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Can someone give me a specific definition of i+1? - vtx4848 - 2015-06-25
I cannot seem to find one anywhere. I understand it as an abstract concept, something slightly above your level, but slightly doesn't seem to be defined anywhere.
Can someone give me a specific definition of i+1? - PMotte - 2015-06-25
As long as you don't define "i", nobody can give a definition of "i+1".
Can someone give me a specific definition of i+1? - john555 - 2015-06-25
PMotte Wrote:As long as you don't define "i", nobody can give a definition of "i+1".Maybe by "i" he means √-1.
Can someone give me a specific definition of i+1? - vtx4848 - 2015-06-25
PMotte Wrote:As long as you don't define "i", nobody can give a definition of "i+1".i is your current level, but if you don't know that then you probably can't answer my question.
Can someone give me a specific definition of i+1? - RandomQuotes - 2015-06-25
i+1 is a basic version of the input hypothesis by Krashen. Essentially, what the input hypothesis posits is that when a learner comprehends material slightly higher than their current level they progress. If you want a more in depth view of it read page 20.
Can someone give me a specific definition of i+1? - vtx4848 - 2015-06-25
RandomQuotes Wrote:i+1 is a basic version of the input hypothesis by Krashen. Essentially, what the input hypothesis posits is that when a learner comprehends material slightly higher than their current level they progress. If you want a more in depth view of it read page 20.I understand that much, but what I was asking for is a definition of what the +1 is in i+1. As in how big is the optimal gap supposed to be.
Can someone give me a specific definition of i+1? - RandomQuotes - 2015-06-25
Did you read the article I linked? The i isn't your knowledge. The +1 is the next stage in competence.
Can someone give me a specific definition of i+1? - vtx4848 - 2015-06-25
RandomQuotes Wrote:Did you read the article I linked? The i isn't your knowledge. The +1 is the next stage in competence.I guess maybe I don't understand. What is the difference between the two? Plus I never even used the word knowledge, but maybe I implied something incorrect I don't know. I used the word "level", which is what you said in your post as well.
I'm just curious what "next stage in competence" actually means in terms of material.
Can someone give me a specific definition of i+1? - EratiK - 2015-06-25
Personally, since i+1 implies discreet items, I always considered i+1 to be one unknown item for a given domain. For example, if you take vocabulary, i+1 would be one unknown word in a given sentence (or paragraph or page, depending on your level). You can apply this to grammar and pronounciation/pitch.
Can someone give me a specific definition of i+1? - RandomQuotes - 2015-06-25
Stephen Krashen Wrote:(a) Statement of the hypothesis
Let us first restate the question of how we acquire: given the correctness of the natural
order hypothesis, how do we move from one stage to another? If an acquirer is at "stage 4",
how can he progress to "stage 5"? More generally, how do we move from stage i, where i
represents current competence, to i + 1, the next level? The input hypothesis makes the following claim:
a necessary (but not sufficient) condition to move from stage i to stage i + 1 is that the
acquirer understand input that contains i + 1, where "understand" means that the acquirer is
focussed on the meaning and not the form of the message.
We acquire, in other words, only when we understand language that contains structure
that is "a little beyond" where we are now. How is this possible? How can we understand
language that contains structures that we have not yet acquired? The answer to this apparent
paradox is that we use more than our linguistic competence to help us understand. We also
use context, our knowledge of the world, our extra-linguistic information to help us understand
language directed at us.
The input hypothesis runs counter to our usual pedagogical approach in second and
foreign language teaching. As Hatch (1978a) has pointed out, our assumption has been that
we first learn structures, then practice using them in communication, and this is how fluency
develops. The input hypothesis says the opposite. It says we acquire by "going for meaning"
first, and as a result, we acquire structure! (For discussion of first language acquisition, see
MacNamara, 1972.)
We may thus state parts (1) and (2) of the input hypothesis as follows:
(1) The input hypothesis relates to acquisition, not learning.
(2) We acquire by understanding language that contains structure a it
beyond our current level of competence (i + 1). This is done with the help of
context or extra-linguistic information.
A third part of the input hypothesis says that input must contain i + 1 to be useful for
language acquisition, but it need not contain only i + 1. It says that if the acquirer understands
the input, and there is enough of it, i + 1 will automatically be provided. In other words, if
communication is successful, i + 1 is provided. As we will discuss later, this implies that the
best input should not even attempt to deliberately aim at i + 1. We are all familiar with syllabi
that try to deliberately cover i + 1. There is a "structure of the day", and usually both teacher
and student feel that the aim of the lesson is to teach or practice a specific grammatical item
or structure. Once this structure is "mastered", the syllabus proceeds to the next one. This part of the input hypothesis implies
that such a deliberate attempt to provide i + 1 is not necessary. As we shall see later, there
are reasons to suspect that it may even be harmful.
Thus, part (3) of the input hypothesis is:
(3) When communication is successful, when the input is understood and there
is enough of it, i + 1 will be provided automatically.
The final part of the input hypothesis states that speaking fluency cannot be taught
directly. Rather, it "emerges" over time, on its own.4 The best way, and perhaps the only way,
to teach speaking, according to this view, is simply to provide comprehensible input. Early
speech will come when the acquirer feels "ready"; this state of readiness arrives at somewhat
different times for different people, however. Early speech, moreover, is typically not
grammatically accurate. Accuracy develops over time as the acquirer hears and understands
more input. Part (4) of the input hypothesis is thus:
(4) Production ability emerges. It is not taught directly.
Can someone give me a specific definition of i+1? - aldebrn - 2015-06-25
This is a fantastic question, vtx4848, and never mind these old farts pooh-poohing your "ignorance". I think the answer is subtle. The excerpt quoted by RandomQuotes (#10) is an excellent but very condensed description, and it shows a potential flaw in EratiK's interpretation, which underlies so much of what people on this forum talk about with Morph Man etc.: the i+1 is not "one new word" or "one new grammar concept", and you can tell this because Krashen in this excerpt de-emphasizes "syllabi that try to deliberately cover i + 1 … a 'structure of the day'".
The most important phrase in the excerpt above to understand i+1 is "given the correctness of the natural order hypothesis". You may think I'm joking but I'm not: without understanding this tidbit the rest is nonsensical. You'll have to refer to the book for details but in a nutshell, the well-tested natural order hypothesis states that both children and adult language learners go through a more-or-less fixed sequence of language topics (grammar, transformations, etc.) to fluency. They find that this sequence is different for adults vs. kids vs. different languages, but within one of these language-age groups, most individuals naturally follow a pattern. There're studies for Japanese that support this hypothesis but I haven't located them. Here's what that average progression looks like for kids and adults learning English as a second language (Table 2.1):
{ing/progressive, plural, copula} -> {auxiliary verbs, articles/the/a} -> {irregular past} -> {regular past, 3rd person singular, possessive}.
Note that everything about the input hypothesis and i+1 is said within the context of a natural order like the one discovered above for English which happened to consist of four stages. Krashen is a professional linguist and he's using words like "stage" and "structure" in this technical sense, to mean language features that learners acquire in order. "Acquiring (i=2) + 1" is shorthand for saying "you are comfortable with stage 2 above—auxiliary verbs and articles—so your next logical step, assuming the natural order hypothesis, is the irregular past".
Notice how he says nothing about vocabulary optimization a la MorphMan. Note how he specifically de-emphasizes trying to engineer i+1, stating that this might actually be counter-productive. What matters, and all that matters, is that language be comprehended: that the teacher's words, aided by actions and gestures and facial expressions and props, etc., are understood by the student.
Is following a textbook a good way to get comprehensible input? He says no. Is studying a Core* deck optimized by MorphMan a good way to get comprehensible input? Maybe, but if so, only by accident: a Core deck helps only in so far as it provides comprehend-able and comprehended input by limiting new words, not because its optimized. We can do far better than optimizing based on vocabulary: we should be optimizing grammar concepts and language features as general as in the four stages above, in addition to mere vocabulary.
Can someone give me a specific definition of i+1? - Stansfield123 - 2015-06-25
vtx4848 Wrote:I understand that much, but what I was asking for is a definition of what the +1 is in i+1. As in how big is the optimal gap supposed to be.i is your current level of competence. The "+1" is supposed to be small enough so that you still understand the input (where "understand" means that "the acquirer is focused on the meaning and not the form of the message" - that's quoted directly from Krashen).
So "i+1" doesn't mean "one unknown word in a sentence", or anything like that. Far from it.
If you're using an SRS for reviewing a set of sentences, you would have to look at each card, and see if you understand the sentence, as it is written in the question. If you don't, then you would have to suspend it (to be un-suspended at a later date), because it's more than "i+1". A sentence that goes "Apple bzzzt, when freshly baked, is one of my favorite things in the world." is in fact NOT i+1. Even though it's only one unknown word, it's a key word that makes the meaning impossible to understand. On the other hand, "Apple pie, when freshly baked, is one of my favorite bzzzzt in the world." is i+1. Even if you never heard the word "thing" before, you know what that sentence means. That allows you to learn the word "thing" in a manner that, according to Krashen, is optimal (my experience with language learning, especially late stage language learning, confirms that).
And, just to state the obvious, sentences that don't add anything you're not competent with should be deleted because they're less than i+1.
Can someone give me a specific definition of i+1? - yogert909 - 2015-06-25
If all that seems a little complicated, here is my tl;dnr
Most people who talk about i+1 around here are simply talking about a sentence where you know every word but one. You could extend that to include an unknown grammar point in a sentence of well known words. The point of all this is will keep whatever we are studying as comprehensible as possible.
Can someone give me a specific definition of i+1? - yogert909 - 2015-06-25
Stansfield123 Wrote:A sentence that goes "Apple bzzzt, when freshly baked, is one of my favorite things in the world." is in fact NOT i+1. Even though it's only one unknown word, it's a key word that makes the meaning impossible to understand. On the other hand, "Apple pie, when freshly baked, is one of my favorite bzzzzt in the world." is i+1. Even if you never heard the word "thing" before, you know what that sentence means.I take your point, but I'm not sure your examples work for me. In your first example, bzzzt has to be some kind of baked good. But in the 2nd example, bzzzt could mean several different things such as 'thing', 'pie', 'snack', 'meal', etc.. If anything, the first example is more i+1 than the second. In any case, I apologize in being a little rusty on my Krashin, but how exactly are you to learn the meaning of bzzzt words if not in sentences like either of these? I can't imagine a sentence which could make bzzzt much more understandable than either of these two sentences. So are we never to learn the meaning of bzzzt?
Can someone give me a specific definition of i+1? - Stansfield123 - 2015-06-25
yogert909 Wrote:Also from Krashen:Stansfield123 Wrote:A sentence that goes "Apple bzzzt, when freshly baked, is one of my favorite things in the world." is in fact NOT i+1. Even though it's only one unknown word, it's a key word that makes the meaning impossible to understand. On the other hand, "Apple pie, when freshly baked, is one of my favorite bzzzzt in the world." is i+1. Even if you never heard the word "thing" before, you know what that sentence means.I take your point, but I'm not sure your examples work for me. In your first example, bzzzt has to be some kind of baked good. But in the 2nd example, bzzzt could mean several different things such as 'thing', 'pie', 'snack', 'meal', etc.. If anything, the first example is more i+1 than the second. In any case, I apologize in being a little rusty on my Krashin, but how exactly are you to learn the meaning of bzzzt words if not in sentences like either of these? I can't imagine a sentence which could make bzzzt much more understandable than either of these two sentences. So are we never to learn the meaning of bzzzt?
We acquire, in other words, only when we understand language that contains structure
that is "a little beyond" where we are now. How is this possible? How can we understand
language that contains structures that we have not yet acquired? The answer to this apparent
paradox is that we use more than our linguistic competence to help us understand. We also
use context, our knowledge of the world, our extra-linguistic information to help us understand
language directed at us.
Krashen is talking about "input", not isolated sentences. When you use isolated sentences instead of input with more context to it, it does indeed become far more difficult to find helpful i+1 sentences. I think the best thing to do is to either go with multiple sentences from the same source material (sub2srs an entire episode of a show you watched, or something: that way you know the context already, even if it's not specified in the question you happen to be trying to answer), or to go with really verbose isolated sentences, like my example.
I thought my example was pretty good, for illustration purposes (it was not meant as advice on what to study). I purposely picked a sentence that uses way more words than it needs to. The meaning of the sentence, essentially, is that the guy likes apple pie. There really is no information value to using any more words than "I like apple pie", to convey that meaning. All that "it's one of my favorite things" nonsense is pretty devoid of any objective meaning, because you can't really compare your affection for a food item to your affection for your children, or for sex, or for something else entirely unrelated. It's a silly, meaningless comparison. Point is, all you need to get, to understand the sentence, is that the guy likes apple pie. Which you get without knowing what "thing" means. But you don't get it without knowing what "pie" means.
Can someone give me a specific definition of i+1? - Stansfield123 - 2015-06-25
yogert909 Wrote:Most people who talk about i+1 around here are simply talking about a sentence where you know every word but one.You are correct. Most people do indeed misuse the concept around here.
Can someone give me a specific definition of i+1? - EratiK - 2015-06-25
I am aware Krashen never went down the quantifying route, but defining per unknowns always seemed like a good rule of thumb, especially considering when you increase the number of unknowns and mental overload happen, you've definitely quitted the realm of comprehensible input. It's not as much misusing the concept has trying to give it a concrete interpretation. In practice your level of competence is defined by what you can't handle, ie unknowns, so I'm not seeing much of a difference.
Can someone give me a specific definition of i+1? - buonaparte - 2015-06-25
Krashen is a nice guy.
Stephen Krashen, an interview:
Can someone give me a specific definition of i+1? - yogert909 - 2015-06-25
Stansfield123 Wrote:Point is, all you need to get, to understand the sentence, is that the guy likes apple pie. Which you get without knowing what "thing" means. But you don't get it without knowing what "pie" means.I believe the point is you should understand the meaning of the target word from the context of the sentence without necessarily a priori knowing the definition of bzzzt. In your second example, you could understand that the guy likes pie, but learn nothing about the meaning of bzzzt making it essentially a i+0 sentence. While the first example provides more clues about the meaning of the target word.
Can someone give me a specific definition of i+1? - aldebrn - 2015-06-25
EratiK Wrote:I am aware Krashen never went down the quantifying route, but defining per unknowns always seemed like a good rule of thumb, especially considering when you increase the number of unknowns and mental overload happen, you've definitely quitted the realm of comprehensible input. It's not as much misusing the concept has trying to give it a concrete interpretation. In practice your level of competence is defined by what you can't handle, ie unknowns, so I'm not seeing much of a difference.I think you're right: unknown vocab per sentence is a practical and level-headed hack that we use to try and increase the chances of input being comprehensible and comprehended.
Even though Krashen first posits you acquire successive "levels" of competence if you're exposed to each before you understand it linguistically (requiring you to obtain understanding out-of-band), he then explicitly forbids trying to engineer fine-tuned i+1, then (i+1)+ input. Just rough-tune it (page 23-24): have lots of sentences which you're completely comfortable with, have lots of sentences that you've recently understood, have lots of sentences that you don't understand—but whose correct meaning you can obtain via a teacher or your own brainpower. (This last is hard to do on your own! I don't think we properly understand how to apply these parent-guided or teacher-guided research studies to the autodidact case.)
Nevertheless, given that we are forbidden from fine-tuning i+1, we're left with the old pragmatic hack of minimizing unknowns per sentence/paragraph, which has been working away this whole time, trying to increase the likelihood that the input is comprehended!
But I think it's useful both theoretically and practically to understand the difference between "number of unknown words/grammar points" and input hypothesis/i+1. The latter specifies what is necessary for acquisition. The former is this elbow grease technique we apply to try and get there, and hasn't been researched nearly as much.
Can someone give me a specific definition of i+1? - aldebrn - 2015-06-25
buonaparte Wrote:Krashen is a nice guy.I enjoyed watching many of his talks and interviews on Youtube, even though he often repeats himself (he's been trying to tell the same thing to the educators for forty years, I don't blame him). After watching that one, I jumped on Lingq. Boy was I disappointed, with that so-close-yet-so-far feeling. Horrible word segmentation, totally user-driven definitions (authors can't specify what definition to use for their own words), useless for getting comprehensible beginning Japanese input. So………
Stephen Krashen, an interview:
Can someone give me a specific definition of i+1? - vtx4848 - 2015-06-26
Thank you for all the responses, I think I understand a bit better now. @RandomQuotes I actually did read that, but I didn't understand it, although rereading my responses I actually didn't put that in any of them.
So I guess "slightly" is a lot more slight than I thought, like not even using a dictionary type of slight.
Can someone give me a specific definition of i+1? - PMotte - 2015-06-26
That "i+1" gives me the impression to be one of those formulae which are used in human sciences which give the impression that they messure something, but they actually don't and can't.
"i" is the current level, "+1" means one level higher.
So, it could as well mean one year high in the eductional system, as the next lesson in your textbook, as one word learned.
It's more usefull to make communication about learning and growing knowledge a bit easier, but it's not like "i+1" in wich "i" is the length of a given person at given time, and "+1" means "+1 cm" if they have grown.
It helps reasoning about the problem a bit, but at the same time you could argue: "Why not just say "one higher level"?"
Can someone give me a specific definition of i+1? - vtx4848 - 2015-06-26
Can I ask another question? How does this acquisition method work for pronunciation? This is the one thing that's tough for me about just guessing meaning and that's it. You don't know if you are pronouncing something right. Even if you were learning English, you could easily learn an incorrect pronunciation.
Can someone give me a specific definition of i+1? - jcdietz03 - 2015-06-26
i+1 can only apply to a sentence.
An "i+1 sentence" has exactly one thing you don't understand in it. That's what I gathered. This is a relative definition and not an absolute one.
To improve your ability, you must understand (eventually) what you currently don't. That applies to anything. It's basically a tautology; don't read too much into it.
For a learner, in a work that's too difficult for you, there will be easy sentences and hard sentences. Some of the hard sentences will have one thing you don't understand and those are the i+1 sentences. Some of them will have more than one thing you don't understand, and some of them will be understood, as well.
Teachers (in the USA, at least) want their young students to read "at or above grade level" to ensure that that material they're reading has some stuff in it they won't understand. It's a similar concept, I think.
---------------
I wouldn't worry too much about pronunciation. Japanese is easier to pronounce than English, I think. You just convert to hiragana and then pronounce it that way, right? I feel like I don't struggle pronouncing Japanese. Much more difficult for me is forming (thinking of) a grammatically correct sentence that says what I want to say and can be understood.
Learning correct English pronunciation is very difficult because there are many more exceptions than in Japanese for pronunciation, and also many more syllables.