A person constantly encounters abstract objects. Sometimes they are talked about in a negative way. For example, when it comes to far-reaching plans that are not clear how to implement. But abstraction can have a positive connotation.
Abstract drawing
In psychology, this is a neutral category denoting a mental operation or type of thinking. So, what is abstract, what can this concept mean?
Definition from philosophy
In philosophy, there are two categories that indicate the stages of knowledge of reality: abstract and concrete. The differences between them are easiest to understand intuitively using the example of the relationship between the concepts “man” and “Socrates”. The first is the most general category, devoid of details and details. Socrates is a specific person. Thus, abstract is the most generalized object that cannot be touched.
Abstract objects are a very interesting subject of study for many philosophers because they point out problems with some popular theories. They are interested in the question: if an object is abstract and not present in space, then how do people know about it and even influence their emotions?
Abstract picture
Moreover, philosophy is generally a science of abstractions, because it studies the most general features of the universe. What does “abstract” mean in everyday consciousness? An ordinary person defines this term as something unrealistic and vague.
An abstract concept is a term that cannot be expressed visually directly, only through symbols, actions or a situation. For example, the word “distract” can only be depicted through a drawing that shows one person trying to say something to a colleague working at a computer.
Synonyms for this word, depending on the situation, can be “abstract”, “blurred”, “unrealistic”, “ideal” and so on. Each of these concepts corresponds to a specific context in which abstraction appears.
Concept of abstraction
Abstraction is a mental operation as a result of which a specific object becomes generalized. This is a broad definition. For example, as a result of abstraction, the following chain is created: smartphone - telephone - equipment - electronics. As a result, a concept appears that cannot be touched, seen or otherwise experienced. Electronics does not exist in object form. But this does not prevent a person from understanding the meaning of this word. As a result of abstraction, abstract ideas and expressions appear. These are mental constructs that describe real-life phenomena.
Abstraction is a necessary component of learning
In a narrower sense, it consists in highlighting one or more features against the background of all others. To generalize the concept of “smartphone” to “electronics”, it is necessary to highlight an abstract feature - powered by electricity and make an abstract concept based on it.
Abstraction can also be a method of scientific knowledge. It allows you to form a hypothesis and then confirm it. This operation makes it possible to analyze abstract things. This could be crime in society, economic growth, etc.
What is the power, brother?... The benefits of mastering MM skills
It is obvious that developed mathematical thinking helps a child, a schoolchild, and any person to easily cope with mathematical problems. However, the benefits of mastering thinking skills are much broader.
“I have successfully identified 5,000 ways that are no good. As a result, I’m 5,000 ways closer to the way that will work.” Thomas Edison
A person with developed mathematical thinking:
- I am sure that every problem has a solution;
- is able to decompose the search for a solution into successive stages - tasks and subtasks;
- ready to perceive mistakes not as obstacles and defeat, but as steps on the path to the right decision.
MM promotes successful studies
The habit of breaking down complex problems into simple subtasks, holding and operating a large number of concepts in your head, not being afraid of difficulties, looking for connections and delving into the essence of things helps in mastering any science and subject, not just mathematics. Moreover, people who consider themselves to be humanitarians—who are good at both their native and foreign languages, social studies, and history—already know the basics of mathematical thinking, they simply do not suspect it.
Develops the skill of critical information analysis
Jordan Ellenberg, professor of mathematics
and author of articles in the New York Times, The Washington Post and Wired, in the book “How Not to Make Mistakes” writes:
“...mathematics is not abstract ideas far from real life. Mathematics permeates everything that surrounds us, and allows us to look beyond the disordered and chaotic surface of our world, to see the structures hidden behind it.”
A person who thinks “mathematically” perceives the world around him with a degree of healthy skepticism, is able to distinguish truth from fiction, and does not believe in the “magical” nature of things. In other words, he will not be satisfied with the formulations “it just happened,” “lucky,” “finger of fate,” etc. It is very difficult to deceive a person who thinks mathematically (read: critically and logically) and thereby get into trouble.
Helps make vital decisions
Mathematical thinking habitually puts the solution of problems into “shelves”, into components, stages, possible obstacles and consequences. Confidence that problems can be solved, and mistakes are at least correctable, allows you to confidently take responsibility, avoid doubts and fears, and, at a minimum, formulate a clear plan of action for yourself in any situation.
Jordan Elenberg in the book "How Not to Make Mistakes"
, states that mathematics is “the science of not making mistakes, and mathematical forms and methods have been developed through many centuries of hard work and discussion.”
“Mathematician Thinking” Helps Overcome Procrastination
Procrastination is the sad habit of putting off until tomorrow what was needed yesterday. But not because you’re lazy, but because it’s scary: the problem/task is scary in its size. Often people, classifying themselves as “humanitarians,” justify their fear and inaction in the face of the new, unknown, and incomprehensible. That is, they may even simply, out of habit, give in to solving certain types of life problems.
Reasoning “mathematically”, a person:
- will analyze the upcoming difficulties and, in general, will not even consider the task as “unsolvable”;
- “figure out” what can be done in the current situation based on his own experience;
- determine what questions still need to be clarified for yourself, what to study in order to better navigate the topic;
- will break the solution into stages and set deadlines.
With the described way of thinking, neither a “technician/mathematician” nor a “humanitarian” will look for reasons to postpone solving the problem “until better times.” They simply won’t have a “reason” for this!
Types of abstractions
A man says he misses a woman - what does that mean?
The classification of types of abstraction is based on the purposes of this operation :
- Isolating abstraction. A specific phenomenon is isolated from the general background and studied. For example, there is an orange on the table. A person identifies two characteristics from it: orange color and sweet-sour taste. Such an abstract (this is a construct formed in the process of abstraction) allows us to further compare it, for example, with tangerines.
- A generalizing abstraction is necessary to obtain a general image, for example, to create a theoretical or empirical model of research. An example is mathematical equations that are solved as a whole, without breaking them down into components.
- Idealization is needed to create an ideal picture of the phenomenon being studied to achieve certain research or practical goals.
The purpose of abstraction for performing a certain class of mental operations may vary, but it is always associated with a specific task and its inclusion in the broader context of cognitive activity.
What does it mean to “think like a mathematician”
Mathematics is a broad science, it is not only about complex, obscure formulas, long calculations or equations with three unknowns.
First and foremost, mathematics is the study of “structures, order, and relationships” (Encyclopedia Britannica). Even the most complex mathematical constructions are built on universal logical laws. The fundamental difference between mathematical thinking and everyday, “philistine” thinking is the skill of “digging deeper”, the criticality of perceiving information - not blindly accepting any statements or established patterns on faith. Critical thinking does not mean that a person will be dissatisfied with everything in the world. He will only strive to look for meanings, reasons, to find out the essence of phenomena and concepts. Let's show it with an example.
| Philistine thinking | Mathematical thinking |
| “He invented an operating system for the computer, and now he makes thousands of dollars every second. What a lucky guy!” | “He has been programming since childhood, even spending nights and weekends in the computer class. Then I found a talented and hardworking like-minded person, made hundreds of attempts and wrote hundreds of programs before I came up with a product that sells well.” |
| “She gets straight A’s, just like her parents. What can I say? Heredity!" | “My parents once did well in school, but now they taught her discipline and hard work. Perhaps she is naturally inquisitive. In addition, she is always ready for lessons, so she gets excellent grades. If I put in the effort, I will also become an excellent student.” |
Who is an abstract person
Pyromaniac - what does it mean?
An abstract person is a personality that a person has drawn for himself in his imagination. It may not exist in the real world. For example, when a girl imagines the guy of her dreams, she draws an abstract prince on a white horse. Another option is to idealize someone. If a person falls in love, he experiences these feelings in relation to an abstract image, and not to a real person. That’s why so many people say over time: “He/she has changed so much.” In fact, the person is what he was. It’s just that an abstract character has turned into a concrete one.
Such a person may be the image of an ideal person to be equal to. When people say, “I want to be goal-oriented, rich,” they are painting an abstract image of how they want to see themselves in the future.
What is abstract personal thinking?
Cancerophobia - what does it mean, symptoms
If abstraction is the process of creating abstract mental constructs, then abstract thinking is the ability to operate with them. This allows us to think about categories that do not exist in nature.
Example . A strict teacher criticizes a young man who “possesses too much water” during an exam: “Let’s get to the heart of the matter.” Why does the student use such clever phrases? Its task is to hide gaps in knowledge or even their complete absence. This is the essence of abstract thinking.
Human knowledge about the real world is not complete, comprehensive, or specific. But a person must somehow navigate the unknown, which is why he thinks abstractly. This is a unique ability of humanity, which allowed it to create all the benefits that people still enjoy today.
Abstract thinking is a form of cognition that can overcome dead ends in reasoning. It allows, at least at a general level, to describe various phenomena. Abstract thinking also allows you to see a problem from different angles. It is this human ability that ensured the creation of various religions. God is the generalized goodness and power in almost every culture.
Abstraction - what is it in psychology?
Abstraction is a process of cognition in which abstraction occurs from unimportant properties, parameters, connections of phenomena or objects in order to identify their more important generalizing patterns.
In other words, this is a generalization that can be made over objects or phenomena, processes, abstracting from some of their properties.
The following concepts are associated with abstraction:
- Abstract logic. It reflects a person’s ability to reason, think, construct statements, operating not with specific data, but with concepts.
- Abstract images are images that do not correspond to any real object.
- Abstract conclusions are a thought that was formed on the basis of several judgments about something.
Read about the main principles and ideas of Gestalt psychology here.
Forms of abstract thinking
Abstract thinking manifests itself in several forms: concepts, judgments and inferences. All of them are used comprehensively. Abstract concepts reflect an object or a group of them in one or more essential characteristics.
Concepts are the most important component of thinking
In speech, a concept is expressed in one or more words. For example, “horse”, “tractor” or “research institute employee”, “blast wave”. This is an abstract image that cannot be represented directly in visual, auditory or kinesthetic form, but can be understood. Judgments contain an affirmation or denial of some fact. They are divided into simple and complex.
Example . The sentence: "Karate is amazing" is an example of a simple proposition. It consists of one premise. The complex one is: “The train has left, the platform is empty” contains two interrelated facts. Judgment is always made in narrative form.
Inference is a form of thinking that allows one to draw a conclusion in the form of a new judgment from one or more interrelated premises.
How can you help your children or grandchildren develop mathematical thinking power?
The tips described above are universal, but are intended primarily for adults. If you want to teach your child to think like a mathematician and develop his mathematical and logical thinking, invite him to solve entertaining problems.
Your assistant is LogicLike.
At the very beginning of the “path”
Be sure to work with your child, see how he copes with failures, advise ways to avoid mistakes (read and listen to the problem again, take a break to think, ask for a hint).
Further
Make time in your family schedule for regular activities, praise and encourage your child, support his enthusiasm in every possible way and thereby help him turn this activity into a hobby.
Children learn better in practice, without long and obscure theoretical explanations, but through vivid, playful, interactive examples. By solving educational problems on the LogicLike platform, children acquire mathematical and logical thinking skills, learn not to be afraid of mistakes, build and test hypotheses, look for sequences and think without patterns. Like mathematicians!
Abstract Thinking Tools
Words are the main tool of abstract thinking, so it can only be manifested in speech. In the process of speaking, a person builds concepts into a coherent logical sequence.
Therefore, words simplify thinking. If something is not clear, you can try to tell someone about this problem. During the discussion, the answer will be found. If there are no interested parties, you can talk to yourself. This is even more effective, because reflection does not stop, and you don’t have to be shy.
Example . A man sensibly explains to someone how to solve his problem. But, if he himself finds himself in such a situation, he no longer acts as wisely as he advised. The fact is that he talks through someone else's problem and finds ways to solve it. And when he himself finds himself in difficult life circumstances, his speech flow often takes on a different course: “everything will end badly, I’m screwed,” and so on.
Therefore, instead of solving the problem, a person only makes it worse. In both cases, abstract thinking works. If he tries to talk to himself, he is more likely to come to the right decision.
Thus, abstractness is a concept that expresses the maximum degree of generality.
Learning to think like mathematicians
You can, of course, study volumes of smart books in an attempt to achieve enlightenment and acquire a “mathematical” view of the world. A less intimidating option is to enroll in a suitable online educational course and conscientiously study all the lectures offered. Then complete tests, homework and do not forget to use the knowledge gained.
LogicLike offers 9 simple tips that will help train mathematical thinking in general, and take on solving mathematical, logical and developmental problems without fear.
Accept yourself and your characteristics
It's not about accepting the label "humanities" or even "not given", but about taking into account individual character traits, temperament and ways of overcoming problems. If you usually need time to “think things through,” don’t make it your goal to “figure things out as quickly as possible.”
"Use your imagination"
When faced with an unfamiliar task or solving a complex problem, try to look at it from a slightly detached and new angle.
Choose analogies that make more sense to you
Barbara Oakley gives this example: if you don’t understand the essence of equations, look for poetry in them, because an equation is a mathematical phrase with a coded meaning, just as a poem is a poetic phrase with a philosophical, deep meaning. Thus, Einstein, in an attempt to understand the essence of the photon, imagined himself as a flying photon and tried to guess how other photons related to it.
Develop a Habit of Action
Absorb knowledge in chunks and break complex tasks into several small ones. Start solving problems (even complex and scary ones) right away, right off the bat. Use any time management techniques that work for you. Thus, the “Pomodoro method” helps with procrastination.
Start solving a problem with inner “ease”
Do not try to immediately dig into the granite of science: it is better to “run” mentally and with your eyes over the material, familiarize yourself with it superficially.
Avoid the "installation effect"
Do not allow existing thoughts and ideas, as well as existing ready-made and/or standard solutions, to interfere with the process of solving a new problem and hinder it.
Tune in for dialogue and discussion
Be prepared to argue: fear of conflict and constant “agreement” nullify the creative process of solving a task or problem.
Convince yourself that any problem can be solved
A successful way out of any situation, the ability to solve any problem in most cases depends not on external circumstances or innate genius and abilities, but on one’s own perseverance and hard work.
Practice!
Want to help children develop mathematical thinking? Solve math and logic problems. Do not limit yourself to tasks from the school or university curriculum. Practice your skills with puzzles, logic games, and entertaining tasks.
