Tag: Mathematics Evolution

Experiential Learning: An Effective Teaching Strategy for Mathematics

Mathematics is undeniably a hard subject. Even the great minds of the past such as Albert Einstein know for a fact that there are difficulties in learning the matter. No wonder Math teachers experience difficulties in the way they teach students. The lecture approach where teachers let students memorize mathematical facts has long been gone. Today, teachers are called on to teach new and effective teaching methods to develop not only mastery, but comprehension as well.

Mathematics requires experiential learning where students are involved in their own understanding of mathematical concepts and practices. Through this type of learning, students are able to identify problems, use constructive reasoning to make viable arguments, and applying mathematics in real-life problems.

On improving mathematical concepts, a recent study explained that problem solving in mathematics is not a natural talent, but learned. The teacher’s role is to guide students through practice, provide both routine and non-routine problems, and help them develop their own strategies in solving those problems. In addition, the study highlights the importance of including the students in developing skills in problem solving and sharing them through argumentative discussions.

Traditionally, math textbooks often just provide fixed examples without providing rich experiences in problem solving. Teachers too often review the answers immediately without explaining what strategies students use to solve the problems or if the solutions can be explained by the students themselves.

For teachers to build their students’ mathematical problem solving strategies, they need to provide instruction that explores new concepts through scaffolding. Scaffolding includes asking guide questions that lead to answers rather than supplying them immediately.

In regards to experiential learning at the high school level, teachers need to focus on reasoning and acquire a sense of using mathematics on their daily lives. This is because U.S. high school students have the inability to apply math to solve problems in a variety of situations. This trends needs to be improved through experiential learning.

Mathematics History

In the history of mathematics, there is no lack of debate over the credibility of statistical justifications. Berkeley’s prolonged review of the techniques of the calculus in The Analyst (1734) is one example. Another is the “vibrating string controversy” among Leonhard Euler, Jean d’Alembert, and Daniel Bernoulli, hinging on whether an “arbitrary” continuous function on a real interval could be represented by a trigonometric sequence. Carl Friedrich Gauss is usually acknowledged with offering the first appropriate evidence of the essential theorem of geometry, saying that every non-constant polynomial over the complicated figures has a root, in his doctorate thesis of 1799; but the history of that theorem is especially knotty, since it was not originally obvious what techniques could properly be used to set up the existence of the roots in question. In the same way, when Gauss provided his evidence of the law of quadratic reciprocity in his Disquitiones Arithmeticae (1801), he started with the statement that Legendre’s claimed evidence a few years before contained a serious gap.

Mathematicians have always been reflectively aware of their techniques, and, as evidence increased more complicated in the Nineteenth century, specialized mathematicians became more precise in focusing the part of rigor. This is obvious in, for example, Carl Jacobi’s compliment of Johann Chris Gustav Lejune Dirichlet: “Dirichlet alone, not I, nor Cauchy, nor Gauss knows what a completely extensive statistical evidence is. Rather we understand it first from him. When Gauss says that he has shown something, it is very clear; when Cauchy says it, one can bet as much pro as con; when Dirichlet says it, it is certain…” (quoted by Schubring21).

Mathematics has, at crucial junctures, designed in more speculative methods. But these times are usually followed by corresponding times of retrenchment, examining fundamentals and progressively implementing a tight deductive design, either to take care of obvious issues or just to make the content simpler to educate convincingly.

The Beauty of Mathematics

As a ‘language of natural sciences’ ever since antiquity, mathematics has always been a main device for describing and knowing the world. It has assisted to examine the framework of the galaxy. Information acquired through mathematics has not only led to improvement in organic sciences, but to following significant cultural-historical success that have modified everyday life. Merchants, for example, required statistical knowledge for keeping track of and calculating, but it was also essential for calculating time, which progressively started to regulate individuals’ life throughout the season, or for cartography, the art of creating charts of the world and skies, which established the foundation for the conquer of our world.

Mathematics was an allegory for the procedure of purchase that led from chaos to order, which was considered as the essential idea of the source around the globe. “Cosmos” in Greek also indicates “order” and represents the feeling of balance. For Pythagoras, the balance around the globe was based on the fact that everything within it is controlled by statistical percentage. The standard idea of excellence had resided on in Christian thought for a long period. In the Age of Enlightenment, it was again taken up by the Freemasons, with God showing as Creator of the Universe, having the compasses as a indication of His sublime omnipotence.

Mathematics was also an essential source of motivation and one of the essential concepts of official reasoning and rational appearance for art and framework in the last millennium. It provided concepts for the methodical research of components and procedures, both intellectually and materially in art types such as constructivism, concrete art, minimalism, op art and kinetic art. What they all have in common is a clearly described procedure of improvement and the convenience and complete visibility of their means; the stunning aesthetic of primary forms; for example, provides generally recognized visible primary terminology for learning the advanced and intelligent concepts of formal phenomena. The use of methods, in turn, decouples the advance result from the artist’s personal trademark, thus satisfying the responsibility to deconstruct and objectify the procedure of highbrow advanced development and to make it understandable for everyone without exemption.

Mathematics is Fun

We are all conscious of the inadequate condition of our mathematics education and studying to accomplish a sufficient level of grades in math in our primary education and studying program and the effects that this has on our community, e.g. not enough engineers, who need an advanced stage of mathematics, are being qualified. There are many factors for this circumstance.

While we know that there are many factors for this, it is crucial that we need to instill interest and passion for mathematics among all the stakeholders engaged with education and studying, such as the parents. This could be a massive process, but it is one that must be performed.

Mathematics is one of the only places of information that can logically be described as “true,” because its theorems are a result of genuine reasoning. Compared with, say chemistry and physics, where there can be discussion or debate about trial outcomes or concepts, mathematics always symbolizes the truth: 7+5 will always equal 12, it cannot be anything else. Albert Einstein is quoted as saying:  “Pure mathematics is, in its way, the poems of sensible concepts.”  To some specialized mathematicians, “math is like love, a simple concept, but it can get complex.”  The biggest time in the life of a math wizard is when after he has shown the result, but before he discovers the error. This does not matter; the excitements of getting the outcomes exceeds the frustration of discovering the error and, in any situation, spurs him on to recalculate and again experience the high of a new outcome. Charles Darwin, however, had a rather depressing perspective of mathematics: “: “A math wizard is a sightless man in a black space looking for a black cat which isn’t there.”