This study develops a Fibonacci-based algorithm to measure foreign language vocabulary knowledge more quickly and effectively, using Russian as an example and referencing a frequency dictionary (Ляшевская & Шаров, 2009) where words are ranked according to their usage frequency. In the Fibonacci sequence, which progresses as the sum of the two preceding numbers, the initial intervals are close to each other, while in later stages, the intervals gradually increase. In frequency dictionaries, words are ordered from most frequently used to least used. When the words in the frequency dictionary are asked based on the natural increase pattern of the Fibonacci sequence, the difficulty level of the test can be adaptively adjusted. The basic working principle of the algorithm is as follows: The student is asked the word that ranks first in the frequency list. If the student knows the word, words from the list are asked by increasing the ranking according to the Fibonacci sequence's increase pattern: "+1, +2, +3, +5, +8...". If the student continues to answer correctly, they will encounter one of the rarest used words in Russian, ranked 46,368th in the list, at the 23rd question. When the student gives an incorrect answer, the increase pattern of the Fibonacci sequence is reversed, and words corresponding to the list are asked by decreasing the ranking as "-1, -2, -3, -5, -8...". If the student continues to give incorrect answers, they will quickly progress towards more frequently used words. The asked words are listed as known and unknown words. The words in these lists are not asked again to the student and are used as data for final evaluation. In this way, the range of the estimated number of words known by the student can be measured quickly and effectively. For example, if the student is ranked between 7500-10000 in the word list after the 20th question, this range will be the student's estimated vocabulary knowledge. This measurement should be considered not as a definitive result for final evaluation, but as important data about the student's vocabulary knowledge. Using this data, a special evaluation can be made by the instructor. Within the scope of the study, a PHP and MySQL-based web application was developed for the implementation of this algorithm. This algorithm design can be used not only for Russian but also for other foreign languages for which word frequency lists have been created. The theoretical foundations of the study are thought to be useful for technology-supported personalized learning approaches in language education.

Keywords: Vocabulary, measurement and evaluation, Fibonacci sequence, Russian language

Reference

О. Н. Ляшевская & С. А. Шаров. (2009). Новый частотный словарь русской лексики. http://dict.ruslang.ru/freq.php.   (Retrieved August 5, 2024).