Yeah, I spend a little bit of time thinking about this stuff. As you may know, I work in a public library. These days, a big part of my work is technical education, especially with low-literacy adults. For the kind of stuff I do, the bottom-up style is far more effective--people perceive it as pragmatic rather than theoretical. It leads folks to think of the computer as a tool for getting things done, rather than a baffling black box. And rather than thinking of me as a pointy-headed expert/authority-figure who likes to think about technical problems just because they're interesting (sad to say, pretty accurate), they think of me as an ally, someone who shares the common goal of getting them signed up for an email account so they can fill out this job application (or whatever).

It seems, in my experience, that the top-down stuff is most effective among people who would be good learners anyway. The bottom-up style, though, might be more universally effective, at least when it comes to the kinds of things that I use it for.

Another model that might prove useful to you, Wolfdog, is the Myers-Briggs "intuitive vs. sensing" split; I think it follows your model fairly well (though I just skimmed that link, so if it's totally kooky, I can find some other info for you). I test way the fuck over on the intuitive side, and I definitely notice it in my learning -- if you give me details or examples without giving me a theory to hang them on pretty quickly, then the specific facts just fall through my fingers. If I have the theory to start with, however, then the concrete bits have a "place" to live, and I can see their significance and value.

Most people in the population are sensors, though, and prefer starting with the concrete in order to prop up the abstract.

I think of it mostly as: I learn as if I'm stringing together a necklace; I need to start with the string and then build up beads to see the whole picture, but without the string I've just got a collection of unrelated, indistinguishable beads. Others learn as if building a brick wall, where you have to lay each brick down carefully, one on top of the other, and then you can step back and see the finished product. (Intuitives also tend be big on metaphors....)

In terms of my own learning and teaching styles, I definitely see it coming into play. In learning, I *hate* survey courses; they end up just plopping a bunch of facts on me without giving me enough structure. So I tried to stick with classes that had a really narrow focus ("Shakespeare" instead of "English lit," "Michelangelo" instead of "Renaissance art") so that I could find those strings, those connections between the "examples" (in these cases, works of art), most easily. From *that* base, I could then branch out and add more information.

I have also found myself completely avoiding professors who don't teach in a way that fits my notetaking style, which relies heavily on categorizing facts under subject-headers. Profs who just throw out facts without grouping them into some sort of narrative structure drive me up the wall.

In teaching, though mine is mostly informal, I have a devil of a time remembering to include enough concrete details/examples for other people to follow me. I've had instructors comment on it in regards to my counseling style, as well. I'm always looking for patterns or theories and too often ignore facts or specific details. I try, with the couple friends who I know get frustrated with that, to start from the concrete and move toward the abstract, but even when I'm speaking about something I know well, I tend to get lost when I do it that way. Definitely something I'm trying to work on.

More info on Sensing vs. Intuitive learners, specifically with regards to teaching (scroll down to the "Sensing (S) versus Intuition (N)" section). And statistics that back up box's point about good students tending toward the "top down" (intuitive) approach:

Based on data from the Center for Applied Psychological Type (CAPT) between 56% and 72% of over 16,000 freshmen at three state universities were sensing students. Interestingly, almost 83% of national merit scholarship finalists and 92% of Rhodes Scholars were intuitive students.

From my last link (and then I swear I'll stop serial posting!), as a suggestion for teaching Sensing students:

In the what must be known (WMBK) method, we first ask: What is (are) the topic's most essential general principle(s) or goals? Place the answer in a goal box. We then ask: What topic(s) must be known such that students could achieve the goal? Place these subgoal boxes below the goal box and show an arrow leading from each subgoal box to the goal box. Continue to ask WMBK questions until you interface with material previously covered. You would then present the lecture by starting at the bottom of the diagram and work up towards the goal box.

That made me giggle. That's what I *try* to do when teaching people who need more concrete facts than I do; I try to go at it "backwards" from how it's structured in my head. But I notice huge resistance coming up for me in giving someone details before giving them general principles -- to me, it makes it feel like I'm forcing them to play a guessing game, and (in my mind, at least) it suddenly establishes a hierarchy: I know something they don't know, and I'm going to keep back the important parts until they "prove" to me that they understand the details. It feels reeeeeeally unnatural and uncomfortable to me.

Ah, all very interesting. I'm familiar with Meyers-Briggs and know the difference between N and S but hadn't thought about that in this context.

I worked on that theory that most people would do better with concrete examples first for some time, tending to plan almost everything in a bottom-up fashion, but like I said, I found that led to difficulties with people being unable to extract any essential principle; or perhaps getting the idea that a (more than likely partial) understanding of some examples is sufficient. It rarely is, but that seems to be the message that gets across. Big-picture stuff, I would say, tends to get treated as footnote-y or irrelevant when it comes last.

Of course when we test to see if the principle has been understood well, the problem doesn't necessarily look like the few examples, at least not superficially. This tends to lead to a lot of, I believe the word is, FAIL, and the all-too-common complaint of "We never saw anything like that before!" or "The test was nothing like what we did in class!"

...well, of course it was, and what you're being tested on is your ability to see how it really is exactly what we did do in class. On cynical days I think of this like a class in Introductory Hammer Theory where we spend a couple of weeks hitting assorted shit with hammers, then the final consists of being locked in a glass room and being instructed to find a means of escape. "Oh!" bewails the poor soul, still sadly imprisoned at the end of three hours, "how was I supposed to prepare for that? We never did one of those before."

So now I do tend to like to say right up-front, "Here's a general principle. It's probably too general to make sense right now, but you have to, at the least, know what it says. We'll take some time to unravel what it means, but you need to be able to recognize it when it crops up in various guises."

"Oh!" bewails the poor soul, still sadly imprisoned at the end of three hours, "how was I supposed to prepare for that? We never did one of those before."

Heh.

Sensing Learners
...Resent being tested on material not explicitly covered in class.

Intuitive Learners
...Don't mind being tested on material not explicitly covered in class.

I've thought a lot about this as it pertains to the way I've learned over the years and the way I teach my students. I think what you said in your last paragraph, Wolfdog, is how I (try to) approach things with my students. It's like, give them the big picture, then break it down and build it up again with them as participants (and hopefully doing most of it themselves).

Does anybody else even think about this?

Yes, of course, the whole area of study known as pedagogy is concerned with it! Systems like the Meyers-Briggs, the 4MAT system (extremely useful for teachers) Gardner's multiple intelligence theory and the insights that underlie learning style inventories by various test designers are all built on theory that posits that different people process incoming information differently. Most of them build on a very longstanding basic contrast between the classical and romantic thought tendencies in Western culture. There's so much to say about this that I hesitated to even comment, but yes - it's an entire field of study, and instructional design (the kind of question you're asking, which you've classed as top-down and bottom-up, which is a question about how to frame the lesson) is built on studies in cognitive science. The shortest answer to the specific dichotomy you present is: they're both right for some of the people, some of the time, in some topics.

I am a solid 4MAT 1, and before you start talking definitions with me, I need to know why you think this information is important. How did it come about, and why do I need to know it? So lessons that begin with detail and terminology without providing context and justification upfront generally confuse me - I end up having to back-build my own framework when I've finally discovered the utility of the topic, at which point I wish the instructor had just begun by discussing the utility. Meanwhile, a 4MAT 2 would be thrilled - they don't care about justifications, it's enough that the teacher (or the field) thinks it's important, and they just want to cut to the chase and know WHAT right now.

And so on.

But if you continue to teach, you will find that patterns of information acquisition will repeat in your students. It's grouping people's responses into repeating patterns that creates these systems of classifying individual intellectual approaches. They're not totally prescriptive, but they're pretty damn valid at a practical level.

Yes, of course, the whole area of study known as pedagogy is concerned with it!
Yes, that is not an unknown field to me. I confess I did mean more specifically I'm interested whether it's an issue anyone here thinks about much, and where you all find yourselves on the spectrum.

There's a (maybe understandable) tendency to view pure pedagogists as purveyors of both -- to be rude but accurate to the perception -- "yeah, no shit" type of insights ('theory that posits that different people process incoming information differently!') and grandiose, Teutonic classifications and schemes ('the complete 4MAT system model!' 'Standards of Learning!') that look brilliant on paper -- I mean, seriously, how can you argue with concentric circles... cut into sectors... and directional arrows? Well, this is unfortunate if it discourages anyone from doing their own thinking about pedagogy by making the field seem disreputable. (In math - I don't know about other fields - it doesn't help that math ed departments, besides being home to some students who are genuinely interested in cognition and pedagogical problems, are also frequently home to others who are just there because, well, doing middle-school maths again is all they're really up for.)

From the link: ...each lesson contains "something for everybody,"...

I think this is one of those things like that has a good ring to it (and I certainly expect to see it when reading teaching philosophy statements on job applications), but is very problematic when it is taken rigidly; adherence to schemes like this can tip over into really shitty design-by-committee schizophrenia, of the sort too many public school teachers are subjected to. "No Child Left Behind" has never exactly been my rallying cry, although I'd appreciate if no-one parlays that into some sort of ruthless "Cull The Weak With No Sign of Mercy" philosophy on my part either.

Put another way, I've generally been more impressed by, and inclined to imitate, teachers that are FUCKING AWESOME for some (and do no harm to the rest), than ones that everybody agrees are, you know, pretty OK. Best of my experience is the ones in the former group are more likely to be quite idiosyncratic, the ones in the latter group are more likely to be carefully measured script-followers. The latter will probably also have a smaller standard deviation in their test scores at the end.

if you continue to teach...
I've been teaching for, like, half my life, and probably wouldn't expend so many words on the subject (maybe you notice I'm not generally so verbose?) if I didn't imagine I might give it a go for another term or two. Also wouldn't if I didn't think I've still got lots to learn, of course. :)

This reminds me of something my yoga teacher said this morning: "If you're not frustrated at me -- or completely hostile to me -- at some point during each class, I'm not doing my job well. If you're not frustrated, you're not learning."

One of my favorite grad school professors definitely pays a lot of attention to different learning styles, and I find that during her class, there's always at least one activity that makes me roll my eyes and grit my teeth and think, "Oh god, do we *really* have to do small-group work / oral presentations / role plays / hands-on play? Because it seems like a *complete* waste of time to me." But I'm often surprised (not always, but often) at how much it helps me to step a bit out of my comfort zone and try a different learning style for a bit. So I think she's a better teacher to me because she's specifically not teaching to me at times.

I'm not sure that last sentence made total sense, but you know what I mean.

But I think that's different from the horrific "teach by committee" thing you're talking about, Wolfdog. But I think it can be helpful for everyone when an individual teacher varies his or her approach during a class session (it helps, though, that our class periods are 2 1/2 hours during the semester, and 5 hours during the summer, so there's a bit of time for playing with different activities).

So I think she's a better teacher to me because she's specifically not teaching to me at times.

Absolutely, because when she's not being a better teacher to you, someone else in the class is internally saying "FINALLY, something I can work with!" Teachers are always privileging one learning style over another. The trick is to be cognizant of it and provide a mixed slate of approaches. That's also flat-out more interesting, too, because it includes qualities of intellectual "interestingness" such as variation and surprise.

dherence to schemes like this can tip over into really shitty design-by-committee schizophrenia, of the sort too many public school teachers are subjected to

You might be tilting at windmills. I don't think this harm occurs nearly as often as the harm done by the majority of teachers who refuse to shift modalities.

Sometimes systems and schemes look bad because they are offered as crutches to people who have no teaching skills whatsoever, and then inexpertly employed ineffectively by those people. (Incidentally, I see them as politically diametrically opposed to the thinking of "No Child," which assumes one sort of measure to be supreme - not aligned with it.) But that doesn't mean that they are themselves intellectually weak systems. While they may seem obvious, they are simply biases unless supported by evidence and organized into a utilitarian approach to teaching.

I disagree that teachers who seem AWESOME to some people and are mediocre to the rest are truly better. They are only better to the minority with whom they connect, and there will always be an easy minority with whom we as individuals connect. The challenge is to get beyond that easy level.

I suppose the aims of the particular educational institution, level, and format need to be considered - a professor at the graduate level can be far less concerned about presenting to all modalities than a sophomore English teacher in a public inner-city high school. The concerns of equity and fair access to knowledge are much smaller at the graduate/private instutition level, and the aims of the education more finite. It can be assumed that the graduate student has already self-selected for employment within a field which will reward his or her approach. That is not true below that level, though.

But, on the whole, the best teachers, the most desirable teachers, are not those who inspire only a few to great heights, but who are actually able to begin teaching students where they are, and use whatever techniques necessary to create demonstrable progress in each person. Whether they achieve an arbitrary standard is a bit less important than whether they made progress, in general. Arbitrary standards (such as those imposed by No Child testing) are no measure of teaching skill or learning success. But neither are the few outlying students who are successful due to simpatico personalities with the teacher - especially when those few succeed in spite of a teaching style that falls flat for a majority of students.

The medieval apprenticeship with the master (which is by its nature unavailable to the ungifted) has its place, but honestly, it's usually in graduate school.

I don't like the classifications of my quick mentions of the tremendous body of work on the cognitive science of learning, instructional design, and teaching strategy as "no shit!" theory. Sure - I agree - this stuff is totally intuitive to a bright thinker interested in teaching and learning. It's what we do already. But guess what? That doesn't mean it's known to all, qualified and demonstrated and replicated. It's easy to be dismissive of it, but instead, it would be to your advantage to master the theory and language in case you want to mount significant paradigm-changing critiques.

The people who developed these systems actually developed the instruments, called on hard data, gathered enough evidence and proved the utility of their systems in practice. They are useful tools that manage to help teachers who would otherwise not address a variety of modalities, and would stick to the same rutlike methods and achieve the same limited success with already able students, and consider themselves satisfied with their work to reach new levels of student achievement and understanding. That is a good thing, in my view. You may wish to dismiss them, but you should first learn the landscape of the field of pedagogy so that you can address shortcomings you feel there are in the terminology or construction of these theories in language other than your own "top down/bottom up" construction, which is framed and termed differently by different theorists. You have definitely identified one element of several of the two-axis classification systems, but it's still only one axis. I think you would be interested in taking a closer look at the applications of all of these theories, and certainly by reading Gardner, if you haven't.

In education, there are so many ideas that appear simple and obvious, yet with an insistence on demonstrated success and basis in cognitive science, much of what we assume is "good teaching" goes right out the window. Judging any system only by its successes is nothing more than tokenism. What do we learn when looking at failure?

There will always be a few successful students, already bright and facile, and sometimes they will even share your own prejudices for learning style and modality. When you hit that wonderful relationship, of course it's awesome. There's chemistry; you understand one another. It's like falling in love. To teach to them only is certainly very satisfying. You connect and understand one another and you feel you are bringing them along by leaps and bounds; they become your proteges, your research assistants, your special students that you check back in with 20 years later.

But they are the easy ones.

The challenge of teaching is to teach to everyone, not just the easy ones with whom you began with a cognitive match. In order to teach outside your own modality, you need to stretch; to accept, at nothing more than their word, that other people construe the world differently, and to bring them experiences that meet your goals but offer them an entry point, even when it means that you're operating outside your comfort zone. That means operating blindly, sometimes: employing tactics that are uncomfortable and unnatural for you, but continuing them if they result in learning, on average. It means paying attention to the areas in which you have resistance (such as, for instance, looking seriously at curriculim planning systems which would have you be sure to balance your approaches within four broadly defined but distinct modalities).

There is no one best way. It is actually much harder to teach using multiple modalities and entry points and a variety of strategies. It requires more planning and more time spent doing things you're skeptical about. It requires questioning your own intellectual biases. But the service you can provide others by treating your teaching as something that needs to be planned with a variety of approaches that address varying ways of contructing the world is far better than what you might provide the few at the expense of the many.

I'm not sure what "teaching by committee" means, as I have never done it.

But I have taught for most of my career and have a degree in education, and though I will always believe that all learning theory is necessarily reductive - scrawled in broad strokes for utilitarian purposes of communal effort, in a world in which individual variance is always greater than group norms - I also strongly feel that when it's ignored, belittled, or dismissed, human potential goes unrealized.

When I taught, I usually started with skills and worked to develop them so that the students could synthesize them into a larger project.

For example, for 7th graders, I taught them skill of calibrating their stride, arm span, and hand span so that they could measure many things without going for a meter stick. For this they needed to know how to measure and how to average. Then I had them make a basic theodolite and use that and their calibrated bodies to measure the height of things they couldn't reach. Then I worked on Newton's third law (rote memorization - for every action their is an equal and opposite reaction), and had them do their big project: to build soda bottle rockets and be able to measure and record the height of their peers' rockets.

For many of my classes, I used Socratic method for explaining things. It took longer, but it was, I felt, more effective. Sometimes, I would start with stories. Telling about Sergei Mikhailovich Prokudin Gorskii or Eadweard Muybridge worked well because both men had fairly fascinating lives in a "once upon a time" sense.

I tried to make sure that projects and skills had elements of visual, auditory, and kinesthetic learning styles and that tests really pushed kids as far up Bloom's taxonomy that was reasonable.

There's quite a lot there and all food for thought. Thanks.

...on the whole, the best teachers, the most desirable teachers, are not those who inspire only a few to great heights, but who are actually able to begin teaching students where they are, and use whatever techniques necessary to create demonstrable progress in each person.

Yeah, I get that, actually. Well, sort of. To be a great teacher, in my opinion, you have be able to send some to great heights, you really do, and you won't do that automatically because you 'just click' with some fraction of people on general principles. But if you're reading into what I've written that I'm OK with jettisoning the rest - or, in fact, that there is a well-defined "the rest" and I've got my Chosen Few picked out in advance, then that misses the mark pretty badly. I really enjoy working with students with all kinds of preparation, different attitudes and preconceptions toward the subject, different styles of learning (and, bless me if I haven't identified more than just one dimension to learning styles, even if that's the one I was in the mood to chat about at the moment! gosh!), different motivations and ambitions. Every one's a different challenge, and it's one of the joys of the job to figure out what will work for an individual. A little puzzle, if you will, and little puzzles are what we are all about.

So, anyway, lecture time is a part of what I do. It's not the only part for sure, and debatable even how important a part it is, but it's the most visible part, anyway, and so it has to set the right tone for the course even if the most learning takes place elsewhere. Teaching large classes at a state school I figured out rather rapidly that it wouldn't work for me to make each day's lecture -- short classes, not the 2-hour or more stretches occhiblu's talking about -- bear the weight of addressing 40 different (and very widely ranging) individuals' needs. Not even if I reduce to the problem of providing for four (or three or two or six according to your favorite classification) styles. Some people there taught like that, like what Occhiblu describes, with a regiment of different styles each day. (I watched them. I sat in on their classes. I sit in on EVERYBODY's class that will let me.) Some of _those_ people would have been successful whether they were doing Moore method, round-table seminars, thinking-pairing-sharing all day, or the underwater synchronized balletic method, or whatever, because they were just good. Others pretty clearly found it to be an amenable framework to hang their ideas on, which gave them support and structure; and still others pretty clearly were doing it because they'd heard it was a good idea.

That wasn't right for me. It was in vogue; I was going to regular seminars that were available for discussing teaching strategies and this was very much viewed as The Thing at the time. But it wasn't for me, and kids can spot a phony a mile away. That can mean a lot of things, but it includes sensing when someone's trying to wear a fashion that doesn't fit, literally or figuratively, and when they get that sense the whole rapport is weakened. (There's one prof here that I admire a great deal - he's one of the Just Plain Great Ones - and have watched a lot, and realized that as much as I admire the guy, trying to imitate him in almost any way would be essentially suicide for me, not just wearing a little bit wrong fashion but the equivalent of my wearing earnestly putting on a dress, a fur hat, a bow tie, and sparkly high heels.)

So I had to, and have to, build those good things into my course in different, maybe little bit subtler ways. I've already said I conscientiously vary the strategy from day to day, in various dimensions independently. That's not hard to do, honestly, and hardly qualifies as subtle; the material itself tends to suggest different organizations from day to day as long as you're awake and attuned to the fact it's saying something you have to listen to. (A pleasingly Sibelian notion.) It's important to me that the motivation for the use of a style or strategy or even gimmick emerges from the material itself, rather than a list of time quotas. Occhi's WMBK's for example, are a regular fact of life for me at a large scale. A second term class in algebra is generally aimed at some large, beautiful 'capstone' result at the end of the course. Maybe ruler-and-compass constructions, maybe Burnside's Theorem, maybe something else, but generally there's a term-long target that structures the entire 12 weeks preceding in terms of WMBK. Inverting the structure at that scale is ludicrous; it's a clear case of material dictating formal organization. The satisfaction of seeing a lot of disparate parts suddenly slot together may not be a universal pleasure, but it is what that course can offer. Of course, because the goal is so large, then each subgoal is also still rather large and leaves room for a variety of approaches, each suited to the needs of the varied topics.

I make the small step of mentioning in lectures what mode we're working in so students are at least attuned to the difference. I have class days that aren't lectures at all. I frame a question differently depending on who I'm asking, and one of the few quota-like things I do aim for is that everybody in the class should be speaking frequently throughout the class, and have a shot at questions I know they'll be well-poised to answer as well as things that put them on the spot a bit more. Many more little tricks, too.

And most of that is still a drop in the hat, because actual lectures are still one-to-many and HAVE to involve compromises because of that, no matter how you choose to spread it around. So actually more than all that, it's far more important to me that my door's open all the fucking time and I can sit down with X and figure out how to explain the one or two things X is confused about in a way that X is comfotable with in a few minutes.

I hope it's kinda clear that I am the enemy of rut-like behaviour. I'm no friend of complete chaos, either, but I'd be bored to death with most of my classes if I weren't constantly ripping things apart in search of new ways to look at them. If there's one small sort of innate gift I do have as an instructor, I think it may be sharing the glee of discovery in a way that gets those "I never really liked math, but this guy's passion for the subject rubs off on you" comments on the course evals.

It's probably good to understand that one of the things that I'm quite explicitly supposed to be achieving with students is building the capacity for thinking in long lines that ultimately makes it possible for them to reach large goals. It's one of the things my subject offers that makes it a part of a balanced undergraduate education. This is true, and important, even in the lowest level classes (lowest level here means Calculus, so gauge accordingly), just as much as in the upper-level algebra class I talked above. So there have to be some days, whole days, when students force themselves to follow an arc all the way through, whichever direction the arc is moving, or I am not doing my job, even if it's a job that fosters some pain and resentment. Likewise, with my silly hammer analogy and occhiblu's quite accurate point that a large fraction of the students will resent being tested on things not explicitly covered in class - part of what I am by job description supposed to be doing is producing students who can, resentfully or not, use tools to solve problems that haven't already been solved for them. Again, this is one of the things that mathematics is good at and so is charged with doing, by the university, as part of its role in the large culture. The art in what I do is in judging the difference between merely throwing them to the wolves and giving them a challenge they can fairly be expected to reach if they stretch.

I'm quite fortunate to work with a department entirely full of people I can respect and admire in the classroom. I have no qualms telling any student to take any prof for any math course; they're all good. And I think all of them have styles that evolved slowly, in very personal ways: watching others, reading pedagogical literature, conducting various assessments of their effectiveness and identifying problems and so on. But it _is_ very personal and it is very selective; one takes bits here and there that seem useful and seem to fit one's style, and one does so at one's own pace. Among those sort of people, a teacher of teachers has to be careful, I think, to avoid even the impression of rushing in and telling "how it has to be done", breathlessly relating what the latest greatest all-encompassing theory is, or even too forcefully pinning shiny new terms on ideas people have already formulated in their own fashion (specialized vocabulary is powerful, and sometimes even intoxicating, but nonspecialists should be left to acquire it in measure to their need for it.) My mode of progress, and I think that of the majority of my colleagues, is a learning style in its own right (and it's not _just_ the "Stubborn Goddamn Sonofabitch" style -- SGSOB1) which has to be treated with some understanding and respect by those who most sincerely wish to help.

Wolfdog, so much of what you say about finding your own style overlaps with therapist training -- it's all well and good to say, for example, "Cognitive Behavioral Therapy is the latest thing!", but it doesn't fit a lot of therapists, and it's counterproductive to have a therapist trying to do a style of therapy that he or she is neither good at nor particularly interested in. The best professors in our department (which, coincidentally or not, is part of the School of Ed) really emphasized taking bits and pieces of what makes sense to each of us, and finding our own meaning and style and authenticity -- because, as you mention, if you're not authentic as a teacher or guide, people are going to write you off pretty quickly.

I think we try to all strive to bring the best of our experiences, interests, and lives to our work, and so, to me at least, it makes more sense to shape the theories to fit our selves, rather than vice versa.

This, of course, assumes that we do have a solid basis in the theories, though. I see a lot of my classmates picking and choosing without really understanding what they're doing -- just kind of randomly grabbing things without thinking about why -- and that's no good, either. So I guess one just has to learn a ton, analyze a ton ... and then forget all of the intellectualization and just do it, figuring the work you put in will be there when you need to call on it.