The article studies the formation of an algorithmic culture of students and pupils in learning mathematics, computer science, and project activities. The objective of this work is to study the level of involvement of the algorithmic approach in the educational process with the help of various educational technologies in the study of mathematics, computer science, and the use of project approach in future engineers' training. The introduction discusses the historical aspect of the origin of the terms "computational thinking" and "algorithmic thinking" and their relationship with different types of learning activities in mathematics, computer science, and engineering education. It is further noted that the terms "algorithmic approach" and "algorithmic culture" are used in the context of the usage of the concepts "algorithmic thinking" in solving educational and research tasks. In the main part of the work, the problem of using algorithmic thinking is considered using multiple examples. The authors also analyze the problem of using an algorithmic approach in training future teachers of mathematics and computer science, in basic training of engineers and computer software specialists. In conclusion, the authors suggest that the algorithmic approach and algorithmic thinking are among the fundamental factors that determine the quality of mathematical and computer education. The algorithmic culture of future specialists should be developed and maintained throughout the training process.
The modern education system imposes new requirements on students that determine the amount of knowledge and skills that they should get by taking part in the educational process. An important place is given to the way or culture of thinking that contributes to the better assimilation of this knowledge. This is largely due to the rapidly * growing need to train not only highly qualified information technology professionals, but also people who could get only familiar with these technologies at least at the basic level.
Experienced teachers note that the result of students' activities at different levels depends on how clearly and consistently the student realizes and implements the algorithmic value of their actions. What and in what sequence he does, as well as what he needs to acquire and what the expected result of his actions should be are only a few examples of what to be thoroughly understood. To a larger extend, this is related to the algorithmic culture of the person, which is characterized by the ability and willingness of the student to make and use various algorithms as part of the educational and extracurricular activities. In this regard, it should be noted that the constant use of algorithms in the classroom should guide students to the understanding and awareness of every step and action.
In educational communication, awareness and handling of linguistic and algorithmic elements are an important integral part of the educational process. Due to this, in modern education there is a new school subject – Algorithmics, which is aimed at the formation and development of algorithmic thinking of students, providing for learning basic algorithmic structures and algorithms of various types.
We know that foreign scientists also carry out research that is related to algorithmic
culture and algorithmic thinking. It suffices to say that historically, we encounter the
term "computational thinking" first. Wing's works, (Wing, 2006, 2008) [
A lot of works has been dedicated to the development of both computational and
algorithmic thinking among students and schoolchildren. The authors of the paper [
Thus, we have shown that the problem of educating algorithmic culture and using algorithmic thinking has not lost its relevance in different educational systems over the years.
Now, we are going to see to what extent the algorithmic approach can be introduced into the educational process with the use of various educational technologies.
Forming of the algorithmic culture of students contributes to the conscious perception of educational material. When building a training algorithm, the following components are to be remembered: understanding the basics of the algorithm and its properties; understanding the basics of the language as a means to write an algorithm; knowing of techniques and tools for recording algorithms; understanding the algorithmic nature of the subject's methods and their applications; being competent at school course algorithms; understanding the basics of computer programming.
It should be noted that the formation of the algorithmic culture of students can be carried out by various methods and means. Such tools can be selected, for example, through project training, practical work in a group, drawing up algorithms, reporting an algorithmic model on a training topic, etc.
The characteristic of the algorithmic approach to learning for different categories of students indicates the features of its use in different educational environments. Here are some examples.
In shaping the professional focus of future mathematics teachers, students are offered to construct some algorithms. In this regard, it is important to know that the school course of mathematics in this aspect offers a wide range of algorithms, e.g., the algorithm of reduction of fractions to a common denominator; the algorithm for the solution of construction tasks; the algorithm study of the function and construction of its graph; the algorithm for calculating the area of a curvilinear trapezium; the algorithm study of the mutual location of two straight lines, etc.
Analysis of the educational experience in school leads to the conclusion that teaching mathematics necessarily involves learning algorithms, therefore, the ability to formulate and apply algorithms in the study of any subjects of the school course of mathematics is extremely important. The advantage is, of course, the method that allows students to open the necessary algorithms on their own. In this case, it involves the implementation of three stages of learning mathematical material, which is summarized in Table 1. Describing training activities with specific regulations or rules is a substantial part of the process of building algorithmic elements. Further, specific subject content can be presented in the form of "a teaching algorithm", which has a methodological focus. For this purpose, to build an algorithm for a training session, students who study to be math teachers should learn to analyze the content, goals of training, the students' activities for learning it, and the teacher's activities for organizing this learning, and to build an algorithm for studying a specific mathematical topic.
We believe that algorithmic problems play an important role in forming the algorithmic culture of students. Moreover, the compilation of algorithms in the course of mathematics is also valuable for a variety of problem types. Educational practice shows that the most effective of them is the execution of tasks according to the algorithm, the development of a sequence of actions with justification, the compilation, and testing of algorithms, and the design of algorithms. About a particular subject area, in teaching to solve stereometric problems as part of a course on analytic geometry, these are algorithms that are used to solve such problems using a vector-coordinate method to find the angle between the crossing right lines, as well as the angle between the planes, between the line and the plane, the distance from the point to the right line, the distance from the point to the plane and the distances between the crossing right lines.
Some effective ways of using algorithms in the educational process in doing graphic tasks in the process of teaching graphic disciplines, as part of, let’s say, the study of design geometry, have been proposed by teachers of Novosibirsk State Architectural Construction University (SIBSTRIN) [13; 14].
Another example in our research concerns using an algorithmic approach and presents the field of further education. It associates with work on interdisciplinary projects, which are based on the use of information technology. In Fig. 1, we show a block diagram of the algorithm that is based on a similar project. At the beginning of the project session, the project manager explains to the project team that the work on the project will be most efficient if the entire design process is divided into a certain number of steps performed in a given sequence. The work on such projects should begin with formulating a problem (elaborating technical specifications). Simultaneously the team should examine the relevance of the issue and reveal "the interested parties". At the next step, the whole group participates in the search for possible solutions to the problem. The expected outcome of this work should be finding conceptual solutions to the problem. Once the conceptual solutions are chosen, the team performs the architecture design of the project, i.e. working out the component-relating details. This step can be associated with the construction of a structural model of the project.
After that, the choice of basic components and a description of the rules of interaction between them (the construction of a functional model) are made. The next stage involves drawing up tentative estimates of costs of the project and the creation of a prototype device (in most cases devices are technical solutions). The final phase of work is to defend the project with a demonstration of positive and negative features, justification for the need for development, and showing the uniqueness of the development. Before the final part, the prototype must be tested and information about the test results is used to finalize the project.
The functional model can also be described as an algorithm for the functioning of the developed device. The fact that it is one of the models used in the design process once again confirms the need to develop algorithmic thinking among students and schoolchildren who are involved in project activities.
As an additional example of using the algorithmic approach, we can review the
experience of projects that used the interface method [
The project was divided into four project modules, each had its interface with other
modules and with the "environment". The functioning of each of these design modules
is easily represented in terms of a simple "quasiparallel" algorithm (part of the steps
that can be performed simultaneously). "Ozonation": the creation of devices that
generate a controllable portion of the ozone; "Analysis of concentration": the development
of chemical analysis technologies ozone concentrations; "Processing": development of
technology for processing of vegetables; "Quality Analysis": the analysis of quality of
vegetables [
In the process of implementation of the pilot version of "The measuring polygon",
the project was divided into smaller complementary projects, the work on which was
carried on for three years. Thus, the research team singled out and realized the
following modules: "Measurement and monitoring", "Data pre-processing and archiving",
"Visualization and search of events" and "Research and modeling". All such projects
can be managed either by one person, or a project team consisting of several students,
postgraduates, and teachers. The algorithm for the interaction of the project modules in
"The measuring polygon" is shown in Figure 3.
There is a positive experience in project work that is based on using the algorithmic
approach. We refer to the project "Establishment of a network of schools implementing
innovative programs to test new technologies and content of training and education
through competitive support of school initiatives and networking projects", held in the
framework of special federal programs designed for education development in 2016–
2020. The work was carried out at "Gorno-Altaisk Lyceum-School No. 6 n.a. I.
Z. Shuklin", where the algorithmic approach was applied to a project "Intelrob
Resource Center of Educational Robotics" [
In the system of basic school education, the algorithmic approach is introduced into the educational process, when the case-study method is used as a means to form metasubject universal educational actions in school students.
To determine the effectiveness of the usage of the case-study method, a variety of
techniques have been used by researchers [
When we use the project method, the implementation of the pedagogical potential
of case-projecting in the development of meta-subject universal educational actions
makes it possible to determine the need for scientific verification, development, and
testing of this technology and to consider it as an effective means of developing the
investigated quality in students of the school. In the process of experimental work that
was carried out based on School No. 5 of the Altai Krai in Altai District, the case-study
technique was developed and introduced at the level of general education [
The assessment of the level of how efficiently the meta-subject results form and develop in students when the case-study method is applied reveals positive dynamics of the development of meta-subject of universal educational actions of the students at the level of general education. 3
The examples of the application of the algorithmic approach in the process of teaching students help to the conclusion that the algorithmic approach and algorithmic thinking are among the fundamental factors that determine the quality of mathematical and computer education. We believe that the algorithmic culture of future specialists should be educated and supported throughout the teaching process.
The study was carried out with the financial support of the Russian Foundation for Basic Research and the Government of the Altai Republic within the framework of scientific project No. 20-413-40003 р_a "Study of the effectiveness of the method of project interfaces using when implementing the project approach in the training system for engineering personnel and artificial intelligence specialists in the Altai Republic"