Adaptation of Educational Content when Learning Mathematics in Bilingual Condition* Julia Vainshtein1[0000-0002-8370-7970], Mihail Noskov1[0000-0001-8966-3633], Victoria Shershneva1[0000-0001-6661-5591] and Mengy Tanzy2[0000-0001-5710-0676] 1 Siberian Federal University, Svobodny, 79, 660041 Krasnoyarsk, Russia yweinstein@sfu-kras.ru, mnoskov@sfu-kras.ru, vshershneva@sfu-kras.ru 2 Tuvan State University, Kolkhoznaya, 125, 667004 Kyzyl, Russia tmengi78@mail.ru Abstract. Adaptive learning is an advanced technology providing personaliza- tion of educational process in e-learning environment. It is deemed currently important to develop and use e-learning courses that include mechanisms of adapting educational content to language peculiarities when teaching students originating from Russian indigenous minority peoples. The article represents an approach to adapting educational content when teaching mathematics in Rus- sian-Tuvan bilingual conditions. The authors have chosen LMS Moodle as a software environment for implementing e-learning courses. It has the functional of educational content mechanism implementation via the accessibility settings of the e-learning course. The authors have developed an adaptive e-learning course (AELC) in discrete mathematics which supports automated course con- tent navigation and is aimed at developing Russian language competence along with mathematical competence. Adaptation mechanisms have been put into ac- tion in the AELC by designing the rule base of educational content choosing and their binding to corresponding elements of the AELC, the access of stu- dents to which executes their activation by established conditions. Module “Sets and Relations” of the adaptive e-learning course “Discreet Mathematics” has been piloted and showed its effectiveness in training future mathematics and computer science teachers at the Faculty of Physics and Mathematics of Tuvan State University (training program 44.03.01 – Pedagogical Education). Over the longer term it is planned to optimize adaptation mechanisms of the AELC by means of including the conditions of student e-learning environment activity accounting into the rule base of educational content choosing. Keywords: Adaptive learning, Personalization adaptive learning, E-learning, Teaching mathematics, Bilingualism. * Supported by the Russian Science Foundation, grant No. 18-013-00654. The research was carried out within the state assignment of Ministry of Science and Higher Educa- tion of the Russian Federation (theme No. FSRZ-2020-0011). Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). Proceedings of the 4th International Conference on Informatization of Education and E-learning Methodology: Digital Technologies in Education (IEELM-DTE 2020), Krasnoyarsk, Russia, October 6-9, 2020. 1 Introduction Nowadays digitalization of education is characterized by the orientation of education- al programs on intensive use of innovative e-learning technologies providing person- alization of educational process in e-learning environment. Many researchers consider adaptive learning to be an advanced technology providing personalization [1, 2]. Its main purpose is to organize educational content in the e-learning environment provid- ing the variability of educational content with regard to student personal characteris- tics [3]. Many Russian higher educational establishments take efforts in this direction. For example, the Institute of Information and Space Technology of Siberian Federal University develops adaptive e-learning courses (AELC) where the adaptation of educational content is put into practice depending on learning content acquisition and student individual style [4-7]. Introducing the AELCs into the educational process for IT-majoring students shows their high performance on the part of educational content acquisition quality improvement [8]. However, the range of individual characteristics is very wide including cognitive and personal features of students. For example, when teaching students originating from Russian indigenous minority peoples, it is necessary to use mechanisms of adapting educational content to language peculiarities. It is particularly true for junior years when teaching basic disciplines including mathematics. 2 Adaptive learning in Russian-Tuvan bilingual conditions Let us consider the Republic of Tuva, which is located in isolation from the rest of Russia and represents a specific cultural world [9]. By and large, the republic has a bigger percentage of population to speak the Tuvan language natively than in other national regions of Russia. It leads to the fact that many applicants do not have a suf- ficient command of Russian or only speak everyday Russian. It causes a specific edu- cational process organization problem that resides in the necessity to develop Russian language competence alongside with subject competences because Russian is the instruction language at the university [10, 11]. The authors suggest using adaptive e-learning courses to organize mathematics training in Russian-Tuvan bilingual conditions. When creating the courses, it is im- portant to take into account the level of Russian comprehension of students and make provision for combined development of both mathematical and Russian language competences. Herewith, one of the educational objectives is to acquire learning mate- rials and get the course credit completely in Russian. The authors have chosen LMS Moodle as a software environment for implementing e-learning courses. It has the functional of educational content mechanism implementation via the accessibility settings of the e-learning course. The authors have used the microteaching strategy when designing the adaptive e- learning course in discrete mathematics. Educational content model represents a col- lection of micro-chunks for learning material represented in several ways with the difference in the extent of Russian use. The learning material variant designed for a student with a low command of Russian is formed simultaneously in Tuvan and Rus- sian. It enables students to adapt to new learning conditions. The next variant of the material is designed for the students who have a medium command of Russian, i.e. those who can speak everyday Russian. This variant contains Russian formulations of statements and definitions and is accompanied by Tuvan translation, also including a mathematical term glossary. The number of fragments in Russian in each micro- chunk increases from version to version and finally reaches an entirely Russian vari- ant. When structuring the knowledge domain of the discreet mathematics course with the workload of 180 academic hours, 28 micro-chunks of educational content were formed in three different versions, and 62 terms were included into the subject field glossary. Let us consider the representation of the educational content of the micro-chunk “Relations”. This is how the definition of relations is represented in the Russian ver- sion: ОТНОШЕНИЕ – это способ задания взаимосвязей между элементами. Strict definition: N-АРНОЕ ОТНОШЕНИЕ НА МНОЖЕСТВЕ А называется любое подмноже- ство упорядоченных n элементов этого множества. The definition is given in Tuvan for the students who do not have a sufficient command of Russian: ХАРЫЛЗАА – дээрге кезектернин бот-боттарынын аразында онаарынын аргазы. Strict definition: А БӨЛУГДЕ N-АРНЫГ ХАРЫЛЗАА дээрге ол-ла бөлугнун подмножествонун чурумчудуткан n- кезектери. For the students with the low command of Russian, the material contains Russian formulations of statements and definitions but it is accompanied by the Russian- Tuvan glossary of mathematical terms, a fragment of which is shown in Table 1. When preparing educational content of the e-learning course the methodical tech- nique “Language communication technique variability” has been used. It is aimed at the simultaneous use of two languages – Russian and Tuvan to create better learning conditions in the realm of intelligibility and perception of the material learnt. The AELC provides for automated navigation between the material versions de- pending not only on the command of Russian but also on the level of acquiring learn- ing material. Students are offered a version of learning material to study. Then the acquisition of new material is checked automatically and, depending on the results obtained, these stages follow: - if there is a problem acquiring language-related learning material, the course au- tomatically offers the learning material version with more material in Tuvan corresponding to the current Russian level of the student; - if the problem lies in the lack of comprehension of the course material, the stu- dent gets assistance in the form of automated heuristic prompts and explaining examples embodied as a training test. Table 1. A Fragment of Russian-Tuvan glossary of AELC. Concept in Russian Concept in Tuvan language Отношение , заданное на множестве Бир эвес x  A : ( x, x)   харыл- А, называется рефлексивным, если заа кылдынып турар болза, А деп x  A : ( x, x)   . бөлугде онап каан деп харылзааны Например, отношение жить в одном рефлексивный дээр . городе на множестве людей. Чижээлээрге, чангыс хоорайга болуг кижилернин чурттаар харылзаазы Отношение , заданное на множестве Бир эвес x  A : ( x, x)   харылзаа А, называется антирефлексивным, кылдынып турар болза, А деп бөлугде если x  A : ( x, x)   . онап каан деп харылзааны Например, быть сыном. антирефлексивный дээр. Чижээлээрге, оглу болуру. Отношение , заданное на множестве Бир эвес x, y –ке (х, у)ϵ p болгаш А, называется симметричным, если оон уламчызы (у, х)ϵ p деп харылзаа x, y из того что ( x, y )   кылдынып турар болза, А деп бөлугде следует, что ( y, x)   онап каан деп харылзааны Например, быть соседом. симметричный дээр Чижээлээрге, кожазы болуру. Отношение , заданное на множестве Бир эвес x, y –ке мындыг харыл- А, называется антисимметричным, заа кылдынып турар болза (х, у)ϵ p биле если (у, х)ϵ p, болгаш оон уламчызы х = у x, y из того что ( x, y)   и ( y, x)   болза, А бөлугде онап каан деп ха- следует, что x  y рылзааны антисимметричный дээр. Например, быть потомком Чижээлээрге, салгакчы болуру. Бир эвес x, y –ке мындыг харыл- Отношение , заданное на множестве заа кылдынып турар болза (х, у)ϵ p биле А, называется транзитивным, если (у, z)ϵ p, болгаш оон уламчызы x, y из того что ( x, y)   и ( y, z)   (х, z)ϵ p болза, А бөлугде онап каан следует, что ( x, z )   деп харылзааны транзитивный дээр. Например, быть старше. Чижээлээрге, улуг болуру азы Adaptation mechanisms have been put into action in the AELC by designing the rule base of educational content choosing and their binding to corresponding elements of the AELC, the access of students to which executes their activation by established conditions. For example, the rule of automatic presentation of other version of the educational content to the student who has not acquired learning material and shown medium command of Russian is set as follows: IF [Parameter «Command of Russian» : = «Средний» AND Parameter «Term i acquisition level» : = «Insufficient» (from 0 % to 50%)] ELSE [Parameter «Term i intelligibility » := TRUE AND Parameter «Version» := «Version B» AND Parameter «Detalization» := « Maximum»]. At the moment the authors are designing the elements of the adaptive e-learning course that include training tests providing step-by-step solution of multistage prob- lems and peer review individual project assignments. The proposed approach was tested in the educational process of students of Tuva State University. Before the study, the control and experimental groups of 19 people were formed. The construction of the educational process in the control group was carried out traditionally, and in the experimental group using the approach proposed in the work using AELC. The positive dynamics of the formation of mathematical and russian- language competence in the control and experimental groups when teaching discrete mathematics, Fig. 1. 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Control group Experimental group Mathematical competence Russian-speaking competence Fig. 1. Dynamics of educational results Assessment of the level of formation of competencies of each student was carried out on a 100-point scale. 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