Intuitive thinking: Perspectives on intuitive thinking processes in mathematical problem solving through a literature review

Abstract The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical problem-solving is still limited. This research aims to provide a comprehensive overview of intuitive thinking in mathematics learning at the elementary, middle, high school, and college levels through the following questions: What is the role of intuitive thinking in solving mathematical problems? What is the process of intuitive thinking in solving mathematical problems? What steps are taken to improve mathematical problem-solving through intuitive thinking? What are the implications of intuitive thinking for mathematical learning? Additionally, this research reviews the literature related to intuition in mathematical problem-solving. The protocol used in this SLR is PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyzes). The results show that intuitive thinking can help improve mathematical problem-solving for topics such as number, geometry, algebra, functions, and calculus. The process of intuitive thinking is produced by 1students having high levels of confidence, 2justification not always being the same as an intuitive response, and 3students rejecting intuitive answers. This research can provide insights and input for educators, researchers, and education policymakers in developing better mathematics education. Future research can further explore intuition in mathematical problem-solving and develop effective learning models to improve mathematical problem-solving abilities through intuitive thinking.


PUBLIC INTEREST STATEMENT
This research discusses intuitive thinking in solving mathematical problems through a literature review.Intuitive thinking, often regarded as a mysterious and innate ability, plays a significant role in understanding and solving mathematical problems.By examining various studies, this paper highlights the importance of intuitive thinking in enhancing mathematical problemsolving skills.Furthermore, the paper emphasizes the significant role of knowledge and experience in developing intuition for effective mathematical problem-solving.By presenting these insights, the paper aims to engage non-specialist readers by highlighting intriguing aspects of intuitive thinking in mathematics that are relevant to the general public.

Introduction
Intuition is a person's ability to understand something without reason or standard rules (reasoning and intellect; Tieszen, 2015).Because understanding something is the first step in solving mathematical problems (Apriliani et al., 2016), intuition is a useful tool for improving our ability to solve mathematical problems (Wijaya et al., 2021).Recent research shows that intuition can improve problem-solving skills in geometry (Cengiz et al., 2018), and other research suggests that intuitionbased learning is better than conventional learning (Hirza et al., 2014).
Students' intuitive thinking can be used as an approach to learning mathematics that is different from other learning approaches (Sáiz-Manzanares et al., 2021).Two decades ago, in 1996, Debbie A. Shirley and Janice Langan Fox (Shirley & Langan-fox, 1996) conducted a literature review on the importance of intuition, how intuition works, and the role of intuition in the learning process.As a result, intuition in relation to solving mathematical problems develops later in other studies.Students must solve mathematical problems in any mathematical subject (Wuryanie et al., 2020;Yanto et al., 2019).Several other studies have shown that intuitive thinking is widely used in understanding concepts, problem solving, creative thinking, and higher-order thinking in mathematics learning (Puspitasari et al., 2018).However, the conceptual definition of intuitive thinking looks diverse but still has the same concept.Some researchers claim that intuition improves problem-solving skills and creative thinking, while others claim that intuition is part of higherorder thinking (Jiang et al., 2019a) and reveals the level of intuitive thinking, namely that students have an immature intuition level and students at the intuition level (Cengiz et al., 2018).
When learning mathematics is delivered through an analytic approach, namely, an approach that emphasises standard rules and formulas, students tend to respond un-reactively or unenthusiastically and are not motivated to follow their learning (Zaporojets et al., 2021).Another approach that makes students motivated to participate in learning mathematics can be used by linking the basic knowledge that students have previously acquired so that students can automatically grasp the material for learning mathematics (Sugiharto et al., 2019).The basic concept of intuitive thinking is using previous basic knowledge as an understanding that is being studied and then being able to find it on its own (Tieszen, 2015).
Students' intuitive thinking can be used as a different approach to learning mathematics than other learning approaches (Zaporojets et al., 2021).Several studies have shown that intuitive thinking is widely used in understanding concepts, problem solving, creative thinking, and higher-order thinking in mathematics learning (Pétervári et al., 2016).However, the conceptual definition of intuitive thinking looks diverse but still has the same concept.Some researchers, for example, claim that intuition improves problem-solving skills and creative thinking, while others claim that intuitive thinking includes high-level thinking and reveals a level of intuitive thinking; that is, students have immature intuition levels, and students at the intuitive level are mature (Tobias et al., 2017).
In this review, "intuition" is defined as a person's ability to understand something without going through rational reasoning, getting a solution as soon as possible, or suddenly (Lerman & Fischbein, 1988).In mathematics, intuitive thinking is a cognitive process that generates ideas as a strategy for making decisions in problem solving by generating or spontaneous responses (Fischbein, 1999).The current review of intuitive thinking in mathematics education focuses on the relationship between intuition and symbolic mathematics in the areas of arithmetic, geometry, probability, and fuzzy theory.But a little in the context of learning processes that involve intuitive thinking at both the middle school, senior secondary, and tertiary education levels.
To help the process of learning mathematics that involves intuitive thinking both at the elementary, middle, high school, and tertiary levels, the purpose of this study is to provide a comprehensive overview of intuitive thinking in mathematics learning at the elementary, middle, high school, and college levels.In this study, the author wants to find answers to the questions asked to get reviews, What is the role of intuitive thinking in solving mathematical problems?What is the process of intuitive thinking in solving mathematical problems?What steps are taken to improve mathematical problem solving through intuitive thinking?
What are the implications of intuitive thinking for learning mathematics?

The Benefits of intuitional thinking
Intuitive thinking allows students to better understand themselves through expressing thoughts and experiences in solving mathematical problems, which can also improve the quality of their learning in the future (Tajer, 2020).Internally, individual students can explore experiences while believing in the truth value of the solutions obtained, and then issues or ideas emerge spontaneously (Johnson & Steinerberger, 2019).This requires continuous practice and adds insight for students so that they can then find ideas spontaneously, but experience and insight are the main things in thinking intuitively (Hintikka, 2008).Despite many differences of opinion and criticism, intuitive thinking as an approach and design to learning mathematics still provides an important foundation for students to be able to solve mathematical problems, is capable of improving creative thinking skills, and contributes to students' views on a mathematical problem, consciously or unconsciously.
There is a lot of research on intuitive thinking in mathematics learning; some of it addresses the role of intuitive thinking in mathematics learning design through experience and knowledge possessed by students and links it to the learning process in the classroom, assisting students in the process of solving mathematical problems and assisting teachers in identifying the needs of the teaching process in the classroom.For example, K.G.Vozdic and E. Sander revealed that pedagogical content knowledge as a learning strategy for students still involves intuitive conceptions, and between the two there is no significant difference in learning outcomes (Gvozdic & Sander, 2018).According to other research, students with a field-dependent cognitive style use intuition with direct, clear, extrapolation, intrinsic certainty, coercive, and conclusive characteristics, whereas students with a field-independent (FIcognitive style use intuition with direct, selfevident, innate characteristics, intrinsic certainty, coercive, and conclusive characteristics.Various styles of student cognition seem to involve intuition.This intuition provides benefits for increasing students' understanding of mathematics, so learning to use intuitive thinking approaches and designs in the future not only helps with understanding mathematics but also improves higherorder thinking skills (Dreyfus & Eisenberg, 1982).

Student approach to intuitive thinking
Students' approaches to intuitive thinking vary based on characteristics and categories.The characteristics of intuitive thinking in general include: (1"Self-evidence," a cognition process that can be accepted directly without any further proof and can be accepted by itself (Fischbein, 2011), is what is meant by "self-evidence.This characteristic of intuition can be seen in the following example: A straight line connecting two points has the shortest distance between them.Of course this statement can be accepted directly without having to show evidence, and of course the student's reasoning process can accept it directly.(2intrinsic certainty; The certainty of intuitive cognition is usually associated with a certain feeling of intrinsic certainty.The statement about the straight line above is subjective; it feels like it has become a rule.Intrinsic means that no external support is needed to obtain some kind of direct certainty, either formally or empirically.(3Coerciveness: The intuitive has coercive properties in its individual reasoning strategies, hypothesis selection, and solutions.This means that individuals tend to reject alternative interpretations that would contradict their intuition.For example, students usually believe that multiplication makes things bigger and division makes things smaller.This is because we became accustomed to operating with natural numbers in childhood.Later, after learning rational numbers, it was still felt necessary to acquire the same beliefs, which were clearly no longer appropriate.(4Extrapolative Ness: An important characteristic of intuitive cognition is the ability to predict beyond all empirical support.The statement "through a point outside a line, only one and only one line parallel to that line can be drawn" expresses intuition's extrapolation ability.There is no empirical or formal evidence that can support this statement.Nevertheless, it can be accepted intuitively, with certainty, as self-evidence.(5Globality (general).Intuitive thinking is a global thinking activity that is opposite to logical, sequential, and analytical thinking activities.The global nature of intuition shows that people who think intuitively look more at the whole object than its detailed parts (Fischbein, 1971).Furthermore, Fischbein categorises intuition in three ways, namely: (1affirmatory intuition: this category of intuition is a statement, representation, interpretation, or solution that individually can be accepted by itself and can be received directly, self-evidently, globally, and sufficiently intrinsically.For example, a straight line can be formed with at least two points.(2anticipatory intuition: this category of intuition occurs when someone needs a way to solve a problem.Anticipatory intuition is a representation of global views, conjectures, and initial claims in problem solving that usually precedes formal evidence.(3Conclusive intuition: This category of intuition is one's attempt to summarise in general the basic ideas of problem solving that have previously been explored.This shows that intuition is also influenced by one's knowledge when connecting problem-solving patterns (Lerman & Fischbein, 1988).

Research gaps in learning mathematics
There is still no comprehensive review of intuitive thinking in solving mathematical problems at the elementary, middle, high school, or tertiary level, where the era of student-centred learning uses various learning approaches such as problem-based learning, inquiry, and project-based learning (Temitayo Sanusi & Sunday Oyelere, 2020).In the context of student-centered learning, several learning approaches such as problem-based learning, inquiry, and project-based learning are often used to encourage students to be more active and creative in solving problems (Wijaya et al., 2022).However, due to the lack of a comprehensive review of the use of intuitive thinking in this context, it is unclear how these approaches might influence students' abilities to think intuitively.In addition, because intuitive thinking is a cognition process that involves previous experience in spontaneous problem solving (Sahadevan, 2022), it takes time for students to train until the use of intuitive thinking can be used properly; this, of course, depends on the students themselves.

Literature search procedure
The research literature search procedure involves visiting, searching for, and identifying literature that is within the scope of this research review.The search sources are focused on electronic databases, including the Education Resources Information Center (ERIC), Scopus, and ScienceDirect.The databases Sciencedirect, ERIC, and Scopus were chosen as the sources of articles for our research, taking into account several factors.ScienceDirect focuses on scientific journals in various disciplines, including the social sciences, biology, medicine, and engineering.ERIC is a database that focuses on education and related issues.Scopus, on the other hand, is a multidisciplinary database that includes resources from various fields of study.With these considerations in mind, the selection of articles will be facilitated by selecting articles that meet the criteria from these databases.We allotted four months of time, namely from January to April 2022, to search for literature in the three electronic databases.
The research instrument used was a protocol related to inclusion and exclusion criteria, which could be in the form of observation sheets.These criteria are based on the year of publication, education level, and material used.The protocol used in this SLR (systematic literature reviewis PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyzes).The selection process refers to the four stages of PRISMA: identification, screening, eligibility, and inclusion.
The search process uses keywords with boolean structures to get the expected results, namely "intuition" OR "intuitive" OR "intuition thinking" OR "intuitive thinking" OR "intuitive thought."Then the collected literature will be sorted according to the following criteria: (1) Published in a peer-reviewed journal (2) Empirical research (qualitative, quantitative, or mixed methods) (3) A detailed description of the research design, method, data collection, and analysis procedures (4) Clearly articulated results or findings (5) Present sufficient data to support the results or findings.
(6) Concentrate on intuitive thinking in mathematics learning.
(7) written in English If literature is not published in peer-reviewed journals (e.g., books, reports), then we do not choose to include it in the list for analysis.Other forms of literature, namely, literature that is not from qualitative, quantitative, or mixed-type research (e.g., literature reviews), are also neglected and should be analysed.The focus of the literature that we analyse is that it includes discussions on intuition in learning mathematics, uses clear research methods, presents research data clearly, and clearly articulates the findings.
From figure 1, the first step was to obtain search results for the keywords we had determined, which returned 65,785 articles (Details are in Table 1).In the second phase, we did an initial screening of the articles by looking at the suitability of the title, abstract, and keywords in the article, and we identified 39 articles that contained according to keywords (intuition OR intuitive OR intuitive thinking OR intuitive thinking OR intuitive thought OR intuitive thought OR intuitive thought OR intuitive thought OR intuition mathematics education), we will look at the article as a whole.Does the article discuss "intuition in learning mathematics" or not?If not, we will remove it, and we will define 36 articles from this phase.In the fourth phase, we determine 16 articles that fit the criteria.
The research article search flowchart is adapted from Moher's opinion, as shown:

Data analysis
An explanation of the author's process in searching, selecting, and analysing the literature data that has been obtained is as follows: First, the author reads each piece of literature, then sorts and abstracts the characteristics of the literature, which include: (1the year of publication; Second, the writer reads the literature abstract to determine the characteristics of the existing literature in the first step; if these characteristics are not completely found, the writer looks for them by reading the text as a whole.Third, the authors further examine any literature that has been set in accordance with predetermined standards.Fourth, in this fourth step, we summarise the findings in terms of themes and categories to see the use of intuitive discussion in solving mathematical problems and teachers' strategies in carrying out learning mathematics that involve intuition, so that obstacles to solving mathematical problems can be overcome.In this review, the authors confine the scope to 16 selected articles.These articles exclusively address mathematical content, with a special emphasis on aspects of intuitive thinking and problem solving within the domain of mathematics.Finally, to ensure the reliability of reviews of any literature, all authors discussed together and asked for input from colleagues with doctoral degrees regarding the results of the study.

Results
There are 16 articles that can be collected according to the inclusion criteria.Between 2013 and 2021, articles that promote intuitive thinking in the solution of mathematical problems involving a variety of mathematical content or material, such as numbers, functions, probability, geometry, or clumsy or real analysis, will be published.The study reviews articles with research conducted in thirteen countries, including three in the United States, two in China, and one in Portugal.Indonesia, Israel, Italy, Turkey, Iran, Greece, and the United Kingdom; interestingly, one study was conducted in two different countries, namely Senegal and the Netherlands.The majority of the research was conducted on elementary school student subjects (n = 7); only two were conducted on junior high school students, university students, and teachers; one was on mathematicians; a combination of students and students; and one was not identified.In this type of research, qualitative research places the research that is mostly done, namely nine studies: four experimental studies, eight qualitative research studies, two research design studies, one research phenomenological description, and one correlational study.The data collection methods in the reviewed literature show that all of them involve collecting data using test techniques, interviews, or combining the two techniques.
From Table 2, it can be seen that most research methods are carried out through qualitative descriptions; the researchers might want to do a qualitative review of intuitive thinking.The content that is mostly taken as research involves content involving numbers, and the subjects that are most often carried out as research are elementary school students.
The theme chosen for research must be the main discussion in the article and be in accordance with the established criteria.In doing so, the article will meet the set criteria and make a meaningful contribution to research and thinking in the relevant field.In addition, the chosen theme must be of significant importance to the reader and provide useful insights in their research.Topics that are considered important and interesting are often the main focus in scientific publications.The discussion of intuition in the articles we review refers to categories that are relevant to the topics discussed.The categories are introduced as part of the analysis carried out in the article and are used to systematically organize and present the data.In this context, categories are selected based on their suitability and relevance to the topic, so that they can help the reader understand more deeply about the phenomenon under study.By paying attention to the appropriate categories, the discussion of intuition can make a significant contribution to research and thinking in relevant fields.In the articles we discuss, "content" is defined as topics related to mathematics, which are the focus of the research conducted.The selection of this topic is based on the criteria that we have set, including the significance and relevance of the research being conducted.In this context, content topics are considered important to investigate because they can provide new insights into the understanding of mathematics and can contribute to the development of this scientific discipline.
Table 3: The researcher wants to show the relationship between categories, themes, and content.The category in question is part of the research discussion included in the criteria.Themes are ideas from research that fit the criteria.Content is a component of mathematics that becomes information, as well as research content that meets the criteria.

Discussion
Intuition is part of cognition; in the process of thinking, one can do it implicitly (automatically or unconsciouslyor explicitly (controlled or consciously).Thinking that is done automatically or unconsciously is an indicator of thinking that involves intuition.In problem solving, intuition serves as a bridge.Mathematics is formed through problem solving, so intuition plays a role for students in learning mathematics.Tables 2 and 3, from 16 articles, identified the role of intuition: Intuition can improve spatial geometry skills, intuition can improve academic achievement, and intuition can show meaningful mathematical structures.In the articles we reviewed, the research was conducted on elementary school and college students for geometry, probability, and number content.
The role of intuitive thinking in solving mathematical problems has been revealed by researchers through various studies using experimental, correlational, and qualitative methods.The findings of these studies indicate that the process of intuitive thinking can help students understand spatial geometry, numbers, and probability.Intuition also plays a role as a mediator in mathematics education  et al., 2014;Jiang et al., 2019b;Liu et al., 2020) Qualitative descriptive 8 (Patkin & Gazit, 2013a;Furlan et al., 2016a;Vitale et al., 2014;Barahmand, 2019a
During problem solving, intuitive thinking processes emerge.According to Ali Barahmand's research, intuitive thinking processes can be identified through the following indicators: (1A high level of trust In solving problems, students do not use deep thinking but instead use tools (calculators).(2Justification is not always the same as an intuitive response.Students solve problems by making initial guesses (which can happen in a specific order or according to a specific ruleand then checking them.(3Reject intuitive answers.In solving problems, the solutions obtained can be wrong after students reflect on them with other rules or procedures (Barahmand, 2019b).Zagorianakos and Shvarts (2015) research classified student actions as "intuitive behaviour," which includes intentionality, closeness, and feelings in determining certainty (Zagorianakos & Shvarts, 2015).Karen Allen Keene, William Hall, and Alina Duca (2014revealed the results of their research on understanding the limits of number sequences in relation to the concept of limits.Studies show that not all students can bring up axiomatic intuitive thoughts on the concept of limits; students need to first understand the rational function material (Keene et al., 2014b).This shows that intuitive thinking cannot appear properly if you do not have prior knowledge, meaning that knowledge and experience are the most important parts so that intuition can develop properly in solving mathematical problems.
The thought process is an activity carried out by a person in an effort to recall knowledge that has been stored in memory.This is done in response to the information he receives, then he processes the knowledge that appears, and finally he draws a conclusion.There are steps for someone in carrying out the thinking process, including: first, information is received by the brain to be digested or required for solving problems; second, responding to information by recalling knowledge that supports the incoming information; third, managing stored knowledge in an effort to answer information; and fourth, concluding the linkage of knowledge to the information it receives.According to Martin Griffiths' research, students are able to create mathematical structures in solving problems, in this case arithmetic, through intuitive thinking, syntax, or their own experiences in learning in class (Griffiths, 2013b).
Intuitive thinking processes are not much different from thinking processes in general.At the stage of receiving information and thinking that will involve intuition, usually the information is in the form of problems that require complex or difficult solutions to solve; this is what we call cognitive pressure.At the stage of responding to information, it seems to be the same as thinking processes in general, namely, trying to recall one's knowledge and experience that have been stored in memory.One's response to going through the problem-solving process is strongly influenced by one's knowledge and experience, so that determines the process.Consider the knowledge that one possesses.The next stage is known as "thought deadlock," and it occurs as a result of complex problems that cannot be easily resolved, necessitating "deadlock" in order to obtain a solution.When experiencing a thought deadlock, a person usually diverts his thinking process to other things, but still hopes that what is thought can help in obtaining a solution.The next stage, which experts call "aha" or "eureka," appears suddenly and spontaneously in finding a solution.The last stage is the validation stage, where the solution that suddenly appears will be validated so that a valid conclusion is obtained.
Students in the process of solving mathematical problems certainly do not only do it by thinking explicitly, which usually involves standard rules in the process of finding solutions, but may also do more implicit thinking processes, meaning that students do search for solutions that do not involve rules.analytically.This is a consideration for educators in the student learning process: involving intuition as a way of obtaining solutions to mathematical problems.
Researchers have revealed that there are steps that can be taken to enhance mathematical problemsolving through intuitive thinking.One of these steps is the utilization of e-strip activities, which involve students' intuitive thinking and aim to enhance their knowledge and experiences.Used e-strip activities in an effort to develop student intuition, which then influences student learning of subsequent topics (Roh & Lee, 2017b).For students who do not have prior knowledge or do not understand the proof process, an e-strip activity can help them find the concept of limit sequences by reading symbols (Roh, 2010).In quantitative research, the researchers conducted learning experiments that involved intuitive thinking, whose results showed that learning based on intuition had better results than learning using conventional learning.Intuition can also improve problem-solving skills for both students who have low-level thinking levels and those who have high-level thinking levels.high (Hirza et al., 2014).
Like any effort on the part of educators to help students develop thinking processes that involve intuition in solving mathematical problems.We argue that if, in solving maths problems, students are given steps or stages in solving problems, then intuitive thinking will disappear.Because at the moment a person experiences a deadlock, thinking does not occur, an "aha" or "eureka" (a solution that suddenly appearswill not be obtained.It is possible to improve problem-solving skills through intuitive thinking by increasing students' knowledge and experience.
From several articles that were explored in depth, the implications of intuition for learning mathematics can be found as follows: (1) In teaching mathematics, teachers can choose to use intuitive thought processes to understand the concepts of limits, number sequences, functions, derivatives, and integrals (Keene et al., 2014c).
(2) Mathematics teachers must consider that intuition cannot yet be used as valid evidence in mathematical statements or proofs but still requires confirmation through other rules, for example, through definitions, theo-accepts, propositions, and others (Van-Quynh, 2019).
(3) When teaching mathematics, the teacher can use realistic mathematics learning (RML), which can help students improve their intuitive abilities (Hirza et al., 2014).
(4) In materials that involve visuospatial working memory, such as geometry, intuitive thought processes can be involved (Giofrè et al., 2013), so intuitive thinking steps can be applied to this material.
(5) The fuzzy trail theory states that intuitive thinking will bring students to the peak of cognitive development; this indicates that to increase students' levels at the higher level of thinking (HOTS), intuitive thinking steps need to be an option in the learning process, for example, in probability material (Furlan et al., 2016b).
(6) An integrated pattern of teaching mathematics by paying attention to things such as bringing up intuitive concepts, introducing new concepts, and generating students' ideas even though they are different (Vitale et al., 2014).
The researchers seem to be trying to say that they think intuitively in the student learning process, either through learning methods or by sorting and selecting mathematical content that can be taught and understood by students with an intuitive approach.Intuition arises naturally, without awareness, and is influenced by one's knowledge.The level of knowledge of a person who is more mature will affect the development of cognition, so that the determination of teaching patterns and teaching methods, which determine the content of pursuits carried out by educators, will pay attention to the knowledge and experience of their students so that educators will easily assist in bringing out students' intuitive thinking.This is an opportunity for further research: how can we help bring out students' intuition in the process of learning mathematics?

Conclusion
Given the importance of intuitive thinking processes in improving mathematical problem-solving abilities, researchers call for educators to collaborate on intuition in other learning models.However, even though there are still challenges to the findings of other studies that argue that intuition cannot be used as a valid justification, it still requires other ways to confirm its truth, and the fuzzy trail theory that intuition can increase students' higher-order thinking levels needs to be considered.teachers to be able to consider the implementation of the teaching process.The realm of intuition is a consideration for policymakers, educators, and school leaders when determining the level of achievement of learning outcomes.Promoting intuition-based teaching is certainly an intriguing topic, and it may become a future research focus.
According to our findings, intuitive thinking can help with problem-solving skills in a wide range of mathematical content, including geometry, numbers, probability statistics, algebra, and calculus.But there are still differing views about intuition, which cannot be used as a valid proof of justification and still requires other ways to verify its justification.Regarding the important role of intuition in learning, we agree with Martin Griffiths in his research, which revealed that through intuitive thinking syntax or students' experiences in learning in class, meaningful mathematics learning is produced when students are able to create mathematical structures in solving problems (Griffiths, 2013b).The intuitive thinking syntax is needed by the teacher to be a guide in the student learning process in order to reach a higher level of thinking, which is then able to solve problems in content related to mathematics.
Our review found that, in general, teachers need thinking strategies that involve intuition in students' learning processes when solving problems.Intuitive thinking helps students understand mathematical concepts by describing definitions and then finding theorems, or propositions, to serve as the foundation for mathematical proof.The most basic need for teachers is to plan learning steps to help students realise their full potential.
A different view of intuition is that it is used as justification for new concepts, like proofs in mathematics, and not in the learning process.Learners who use intuitive thinking processes may help developing students solve mathematical problems as a bridge to understanding mathematics in general.The development of intuition-based learning models is a new offering that teachers might develop.Zonmes even offers to add one domain to Bloom's taxonomy, namely the realm of intuition, as part of the evaluation of learning as a level of achievement that teachers need to investigate, not only in the cognitive, affective, and psychomotor domains (Sönmez, 2017).
Based on the findings from our review, intuitive thinking processes can bring students to a higher level of cognitive development, improve problem-solving abilities, understand concepts, and involve visuospatial working memory.Intuition cannot be used as valid evidence in mathematical statements, but other ways or rules are still needed to confirm its truth value, so the steps for intuitive thinking need to be arranged in a lesson plan so that the learning process will become clear.Mathematics teachers in particular make efforts to improve problem-solving abilities through intuition-based learning, but they also need support and guidance from education policymakers and school leaders to facilitate this.
Although tremendous effort has been made to develop intuitive thinking in problem solving in mathematics education, much remains to be done to develop it in the classroom.Experts who discuss intuition such as Immanual Kant, Jung, and Fischbein have made the basic definition of intuition in its application to solving mathematical problems, so future research is very important to gain more insight about intuitive thinking, especially in strategies and effective learning models.
Intuitive research seems to be mostly done on elementary school students; this may be because elementary school mathematics content is easy to reach with intuitive reasoning processes.This supports the dual-process theory of multiple thinking processes through intuitive reasoning and analytical reasoning.At the level of junior high school students, high school students, and university students, little research has been conducted.This is probably because their thinking processes have been influenced by analytical reasoning, namely using rules or standard methods that are generally used in solving mathematical problems.