# Laboratory 'Innovative technologies of teaching mathematics in schools and universities' (LITTM)

**About**

The Laboratory of Innovative Technologies for Teaching Mathematics at School and University (LITTM) is a part of the N.I. Lobachevsky Institute of Mathematics and Mechanics in Kazan Federal University. The laboratory focuses its research activities on two important areas of information technology, namely the development of educational mathematical ontology OntoMathEdu and the design of an individual digital space in the system of school mathematics education using intelligent recommender systems.

**The main directions of research **

**Development of an educational ontology of mathematical knowledge in school mathematics OntoMathEdu **(Certificate of state registration of the database No. 2019622208 Educational Ontology of mathematics "OntoMathEdu").

The OntoMathEdu ontological resource (https://github.com/CLLKazan/OntoMathEdu) is intended to present mathematical knowledge on Plane geometry for high school. Ontology includes a hierarchy of object types, a hierarchy of roles, a hierarchy of materialized relationships, and a network of points of view.

The level of subject ontology is built, which contains language-independent concepts related to the school geometry course. There are many basic concepts that characterize general mathematical knowledge, as well as specialized concepts from various sections of Plane geometry. The OntoMathEdu ontology includes over 800 concepts and seven types of relationships. The names of the concepts are given in three languages (English, Russian and Tatar), the descriptions of the concepts contain links to the Wiki, to the Russian educational resource, to the English educational resource.

A distinctive feature of an ontology is a set of relations linking the concepts of ontology. The set of relations includes both explicit dependences of concepts in the area under consideration, and special relations that allow organizing conceptual knowledge in accordance with the educational goals of using the ontology.

A semantically annotated corpus of educational mathematical texts in Russian is being created. The corpus consists of mathematical statements extracted from educational mathematical documents, where each statement is manually annotated with its formulaic representation in the LaTeX system and the formalization of the formula in the OpenMath standard. The developed method for annotating the structural elements of a mathematical text (definitions, statements, theorems, etc.) is based on the use of lexico-syntactic templates and rules describing the structural characteristics of the corresponding language structures in scientific, technical and educational texts in Russian.

**Designing an individual digital space in the system of school mathematics education using intelligent recommendation systems**

The personalized digital model of teaching school mathematics has been created at the distance education site of Kazan Federal University. The semantic core of the model is the educational mathematical ontology OntoMathEdu. We also offer a new intelligent recommendation system for school mathematics, which is an important component of a personalized digital model.

To implement the principle of consistency and continuity in the study of concepts of the subject area, we introduced the concept of an educational level. To represent different language versions of ontology concepts, taking into account the task of educational levels, a model of ontology projections was developed.

We are designing an electronic course that provides for the use of various methodological elements (gamification, creation of conditions for individual and group creativity, the choice of alternative ways in solving educational problems, etc.). The ontological approach when creating a course makes it possible to use ontology as a reference system, as well as a basic component for building an individual learning trajectory and generating tests. The recommender system provides a set of links to useful external sources, including using a keyword search engine.

**People**

Liliana R. Shakirova (head of laboratory) Liliana.Shakirova@kpfu.ru Head of the Department of Theory and Technologies of Teaching Mathematics and Informatics at the N.I. Lobachevsky Institute of Mathematics and Mechanics focuses her research activities on the problems of mathematics education, digital technologies for teaching mathematics, and training future mathematics teachers. | elipachev@gmail.com |

Olga.Nevzorova@kpfu.ru Associate Professor, Kazan Federal University, Institute of Computational Mathematics and Information Technologies, Department of Information Systems. Research interests: e-learning, semantic technologies, ontology modeling, natural language processing. | |

mmwwff@yandex.ru Associate Professor of the Department of Theory and Technologies of Teaching Mathematics and Informatics of the N.I. Lobachevsky Institute of Mathematics and Mechanics and a researcher of the LITTM laboratory, focuses her research activities on the problems of mathematics education, digital technologies for teaching mathematics, and training future mathematics teachers. | aedyupina@kpfu.ru Engineer of the Department of Theory and Technologies of Teaching Mathematics and Informatics of the N.I. Lobachevsky Institute of Mathematics and Mechanics, master's graduate, a young scientist in the field of teaching mathematics using modern methods, digital technologies. |

**Conferenсes and workshops**

International conference "Mathematical education at school and university" (MathEdu)

The purpose of the MathEdu Conference is to unite the efforts of scientists and teachers of educational institutions of various levels in the search for ways to improve mathematical education at schools and universities in the context of the transition to new educational standards. At the conference sites, modern methods and technologies of teaching mathematics and computer science at school and university are analyzed, specific measures are proposed to improve the multi-level training of teachers of mathematics and computer science in the conditions of undergraduate and graduate programs; the main problems of school and university mathematical education in the countries of near and far abroad are discussed.

Workshop "Digital Technologies for Teaching and Learning (DTTL)"

The DTTL workshop will address the following topics: digital resources for teaching and learning, ontologies in e-learning, intelligent learning systems, new software for teaching and learning, mathematical models of learning, digital learning platforms, models and algorithms of educational data analysis, linked data in education.

Conference "Information Technologies in Education and Science (ITES)"

The conference allows attracting talented scientists to conduct fundamental research in the field of information technology and artificial intelligence.

Republican seminar for teachers of mathematics and computer science

In the context of reforming mathematics education, improving and deepening the relationship between school and university becomes one of the most important directions in the development of the modern education system in Russia. The staff of the department, 2 times a year (in autumn and spring), organize a seminar - a platform for the exchange of experience between teachers of the Republic of Tatarstan and all of Russia, and teachers of the higher education system.

All events are part of the large International Forum of Mathematics Education (IFME).

**Science for schoolchildren and students**

Competition of local history mathematical tasks for schoolchildren

The humanitarian potential of mathematics education and its culturological function can be realized by including integration and research tasks in teaching, combining history, mathematics and local history. The use of elements of local lore and history of the native land in the course of mathematics contributes to the formation of motivation for learning and personal values of students, fostering a sense of patriotism in them, understanding of interdisciplinary connections, the importance of mathematics in life. Thanks to the familiar from childhood surrounding objects-sights, abstract mathematics becomes more attractive, real and "earthly".

Competition "Lobachevsky and XXI century"

The competition allows us to attract students to scientific, research and search activities; to acquaint with the biography and contribution to science of the great geometer Nikolai Ivanovich Lobachevsky and his followers.

**Projects**

**Publications (last 5 years)**

- Olga Nevzorova, Liliana Shakirova, Marina Falileeva, Konstantin Nikolaev. Towards Ontology-Based Software Services for Teaching School Mathematics // L. Gómez Chova, et al. (eds). Proceedings of the 15th International Technology, Education and Development Conference (INTED 2021), March 8th-9th, 2021. IATED, 2021. Pp. 5288–5297. ISBN: 978-84-09-27666-0, ISSN: 2340-1079
- Liliana Shakirova, Marina Falileeva, Olga Nevzorova, Konstantin Nikolaev. Design and Implementation of a Personalized Digital Learning Model // L. Gómez Chova, et al. (eds). Proceedings of the 15th International Technology, Education and Development Conference (INTED 2021), March 8th-9th, 2021. IATED, 2021. Pp. 6340–6348. ISBN: 978-84-09-27666-0, ISSN: 2340-1079
- Dyupina A, Falileeva M., Problems of Designing Polylingual Ontology OntoMathEdu // Communications in Computer and Information Science. - 2020. - Vol.1242, Is.. - P.179-190.
- Shakirova L, Falileeva M, Kirillovich A, Lipachev E., Nevzorova O., Nevzorov V. Modeling and evaluation of the mathematical educational ontology//CEUR Workshop Proceedings. - 2020. - Vol.2543, Is.. - P.305-319
- Alexander Kirillovich, Olga Nevzorova, Marina Falileeva, Evgeny Lipachev, Liliana Shakirova OntoMathEduEdu: A Linguistically Grounded Educational Mathematical Ontology // Intelligent Computer Mathematics. Series: Lecture Notes in Computer Science, Year: 2020, Volume 12236, Pages 157-172. ISBN : 978-3-030-53517-9. https://doi.org/10.1007/978-3-030-53518-6 Q2
- Damir Mukhamedshin, Olga Nevzorova, Alexander Kirillovich. Using FLOSS for Storing, Processing and Linking Corpus Data // Vladimir Ivanov, et al. (eds). Proceedings of the 16th IFIP WG 2.13 International Conference on Open Source Systems (OSS 2020), Innopolis, Russia, 12–14 May 2020. IFIP Advances in Information and Communication Technology, vol. 582. Springer, 2020. Pp. 177–182. doi:10.1007/978-3-030-47240-5_17 Q3
- Kirillovich, A.: OntoMathEdu: Towards an Educational Mathematical Ontology/ A. Kirillovich, O. Nevzorova, M. Falileeva, E. Lipachev, L. Shakirova // CEUR Workshop Proceedings, 2020. V. 2634. P. 1-10. http://ceur-ws.org/Vol-2634/WiP1.pdf.
- Nevzorova, O.: OntoMathEdu Educational Mathematical Ontology: Annotation of Concepts / O. Nevzorova, L. Shakirova, M. Falileeva, A. Kirillovich, E. Lipachev // CEUR Workshop Proceedings, 2020. V. 2648. P. 157-168. http://ceur-ws.org/Vol-2648/paper13.pdf.
- Liliana Shakirova, Marina Falileeva, Alexander Kirillovich and Eugeny Lipachev. Problems and Solutions in the Design of Formal Taxonomy of Concepts of Geometry // L. Gómez Chova, et al. (eds). Proceedings of the 13th International Technology, Education and Development Conference (INTED2019), Valencia, Spain, March 11th-13th, 2019. IATED, 2019. Pp. 6793-6801
- Nevzorova O., Nevzorov V. (2019) Ontology-Driven Processing of Unstructured Text. In: Kuznetsov S., Panov A. (eds) Artificial Intelligence. RCAI 2019. Communications in Computer and Information Science, vol 1093. Springer, Cham, pp 129-142. DOI https://doi.org/10.1007/978-3-030-30763-9_11 Q3
- Mourat Tchoshanov, M. Cruz Quinones, Elena Ibragimova, Liliana Shakirova, Kadriya Shakirova. Lower Secondary School Mathematics Teachers' Topic-Specific Content Knowledge in the U.S. and Russia (Предметно-тематические знания учителей математики средней школы в США и России), EDUCATION AND SELF DEVELOPMENT, vol. 14, N 1, 2019, pp. 31-44
- Shakirova Liliana R., Falileeva Marina V., Dupina Anastasiya E., DYNAMICS OF STUDENTS' ACTIVITY STATES IN THE PROCESS OF SOLVING MATHEMATICAL TASKS//IIOAB JOURNAL. - 2019. - Vol.10, Is.. - P.122-127.
- Alexander Kirillovich, Liliana Shakirova, Marina Falileeva and Eugeny Lipachev. Towards an Educational Mathematical Ontology // L. Gómez Chova, et al. (eds). Proceedings of the 13th International Technology, Education and Development Conference (INTED2019), Valencia, Spain, March 11th-13th, 2019. IATED, 2019. Pp. 6823-6829
- Mourat Tchoshanov, Maria Quinones, Kadriya Shakirova, Elena Ibragimova, Liliana Shakirova. Mixed Methods Study of Middle School Mathematics Teachers' Content Knowledge in USA and Russia Using Sequential Nested Design // ARPHA Proceedings 1: V International Forum on Teacher Education : Part I: Teacher Education and Training. Рр. 687-700. doi: 10.3897/ap.1.e0651
- Mourat Tchoshanov, Maria Cruz Quinones, Gulshat Shakirova, Liliana Shakirova. CROSS-CASE EXAMINATION OF MIDDLE SCHOOL MATHEMATICS TEACHERS' TOPIC-SPECIFIC CONTENT KNOWLEDGE IN THE U.S. AND RUSSIA. Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. St Louis, MO: University of Missouri, USA, November 14-17, 2019. Pp. 756-761
- Tchoshanov M. Examining College students' conceptual metaphors of infinity across Calculus coursework sequence / Tchoshanov M., Babarinsa G., Ibragimova E., Falileeva M // INTRUM. Second conference of the International Network for Didactic Research in University Mathematics, April 5-7, 2018, Kristiansand, Norway. - 64-73.
- Alexander Kirillovich and Olga Nevzorova. Ontological Analysis of the Wikipedia Category System // David Aveiro, Jan Dietz, Joaquim Filipe (eds). Proceedings of the 10th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2018). Seville, Spain, 18-20 September, 2018. Volume 2: KEOD. SCITEPRESS, 2018. Pp. 358-366
- Shakirova L.R, Utkina T.I, Falileeva M.V, Elgushova, A.S. Quality assurance system for post-graduate student training in mathematics and its computer support//Journal of Advanced Research in Dynamical and Control Systems. - 2018. - Vol.10, Is.2 Special Issue. - P.2226-2229
- Rizvanov Zimfir Z., Abaturova Vera S., Malo Irina E., Shakirova L.R. The methodical projects as a method for learning future teachers//AMAZONIA INVESTIGA. - 2018. - Vol.7, Is.15. - P.172-177.
- Elizarov A.M., Kirillovich A.V., Lipachev E.K., Nevzorova O.A., Shakirova L.R. Open linked data and ontologies in mathematics education (Открытые связанные данные и онтологии в математическом образовании) // V. Voevodin, et al (eds). Proceedings of the 20th Conference Scientific Services & Internet (SSI-2018). CEUR Workshop Proceedings, vol. 2260. CEUR-WS, 2018. Pp. 186-196
- Examination of Lower Secondary Mathematics Teachers' Content Knowledge and Its Connection to Students' Performance / M. Tchoshanov, M.D. Cruz, K. Huereca, K. Shakirova, L. Shakirova, E.N. Ibragimova // International Journal of Science and Mathematics Education. - 2017. - Vol.15, Is.4. - P.683-702. (SJR=0.893)
- Tchoshanov, M. А. Cross-national study of lower secondary mathematics teachers' content knowledge in USA and Russia / М. А. Tchoshanov, М. С. Quinones, К. В. Shakirova, Е. N. Ibragimova, L. R. Shakirova // CERME 10. 10th Congress of European Research in Mathematics Education. - Dublin, 2017. - TWG 11. Р. 1-9.
- Shakirova L. ASSESSMENT OF THE LEVEL OF STUDENTS' PRODUCTIVE ACTIVITY IN SOLVING MATHEMATICAL TASKS / L. Shakirova, M. Falileeva, M. Kinder // 9th International Conference on Education and New Learning Technologies, EDULEARN17, July 3rd-5th, 2017. – Barcelona, Spain. ISBN: 978-84-697-3777-4, pp. 1570-1575.
- Tchoshanov M, Quinones M.C, Shakirova K.B, Shakirova L.R. Analyzing connections between teacher and student topic-specific knowledge of lower secondary mathematics//Journal of Mathematical Behavior. - 2017. - Vol.47C, P.54-69 (SJR=0.923)
- Comparative analysis of mathematics teachers' content knowledge in USA and Russia through the lens of TIMSS results / Mourat Tchoshanov, Maria Cruz Quinones, Kadriya Shakirova, Elena Ibragimova and Liliana Shakirova // Education and Self-Development, 2017, 12(1), 23-33. DOI: 10.26907/esd12.1.02
- Shakirova L., Falileeva M., Kinder M., ASSESSMENT OF THE LEVEL OF STUDENTS' PRODUCTIVE ACTIVITY IN SOLVING MATHEMATICAL TASKS//9TH INTERNATIONAL CONFERENCE ON EDUCATION AND NEW LEARNING TECHNOLOGIES (EDULEARN17). - 2017. - Vol., Is.. - P.1570-1575
- Tchoshanov M, Quinones M.C, Shakirova K., Ibragimova E., Shakirova L. Analyzing connections between teacher and student content-specific knowledge of lower secondary mathematics. Presentation at the Psychology of Mathematics Education (PME-NA) Annual Conferense, Indianapolis, USA, oct. 5-9, 2017.
- Nevzorova, O (Nevzorova, Olga); Nevzorov, V (Nevzorov, Vladimir); Kirillovich, A (Kirillovich, Alexander) A Syntactic Method of Extracting Terms from Special Texts for Replenishing Domain Ontologies // Proceedings of SECOND RUSSIA AND PACIFIC CONFERENCE ON COMPUTER TECHNOLOGY AND APPLICATIONS (RPC 2017), 2017. Pp. 127-131 WoS
- Mukhamedshin D., Nevzorova O., Khusainov A. (2017) Complex Search Queries in the Corpus Management System // Computational Collective Intelligence. ICCCI 2017. Lecture Notes in Computer Science, vol. 10449. Springer, Cham. Springer International Publishing AG 2017. Pp. 407-416. Q2