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Abstract
There are numerous theories of second language vocabulary acquisition and teaching. This research employs a mixed methods with a grounded approach to determine how second language students learn new vocabulary and to propose a theory of vocabulary learning. Students attending the total immersion German Deutsche Summerschule (June 2019) logged 1,514 new vocabulary words. Word frequencies were determined by comparisons to available textbooks and to five German linguistic corpora. After plotting vocabulary frequencies and comparing the results to a variety of mathematical explanations, it was found that learning could be explained by specific mathematical equations, showing that vocabulary memory was constructed in the form of an expanding neural network, with commonly used words representing nodes being connected to words and collocations.