The Duolingo mobile app provides a particular case study for encountering the overlap between symbolic and machine language systems in SLA (Second Language Acquisition). Although Duolingo is built upon both natural language as a trésure des significant, as well as the syntactical system of machine code which underwrites the application’s backend processes and frontend interfaces, its pedagogic pipeline bears certain particular features and underlying logics which structure the user’s experience. These features will be analysed presently.
In 2016, Duolingo started using their half-life regression (HLR) algorithm which superseded the previous method of crowdsourcing real-life translations (the so-called ‘Immersion’ module). It thus became an app for providing courses, rather than for platforming crowdsourced learning and translation to third parties. Currently, the user experience of the courses is wholly crafted by the HLR algorithm, which is continuously being further developed based on the individual user’s inputs. This process enhances personalization and develops the learning experience for individual users.
In their essay “A Trainable Spaced Repetition Model for Language Learning,” the creators of HLR provide insight into some of the sources which prompted the programming of the HLR’s current architecture.
Ebbinghaus’ Forgetting Curve
One of the fundamental models for the development of the app’s contemporary version was the so-called Ebbinghaus forgetting curve (fig. 1). In 1885, the linguist turned psychologist Hermann Ebbinghaus came up with a function for computing human memory retention through engaging in a series of self-administered tests. During these tests, he noticed that an individual item of memory (in his case a random three-letter glyph which could not be a cognate with an already existing word – like ‘PTL,’ for example) exhibits a certain predictable duration of retention within a person’s memory. Ebbinghaus went on to define the statistical half-life of memory retention, finding that “memory decays exponentially over time.”
This is the basic Ebbinghaus curve function, where R is retrievability (how easy it is to retrieve a piece of information from memory), S is stability of memory (how fast R falls over time in the absence of training, testing or other recall), and t is time.
Ebbinghaus derived two effects from this function: the spacing effect and the lag effect. The spacing effect consists in a person memorizing a target item better, if they revisit it repeatedly and after a certain period of time has elapsed – if there are spaces between studying sessions the subject will retain the target item better than if she were to ‘cram.’ The R value for a target item will become more robust, showing less subsequent decay. The lag effect then posits that the longer the interval between the individual study sessions of the target item, the more effective the retention will be. A proportional increase of time lag between the individual sessions in fact strengthens the associations and makes the retention in memory even more robust. One must learn to forget for a while in order to remember the given item better.
By affixing a certain weight to various lexemes within the words presented to the user Duolingo ‘s HLR fine tunes and personalizes the forgetting curve for its individual users (these weights are also based on the frequency of the target item’s appearance and successful/failed recall). For this, it uses a computed version of two standard methods of learning languages: the more aurally-focused Pimsleur method and the spaced-repetition model of the Leitner method.
The Leitner method is more interesting in terms of the underlying logic of the spacing and lag effects which HLR uses and provides an entry point for a critique of computational thinking in the field of second language acquisition.
Leitner’s Spaced repetition algorithm
The Leitner method was originally devised in 1972 by Sebastian Leitner for better memorization by using a number of boxes and flashcards. The learner first puts all the flashcards into the first box and attempts to memorize them, then recall them. The ones whose recall was successful get placed in the second box, while the ones which were not recalled correctly stay in the first or get moved into the previous one if possible. The number on the boxes indicates the days after which the cards in the given box are reviewed (1<>2<>3<>4<>5>…). Already, we see the same basic learning algorithm which works with the spacing and lag effects in the analogue – it is what’s called a spaced repetition algorithm.
According to the authors of “A Trainable Spaced Repetition Model for Language Learning,” the Leitner method yielded the most effective recall on the part of the learner of all the considered spaced repetition algorithms.Duolingo’s HLR further builds on this algorithm and effectively manages to increase the predictive capacity on the part of each individual learner. This was done by adding granularity and personalization to the data which the user is presented with. So-called lexeme weights were added to individual words in order to compensate for their specific qualities: “Positive weights are associated with cognates and words that are common, short or morphologically simple to inflect; it is reasonable that these words would be easier to recall correctly. ”
Students were randomly assigned to two groups of which one used the Leitner method (control group) while the other used Duolingo’s HLR with lexeme weight analysis (experiment group). The mean absolute error of prediction (an indicator of how closely predictions match the students’ resulting outcomes) was reduced by “at least 45%” with using the HLR.
A study conducted in 2012 shows that the students gradually lose interest in the app and study sessions of Duolingo tend to drop off after a certain point. It also shows that two things are central to the effectiveness and retention on the part of the students: motivation and the initial level of knowledge of the target language. The most motivated people were those who studied in order “to travel,” while those “who studied mainly for personal interest and school had more modest improvement.” The second main contributing factor to activity on Duolingo was initial knowledge of the target language: “People who were beginners (Semester 1) had the biggest improvement and more advanced people (Semester 2 and 3) had the smallest improvement.” The literature is very sparse on this account, however a general rule can be observed from the interaction of the steepness of the user’s learning curve in comparison with the motivation for learning through the app: the steeper the learning curve, the more dedicated the learner is and the more she returns (fig.3) until a certain point, after which the use of the app wanes.
A conclusion can be drawn from this: Duolingo indeed curbs the higher order functions of language, including their non-conforming anomalous features (such as local dialects, slang, argot, ad hoc formations, and pragmatic meaning), in favor of a standardized and largely discretized canon of linguistic tropes. Duolingo provides a tool for getting a procedural understanding of the target language, such as basic morphology and syntax within a certain zone of the student’s development. The shift in policy and service after the ‘Immersion’ module in favor of a closed application makes for a lack of such a dimension. The shift to HLR has made Duolingo a personalized application for basic grammatical entrainment but lacks the element of human counseling and guidance.
This case study provides a very interesting perspective on the transposition of generic computational algorithms of thinking into the digital. The move from immersion to HLR is a minor one on a structural level, yet the method’s existence as a digital twin allows for particular affordances: the method can be reproduced on every digital device in the most varied of settings, the data can be mined in order to better understand success and failure rates on the part of the student, and this data can (and is) then extrapolated into the application’s “feature sets” for the app’s further development, or for creating deeper personalization on the level of user experience. Due to the computational infrastructure which enables the application, Duolingo is a great example of what Kenneth R. Walsh terms an “adaptive tool […] based on user learner responses,” which he sees as the ideal future for educational practices. Such a tool “can present more advanced information to those who have mastered certain levels and present remedial material to learners who are not progressing.” It can, in other words, very effectively discern the student’s ‘zone of proximal development’ as framed by Soviet psychologist Lev Vygotsky. In his work The Development of Higher Psychological Processes, Vygotsky defines the ZPD as
the distance between the actual development level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with a more capable peer.
By means of effectively iterating the weighted lexemes and words, Duolingo is able to work within the user’s ZPD. Although the application cannot be considered “adult guidance,” can it be considered a “more capable peer”? In what way does a digital interface process inter-personal transference? The capacity for algorithms to comprehend and design a personalized Zone of Proximal Development for Second Language Acquisition must be further explored.
This essay was made possible with the gracious help of Dott. ssa. Alessandra Romano (University of Siena).
 Jacques Lacan, “Subversion du sujet et dialectique du désir dans l’inconscient freudien,” Écrits 806
 Duolingo Wiki, “/Immersion,”accessed 22 May, 2020<https://duolingo.fandom.com/wiki/Duolingo_Wiki:Archive/Immersion>.
 Duolingo, “How We Learn How You Learn,” Duolingo Blog, accessed 22 May, 2020 <https://blog.duolingo.com/how-we-learn-how-you-learn/>.
 Burr Settles, Brendan Meeder, “A Trainable Spaced Repetition Model for Language Learning”
 Hermann Ebbinghaus, Memory: A Contribution to Experimental Psychology, Translated by Henry A. Ruger & Clara E. Bussenius, accessed May 22,2020< http://nwkpsych.rutgers.edu/~jose/courses/578_mem_learn/2012/readings/Ebbinghaus_1885.pdf>.
 Settles, Meeder 1851
 Duolingo, “How We Learn How You Learn”
 Settles, Meeder 1853
 Settles, Meeder 1851
 Settles, Meeder 1854
 Settles, Meeder 1853
 Roumen Vesselinov, John Grego “Duolingo Effectiveness Study: Final Report,” accessed 22 May, 2020< http://static.duolingo.com/s3/DuolingoReport_Final.pdf>.
 Vesselinov, Grego 19
 Vesselinov, Grego 19
 Immersion in Duolingo was one of the most remarkable examples of human computation: “Duolingo, a free language learning platform, was built upon a project started at the end of 2009 by CMU professor Luis von Ahn (creator of reCAPTCHA) and his graduate student…the idea is to create a program that served two purposes, a ‘twofer’ as Luis von Ahn said, teaching its users a foreign language while having them translate simple phrases in documents.” <https://digital.hbs.edu/platform-digit/submission/duolingo-using-the-wisdom-of-crowds-to-translate-language/>. The entrepreneurial ethics underpinning such a platform service have not disappeared and Duolingo keeps most of its data as intellectual property and unavailable, honing its language algorithms based on the input of its millions of users.
 Settles, Meeder 1852
 Kenneth R. Walsh, “Human Machine Learning Symbiosis,” Journal of Learning in Higher Education (Spring 2017, Vol. 13, No. 1) 55.
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