In the contemporary schooling, a range of learning methods has been inevitable. The idea behind every method is to facilitate an easy comprehension of ideas behind a concept. Several learners have experienced conflict of learning styles, where their learning preferences fail to align those of their instructors. This resulting frustration causes a communication breakdown, a situation which hinders progress in teaching and learning in the classroom (Department of Education, 2000). Individuals are, therefore, encouraged to establish their natural learning preferences so as to expand their manner of learning as this would enable them to learn through other methods in addition to their preferred style. By appreciating a variety of learning styles, an individual finds it easy to fit in an environment where learners with multiple styles are accommodated (Pratt-Adams et al, 2010).
Once an individual learner understands where his preferences lie, he/she begins to accommodate other preferences as they seek to develop a balanced approach to education. In this regard, an individual is able to perceive the world through a variety of ways, a situation which improves the effectiveness of learning. It is important to balance as the learner avoids over-emphasizing on a single dimension of learning.
A single dimension of learning limits the ability to accommodate new information and, consequently, the ability to make sense of that information in a quick, accurate, and effective manner. For instance, if a student over-relies on sensing, he/she tends to opt for what is familiar. They, therefore, concentrate on the facts that he or she knows instead of getting innovative and adaptive to new situations. His/her learning focuses on seeking opportunities to acquire theoretical information before availing facts to negate or support the hypotheses in question. On the other hand, over-reliance on intuition presents the risk of missing vital details, and this may reduce the capacity to make decisions. A student should, therefore, be taught how to memorize data as well as to learn facts that enable him/her to criticize or defend a procedure or theory. This would facilitate the evaluation of some of the details which make learning effective (Mason & Stacey, 1982).
Intuition is defined as the ability to learn without inference, i.e., without the application of the reasoning capacity. This ability provides an individual with beliefs that may not be justifiable. As such, psychologists have been prompted to engage in the study of intuition as they seek to uncover those aspects of a human mind which do not exist in a manner that is definable in accordance with natural laws. A significant number of these studies have indicated that intuition is closely associated with scientific discoveries as well as other types of discoveries. In fact, the subject has been dominant in a section of psychological papers that deals with cognitive processes of acquiring knowledge and skills (Mason & Stacey, 1982).
According to Carl Jung, intuition is an irrational function that is presumed to be in direct opposition to rational function. Jung argues that intuition is a form of perception which occurs in a manner that avails ideas, possibilities, and resolutions unconsciously. Studies have revealed that ‘intuitive type’ individuals are those who act on the basis of the intensity of perception and not on rational judgement (Nunes & Bryant, 1996). For instance, various studies have revealed that most mathematicians possess an intuition for the science or a group of closely related sciences that deal with the logic behind shapes and arrangements. Such an intuition enables them to possess a quick recognition of the instances when results fit in a reasonable framework of a specified theory.
Philosophically, intuition has been regarded as a form of cognition or knowledge, which is independent, or reason and experience. The intuitive knowledge as well as the intuitive faculty itself is presumed to be of inherent qualities in the minds of human beings. The term intuition, however, has been applied in reference to different senses. While some philosophers regard intuition to be a mathematical idea, which is self-evident, there are those who presume it to be the truth that exceeds the intellectual capacity of the mind (Nunes & Bryant, 1996).
Intuition was an important aspect in the Greek philosophy. For instance, mathematicians like Pythagoras and his college found the concept to be of a great significance as it could prompt learners to make discoveries in a manner that was seemingly boundless by preconceptions. Intuition was also important to such philosophers and scientists as Henri Bergson, Immanuel Kant, and Baruch Spinoza. Spinoza regarded intuition as a form of knowledge that surpasses both scientific and empirical cognitions as it cannot be derived from senses or experience-based reasoning. In fact, his argument was that intuition would enable an individual to comprehend the orderliness and unity in the universe and, therefore, permit a human mind to become a part of an infinite being.
At times, a real life testing of the results that have been recognized through intuition indicate shortcomings in the manner where people conceive mathematical concepts. This is due to the way in which an over-simplification of a notion disguises some of the underlying principles. In this regard, intuition tends to produce a set of results that are formulated elementarily, and this is of little significance as far as the science of mathematics is concerned. Nevertheless, it can result in a profound definition of some real world situations and as such, be a significant advancement of the scientific concepts behind mathematics. This review of literature examines some of the elementary concepts behind this phenomenon in a manner that explicates how math students can test their capacity to intuit. Moreover, the review evaluates the manner in which pocket size devices like iPads can be utilized as a teaching tool (Selden & Selden, 2005).
Intuition in Mathematical Philosophy
Mathematics is a series of intuitions that have been carefully organized and sifted over hundreds of years. Philosophers of math have been engaging in debates with the aim of resolving difficulties and paradoxes that emerge in the midst of their intuitive convictions. They, however, tend to lay emphasis on the domain of possibility, and unlike learning through senses, intuitive learning avails considerable possibilities, ideas, as well as potential outcomes. Unlike sensory learning, where learners are interested in the contemporary circumstances, intuitive mode of learning incorporates imagining the future, abstract thinking, as well as day dreaming. Statistics indicates that around 35 percent of math students are intuitive learners (Olvera, 2006).
Intuitive learners have unique characteristics that differentiate them from those who utilize other styles of learning. For instance, they appear to favor working in short sessions instead of accomplishing a task on a single occasion. They also enjoy exploiting unprecedented situations, experiences, and challenges. Nevertheless, they have a liking for abstract ideas and theories, although they prefer working with a general idea instead of narrowing it down into details (Silverthorn, 1999). In fact, according to Myers, intuitive learning is presumably a holistic style of learning where students begin with an overview and theories before proceeding to the search for possibilities and links. Myers argues that these learners have an enhanced capacity to grasp concepts, a situation which empowers them to deal with various imaginative possibilities (Silverthorn, 1999).
Unlike in sensory learning, intuitive learning enables students to proceed from theory to practice as they focus on the characteristics of data, ideas, as well as the interrelationship between such ideas. They seek to comprehend the construction of ideas as well as how and why situations happen to exist as they do. Intuitive learners are enthusiastic about experimentation and, in this regard, they manage to deduce relationships amongst pieces of information. They find it easy to work with symbols as they accord them a heightened degree of liberty. Moreover, working with symbols quickens insight as well as the perception of relationships, and as such, students are able to comprehend most of general concepts, a scenario which makes them be imaginative (Tall & Harel, 1991).
Intuitive learners are driven into reading as this enables them to discover concepts instead of waiting for their teachers to avail them systematically. The utility of the teachers’ professionalism becomes apparent as they provide their students with open-ended instructions.
Need and Relevance
Studies have revealed that mathematics and other types of scientific knowledge are an important boost to the quality of life. With the emergence of knowledge-based societies, teachers have been called upon to nature their students’ understanding on the basis of the habits that facilitate competent functioning in a modern society. These calls have been prompted by the reports that despite being a central subject, students find math to be difficult, even after a host of teaching methods have been devised. Over the last few decades, educators and psychologists have sought to evaluate the causes of these challenges in their endeavor to devise ways of promoting human thinking (Orey & Branch, 2011).
Intuitive knowledge has been identified as a vital element in any scientific reasoning. This is because of the manner in which human responses to scientific tasks relate to features that are, otherwise, considered to be irrelevant as well as a host of varied ideas and concepts. Therefore, describing a certain task facilitates the prediction of the style in which the subjects will respond, especially on the basis of specific and external features that indicate a relation to a finite number of intuitive principles (Orey & Branch, 2011).
The theory behind innate knowledge dates back to the time of Plato. According to the University of Missouri News Bureau, all children possess an intuitive knowledge of the science of matter, energy, as well as their interaction. They also possess an innate knowledge of the idea behind relativity as well as the blueprint for the laws of motion as they were laid down by Newton. In fact, this knowledge appears to be more complex than the previous perception of researchers. Nonetheless, there has always been a perception that infants possess some expectations regarding some of the objects in their surroundings, and this knowledge has been perceived as a skill that that has never been taught. As children develop, the intuitive knowledge is refined, and it eventually results in some of the abilities that adults utilize (Mezirow, 1997) .
After reviewing scientific literature, vanMarle established that two month-olds demonstrate an intuitive comprehension of the force of gravity as they anticipate in the fall of unsupported objects. As they grow older, it becomes clear that they expect non-cohesive matters such as water and sand to lack the characteristics of solids. vanMarle argues that intuitive science and mathematics include those skills that individuals utilize on a daily basis. In fact, such skills are the ones that facilitate individuals’ daily interactions with their surroundings (Sterrett, 1992). In the same regard, children are perceived to possess the ability to anticipate and predict some of the behaviors of substances and objects with which they interact.
Exploiting intuitive knowledge in the appropriate manner enables the student to improve his/her learning capacity to a level which would enable one to become an independent learner/researcher. As much as the teachers attempt to devise the best teaching method, an effective skill development would only be possible if parents could encourage their children to interact and play with objects upon their arrival from school. Learning is a cooperative process, and a combined effort between teachers, parents, and other stakeholders is the best way to assure success in education. Studies have indicated that parents are the most effective players in facilitating natural interactions with their children (Sterrett, 1992).
Effective Intuitive Learning
Teachers have always been interested in finding the methods of learning that would improve knowledge acquisition amongst students. This is because the time that students have for learning new ideas is limited, and it is necessary for them to acquire the most within the shortest time possible. Nevertheless, transfer, recall, and retention are also important for the learning to be effective. In this regard, students should be in a position to accurately recall much of the information they learn. Effective recalling would enable them utilize such knowledge in a variety of situations (Stultz, 2008).
Memory Improvement Basics
Some of the best methods of facilitating memory improvement include the improvement of focus, avoidance of cram sessions, as well as the structuring of the study time in a manner that improves efficiency in learning (Stultz, 2008).
Keep Learning and Practicing New Things
Improving effectiveness in learning necessitates retaining the simplicity in studies. While learning new concepts, students should be encouraged to keep practicing so as to maintain most of the gains that have been achieved. Inadequate practicing results in a loss of some concepts in the brain process, which is commonly referred to as ‘pruning’. Pruning maintains certain pathways while eliminating the others, and the retention of new information can only be achieved through constant rehearsals and practicing (Tsang, 2010).