Why didn't you tell us about that?

I never heard about any of this in my school of ed

Statements like this occasionally pop up in my Twitter stream - usually during something like #edchat. Given my involvement in teacher preparation, it is easy to get defensive about these Tweets. So I try to ignore them. Last week, however, was Twitter Math Camp (TMC) and the following was Tweeted at the end of the sessions: "None of this stuff we've talked about these last three days came up in my education program." Sorry, I couldn't ignore this one.

I am not here to defend the current state of teacher preparation. There are certainly issues that need to be addressed. But introducing the latest popular instructional approaches is not the answer. In fact, chances are your education classes were talking about ideas that were popular at some point in time.

Hattie (2011) suggests that schools of education often put too much emphasis on particular methods of teaching, thereby ignoring what is most important - learning. Reading this reminded me of a time when I made sure all of my preservice teachers were proficient in writing Launch, Explore, Summarize (LES) lessons. What I considered to be one of the best middle school mathematics curriculum, Connected Mathematics Project, used this format and I wanted my students prepared to use it. Then I got an email from a former student who had just got a teaching position in a middle school that used Saxon Math which follows a much more traditional approach. She was at a loss about how to apply the LES format. I was preparing teachers to use a particular method but not necessarily to support learning.

For Hattie, teaching for learning requires educators to gather data on and analyze the effectiveness of the instructional methods being used. Reading this was affirming since after several episodes like the one described above I moved from pushing the LES approach to encouraging a certain stance. I wanted the preservice teachers to see themselves as educational researchers in order to determine what was and wasn't working for their students.

The push-back from some of these future teachers has been interesting. I usually get a few each semester who ask, "Why don't you just tell us the best way to teach math?"

I respond, " I don't know what grade level you're going to teach. I don't know where you're going to teach. I don't know what text you're going to be using. Deciding the best approach to use is dependent on these factors and many more. My goal in this class is to provide you with opportunities to practice using the tools that will support you in making those decisions. I want to help you to develop educational phronesis: practical wisdom that allows you to consider what's currently available to foster learning and what's worth doing under the circumstances."

Does this mean that my students might not be familiar with 3 Acts or foldables or "My favorite no" or some other great ideas the mathtwitterblogosphere comes up with in the coming years? Probably. But if these preservice teachers become educators who attend TMC and critically consider how to adapt what they hear for their students, then I will be happy.

Do you ever make mistakes?

The above was on my Facebook news feed this past week. As a young adult, I remember watching Bob Ross on our local PBS station, WNMU. If you are not familiar with his work, watch this short sample.

Anyone considering making online teaching videos could learn a lot from Bob Ross. He treats the viewer as an apprentice. We get to watch him engage in an authentic act. And as he engages in this act, he describes what he is doing and why he is doing it. Let me amend what I wrote at the beginning of this paragraph: Any teacher could learn a lot from Bob Ross.

PS: When John Golden (@mathhombre) found out I was writing this post, he asked me to include the following. I do it gladly. The idea of "happy accidents" fits with my efforts at graceful imperfection.

What goes here?

I look forward to learning with you.

The day before a teaching observation I send out an email confirming that I have the correct details and reminding the teacher that I will need an action plan beforehand to focus my attention. I try to end each of these emails with the statement provided at the beginning of this post. It serves as a reminder that the observation will be a learning opportunity for both of us and not just a dog-and-pony show.

Sometimes, I take for granted my role as a learner in these experiences. I was reminded of this during a recent observation. The teacher wanted me to focus on whether or not she was providing adequate support to students as they were learning how to multiply and factor polynomials. This was in an eighth-grade class and they were halfway through the unit - just wrapping up multiplication of polynomials.

The lesson went well and the students were engaged in what Fisher and Frey call Collaborative work. This entailed a few items that provided students practice multiplying polynomials and a worksheet called Polynomial Puzzler that the teacher had modified from a lesson found on Illuminations. The teacher went over the instructions,

Fill in the empty spaces to complete the puzzle. In any row, the two left spaces should multiply to equal the right-hand space. In any column, the two top spaces should multiply to equal the bottom space,

 and demonstrated using the first puzzle.

As I looked through the entire worksheet, however, I identified an area I thought would give the students trouble; there were places where the four entries in the upper left were missing entries. This meant the students would need to factor some polynomials in order to complete the puzzle. The teacher had not provided the necessary support for student success. I made a note to talk about this during the debriefing.

Sure enough, after students had completed the first puzzle and multiplied what they could in the second puzzle, many started to ask, "What goes here?"

The teacher responded with something like, "That's a great question. I guess I didn't give you enough support." She pointed to the upper right corner and said, "We want to find out what goes here. In other words, what times this {pointing at (-15x+3)} will equal this {pointing to the lower right corner}? Okay?"

I thought to myself, "No. Not okay. They need to know how to factor." But the students seemed satisfied and went on about their work. And the surprising thing was that they were okay. In fact, they were better than okay. They were amazing.

The students at the table nearest me began looking back at the work they had already done and sharing what they noticed. "Look. -4x+10 divided by 2 is this one {pointing at -2x+5}," one of the girls exclaimed with more enthusiasm than I usually see in math class. The group then began talking about dividing the polynomials to find the missing entries. Sometimes they tried using guess-and-check to identify what was missing. The main point for me was that they did not just give up.

They seemed to be embracing the struggle that so many students in math class are determined to avoid. And they weren't alone. I heard several ahas from students seated in different groups around the classroom. I do not know why this class acted so differently than others I have seen. The cooperating teacher is a former GVSU graduate, so I would like to think that the learning environment had something to do with it. Or maybe it was the fact that it was a puzzle and not homeWORK.

After the lesson, I asked the teacher if she had anticipated any problems. She had thought that the instruction might be confusing. When I pressed about the factoring, she acknowledge that it could have been a problem but that she thought it was actually good that they did not know exactly how to do the puzzle our way because then they would obsess about doing it right. "Besides," she said, "I just wanted it to foreshadow factoring. Now they're ready for the next lesson."

I love my job. I learn something everyday. Even on those days when I think I'm the teacher.

Where does it hurt?

Me: (after a fairly lengthy description of open questions) So what did you hear? What are you thinking?

Teacher: (long pause) I don't know what you want me to say.

Exchanges like this happen more often than I like. People have been trained to believe that when a teacher asks a question, he or she is looking for a particular answer. We want to be good students which means providing the expected answer. It reminds me of a book discussion on Diane Rehm about how patients and doctors fall into a routine that can result in mistaken diagnoses and unnecessary tests.

Proud parents with Dr. Hilary at MSU COM graduation

This book came to mind when the teacher responded as she did. You see, I have tried to get in the habit of asking questions I do not know the answer to; it ensures that I avoid falling into an educational rut, and it makes my job as a teacher much more interesting. I tried to explain to the teacher that my question was an attempt to gather some information about what she had attended to in order to make a decision about our next steps. I said something like, "Think of me as a doctor trying to make an accurate diagnosis of your 'health' in regards to understanding of this topic. It's like I'm asking, 'Where does it hurt?'" She laughed and then went on to describe what she had understood about open questions. As the discussion went on, I would stop every now and then to ask, with a smile, "Where does it hurt?"

This is one of the ways we might use warm-ups more appropriately (see last week's post for my perspective on this problem). We could treat it as a way to diagnosis the readiness of the learners to move on or determine what issue we might need to address. (Here is an example of the latter.)

I saw an example of this earlier in the week. Students worked on some scale drawing questions, and after giving the answers the teacher asked if there were any of the questions students needed help on. A student called out a number. So far, so good. However, instead of doing more of a diagnosis, the teacher fell into the rut of showing the student how to find the answer. After a couple of minutes, the teacher stated, "That means the answer is 1/2 an inch. Okay?"

Fortunately, the student responded, "So 6 centimeters, right?"

Now the teacher could do an accurate diagnosis. The problem was not in finding the answer - it was interpreting the answer. "This is 1/2 an inch (holding his thumb and index finger close together). 6 centimeters would be more than two inches (expanding the distance between his thumb and finger). I wonder - were you thinking that 6 inches is half of a foot, so half of an inch is 6 centimeters? (She nods yes.)"

How often do we jump into treatment before doing an accurate diagnosis? I know that it seems inefficient to spend time listening to the student explain "where it hurts," but is it? Drs. Kosowsky and Wen found that it was important for physicians to take more time listening to their patients in order to get their diagnoses and treatments right. The same could be said for teachers.

Am I getting warmer?

In The Teaching Gap, Stigler and Hiebert examine the details of typical lesson designs found in German, Japanese, and U.S. math classes from the Third International Mathematics and Science Study (TIMSS). A table found on pages 30 and 31 describes three specific lessons and notes whether or not each lesson's features represent the overall teaching in that country. The U.S column looks something like this:

• Teacher asks students short-answer review questions. (Typical to begin with "warm-up" activity.)
• Teacher checks homework by calling on students for answers. (A common way to check homework.)
• Teacher distributes worksheet with similar problems. Students work independently.
• Teacher monitors students' work, notices some confusion on particular problems, and demonstrates how to solve these. (Typical for teacher to intervene at first sign of confusion or struggle.)
• Teacher reviews another worksheet and demonstrates a method for solving the most challenging problem.
• Teacher conducts a quick oral review of problems like those worked earlier.
• Teacher asks students to finish worksheets. (Unusual to not assign homework.)

My work with teachers brings me into a lot of secondary math classrooms, and I can say that not much has changed in the typical math lesson since the printing of The Teaching Gap in 1999. However, I want to focus on just one aspect of the U.S. lesson, the warm-up.

Because of my own interest in engagement, teachers often ask me to focus on when students are engaged (or on-task) during a lesson and what to do when they are not. Probably the most off-task period during many lessons is the first part of the lesson, the warm-up.  This might be for any number of reasons but I have a few ideas.

First, the students find little purpose in this activity. It is rarely collected, usually graded only as a consequence for causing a disruption, and often disconnected from the overall lesson. Without some purpose, it is difficult for students to engage in a task.

Next, there are times when the task is an extension of current work rather than a refresher. It would be like running a race without warming up. Consequently, some learners do not see themselves as having the potential to be successful with this initial task - a tough way to begin a lesson.

Finally, by sixth grade students are familiar with the design of most math lessons. They know that someone will at some point provide the answers to the warm-up. So some students do not work on the warm-up (off-task) but copy down the answers when they are shared (on-task). Others, work on the warm-up (on-task) but pay little attention to the answers because they already have them (off-task). Either way, this seems like an inefficient way to start just about every lesson.

What do you think? Have I accurately portrayed what is going on during the warm-up in many math classes or is this a straw man? If you agree that the warm-up is in need of a makeover, then perhaps in a future post we can discuss the alternatives. Otherwise, I do not want to waste your time any further - going over something that is not really a problem has no purpose and does not make any sense to me.

Why so tense?

from What I Really Do Meme

It's inevitable. Whenever I work with student teachers, there comes a time when we have to talk about the tension they are experiencing between their ideal classroom and the reality of their placement. The discussion goes something like this...

Think of your vision of teaching (the ideal) and what is actually happing in your classroom (the reality) as two points. Now, stretch a rubber band between these points. Many of you will notice that the ideal and the reality are quite far apart resulting in tension between these two points of view.

The tension often results in one of two outcomes. New teachers quit (the rubber band breaks) because the distance between their ideal and the reality is so far apart. Or a new teacher abandons their ideal and snaps back to the reality (i.e. they teach as they were taught).

In order to deal with this tension, I have found it helpful to expand both my vision of the ideal and my perspective of the reality. This means that I maintain my core teaching philosophy while considering what might be negotiable.  I say to myself, "I would be willing to do x as long as I don't have to give up y." When it comes to the reality, I continue to be honest about my situation but I try to be aware of potential areas I might be able to build on. I remind myself, "If I concentrate only on what I dislike, then that's all I will see." As both expand, I look for areas where they overlap; this is where I find the subtle shifts that allow me to survive the situation while gradually subverting the current system.

Here are some examples of how I and other have attempted to make subtle shifts in our teaching.

So this is part of what I do as a supervisor of secondary math student teachers; I try to help them to be aware of what teaching is and what they want teaching to be. And then I try to support them in improving teaching, which is where the fun begins.

Is it a performance or playing?

We spent much of our break between semesters attending concerts by Michigan musicians (Joshua Davis, Max and Ruth, Seth and May, and Starlight Six). As often happens, I began to consider how what I observed during these concerts might apply to teaching. This was especially true when we got to see Joshua Davis at two different venues on December 13th. The first was at a theater in Frankfort, Michigan showing a movie to which Joshua contributed. Later, at an after party, he played in a pub across the Betsie River in Elberta.

At the theater, Joshua performed before the movie while photos from his trip played on the screen behind him. He shared a bit about the project and a few songs that had resulted from the experience. I saw this as a performance because he had limited time to share a planned set of his "best material" in a polished fashion to an audience he could barely see beyond the first few rows. 

His playing at the pub was much different. Joshua was set up on a "stage" separated from the audience by a pathway that many of the patrons used to get from the bar area to the bathrooms. During his set, he joked with the people as they passed by and interacted with the audience. We yelled out requests and he obliged. Furthermore, it was clear that he was trying out some new approaches to familiar songs. I call this playing because it was more relaxed and playful than his earlier performance.

As I reflected on the differences between these two shows, I realized that I need to be better about distinguishing between performing and playing in my practice. There is a place for both in teaching, but I am afraid I have not always made an intentional choice about the approach I will use during a lesson. When there is limited time, little opportunity to interact with the audience, and a need to share my best, most polished material, then a performance might be the way to go. Otherwise (and if I am honest, most times), I would be wise to be more playful in my teaching - trying out new things, seeing how the audience responds, and making the necessary adjustments.

And before too long, maybe I can schedule an "open-mic lesson." Of course, there will need to be intentional efforts to turn over to the audience the responsibility of making music. Still, it would be interesting to hear how they might interpret the music and make it their own. 

Why did you do that?

We just completed another semester at Grand Valley State University, and once again I found myself asking our teachers-in-training some version of "Why did you...?" after many of the observations. I try to make it clear that this is an authentic question not some sort of accusation of wrong doing that demands an accounting. Seriously, I want to know the rationale behind some of their teacher moves. Also, I want them to be mindful of why they make certain decision during their lessons. Consequently, this is what I would call a win-win question.

For example, many student teachers struggle with time management during class, and on their Action Plan they will ask for suggestions about how to be more efficient while conducting a lesson. During the subsequent observation, I often see a typical lesson component. (Stigler and Hiebert were right about there being an often unconscious script associated with teaching math.) The teacher provides some time for individual or small group practice followed by a whole class discussion of the practice items. 

Afterwards, I ask, "Why did you go over all the items? What did you see as you walked around that made you decide that this was necessary?" Again, this is intended to be a serious question, and I sometimes get answers that teach me something about them as teachers and their students as learners. Some of the teachers say something like:

• "I noticed that most of them were struggling on [some aspect of the practice] and decided we needed to look at it as a class." or
• "There were a few different approaches and I wanted the class to see that problems can be solved in multiple ways." or
• "While they got all the practice items correct, I wanted to provide them an opportunity to communicate mathematically. They still struggle with vocabulary and precision and I thought this would be a good time to practice these given that they understood the concepts."

But occasionally, the response I get is, "What do you mean? We always go over the items after their practice. You mean I can skip this.?" The discussion that follows is nearly always goose-bump-inducing as the novice teacher begins to develop phronesis (what could I do here and what's worth doing?).

My goal as a teacher educator is not to develop a bunch of Dave Coffey clones. One is enough. Besides, my approach would not work for all the different teachers I work with over a semester. But if I become the voice in their head that asks after a lesson, "Why did you do that?" - I can live with that.

What's your plan to improve?

One of my favorite activities to do with teachers, both preservice and inservice is the Marshmallow Challenge. I view it as an excellent metaphor for planning and improving lessons. If you are unfamiliar with this activity, then you might want to watch this TED Talk before going any further.

Often, teachers fall into the same trap as others described in the talk. The teachers develop elaborate plans, create tall spaghetti structures, and wait until the last second to put the marshmallow on top (use this bomb timer to add suspense). Usually, the structure cannot support the added weight and it falls or breaks. 

So what does this have to do with lesson planning? I see the same thing happening in developing and implementing lessons - especially among new teachers. There is a great deal of planning beforehand in order to make things perfect. They work until the last minute, trying to get everything ready, but when the lesson finally encounters the learners it falls apart. Novice teachers are not the only ones to experience this phenomenon, however. Personally, I have had my fair share of lessons crash and burn despite massive preparation. In fact, I have wondered if the preparation was sometimes the problem.

Near the end of the talk, Tom asks, "What is your marshmallow?" For me it is a focus on student learning goals. With that in mind, and an awareness of how building on and improving prototypes increases the likelihood of success during the challenge, I have decided to try to plan differently. I want to start by designing a lesson with the least amount of support necessary to achieve the learning goals. Then I will try it out, gather data on whether or not the structure supports my goal, and make the necessary adjustments. If things go according to plan, I can create the next lesson/scaffolding using the same approach - start simple and add on as necessary.

This past week, it was interesting to watch two groups that contained members who had preformed the Marshmallow Challenge in other settings. Each followed the kindergarteners' approach of making successive prototypes. Where they differed was in their acceptance of their circumstances. 

One group kept adding on until the very last minute - continually tinkering with the prototypes. Unfortunately, they ran out of materials and the final structure was unsteady and fell over as the timer went off. A few minutes earlier it was standing tall:

The other group "finished" with about four minutes left. Given more time and resources, they might have been able to build something taller, but under the circumstances they were satisfied with their effort. They ended up besting the only other standing tower by about 6 cm.

It is only a metaphor, but I think the Marshmallow Challenge has a lot for us to think about as we consider improving education. Michigan is in the midst of considering plans for overhauling school funding (and therefore schools) but these plans have the feel of untried spaghetti towers not tested prototypes. As Stigler and Hiebert point out: 

Traditionally, Americans haven been more willing to accept dramatic failures than to applaud or even appreciate, small successes. (page 139 of The Teaching Gap)

If we are to succeed at this challenge of education reform, then we ought to heed the lessons of the Marshmallow Challenge.

What if they ask me a question I can't answer?

I often coach student teachers assigned to teach topics they have not worked with in a long time. The last time many of them had Algebra or Trigonometry was in high school and some "rust" obscures their understanding of the subject. They are understandably concerned about making a mistake while working through examples or demonstrating solutions to homework questions. 

I can empathize having had to teach College Algebra many, many years after my last encounter with the material. Before each lesson I had to reteach myself the topics. (It didn't help that my initial interactions with the College Algebra content were what Skemp would call instrumental.) And when it came time to address homework issues, I was always concerned that I would make a mistake in front of the class. Turns out I had my own issues with math-phobia.

While I am comfortable with the idea of making mistakes in my mathematics education classes, because it represents the learning process, I have found college freshmen and sophomores taking a required math course less understanding than my preservice teachers. Students in College Algebra often have certain expectations of what mathematics teaching looks like and when they encounter something different (mistakes), they can shut down. So early on I want to establish a certain level of confidence for myself and for them.

I share this story with preservice teachers so that they can feel comfortable with the fact that any nagging doubts they have about teaching a topic they need to relearn can be expected and dealt with. There are two suggestions that I make to build their confidence. The first is to avoid answering off-the-cuff questions until they feel more comfortable with the content and the classroom. And the other is to always have the examples they want to share written out ahead of time.

When it comes to questions that arise in class, if it's not something the student teachers have prepared for I tell them it's alright to write the question down and tell the class they will get back to it. This models that all mathematical questions don't have immediate answers and hopefully helps students to become more comfortable embracing the patience required to be successful in learning relationally (see Skemp). Regarding homework questions, I suggest that the student teachers set up a procedure by which students can identify which problems they want support on. If this can be done beforehand (I used Blackboard), then the student teachers can determine which items caused the most confusion and prepare a whole-class demonstration to support student learning. Items identified by a single student can be attended to through a written example or individual conferencing. If there is no way to gather this information beforehand, then I suggest collecting it at the end of the class period when it is expected to be completed and preparing the support for the next period. In either case, have the work written out ahead of time.

When they share their examples, at least early on, I encourage the student teachers not to recopy the work on the board but to use the overhead or document camera to project their work. This addresses several issues that teachers trying to build their confidence often face. First, it tightens up time management. Writing on the board is time consuming and can allow students to get off-task. (Believe it or not, many of them are not copying it down.) I would simply project my work and add my thinking as I go over each step. Second, projecting previously written work alleviates the potential for making a mistake and eroding confidence for those already dealing with this issue. Multi-tasking when stressed is difficult, and I have found that the combination of copying and talking through my thinking can lead to errors even though I have written everything out correctly. Finally, and this is huge for new teachers in front of a class of teenagers, using written work projected on the board usually means not having to turn your back on the class. If you've ever taught in a secondary math class, you'll understand what I mean.

Let me be clear, I am not suggesting that this approach become the norm; it is just the place to start when teaching a new prep that might require some relearning of topics. Once a classroom culture of trust and respect has been developed, I have found that I can go back to responding to questions more immediately. But I still reserve the right to say, "I'll have to get back to you on that one."

What's worse than two guys sarcastically watching a video?

Soon after we first posted Mystery Teacher Theater 2000 Episode 1 and it started getting attention, John and I began to consider, "Now what?" As we so often do, we tried to make this thinking visible by sharing it on Twitter.

In retrospect, I regret using "snarking" and "snark" in this discussion because, as I have written before, the original videos (yes videos, another one came out recently) were meant to be satire. Still, hopefully these tweets demonstrate that John and I try to take a meta perspective when it comes to education. 

Well, that's enough background. We hope the message of this version speaks for itself. Ladies and gentlemen, welcome to Meta Mystery Teacher Theatre 2000.

I hope you stuck around after the credits, there is a surprise waiting for those who persevered through the entire video.

Is it worth it?

The second episode of Mystery Teacher Theater 2000 came out last week.

My partner in MTT2K, John Golden, did an excellent summary of his perspective on Khan Academy here. In this post, I want to give a bit of background on how we came to use this video and expand on John's point that "at some level this is two guys goofing around to make a point about good use of resources."

I first saw Khan Academy's video, Introduction to matrices, while doing an observation of a student teacher. As a part of the lesson, the student teacher decided to show this nearly twelve minute presentation to a class of precalculus students. Throughout the video, the students paid very little attention to the screen and the student teacher ended up going over the basics again.

The idea of having over 3,000 videos on a variety of subjects available to anyone with an internet connection is appealing to me. If the quality of the videos is suspect, it is less attractive but it really is none of my business. When those videos are assigned to K-12 students to watch either in class or after class, then it is part of my responsibility as a teacher educator to question their use. In this case my question would be, "Is this video worth showing in class or could the time be better used?"

In other words, how is this video better than:

• the teacher providing this information through a more interactive lecture;
• the students reading the textbook section on matrices; or
• the class working on an "archeology project" where they try to discover the  basics of matrices using artifacts strategically "found" by the teacher?

Grant Wiggins talks about the juice needing to be worth the squeeze when it comes to assessments. I would say the same could be applied to other instructional decisions like the use of Khan Academy videos as a part of a school's curriculum. In the case of the student teacher, I would say it was definitely not worth the time it took to watch the video and get the students focused back on the lesson.

Perhaps the problem is that the videos were not intended for whole group instruction. A recent post from a Teach for America staff member explains how he used Khan Academy to help differentiate his instruction.

I could point my most advanced students towards videos instructing them on multiple application of a particular theory while I simultaneously walked students struggling with the same notion through a lesson explaining its fundamental premises. It helped me to be a better teacher who reached more of my students more effectively.

Several promotional videos from Khan Academy offer the same testimonial. Teachers assign Mr. Khan's videos to students to watch while the teachers work with smaller groups. Here are two teachers from Eastside College Prep in East Palo Alto, California talking about using Khan Academy in their classrooms.

If Khan Academy helped these middle school teachers to break out of the mindset of simply giving notes to students, then I really do owe a debt of gratitude to Mr. Khan. However, because valuable school time is being used to watch these videos I must push these teachers to think about what comes next. Repackaging the lecture as a video is not a re-imagining of education nor is it true differentiation of learning.

The way they are using the videos sounds more like addressing a classroom management issue than truly facilitating learning. If these teachers are looking for something productive for other students to do while they work with small groups, then I would encourage them to talk to their colleagues who teach reading and writing and manage small groups regularly without assigning videos. I can think of at least a half-a-dozen things that are more worthwhile to do in class than watching a video like the one I sat through during that precalculus lesson. 

I will write another post about alternative activities (if there's any interest) but this post is getting long and I want to give those teachers who assign Khan Academy videos to their classes a chance to respond to the question, "Is it worth it?" Please post your comments below with the understanding that any off-topic comments will be deleted - I would not want you to waste your time.

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.

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.

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.