Friday, July 27, 2012

Who will be the math education savior?

Last night, my wife and I celebrated our 15th wedding anniversary with a house concert. Josh Davis, one of our favorite Michigan singer/songwriters, performed. We had supported his trip to Palestine as part of a project by On the Ground Global, and the house concert was his way of saying thanks. (Below is a video from his trip.)

As a Jewish-American, Josh brought a unique perspective to the trip. He told many stories about the ten days he spent there and sang several songs he wrote based on the experience. In one of the stories, he shared an interchange on spirituality that he had with one of the Palestinians who hosted him. The man gave him a set of Muslim prayer beads with the explanation that everyone needs guidance through the darkness.

This got me thinking about recent discussions related to math education. It might be hyperbole to say that these are dark times to be a teacher but there certainly seems to be a cloud over the profession. Understandably, some might reach out for a savior to guide them. We need to be careful.

I am a firm believer in the power of inspiration - hearing someone else's story or idea and considering ways to apply it to our own situation. My blog is filled with examples of this. But for me, it is even more important that our efforts be authentic. Here is a story from Alan Cohen's The Dragon Doesn't Live Here Anymore that seems appropriate:
There is a story from the Jewish Hassidic tradition that I would like to share with you. Rabbi Zusya, a pious and revered sage, was lying on his deathbed, weeping. His students stood by him perplexed. 
“Rabbi, why do you weep?” one of them ventured to ask, “Surely if anyone is assured a place in the kingdom of heaven, it is you!” 
The sage turned his head toward his beloved students and began to speak softly: “If, my children, when I stand before the heavenly court, I am asked ‘Zusya, why were you not a Moses?’ I shall have no hesitation in affirming, ‘I was not born a Moses.’” 
“If they ask me, 'Why, then, were you not an Elijah?' I shall speak with confidence, ‘Neither am I Elijah.’” 
“I weep, friends, because there is only one question that I fear to be asked; ‘Why were you not a Zusya?’”

While some people may ask me, "Where are your 3,000 videos?", I am not Sal Khan and that medium does not match my skills. And when others ask if I have Meyer-ized my lessons, I can tell them no because it does not match my style. For years I taught as others taught and I do not want to go back to those times. I am comfortable and confident in my teaching but that is not to say complacent. Thanks to all of you, I continue to find ideas that inspire me.

So who will be the math education savior? You will. And you. And you. In fact, there was a large group of them meeting recently at Twitter Math Camp. Check them out here, and be prepare to be inspired.

Updated 6/17/13: Below is an interview and performance by Josh Davis where he describes his encounter with the Palestinian who gave him the prayer beads.

Wednesday, July 18, 2012

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.

Friday, July 13, 2012

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.


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.

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


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?

Friday, July 6, 2012

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.