This post was mentioned on Twitter by ddmeyer: @berkun I don’t think I break too much from c.w. here. Time to upgrade pedagogy. I like David Simon’s sol’n also. http://bit.ly/cq0QXe…

IMHO, facilitating this sort of dynamic storytelling feels easy for a gifted educator and can really look easy, but it takes lots of expertise. It’s like a really good improv group. They make everything look easy and spontaneous, but they have honed their craft.

Aside from knowing how to tell a good story, a great math teacher also needs to know:

1) Math. She doesn’t need to know all math, but needs to know lots of math related to her topic. This includes knowing what leads up to it, what flows directly from it, and how it can be applied.

2) How students build their understanding of the concept and common mistakes people make. Many brilliant mathematicians have no idea about how knowledge is built. They are too smart. It’s like an engineer tutoring a kid in pre-algebra. Many engineers are gifted in math and have no sense of how to help anyone move from one level of understanding to the next.

3) How to listen. I know plenty of smart people who can tell good stories, but can’t really understand questions people ask. When someone interrupts a story with a question, some storytellers misinterpret the question and thus provide bad answers. A great teacher has to be a great listener. A bad listener won’t be able to stop students from steering straight into rocky mathematical cliffs. A bad listener can’t determine where their students are. A great teacher has to be a great listener who knows where her students are and where they are headed.

What have I missed?

–paul

In “What The Best College Teachers Do”, there’s a quote something like, “By the end of the course, I want the students to feel as though they *invented* calculus…” THAT is the feeling we’re looking for, is it not? So I’d prefer to focus on the story of the learner’s *discovery* of the topic… rather than a story *about* the topic.

Just my two cents. Not suggesting I’ve been successful, but we’ve seen how asking our authors for storyboards instead of outlines/TOCs has led to some interesting and very *wrong*(from the learner’s persective) implementations of “story”.

Considering we all learn our first language primarily through observation (induction), it would seem that learning a second language could be inductive as well. I’ve learned two second languages inductively (and one non-inductively), so to speak. The first language I learned this way was German, which was taught using Total Physical Response and a textbook in high school. The first time we heard our teacher speak English was at the end of our second year. My second experience was in learning Chinese, which also involved many ways of learning outside of the classroom. As a bit of background, I took three semesters in a traditional course at USC, and have lived in Taiwan for all but three years since. I studied formally in a local language program while attending a local church. The language program was completely conducted in Chinese, as we had students from around the world. I also learned a lot of characters through singing songs at church. If you see a certain character enough times, and hear it sung repeatedly, eventually you recognize it and know what it sounds like (other than tone). At that point, you can ask someone what it means, or you can figure it out through the context. I learned a lot of language this way.

I think that learning a second language teaches students that words can take on different meanings in different contexts. Definitions even change over time. Different languages have different amounts of rigidity in their grammar. By listening to the language, you begin to develop a sense of what “sounds right”. Krashen talks about how input is the key to learning language, and not production. So, how do we get students to listen to (or read) the language? How do we get them to listen/read actively and observe the language? Production for me is very analogous to applying formulas. Listening/reading develops the intuition, whereas practicing production allows you to respond or initiate in conversation in a smooth fashion. I’m not a second language teacher, but if I were, and I wanted to follow the advice of this blog, I would probably try to get as much input (aural and written) to the students as possible.

From above:

“If I can make you curious enough, there’s this thing called Google. If you’re curious about the New Orleans Indians, or ‘second-line’ musicians–you can look it up…”

“Treme’s pilot, true to Simon’s challenging aesthetic, dumps the viewer into an unfamiliar-but-compelling environment full of unfamiliar-but-compelling people and trusts that, because the whole thing is so damn compelling, you’ll be back the next week to learn more.”

Being dropped into a foreign country and trying to learn the language is like the definition of “unfamiliar-but-compelling”. That’s not 100% feasible in the classroom, but here’s my stab at an ideal language learning classroom. You start with some form of aural immersion (TPR, singing, cartoons, etc.). This gets the students interested and wanting to figure out what’s going on. Let them struggle to figure out how to pronounce a word. Maybe even let them try to spell it from how it sounds. Let the students try to figure out what the word means from the context. Then, give them the vocabulary list (this almost seems optional). Maybe they’ll find out that their spelling was similar to the “correct” spelling. Maybe they’re off just a bit. Maybe their spelling was representative of the actual sound of the word, but the language has little tricks that they don’t know about. An ESL student might spell “rocket” as “rockit”. They would learn that sometimes “e” sounds like a short “i”, without the teacher having to tell them. Now that I think of it, get rid of the vocabulary list completely, and just give them a passage containing many of the words they just heard. This way, they’re exposed to more authentic input, and they are reinforcing the words/structures they just listened to in the aural immersion. You could even reverse the order (aural -> written, written -> aural). Give the students an authentic text (maybe a dialog) containing words the students don’t know (give them a dictionary to look up the words). Let the students try to act it out. Then, show a video of the dialog. Now, they can see the context, and they can listen to find out if they were pronouncing things right.

As the students pick up more vocabulary and grammar, their ability to acquire new words and structures from context will increase. I’ve only had 2.5 years of formal training in Chinese, but I’ve been using context to acquire language constantly since I stopped taking classes about 10 years ago, and I am able to translate Chinese to English professionally as part of my job.

Finally, regarding motivation, I think the biggest joy for me in learning a language is being able to use it. But, I’ll always remember those glorious moments of ordering something in Chinese, and having the exact thing I ordered show up on the table, having someone on the phone tell me that they wouldn’t have known I wasn’t Chinese unless I told them, or telling a joke in Chinese and people actually laughing. These things help me keep pushing to learn, even now, especially when I feel like my mind is in a big, black haze when I’m speaking Chinese, which happens when I’m not sure the other person knows what I’m saying.

P.S. If you’ve seen the video on ConcepTests by Eric Mazur (physics prof at Harvard), I think even that could be adapted for the secodn language classroom. Give the students a fake text message or e-mail from a girl to a boy, and ask (based on the context): Has the girl agreed to go to the dance? 1) Yes, but he has to get a haircut; 2) Yes, but he needs to shave; 3) No, because she doesn’t like his hair; 4) No, because he doesn’t have enough hair to need to shave (ok, this is a pretty lame example, but I made it up on the spot). Have the students vote on the answer. Let them discuss it amongst their peers. Let them vote again. Clear up any conceptual problems. Rinse and repeat.

From my formal undergraduate math experience, I got little to no history of the subject. Most of what I know, I picked up myself out of interest. I suspect the same might be true for many math teachers. To that end, here are two excellently researched math/history books from good authors that have been highly recommended to me:

Mathematics in Western Culture by Morris Kline
and
Mathematics and Its History by John Stillwell

Of course, that doesn’t solve the problem of how to tell a story rather than a dry narrative in class, but maybe it’ll help with the equivalent of background research.

I suspect that as humans we understand narrative better than exposition– case in point being that hilarious moment that becomes a dull series of events when you try to recount it and ultimately have to explain away with a lame “you really just had to be there.”

I don’t think a teacher can tell the story without fully understanding exactly what you laid out, Dan and David, in comments 2 and 3: what came before? What comes after? Why does this all matter? How does it affect everything else we do? And why does it just make sense this way?

First, we all need to understand this (and, from my recent work with math majors, I’m not sure what it takes for even content experts to really truly get it). Then we worry about presenting it to our students.

From Martin Scorsese’s forward:

He knew that is was about acting and editing, action and words. And that more than anything else, it was about practice. Theories are fine, but practice is everything.

…

This book – this invaluable book – is the work of a lifetime, from a man who was passionately devoted to his craft and his art, and who then devoted himself to transferring his knowledge and his experience to his students. And now it’s available to all of us. What a gift.

Consider where you were a year ago, two years ago, five years ago. Your ‘resolution’ for teaching has increased. Your ‘bit depth’ for processing the response of your students has increased. I’ve seen many a teacher go through the progression:

1) “I say what I’m going to say regardless of what the student’s facial expression, body language, questions, etc.”

2) I adjust what I’m going to say based on whether they are “definitely getting it” or “definitely not getting it”

3) I adjust with subtle changes based on subtle feedback from the students.

etc.

When I began with my horses, all I could adjust for were the most gross examples of behavior: doing it or not doing it. I had a bit-depth of 1: on/off, right/wrong. Later, I began to have, say, an 8-bit experience… 256 different shades of behavior.

With those differences, I also needed to learn a matching set of possible responses and the flexibility to self-assess how they were working. At first they were mechanical and with MUCH latency… I wouldn’t know if they were working for quite some time, and often only with external assessment from another observer (or what we call “eyes on the ground”). But eventually my resolution began to increase.

I believe this is no different from improving expertise in virtually ANYTHING. It is always about continually increasing our resolution, and is achieved through a balance of challenge matched with new knowledge + skill, and what the performance experts call “deliberate practice.” We NEED to find ways to offer teachers a chance to learn and practice *the right things.*

Not that different from how one becomes a chess master. Or a martial arts expert. Or a horse “whisperer”. What once looked like magic (or at least innate talent) begins to look more like not just time-on-task, but time-on-the-RIGHT-task.

My sister-in-law is a Sommelier. For me, wine is indeed a 1-bit experience (red or white). At one time, hers was too. Now she can distinguish all those (b.s. I still think) subtleties. She *learned* this. She studied this. She practiced this. She took tests on making these distinctions. She was not born with any particular talent for this, and in the beginning… not even an interest. But the more her resolution grew, the more *interesting* wine became. Now it is her passion.

If this is viewed as increasing a teacher’s resolution for both the feedback of students *and* the possibility for responses, yes, we can teach this. As you’ve suggested in the past, in our books we are doing some of this with ZERO direct feedback from our learners, based on the assumption that we can capture 80% of what is likely to happen in a classroom guided by someone like you, and then do our best to “flatten” that into a 2D page. A pathetic imitation of an awesome class experience, but in part compensated for by the fact that each individual learner is given the time needed for their own unique brain to fill in the spaces we tried to create and inspire.

As to *how* to teach this… well, yeah, I really don’t know. But again to paraphrase YOU–figuring out what the problem really is matters deeply, and I think you and your co-conspirators are converging on a few key tools/skills that could make a huge impact on learning.

People like you make me optimistic about the future. Do not let up.