The Stages of a Thinking Act

complex problems arise, will be resilient in facing difficult problems, as well as have good communication and teamwork skills.

In short, computational thinking will be part of the skill set not only of scientists but of everyone [84]. The prevalence of computational thinking tomorrow will be like the prevalence of computers today. Just as ubiquitous computing was yesterday's dream and has become today's reality, so too will computational thinking be tomorrow's reality.

1.2 SOME BASIC CONCEPTS

1.2.1 Thinking

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Thinking is considered a psychological process belonging to a stage of the cognitive process. Based on the nature of reflection, all cognitive activities can be divided into two stages: sensory cognition (including sensation, perception) and rational cognition (including thinking and imagination). Therefore, the rational cognitive process is also called thinking.

Thinking has been studied by many scientists in many different fields and the concept of thinking has been expressed from different perspectives [6], [12], .

Psychologist MN Secdakov [37] introduced the concept "Thinking is the generalized and indirect perception of objects and phenomena of reality in their signs, common properties and essence" . Thinking is also the perception and creative construction of new, individual objects and phenomena of reality on the basis of acquired generalized knowledge.

In the scope of this study, the author uses the concept of thinking of pedagogues: "Thinking is a psychological process that reflects the essential properties, internal connections and relationships that are regular.

of things and phenomena in objective reality, which we did not know before" [20].

The thinking process has the following characteristics [20]:

- The “problematic” nature of thinking: To stimulate thinking, two conditions must be met at the same time: (1) Must encounter a problematic situation, a situation that contains a new purpose, a new problem, requiring a new way of solving. At that time, to solve that problem, a new way of solving must be found, that is, thinking. (2) The problematic situation must be fully perceived by the individual, transformed into an individual's task, that is, the individual must determine what is known, given, and what is unknown, must be found: at the same time, there must be a need (motivation) to find it. Familiar facts or facts beyond the understanding of the individual will not appear in thinking.

- Indirect nature of thinking: Thinking discovers the nature of things, phenomena and the laws between them by using tools, means (measuring machines) and cognitive results (rules, formulas, laws, etc.) of humans and personal experience. Thinking is expressed in language.

- Abstract and general nature of thinking: Thinking reflects the most essential, common nature of many things forming a group, a type, a category (generalization), and at the same time abstracts from that thing specific, individual things.

- Thinking is closely related to language: Abstract, indirect, general thinking must use language as a means. Thanks to language, people can carry out thinking operations and the products of thinking are judgments and reasoning expressed in words, phrases, sentences...

- Thinking is closely related to sensory perception: Sensory perception is the basis for thinking; conversely, thinking and the results of thinking are

coordinate the reflective ability of sensation, making human sensation more sophisticated, more sensitive, perception more selective and more meaningful.

* The thinking process takes place through the following five stages:

- Identify the problem and express it into a thinking task;

- Mobilizing knowledge and experience related to the problem, creating (in the thinking subject's mind) associations around the problem that needs to be solved;

- Filter associations, eliminate unnecessary ones, and form hypotheses about ways to solve the problem;

- Test the hypothesis on how to solve the problem: if the hypothesis is correct, proceed to solve the problem; if the hypothesis is wrong, negate it to form a new hypothesis and start a new thinking process;

- Solve problems to get results, check results.

KK Platonov summarized the stages of a thinking act in the following diagram (Figure 1.1) .

* Intellectual operations in the thinking process [20]:

- Analysis and synthesis: Analysis is using the mind to separate the object of thought into parts, attributes, connections, and relationships of small components to perceive the object more deeply. Synthesis is using the mind to combine the components that have been separated through analysis into a whole; synthesis takes place on the basis of the results of analysis, conversely analysis takes place on the basis of the model that will be synthesized. Thus, the two operations of analysis and synthesis are closely related to each other.

Problem awareness

Associations appear

Associative screening and hypothesis generation

Hypothesis testing

Problem Solving

New thinking action

Precision

Confirm

Negative

Figure 1.1. Stages of a thinking act

- Comparison: Using the mind to determine the similarities and differences between objects and phenomena. Comparison plays an important role in perceiving the world; it can be considered the "basis of all understanding and thinking".

- Abstraction and generalization: Abstraction is an intellectual operation, using the mind to eliminate unnecessary attributes, parts, relationships, etc. in a certain aspect and only retain the necessary elements for thinking. Generalization is using the mind to encompass many different objects into a group, a type, etc. on the basis that they have some common attributes and nature, relationships that have rules. Generalization is

is a synthesis at a higher level. The two operations of abstraction and generalization are related to each other in the same way as the relationship between analysis and synthesis.

Thinking operations are closely related to each other, unified in a certain direction as determined by the task of thinking. In fact, thinking operations do not necessarily follow a mechanical sequence as stated above. Depending on the task and conditions of thinking, not every thinking action needs to perform all of the above operations.

1.2.2 Computing

According to the Free Merriam-Webster Dictionary , the meaning of computing is a type of calculation that includes arithmetic and non-arithmetic steps and follows a well-defined model (for example, an algorithm, ...)

The concept of computing is a goal-oriented activity that requires, benefits from, or creates a mathematical process called an algorithm that is performed by a computer or a computer.

Computing includes the design, development, and construction of computer hardware and software systems; the editing, structuring, and management of information; scientific research on computers; making computer systems work intelligently; and the creation and use of media and entertainment. The field of computing includes computer engineering, software engineering, computer science, information systems, and information technology.

1.2.3 Computational thinking

The first person to mention the phrase “Computational Thinking” in the book MINDSTORMS (first published in 1980) was Seymour Papert (February 29, 1928 – July 31, 2016), a mathematics professor at MIT and author of the LOGO software and programming language, while wanting to introduce

teaching algorithms using this software to young students.

Author Jeannette Wing (currently vice president of Microsoft) was the first to define the concept of computational thinking, in 2006 [83] which is roughly translated as follows: "Computational thinking involves solving problems, designing systems and understanding human behavior, by drawing on the fundamental concepts of computer science" 1 .

However, in 2011 at a conference, Jeannette Wing proposed another definition [86] which is roughly translated as follows: “Computational thinking is the thinking processes involved in formulating problems and their solutions so that the representation of those solutions can be effectively implemented by an information processing agent.” 2

And in 2014, author Wing continued to add to the definition of computational thinking [87] which was roughly translated as follows: "Computational thinking is the process of problem solving and solution, in which the solution can be effectively implemented by humans or computers or can also combine humans and computers simultaneously." 3

Since the first definition of Wing (2006), many researchers on computational thinking have also given other definitions or perspectives on this type of thinking. For example, in 2009, Denning [66] could be understood as “Computational thinking has a long history in computer science. In the 1950s and 1960s, it was called “algorithmic thinking”, which meant the orientation of thinking to formulate problems in the form of converting input data into output and finding algorithms to perform the conversion. Today, this term has been extended to include the process of

1 Original: “ Computational thinking involves solving problems, designing systems, and understanding human behavior, by drawing on the concepts fundamental to computer science.”

2 Original: “ Computational thinking is the thought processes involved in formulating problems and their solutions so that the solutions are represented in a form that can be effectively carried out by an information-processing agent. ”

3 Original : “Computational thinking is the thought processes used to formulate a problem and express its solution or solutions in terms of a computer can apply effectively.”

think at multiple levels of abstraction, use mathematics to develop algorithms, and test how solutions scale across different sizes of problems.” 4

In addition, the author Hemmendinger proposed a view of computational thinking in 2010 [60] that can be roughly translated: “... [Computational thinking] is teaching them how to think like an economist, a physicist, an artist and understand how to use computing to solve their problems, to be creative and to discover new questions that can be explored favorably.” 5

Or in 2012, author Furber [75] stated and his point of view can be translated as “Computational thinking is the process of recognizing aspects of computing in the world around us, and applying tools and techniques from Computer Science to understand and reason about both natural and artificial systems and processes.” 6

In addition, in 2014, author Yadav and his colleagues also presented a perspective on computational thinking [52] - which can be roughly translated as: "The thinking process to summarize problems and create solutions that can be automated." 7

Through the results of research on some concepts of computational thinking, research on characteristics, structure, path of formation and development of computational thinking, etc. in domestic and foreign documents, it can be concluded that until now there is still no final definition of computational thinking. These definitions tend to focus on the activities and cognitive processes of

4 Original : “Computational thinking has a long history within computer science. Known in the 1950s and 1960s as “algorithmic thinking,” it means a mental orientation to formulating problems as conversions of some input to an output and looking for algorithms to perform the conversions. Today the term has been expanded to include thinking with many levels of abstractions, use of mathematics to develop algorithms, and examining how well a solution scales across different sizes of problems.”

5 Original: “...[Computational Thinking] is to teach them how to think like an economist, a physicist, an artist, and to understand how to use computation to solve their problems, to create, and to discover new questions that can fruitfully be explored.”

6 Original: “Computational thinking is the process of recognising aspects of computation in the world that surrounds us, and applying tools and techniques from Computer Science to understand and reason about both natural and artificial systems and processes.”

7 Original: “The mental process for abstraction of problems and the creation of automatable solutions.”

individuals, to improve cognitive skills and support teaching and learning in affected individuals.

Accordingly, based on finding similarities in concepts and relationships of core components that form computational thinking as well as based on the concept of author Wing, we can propose the concept of computational thinking as follows:

“Computational thinking is a type of thinking that aims to solve a problem through decomposition and identification activities to form the problem and step-by-step construction activities to implement the problem in the direction of automatic processing by the computer.”

The author will use this concept of computational thinking throughout the thesis to understand the characteristics and core elements that make up computational thinking as well as to develop problem-solving approaches that can be applied in the teaching process for students.

1.2.4 Developing computational thinking

The concept of "development" has many different understandings depending on each aspect. Some concepts can be cited as follows:

According to the Vietnamese dictionary [48], development is “to change or cause change from little to much, narrow to wide, low to high, simple to complex.”

According to philosophy, in materialist dialectics, the concept of development is used to refer to the upward movement of things: from a lower level to a higher level.

Author Nguyen Thanh Kinh [25] proposed the concept of development as "improving the old quality status to a new quality status for those who need to be developed, helping them improve their awareness and operational skills on the basis of existing knowledge and skills, through learning and training".

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