Stephen Krashen’s claim was radical in 1982 and is common sense now: you do not acquire a language by studying rules and then applying them. You acquire it by understanding messages, lots of them, pitched slightly above your current level. He called it comprehensible input, and the level “slightly above you” got a name that stuck: i+1.
The strong version of Krashen’s theory says input is not just important but sufficient, meaning that speaking and writing emerge on their own once you have absorbed enough. That part is contested, and I do not buy it; the case against is in the article on the output hypothesis. But the core observation has held up remarkably well: comprehension is the engine. Every durable thing you know in a foreign language, you met many times in messages you understood.
What i+1 means when you sit down to study
The “i” is your current Italian. The “+1” is material where the new elements are few enough that the context carries you across them. In practice you can feel it: an i+1 text is one where you occasionally meet an unknown word, guess it from the sentence, and turn out to be right. An i+5 text is one where you stop guessing and start decoding.
The useful test is mechanical. Open a page and count the words you do not know. Around 3 to 8 unknown words per page, you are in the zone: you follow the story and the story teaches you the words. At zero you are coasting (pleasant, and actually useful, since that is fluency practice). Past ten, the text has become a dictionary exercise, and dictionary exercises are a different strand of work.
Why understanding does the teaching
When you understand a message that contains one new element, your brain gets the new element with its meaning, its context and its grammar attached, for free. The research behind extensive reading shows vocabulary growing steadily from exactly this: repeated meetings with words inside messages that made sense. Grammar rides along too: the article on meeting grammar in texts first covers why a structure you noticed inside a story sticks better than the same structure met on a chart.
The hard part: finding real i+1 in Italian
This is where most learners fail through no fault of their own. Native material is i+10 for years. News is i+7 on a good day. What you need is material engineered to sit one step up, and that is precisely what graded readers are: real books rewritten to a CEFR level, so that “one step above you” is a property of the text, not luck. I keep a guide to which Italian classic works at which level.
In 
amo Italian I made this the architecture rather than a feature. Every novel is built to a fixed rule: twenty chapters, five pages each, a hundred footnotes, and the vocabulary of every book classified word by word against CEFR levels, so a B1 novel genuinely stays a step above an A2 reader instead of drifting. Three comprehension questions per chapter check that the input was actually comprehensible, rather than assuming it.
What input alone will not give you
Honesty section. Input will not give you the ability to produce under time pressure; that needs output practice and fluency work. It will not reliably fix fossilised errors; that needs deliberate work on your own mistakes. Krashen gets you the raw material. The other strands turn it into speech.
But get the input right first, because everything else runs on it. An hour a day of Italian you mostly understand, slightly above your level, is the single highest-yield habit in language learning.
References and attributions: Stephen Krashen, Principles and Practice in Second Language Acquisition, 1982. The input hypothesis and the term i+1 are Stephen Krashen’s; his ideas are paraphrased with attribution and no original text is reproduced. Part of the Science of Learning Italian series.
