Want to #ObserveMe Teach A Lesson To High School Students?

I realized this weekend that if I am suggesting that we should all ask people to observe one another (#ObserveMe), then I should follow my own advice in as public a way as possible.  So, I would like any interested peers to give me feedback on the goals in the picture below and record it on this Google Form.  I believe that it may also be useful to read the feedback others are leaving for me.  So, you can see everyone’s feedback here.

Since we are a global community, I thought the easiest way to share my teaching practice would be via video.  I had a tough choice though in terms of how to share it:

• Option One: share the entire full length video (it would be long and people might skip parts I find important)
• Option Two: turn it into clips that are sped up (much easier to view but parts you may want to see go by too quickly)

Ultimately I decided on option two.  This video was originally filmed in 2013 and shows me using my How Much Shorter Are Staggered Pipe Stacks? problem with some pre-Calculus students.  Prior to teaching this particular lesson, I had worked with this class three other times.  Each time we used a different problem-based lesson so they were already familiar with me and with using a problem solving framework.

It is important to note why I was using this problem.  As I explain in the blog post I just linked, my goal for this class was “Problem completion”.  I wanted to show on video what an entire problem looked like.  The reality is this lesson fit better over two days, so to make it fit in one period I had to make some tough choices and I couldn’t give certain parts as much time as I would have liked.

Before you watch this video, I highly recommend you complete the problem yourself.  Alternatively, you could just read through the problem and see what methods are possible.  It should be said that this problem is NOT easy… and it’s not because of the content standards.  In fact, this could even be solved using 8th grade standards.  What makes it challenging is the level of mathematical modeling required.

The problem begins by asking students to share what they notice about the picture.

After discussing what students wondered, I then asked them to watch a short video to get the conversation going further.  At almost 8 minutes into the class I introduced the question we would explore: “How much shorter are 20 layers of staggered pipes?”

I made two noteworthy decisions up to this point:

• First, while normally the class explores the question(s) students come up with, based on time constraints (we had to finish this lesson in one period) I was the one who gave them the question.
• Second, I invested almost 8 minutes of the class building the context and getting students to notice patterns.  While I didn’t have the language for this then, I was turning up the “math dial.”  This metaphor comes from Dan Meyer and I absolutely love it.  This idea may seem relatively normal, but I used to begin class by immediately giving students the question without warming them up to the context and getting them involved in the problem.  It took 8 minutes of the class, but it was worth it.

From about 8:00 to 14:30, students thought about the information they already knew and the information they needed to know to figure out the answer.  They realized that they needed to know the diameter of the pipe and you see us discussing that at 12:45.

At around 15:40 to 17:00, students placed guesses on the sticky notes and put them on the whiteboard.  In around 2014 I incorporated a place to make a guess into the problem solving framework itself.

By 17:00, students were collaborating in groups on the problem.  It’s also noteworthy that at this point in my practice, I did not have students work on the problem individually first.  Now I do so they have more time to process before interacting.

What I began to realize as students were solving the problem was that they were just making estimated guesses using proportional reasoning.  This was not the strategy I wanted them to use as it lacked precision and had larger amounts of error as the number of rows increased.

I was trying to find a “least helpful” way of nudging them forward.  In contrast, a “very helpful” method would be to tell them everything they did wrong and what they should have done instead.  So, thinking of a question that will give them just the right amount of a push in the right direction can be tricky to find.  Here’s what I did…

Let me take a quick tangent…

I once took a steak cooking class where the instructor said, “If you’re not sure if the steak is done, it’s better to undercook it than overcook it because while you can always throw the steak back on the grill, you can never undo overcooking.”  This is the same with student questioning.  If you give too big of a hint, you can never undo that.  Instead if you ask a least helpful question, you give students a chance to make their own discoveries and you can always come back and give a bigger hint.

Notice how “least helpful” I was with the first group.  I asked questions like “How would you make a formula that’s based on this?”  I didn’t tell them exactly what to do but I gave them a nudge in the right direction.

When I worked with the group at around 29:00, I was still trying to get groups to realize that their proportional reasoning strategy was not efficient enough.

By 30:00 I realized that too few groups were approaching this using a geometric strategy so I decided to intervene.  At around 31:17 I asked students about where the triangle vertices are.  I got no volunteers.  I realized that kids were definitely on task but were either confused or lacking confidence in their answer, so I did another pair share.

We came back together about a minute later and I asked again and then I waited.  Ten seconds went by with no responses.  This could have gotten really awkward, but this time I was prepared…

I decided that I would do a “warm call” as a backup plan.  During that one-minute conversation students had about where the vertices were, I found a group that knew where they were and told them that I “might” call on them.  That way if I asked again and no one said anything, I had an option.

So eventually students start to see the triangular pattern within the circular pattern.  I’m trying to ask questions and facilitate student conversations more than tell them what do.

At around 34:30 I ask my favorite discussion question of all time, “Does anyone else have the same answer/idea but have a different way of explaining why?”

After the conversation about the length of the triangle’s base, all students switched off the proportional reasoning and were exploring geometric strategies.

Knowing that I was about 15 minutes from the end of the class, I called the class back together again to have a student share his breakthrough in finding out the height difference between the pipe stacks with his classmates.

At around 46:40 with about 6 minutes left in the class I sadly had to bring everyone back together to finish the lesson.  I really wish I had been able to give them more time because I think a larger portion of the class would have ended up with an answer closer to the correct answer.

So, I collected all their answers and then compared their answer to their initial guesses.  Then I played them the answer video.  Once we saw the answer, I had them write down their conclusion and reflect on how they approached the problem including what they would do differently.

I hope this was worthwhile to watch.  If you have any feedback for me, I’d love you to send it to me here.

Would you like to use these video files? You can download them all using the button below.