What can we learn from books/movies about teaching?

While it probably does not happen often enough to be considered a trend, I have noticed that many educators on Twitter are using fictional stories to justify what they see as effective teaching. I have seen arguments that Obi-Wan Kenobi's work with Luke in Star Wars suggests that lecture is not all bad. Others point to Mr. Miyagi's teaching in The Karate Kid as evidence that teachers do not need to make their intentions explicit to be effective. Even I have succumbed to the temptation by holding up Tom Sawyer as an example of the way I would like to teach.

I understand why we do it. 140 characters makes it difficult to state our position and defend it all in a single tweet. Consequently, we rely on parts of familiar stories that transmit a shared understanding of our perspective. When I brought up Tom Sawyer, I trusted that people would remember the passage about Tom being sentenced to whitewash Aunt Polly's fence. I am old enough that, although I read the original story, the picture that comes to mind is from the 1973 movie starring Johnny Whitaker.

The problem is that these characters are responding to Tom's approach because that's how it was written not as empirical evidence of my point. Sure, the story resonates with us because it represents some experience or idea that we are familiar with (in my case, the gradual release of responsibility) but it is important to remember that it is fiction not reality. The progression from modeling to mentoring to monitoring will not be as fast as Tom experienced. To suggest otherwise might lead a teacher trying this approach to believe that such a transition will be quick and easy; this is not the case, which could lead to the teacher to experience frustration when it actually takes time and is messy.

I have said it before, teaching is hard. It is understandable that we might try to simplify it by using familiar stories as some sort of allegory. In fact, I cannot say with certainty that I will not use this approach in the future. What I will try to do is ensure that I encourage a great deal of critical thinking around how the fiction represents some reality of education and where it oversimplifies the teaching and learning process. That is my commitment to making the complexities of teaching explicit.

How long until we "Pig Out"? Part II

In an earlier post, I introduced an activity based on the game Pass the Pigs™. The idea is that participants in the activity will consider ways to answer the question, "How many tosses does it typically take before a Pig Out occurs?"  and then pick one of the ways to explore further. Here, I want to share one of the approaches often selected.

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Experiment

I conducted 100 trials. Tossing the pigs until I rolled a Pig Out constituted a trial. The number of tosses in each trial were collected. I also kept track of how the pigs landed in case I wanted to use the data in a different experiment.

Example

1. pink (no dot)-razorback, pink-razorback, dot-razorback, Pig Out [4]
2. trotter-razorback, pink-trotter, pink-trotter, razorback-razorback, pink-pink, pink-razorback, dot-dot, Pig Out [8]
3. dot-dot, pink-pink, pink-pink, razorback-razorback, Pig Out [5]
4. dot-trotter, razorback-razorback, pink-pink, dot-snouter, pink-pink, razorback-trotter, dot-dot, Pig Out [8]
5. Pig Out [1]

Data

Here are the basic data [number of rolls until a "Pig Out"] for 100 trials

Results

Therefore, based on my experiment, a Pig Out occurs, on average, every 4.68 rolls. The dot plot on the right is another way to represent these results. The plot shows that the mode for the number of rolls until a Pig Out is 1, and I determined that the median is 4. This makes me wonder which average makes the most sense to use in deciding when to pass the pigs.

After completing this experiment, I can see some things that I would change if I were to do it again. In collecting data on how the pigs landed, I did not distinguish between the two pigs. It would be interesting to know if the distribution of rolls between the different pigs was consistent. I also want to go back and look at the scores and determine the average score before rolling a Pig Out. Finally, I wonder if there is another experiment or approach that I could use to check this result.

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This write-up provides a basic model which other participants can use to share their findings. Identifying what represents a single trial is difficult for novices conducting probability experiments, which is why I want a model that defines it and then shows several examples. I also want to introduce the idea of gathering as much data as possible during an experiment. Finally, the example highlights the need to reflect on the results and consider other options.

So how might we verify this result or address some of the other issues raised in this write-up?

Why did you do it? Part II

In a prior post, I explained why John Golden and I used satire to critique a Khan Academy video for MTT2K. As Audrey Watters points out in the Tweet on the right and a post at Hacker Education, the approach has worked and started a serious conversation on Khan Academy's role in education reform. (You can add an article on Huffington Post Education and blog posts from Rhett Allain at Wired, Robert Talbert at The Chronicle, and Keith Devlin to the ongoing discussion.) But starting a conversation was only part of what I hoped to accomplish with the MTT2K parody. My primary reason for this project is revealed here.

A few people have attributed MTT2K to my not being a fan of Mr. Khan. This is only partially true. I am a big fan of his idea of moving K-12 education forward into the 21st Century. Anyone who wants to help teachers and students improve learning is someone I would consider an ally. Mr. Khan is not alone in this endeavor to provide online lectures, nor is he the first, but he has an incredible story and over 3,000 videos across several different disciplines.

While I love the idea of Khan Academy, I am not a fan of its implementation. Mr. Khan's videos are reminiscent of the lectures many of us experienced in math class, but they are lacking in some essential elements. As is the case with many people in the U.S. who think they understand education and what is wrong with it, Mr. Khan has a one-sided view of teaching. That side is from behind a student's desk, and because most teachers do not make visible all the work that goes on behind the scene before, during, and after the lesson this picture is incomplete.

As teacher educators, we share the Teaching-Learning Cycle with our preservice teachers in an effort to introduce them to the entire picture of what it takes to be a teacher. The work of assessment, evaluation, and planning often go on unnoticed to the casual observer, so people can be excused for not being aware of them. But in order to foster learning, a teacher needs to not only be aware of these parts of the Cycle, they need to know how to implement them effectively.

Much like the preservice teachers just entering our program, Mr. Khan seems unaware of the importance of each aspect of the Teaching-Learning Cycle. For example, in this Wired piece from last year, he seems to suggest that before his dashboard system, teachers usually "fly blind." This demonstrates a lack of awareness of the multitude of formative assessments that teachers use for evaluation which go far beyond counting video views and the number of right answers.

Furthermore, many of the math videos I have watched from Khan Academy suggest a lack of planning on the part of Mr. Khan. This is confirmed in a recent Time article:

He doesn't use a script. In fact, he admits, "I don't know what I'm going to say half the time."

There is something to be said for a teacher exposing students to an authentic learning experience and expert teachers can make this look easy. But it is not easy. As Mr. Khan showed in the video we critiqued and novice teachers find out on a regular basis, lack of planning can have disastrous results. Teachers who do not know the vocabulary used in the lesson or think the numbers used in the examples can come out of thin air risk fostering misconceptions rather than learning. Novice teachers who make and catch these kinds of mistakes have opportunities to quickly set things back on the correct path. It is unclear how Khan Academy handles this as the video we critiqued was more than a couple years old.

So this is what I hoped people would get out of the video. Yes, Mr. Khan has a good idea - let's improve education by allowing teachers to work more directly with students. He is not a world-class teacher, however. In fact, his videos demonstrate that he suffers from many of the same mistakes that preservice teachers make because they do not understand the complexities of the Teaching-Learning Cycle.

Given this line from the Time article, my greatest concern is that Mr. Khan is satisfied with his current understanding of teaching which perpetuates the idea that teaching is easy:

I think there is an advantage to being an outsider - I'm not colored by the dogma of the Establishment.

Which brings me back to the power of satire. The Time article was done prior to MTT2K hitting the scene. Let's see if it does anything to push Khan Academy to  improve its implementation. There are expert teachers willing to help. All Mr. Khan has to do is ask.

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.

How long until we "Pig Out"? Part I

"What are the chances of a 'Pig Out'? Part I" is the most popular post on this blog. The activity ends by asking the reader to consider how many tosses it would take, on average, to roll a "Pig Out" and lose the points accumulated during the turn. Just in case you are not familiar with the game Pass the Pigs™, or didn't read the earlier post, here are the rules and a figure showing the scoring:

I developed the following problem solving workshop with my colleague, Dr. Mary Richardson, as part of a presentation for a Math in Action Conference.

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Understanding the Problem

In the dice rolling game, Pass the Pigs™, players are always on the look out for the dreaded "Pig Out." If it is tossed before a player passes the pigs to an opponent, the player loses all the points for the round.  A "Pig Out" occurs when the pigs land on opposite sides – dot and no dot (as seen above). Therefore, it would be good to know about how many tosses it typically takes before a "Pig Out" occurs.

Create a Plan

How might you solve this problem?

Please consider several possible solution methods

Carry Out a Plan

Try one of the plans you considered in the previous phase

Looking Back/Ahead

• Use your results to answer the question, "How many tosses would you expect it takes until a "Pig Out" is rolled?"
• Evaluate the plan you used (glows and grows) – What did you like? What would you do different?
• Describe an extension – What other questions arise from this game?

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Before I share our results, I want to provide you an opportunity to try solving the problem yourself. There is a free game here if you want to gather your own data. In future posts, I will describe two approaches we used to answer this important question.

What's your story?

This past Friday we attended the release party of the Harvest Queen cd at Kauffman Auditorium in Marquette, Michigan. (The story of how this project came to be is told here [Kickstarter Video] and here [WNMU interview].) The concert, which included traditional and new waltzes, was amazing, but it was only a portion of the overall event. Crossing Paths was intended to be an opportunity to explore various connections between local food and music.

In the afternoon, Kailin Yong conducted a violin master class for players of all ages and abilities. While my wife attended this hour-long class, I went for some local coffee. When I returned, Kailin was answering questions from those assembled on the stage. Someone asked him to explain when he started improvising in music.

Kailin responded by playing a beautiful, classical melody and then said (to the best of my memory), "I was very good at telling this story - an old Italian's story. But I wanted to tell my own story. I had been playing for years before I felt free to improvise. I do not want my students to have to wait as long as I did, which is why I had you working on improvisation today."

This reminded me of what Jonah Lehrer shared in Imagine about Yo-Yo Ma

"I was nineteen and I had worked my butt off," Ma told David Blume of The New Yorker in 1989. " I knew the music inside and out. While sitting there at the concert, playing all the notes correctly, I started to wonder, 'Why am I here? What's at stake? Nothing. Not only is the audience bored but I myself am bored' Perfection is not very communicative." (p. 86)

In both cases, expert musicians found being perfect was not enough. They longed to express themselves. They wanted to tell their own story or, at the very least, find a way to add a part of themselves into the retelling of the story of some other songwriter.

It seems to me we spend a lot of time in math class trying to get our students to retell someone else's story perfectly. The standardization of the curriculum leaves little room for learners to improvise and add their uniqueness to the mathematics. It is no wonder that most students see mathematics as a static set of rules. Whether we "tell" them the rules or have them "discover" the rules it amounts to the same thing - they are playing someone else's tune.

I am glad that I returned before violin master class was over (It turns out my compulsive timeliness can come in handy.) Thanks to Kailin's answer, I want to plan more opportunities that allow learners to improvise. I, too, do not want them to have to wait as long as I did to pick up this skill.