And then what did you do?

In my experience, middle school students are often reluctant to try a problem they don't already know how to solve and uninterested in using alternative solution methods once they have one that works. Some middle school math teachers I worked with this week have found the same thing. So we considered how we might use techniques from improv to help students get started on a problem and possibly explore an approach they might not normally use. Improv techniques like the "Yes, And..." activity.

We decided to play it using this situation from Context for Learning Mathematics [CFLM] and a couple of starting choices.

Starting Steps:

1) First, I split up the dollar and the 25 cents and multiplied the dollar by 24.

2) First I doubled $1.25 and got $2.50.

We would make teams of three. Two people would engage in the "Yes, And..." activity while the third kept "numeric notes" that could be referred to after the activity. 

Here's how it might work:

Numeric Notes

First, I split up the dollar and the 25 cents and multiplied the dollar by 24.

Yes, and then I added back the 25 cents and got $24.25.

Yes, and then I remembered there were 23 more quarters that I need add.

Yes, and I don't know what 23x.25 is so I did a quarter plus a quarter is a half dollar instead.

Yes, and that reminded me that there are four quarters in a dollar.

Yes, and that made me wonder about how many dollars there are in 24 quarters.

Yes, and I divided 24 by 4 and got 6.

Yes, and that means 24 times .25 is 6 dollars.

Yes, and then I added 6 dollars to the original 24 dollars.

Yes, and that means the total cost of the turkey is $30.

Afterwards, the students reflect on the activity. This is an opportunity to observe their own thinking: what they did; why they did it; and how else they might have navigated the situation. I have done something similar with my college students, who finish up by writing a Metacognive Memoir about their experience.

How does a mathematician see the world?

And how does a math teacher help learners to see the world through a mathematician's eyes?

This was a major challenge during the past semester in my Intermediate Algebra sections. Many of the students came to class expecting me to show them a procedure that they would practice until test time - when they would reproduce the procedure and promptly forget it. Nearly all of the students had seen the Intermediate Algebra content in high school (linear, quadratic, and exponential functions) but it hadn't stuck.

This was the problem. They had seen the content. Now it was time for them to use it to see the world. So I shared pictures and videos and asked them to look at them through a mathematical lens.

At one point, a student said, "Just once, I wish I could see the world through your eyes." Exactly! Unfortunately, they were often so afraid of making a mistake, of breaking the mathematical glasses, that they were not willing to even put them on. They did not know how to be playful with the math we were exploring.

So I introduced them to Yes, And ...; this is a problem finding activity that I developed using a well-know improv game where participants accept and build on the ideas of their partners. Here are the instructions for my version:

• Provide a mathematical context (often pictures or videos) but without any identified problem;
• Pair up the students and find a fun way to identify Student A;
• Student A picks one of the contexts and finds a problem to solve;
• For one minute (this is usually enough time to get started without completely solving the problem), Student A talks through his or her thinking while Student B writes as much as possible down on a piece of paper;
• After one minute, the students switch roles. I say, "Yes, and ...," to signal the switch and to emphasize that Student B ought to build on the work that was already done.
• Student B thinks out loud for one minute while Student A records the thinking on the same paper.
• After one minute, I say, "Yes, and ...," and the roles reverse again.

Yes, And ... can go on as long as the teacher wants. I found six minutes (three rounds) to be about right the first time we played the game. One student submitted this to demonstrate her engagement with the task.

I cannot claim for certain that Yes, And ... changed my students' view of mathematics or helped them to see the world through a mathematical lens. What I know is that for six minutes they played with math. It's a start.

Why did you do it? Part I

When John Golden and I made the Mystery Teacher Theatre 2000 (MTT2K) video we thought 100 or so people might see it. Maybe some of our followers on Twitter would click on the link and others interested in education might find it through a hashtag. We were also prepared for a few of the people that seem so dedicated to Khan Academy to turn up and comment. No big deal.

But then Dan Meyer posted the video on his blog and things got interesting. Khan Academy took down the video we critiqued and replaced it with two new videos (here and here). Justin Reich found out about our parody and wrote a post on his EdTech Researcher blog at Education Week. Justin and Dan even sponsored a contest for teachers to make their own versions of #MTT2K. Then, it got surreal as Slate and The Chronicle of Higher Education picked up the story.

Once the video got some attention, people began asking questions on Twitter and in the comments of the various posts about our approach and what we hoped to accomplish. These questions deserve to be answered. As John points out in his post, I was the instigator, so I will try to address both of these issues. The answers are not simple, however, so I will break this into two posts – addressing the approach now and what we hoped to accomplish in a later post.

This all started on February 1^st of this year in my class on teaching and learning math in the middle grades. The focus of the first workshop of the class that day was the NCTM’s Communication Standard:

Instructional programs from prekindergarten through grade 12 should enable all students to--

• Organize and consolidate their mathematical thinking through communication;

• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;

• Analyze and evaluate the mathematical thinking and strategies of others;

• Use the language of mathematics to express mathematical ideas precisely.

The plan was to watch two online videos about multiplying and dividing integers using the above bullet points as a framework and then consider how well each video met the Standard. Integer computation was the topic simply because it was the next section of the syllabus. In other words, the topic led me to the videos, not the other way around.

In preparation for the workshop I previewed a video from Khan Academy and a video from Mathtrain.TV. These sites were selected because they represent resources teachers are currently using across the country and I wanted the preservice teachers to be aware of their existence. I was a bit surprised by the number of issues in the Khan Academy video but it was a perfect assessment of my students’ ability to apply the Communication Standard to another person’s mathematical discourse.

Again, the plan was to watch the video and then debrief, but once the Khan Academy video got started it was as if my students could not contain themselves. They quickly identified issues related to consolidation, coherence, and precision and it seemed that they could not wait until the end to share what they noticed. Afterward, I told John it was like an episode of Mystery Science Theater, and that I might write a blog post about it. For a variety of reasons I never did – mostly revolving around a desire to remain above the fray typically associated with Khan Academy critiques.

In March, I listened to the audiobook for Tina Fey’s Bossypants and I was intrigued by the idea of improvisation and how it might apply to education. John listened to the book, as well, and when he was finished I asked if he was interested in participating in a bit of educational improv. He was game but we struggled to come up with a scenario that made sense. The Mystery Science Theater idea came up, and we both liked it but again it remained only an idea.

For me, a USA Today article on Sal Khan helped me to get serious about this project. It was the latest piece praising Mr. Khan and the Khan Academy while basically ignoring (or worse) the concerns of educators over some videos’ inaccuracies and pedagogical issues. I called John and told him I thought the time had come to do some Mystery Science Theater improv.

This part is important! We were concerned that some people would see our satire as mean-spirited and immature. Still, being fans of satirists like Mark Twain and Jon Stewart we recognized that there are times when this approach is necessary. This is especially true when there is a need to break through a person or group's seemingly impenetrable veneer. Given the results, I would say we were correct in our concerns and successful in our use of satire.

I trust this explains the evolution of our approach and how we came to use satire in our video.  As for my motivation, this is already a long post, so what we hoped to accomplish will have to wait until a later post. Please stay tuned.