i+1 is Stephen Krashen's shorthand for language slightly beyond your current stage: i is what you have already acquired and +1 is the next structure you are ready for. He argued that you move forward by understanding input containing +1, helped by context, and that teachers needn't aim at +1 precisely, because plenty of understood input contains it anyway.
Where does i+1 come from?
The formula comes from Stephen Krashen's input hypothesis, set out in Principles and Practice in Second Language Acquisition (1982). He frames it as a question: if an acquirer is at stage i, how do they get to stage i+1? His answer is that understanding input which contains i+1 is "a necessary (but not sufficient) condition". By "understand" he means paying attention to the meaning of the message rather than its form.
That raises an obvious puzzle: how can you understand a structure you haven't acquired yet? Krashen's answer is that you use more than your grammar. Context, your knowledge of the world and other clues outside the language fill the gap. Krashen gave the hypothesis four parts:
- It is about acquisition, the subconscious process, not conscious learning.
- You acquire by understanding language a little beyond your current competence, with the help of context.
- When you understand the input and there is enough of it, i+1 is provided automatically.
- Speaking fluency can't be taught directly. It emerges over time once enough input has been understood.
Two details are often lost when i+1 is quoted. First, the +1 is a grammatical structure, the next one in what Krashen called the natural order of acquisition, not "one new word per sentence". Second, i stands for the learner's interlanguage, their own developing version of the language, which nobody can observe directly. Our page on comprehensible input covers the other four hypotheses Krashen built around it.
Should a text be pitched exactly at i+1?
Krashen said no, and this is the part of the theory with the most practical consequences. He drew on research into the way parents talk to small children, which is simpler than adult speech but roughly tuned to the child's level rather than finely tuned. It contains the child's i+1, along with plenty of structures they already know and some they aren't ready for.
He argued that rough tuning beats a deliberate aim at i+1 for three reasons:
| Roughly tuned input | Finely tuned input (the "structure of the day") |
|---|---|
| Covers i+1 without anyone having to guess what it is | A deliberate aim at i+1 can miss |
| Serves several learners at once, as long as they all understand it | Helps only the learners whose next step happens to be the one taught |
| Brings review for free: structures come round again and again | Each structure is presented once, and a learner who misses it may wait a year |
For a self-taught learner, the lesson is reassuring. You don't need to find a text that hits your exact next step, and nobody could tell you what that step is anyway. You need text you mostly understand, in quantity. How to judge "mostly" is the subject of choosing the right reading level.
Is i+1 the same as Vygotsky's zone of proximal development?
The two ideas are often mentioned together, but they aren't the same. Lev Vygotsky's zone of proximal development is the space between what a learner can do unaided and what they can't do even with support. It is about help: a teacher or a more able peer supports the learner within that zone, a process later called scaffolding by Wood, Bruner and Ross. Vygotsky never used that term himself.
Krashen's i+1 is about input rather than help from another person. The next step arrives in what you read or hear, and context makes it understandable. Both ideas share the intuition that learning happens just past the edge of what you can already manage.
i+1 also attracts the criticisms aimed at the input hypothesis as a whole: critics argue it lacks testability and is conceptually ambiguous. Since nobody can measure a learner's i, it is hard to show that a given text contained their +1. Treat it as a useful picture of what good input looks like, not as a measuring tool.
What does the +1 look like from one level to the next?
We looked at the grammar in the free chapters of three Spanish series on Contos, one each at A1, A2 and B1. Every verb in the first two chapters of the A1 series is in the present tense. The A2 series adds past forms. The B1 series uses the subjunctive.
Pero el apartamento está vacío. Alba no entiende.
"Mi gato ha desaparecido", dice. "Alguien lo ha robado. Estoy segura."
Luego preguntó, muy despacio: "¿Ha vuelto a encenderse la luz?". Como si ya lo supiera.
The step up is about more than grammar. Across chapters 1–2 of every Spanish series, the text gets denser at each level:
| Level | Words per sentence (average) | Different word forms per chapter (average) | Word forms in chapter 2 not seen in chapter 1 |
|---|---|---|---|
| A1 | 5.5 | 100 | 57 |
| A2 | 6.5 | 143 | 84 |
| B1 | 11.7 | 186 | 116 |
| B2 | 12.5 | 219 | 147 |
The jump from A2 to B1 is the steepest: sentences nearly double in length. For some readers that is more than a +1, so it helps to sample the next level before you commit: the Contos library shows a "Ready for more?" row of next-level series alongside the series at your own level. You move up when you know enough words: 500 for A2, 1,500 for B1 and 4,000 for B2.
One honest difference from Krashen: when a word stops you, Contos lets you tap it for a translation in your own language. That isn't the context and world knowledge he had in mind, but it does the same job of keeping the message understood.
Read chapter 1 at A1 and chapter 1 at A2, and notice which new forms you could work out from context.
Read free in your browserFrequently asked questions
Who came up with i+1?
Stephen Krashen, as part of his input hypothesis. His fullest statement of it is in Principles and Practice in Second Language Acquisition (1982), where i is the learner's current stage and i+1 the next one.
Does i+1 mean one new word per sentence?
No. Krashen was talking about grammatical structures, acquired in a roughly fixed natural order. How many unfamiliar words a text can contain is a separate question, studied as vocabulary coverage. Our extensive reading page covers those figures.
How do I find my i+1?
You can't pin it down exactly, and Krashen argued you don't need to. If you understand most of what you read and there is plenty of it, the structures you are ready for will turn up. Choose text you can follow comfortably rather than text you have to decode.
Has i+1 been proven?
No. It is part of the input hypothesis, which critics say is hard to test and vague in its key terms. Because a learner's current stage can't be observed directly, nobody can confirm that a given text contained their +1. It remains a useful guide rather than settled science.
How does Contos apply i+1?
Loosely, as Krashen recommended. Each series is written at one CEFR level from A1 to B2, so the text is roughly tuned rather than built around a single structure. A tap gives you the meaning of any word, and you move up a level when your known words reach 500, 1,500 and 4,000.