Let's start by defining adaptive learning. Adaptive learning uses computer algorithms interacting with the students and providing them with individualized resources and exercises matching their unique demands. The system adapts the sequence of learning materials to the students' individual characteristics which are defined based on their previous answers to questions and exercises. Adaptive learning systems are aimed at transforming the learner from a passive recipient of information into an active collaborator in the learning process.

The answer lies in the need of today's users to define the learning outcomes in a clear language and achieve them in the shortest periods of time, while tracking their own progress. One of the things that matter the most is being able to learn anytime from any place.

Thus, modern education should be individualized (i.e. adaptive), granulated (presented in the microcontent format), socialized (communication inside and outside the platform) and continuous.

In partnership with Tomsk State University, ENBISYS has resolved the challenge associated with "leveling out" basic math skill levels among students using adaptive learning technologies in Plario.ru simulator.

There are several reasons we chose math as the subject. First, it's quite easy to decompose math into logical granulated pieces of content. Second, there is a tangible problem: students enrolling in higher educational institutions find themselves at very different levels of math mastery. Their level is often not enough to master more advanced math. Thus, the efficiency of group classes drops, because the lecturer might be struggling to adapt the structure and the pace of the learning materials to the actual mastery level of each student. Besides, many high school students need additional individual work to prepare for the Unified State Examination.

Each module is presented as a set of interconnected skills (from 30 to 60), and each of them corresponds to the certain ability to use a given set of theoretical knowledge to solve practical problems. Each skill is associated with multiple learning materials (theory and practical tasks). Working with those learning materials is the essential part of the learning process.

The state (model) of the student is represented as the sum of pairs (skill, mastery). Mastery is the extent to which the skill is absorbed and confidence that the student has learned this skill. Mastery can take on a value within the range (0, 1]. The skill is considered to be mastered when the confidence is higher than a certain threshold value, e.g. 0.9.

1. When using the system, the student must achieve the target level, i.e. master all skills with the confidence not lower than a certain threshold value, e.g. 0.9. This means that the student will have this skill at the required level with 90% probability.

2. The initial preparedness level helps define which skills the student needs to train and which skill he/she should start with. The system must diagnose the initial knowledge level with detailed analysis of each skill.

3. To achieve the target state, each student needs a different number of learning materials of various complexity levels. The system must provide the amount of various level learning materials that should be sufficient to master each skill. To exclude the chance of the student memorizing the right answer, the content must be redundant.

4. The current student state (mastery of each skill) must be available at any time.

5. The system must provide the student with an individual sequence of learning materials corresponding with his/her current state.

6. All theoretical materials must be available to the student regardless of his/her current state.

Due to the subject domain specifics, we decided to use the extended version of ВКТ algorithm. The differences from the standard version are:

• set individual values to "transit", "slip" and "guess" probabilities for each pair "learning material - skill";
• correlate learning materials with more than one skill;
• create "prerequisite" type dependencies between skills.

Extended BKT in Plario.ru helps to dynamically form an individual learning trajectory, with the trajectory changing after each exercise is completed.

At the first stage of the project, we had no actual data on the learning parameters and outcomes to build the recommendation part of the system (adaptive logic), so we decided to use the materials ranging algorithm that was reviewed and enhanced to meet the system requirements. We are going to transfer to machine learning technologies later, after we accumulate enough data.

The adaptivity of the learning process is ensured by a flexible algorithm recommending student activities that provides:

• accelerated elimination of gaps;
• learning process continuity;
• required prerequisites (mastery level sufficient for moving forward).

The competency framework in each Plario.ru module was developed by the group of experts of Tomsk State University. It is presented as an oriented acyclic graph, where:

• the nodes represent specific skills (e.g. factor out common factor, group summands);
• arcs represent dependencies between skills, where the initial node corresponds with the prerequisite skill and the end node to the dependent skill.
• dependencies have "power" describing the degree of necessity of mastering the prerequisite in order to start learning the skill (where 1 is maximum dependency that does not allow starting to learn the skill unless the prerequisite skill is mastered).

The state of each student at each moment (student model) can be presented as the sum of skills each having a defined individual mastery value (confidence that this student has mastered this skill). By superposing the student model on the skill graph, we get the individual skill graph of this student.

Put simply, the learning process has the student moving through the individual graph from mastered skills to those which have not been mastered yet, following the dependencies between them.

Fragment of skill graph from Simplification of Algebraic Expressions module

The educational content in Plario.ru was prepared by Tomsk State University experts based on the proprietary methodology. It is based on the following principles:

• high degree of granularity - priority on "micro doses" of content which are aimed at clarifying / training a small but complete knowledge segment (applying a certain rule or formula) the mastering of which does not require a lot of time;
• independence of content units from one another allowing to combine them in any order;
• priority of the practical part over the theoretical one.

Educational content in Plario.ru consists of:

• theoretical materials presented mainly as reference data or problem solution examples with explanations;
• practical problems playing a dual role in the system: they have both educational and controlling function.

When educational materials are created in the system, they are described in accordance with the extended BKT algorithm used in Plario.ru. At the diagnostic stage it is important to evaluate the mastery level in a minimal time with maximum degree of certainty. Therefore, diagnostic problems have slightly different requirements:

• the number and the complexity of problems must be selected so that an average student could provide answers to the test within 2 academic hours;
• problems must cover all skills of the modulel;
• if possible, each skill must be covered by more than one problem, to avoid the impact of accidental errors or guessing;
• incorrect answers are a source of additional information about the existing gaps in the knowledge and it should be possible to use this information in the system.

Plario.ru platform was initially designed to function without an instructor. The instructor could oversee the students' progress but not interfere with the process directly.

We are currently completing the system with new subjects and we are adding some functions that would assist the instructor during the learning process.

Plario system will be enhanced and transformed into a digital training package allowing to:

Plario.ru is a solid example of an adaptive system solving a real problem of students and instructors. The concept of the platform matches the priority task of today's educational establishments associated with digitalization of the educational environment.

By using smart algorithms, ontologies and the expertise of the leading mathematicians of Tomsk State University, Plario transforms the process of "leveling out" the students' knowledge. Additionally, it decreases the workload of instructors removing their routine operations, and also reduces the load on the classrooms. In 2019-2021, Plario was integrated in 5 Russian higher educational establishments and 6 schools with the total number of users over 5000.