Today, my son reached a 500-day streak in Duolingo, and, yesterday, I reached a 600-day streak.

I asked Shane whether Duolingo has helped him with French. "Unquestionably," was his response. He said he identifies patterns in grammar more readily, has expanded his vocabulary, has internalized words that were previously all around him but that had gone unnoticed, has improved his pronunciation, and has learned new grammatical concepts in French. I also asked him whether he speaks more French since starting Duolingo. His response: "I don't necessarily speak more French in my life, but I'm much more comfortable when I do speak it." He told me that he speaks French with francophone colleagues out of respect for them and that certain relationships are primarily based on using French.

At the same time, however, he sometimes feels as though he has plateaued in his use of the app, particularly when working through a unit that focuses on language he's less likely to use day-to-day.

I could relate. I felt this way when I had completed the Brazilian Portuguese course in Duolingo. For months, the daily refresher was repetitive, serving up the same sentences and verb tenses day after day. Recently, however, Duolingo changed the content I receive in my daily refresher, offering much harder and more varied vocabulary and sentence structures. I felt challenged and re-energized.

A recent post in the Duolingo blog—Dear Duolingo: What's the right level of difficulty?—helped explain one of the app's learning philosophies. The questioner, who is both a language learner (Spanish) and a language teacher (English), asked Duolingo how it decides what the right level of challenge is for users of the app.

Sharon Wilkinson—who has a Ph.D. in French and Second Language Acquisition and works on Duolingo's French course for English speakers—begins her response to the question by saying,

We give you lessons and exercises with language that's just a little bit more advanced than what you already know. In each lesson, you're taught a handful of new words or structures by seeing them in sentences made up of only familiar words and grammar, plus the specific new thing.

The idea of offering content that's just a little bit more advanced than what you already know, says Wilkinson, was first proposed about a century ago by researcher Lev Vygotsky, who called this the "zone of proximal development." In the 1980s, linguist Stephen Krashen expanded on the idea by referring to "i + 1" where "i" refers to what you know already and "1" to what you don't yet know but can figure out.

Wilkinson says:

The trick for teachers, of course, is to decide what "i" and "1" are at each stage of development, for each learner. If we give you language that is "i + 20"—language that is far beyond what you already know and can use—you'll likely become discouraged and frustrated… and you might give up. If we focus only on language that is "i + 0"—only what you know and feel comfortable with—your progress will stagnate and you'll become bored. Instead, we want that sweet spot of Goldilocks difficulty that's not too easy and not too hard: your "zone of proximal development"!

Duolingo uses this approach in designing its lessons. For example, 5-7 new words are introduced alongside familiar vocabulary. Hints enable users who need help with certain words or concepts to get extra assistance. In stories, 90% of the words have already been presented in lessons, while 10% may be new words or phrases. And to personalize the content for individual users, Duolingo tracks what words or grammar concepts users are struggling with, and focuses on these in personalized practice sessions.

The concept of i + 1 resonates with me. When I was first learning Brazilian Portuguese, I tried listening to podcasts in that language, but they were so far beyond my level of comprehension (i + 20) that I abandoned them quickly. Even in French, which I've studied almost my entire life, I would be reluctant to read a book in that language.

Wilkinson's blog post helped me understand that there's a sweet spot in learning. Content that's too hard leads to discouragement and frustration; content that's too easy leads to boredom. If Shane and I can keep our learning in the Goldilocks zone, we're sure to continue our streak for another 100 days.