on a blog about teaching, we should be concerned about how it actually fits into the big picture. Maybe its only role is having a happy moment in class that leads to better attention and learning afterward. You could even make an argument for that!

Do my kids really learn valuable (but not articulated) information about physics from watching raindrops chase down a window or is that the sum total of the experience?

I’m sorry if I somehow touched a nerve other than that basic question, which wasn’t answered by watching the video.

Lust v. Love might be another analogy. ;-)

6. #### Sadie Estrella

December 17, 2012 - 5:42 pm -

I too am sorry for coming off a little on edge with my response., Jen. However, I guess I am still not sure what you are saying. The ending of the video did start in the discussion about which color “won”? Because the answer that was mathematically calculated on paper was 48.5 secs we were able to discuss how this would look to our eyes. It would be at 49 secs. Why? Because .5 sec is too short for the naked eye to see. Right after this because one students wanted to be the “winner” for the color block he wanted to argue that it was 48 secs when it hit. We used our equation to prove that it wasn’t 48 secs because that answer was less than 98units. We also watched the video many times pausing it at 48 secs to see that little sliver of white to show that the blocks had not hit the red bounding box. When I say we I am being very nice in including myself but to tell you the truth I had no part in this discussion. Students were arguing with each other as to why it was 49 secs or what not. I was a mediator in the conversation to make sure they spoke civil to each other (you know how high schoolers can be) but other than that the conversations/discussions were coming from the students themselves.

So to tell you the truth again I am not sure what you are asking.

Thanks for your response *:)

7. #### shaun

December 22, 2012 - 9:49 am -

I really love this lesson design and wanted to ask what software you used to animate the shape and was interested in exploring similar types of questions. Any suggestion for similar problems? I am not sure how to find other examples like this or how to design problems like this for my students.

I am also going to attempt to construct this sequence with GeoGebra.

Again thanks for the lesson design. Great stuff!

8. #### Dan Meyer

December 22, 2012 - 1:10 pm -

Hi Shaun, my standard toolkit includes Adobe Photoshop, Final Cut Pro, and Adobe AfterEffects (which did most of the heavy lifting in Pixel Pattern). They aren’t tools I recommend for every math teacher, but they do allow us to create some interesting mathematical experiences for students.

9. #### shaun

December 22, 2012 - 8:27 pm -

thanks, my main editing tool has been screenflow, but I love the pixel effects. I am going to try out AfterEffects and attempt to create some similar pile pattern problems. Can AfterEffects actually animate the sequence or did you copy and scale the image with each step?

10. #### Dan Meyer

December 23, 2012 - 9:56 am -

shaun:

Can AfterEffects actually animate the sequence or did you copy and scale the image with each step?

The latter, which was a miserable, miserable pain. AfterEffects includes ActionScript, a pretty powerful scripting language, which probably could have automated the process, but that’s a bit beyond me.

11. #### shaun

December 28, 2012 - 7:37 pm -

I had some fun finding a way to make this work on GeoGebra. It was a big learning experience for me, but I wanted students to be able to tinker with the problem and I wanted to open up the possibility of setting up animations for similar pixel patterns.

I made a quick video showing the Pixel Problem on GeoGebra: http://youtu.be/ON6qcvBdchg

You can also download or use this program here: http://www.geogebratube.org/material/show/id/26401

I will make videos explaining the programming behind it so that other teachers can expand on the idea.

I hope this helps and thanks again for the great problem.

Also, I tried to give appropriate credit to you in the video and program. Let me know if there are any issues.

12. #### Dan Meyer

December 29, 2012 - 7:26 am -

That’s great, Shaun. Really dazzling Geogebra work. So how does the lesson change now that students can just drag the slider to answer the original question? How do you envision the task unfolding now?

13. #### shaun

January 1, 2013 - 5:40 pm -

Good question, I don’t have enough working computers or a projector (yet) to run the demo in the classroom, but I imagine that restricting the slider to a small number of steps (like 10 or 15) would help them think about the problem.

Until I am able to run it in the classroom, I will assign it as a homework with the slider cut to about 15 steps or so. Then I can assign a follow up home work assignment asking a question like, “how would you change the dimensions so that that the pattern will hit the left and right sides first? Each leg at the same time?” Then I might follow up with some other problems that are similar, but perhaps are enclosed in different shapes and perhaps grow in different ways. I would create matching GeoGebra simulations for some, but certainly not all. I eventually want them to visualize without help. That was my orignal goal: to create a variety of pixel patterns that grow in different ways.

What are your thoughts?

14. #### Dan Meyer

January 2, 2013 - 7:59 pm -

I don’t think video is necessarily better than Geogebra or vice versa but their different constraints are interesting. With video, you don’t need computers for everyone. With Geogebra, if you don’t have computers for everyone, you lose what is IMO its best feature, which is that students can scrub the slider around to orient themselves to the context. They can go backwards and forwards in time. If you’re able to fully lock down the system (in a way that’s irreversible by the student) so that the student can’t get the answer to the question in advance, I’d prefer the GGB approach. (All other things like 1:1 laptops being equal.)

I’m not sure it’s possible to lock down a GGB file that tightly, though. Please send it along if it is.

15. #### Andrew Stadel

January 5, 2013 - 2:36 pm -

Giddy up Sadie!
When I first saw this 3Act at Dan’s Palm Springs conference, I immediately became excited because I know I’d be using it with my Algebra kiddos this year. Thanks for sharing you students responses. I love how you now your students will remember calculating the slopes and y-intercepts. In the end, I think the teacher has an opportunity to create those moments in class where students will have belief in the math they are doing. Keep it up!

16. #### Shaun Errichiello

January 7, 2013 - 5:39 pm -

You are right that GeoGebra can’t be entirely constricted (which is why I love it!) However it can be restricted for classroom use if it is embedded in a webpage. I made a quick video tutorial: http://youtu.be/F2D7d0e7N0M

You can download and play with the worksheet here: http://tube.geogebra.org/material/show/id/27042

Does anyone have a collection of these types of problems? I am making more but wanted to see other ideas as I tinker with this stuff.