VisualMath: Waves, color, and light optics and digital imaging
Thepaper gives a description of visual math objects in the followingformat:
Itgives a summary regarding the importance of visual math techniques.It further provides the thesis statement, that is, the purpose of theresearch paper.
Thebody of this research paper is organized into subsections as outlinedbelow:
Major point 1: Why the object was created
Itanalyses on the essentials of the visual math objects to the studentsas well as to the instructors.
Major Point II: How does the visual math object idea connect to the topic?
Thepaper gives a brief description of the aspects of the visual mathincluding color, waves, digital imaging as well as optic by relatingthem to the topic at hand. Here, a detailed explanation of theabove-sighted aspects of visual math is highlighted by correlatingthem to features of visual math.
Major Point II: How visual math objects can be used by the rest of class to enhance the understanding of the topic
Thissection outlines ways in which the rest of the learners can make useof the visual objects to boost their knowledge in Mathematics.
Thisis a summary of the research paper regarding visual math objects. Itgives some features of visual math such as graphs and models andtheir importance in enhancing understanding of mathematics. Moreover,it provides recommendations to the tutors regarding on the importanceof incorporating visual math in their teaching mode.
Mathematicsis a subject that permits precise thinking such that when combinedwith creativity, visualization, openness as well as flexibility, itbecomes alive. Math information is demonstrated visually as atechnique of classifying, extending or replacing other modes ofpresentation. Visual demonstrations in Mathematics entail formationof models that represent mathematical information. Visual math allowstutors to create an arena for interactions whereby students utilizesdifferent ways of solving mathematics problems. The paper willelucidate more on visual math regarding the creation of objectstaking into account waves, color, light, optics as well as digitalimaging.
Theobject was created since visual math enables students to thinkvisually which boosts their understanding on various aspects.Students operate with physical manipulative, drawings and alongsideother which assists them to understand on abstract mathematics.Moreover, visual math encourages higher-level of thinking as well asenabling communication. The object is an excellent idea in teachingsince Visual Math enhances learners’ conception and achievement.Consequently, it boosts students’ confidence and self-motivation byenabling them to perceive themselves as successful learners. They arethree critical components that are incorporated into visualmathematics, they include, visual tools, procedures, and teachingmethod.
Developinga visual depiction to solve a problem is a process that entailsprocessing of the information in the problem, selecting the vitalinformation as well as establishing the goal of the problems. Visualdepiction is an essential skill since higher-level math and sciencetopics primarily draw on visualization and spatial analyzing skillsto work out the problems. Moreover, it is an approach that learnerscan utilize when they are developing the best manners to answer anissue in mathematics.
Thecolor is an essential concept while creating objects in visualmathematics as it enables students to understand the concepts aspresented by the instructor. For instance, in algebra, some studentstend to get confused due to increased utilization of symbols.However, usage of color to distinguish between multiplicationsdivision, subtraction as well as addition have worked wonders to manystudents. Additionally, while teaching sequential step mathematicsproblems, outlining each stage in a distinct color makesunderstanding easy. Also, color enhances readability in graphs,equation, and charts. To sum up, adding of colors to numbers orsymbols increases visual richness and hence helps students to executemath problems speedily.
Anotherreason for creating visual mathematics objects is because itintegrates wave’s function which increases understanding. Waves inmath make us appreciate the natural world surrounding us. Forinstance, we can compute the sound and light waves using mathconcepts. It is done by incorporating light and wavelengths in thecomputations. Examples of mathematics functions that integrate wave’sconcepts include the Trigonometric functions that explain wavebehavior. The features utilize XY plane to demonstrate how the sinefunction relates to the wave plotted on a graph.
Digitalimaging entails formation of graphic pictures such as the internalconfiguration of an object as well as a real view. The term is mostlypresumed to involve the processing, storage, compression as well asdemonstration of images. Mathematics is built-in to digital imaging,for instance, modeling, color, and pictures capture the attention ofthe learners. Present developments in Photoshop, as well as Lightroom, depend on mathematics algorithms and exploitation of fastprocessors. Digital imaging is critical in visual mathematics sinceit helps in the creation of digital images such as photographs,printed messages, artwork via the utilization of digital camera andscanning. Every picture is assembled in a particular quantity ofpixels that are then analyzed onto a framework and kept in a seriesby a processor. Each pixel in a picture is associated with full valuethat helps in establishing its color. Additionally, in digitalimaging, the overall assessment of every pixel is then symbolized ina binary code which is referred to as bits. They are interpreted bythe computer to establish the analog exhibit of the picture. Thebit-intensity and pixel metrics of the picture connect to the colorscheckable in the picture and identifies the dimension of the picturefolder on a processor. Those pictures which have just double-pixelshades, that is, white and black are known as dual. Grayscalepictures are frequently shown in an 8-bit method which symbolizedtheir complexion. Additionally, 20-bit technique, which shows actualshades, is typically the optimal presented approach due to monitorrestrictions. The diverse scale of a picture associated with someshades can be involved in the particular model. An extreme dynamicrange introduces the most pronounced shades demonstrated but does nothave to correlate with the quantity of tones that are produced. Apicture may have a wide variety of diverse range, but a smalleramount of tone demonstrated. Similarly, in digital imaging, a picturemay be several tones but not as broad of a different variety.Consequently, it has the effect on the aspects within the film. Theyare various ways of amassing digital images on a computer. Theordinary ones are BMP and GIF.
Visualperception is a multifaceted process that requires relations betweenthe receptors in the human eye that detect the stimulus as well asthe neutral structure and the brain which are tasked for conveyingand deducing the detecting visual information. The procedure includesvarious neutral, physical as well as cognitive experiences whoseunderstanding is critical to structure effective and efficientimaging explanations. Development of advances in computer visions,information engineering, neuroscience as well as video and pictureprocessing improves the potentiality of the traditional imagingtechniques. Hence, digital imaging concerning the methods andapplications expansively envelops the structuring device,accomplishment and applications attribute of visual mathematics.Consequently, it gives the learners a high, elementary appreciativeof the theory and techniques offering a basis on which the solutionsfor most of the challenging mathematics problems can be built.
Opticsencompasses anything that is linked to light or vision it can be thevisible or infrared light that executes a specified function. Forinstance, optical fiber refers to the kind of wire typically made outof glass or plastic that transmits signals. These signals can bededuced by the computer as data, and it is an instance of how datacan be moved over a system network. In visual mathematics,utilization of optical illusions helps in the understanding of somemath tools such as geometric shapes. They thus contribute tocapturing the interests of students due to their interesting aspects.Other students should use optical illusions to understand the rangeof properties and formulae that are relevant to the shape inquestion. Moreover, optical illusions should be utilized by learnersfor them to be aware of the properties of distinct general manners oftricking the perception into believing something that is changed whenin real sense it is not. It is essential when relating themathematics to the real life scenario, for instance, architecture andbuilding work. Constructions of structures such as Parthenon utilizethis knowledge. Optic illusions are as a result of an error in one ofthe visual intellect which occurs when the senses explain the imagebut the mind results to a false assumption. Hence, introducingactivities in the classroom that entail various kinds of visualillusions is intellectually exciting, mathematically inspiring aswell as the thought-provocative for a variety of learners. Studentscould also utilize the optical illusions in the admiration of boththe physical and perceived world as well.
Insummary visual mathematics should be integrated into schools due tothe nature of knowledge required in our current high-tech globe.Previously, math was based on numeric as well as words but currentlyit is primarily based on images that are useful in enhancinglearners’ understanding. Most organizations own significant amountsof data, and they are employing individuals who can help themcomprehend the sense of these data set by use of patterns and models.To connect learners in vital visual thinking, instructors needs tofrequently ask them to analyze the mathematical ideas according totheir understanding. They should demonstrate this in drawing since ithelps in the formulation of ideas as well as invoke understanding.Moreover, students need to portray the ideas in several ways such aspictures, models, graphs, real objects amongst others kinds of visualaids as they assist in capturing the attention of learners.Demonstrating the visual aids and frequently sight assists thestudents to master the skills. Models facilitate the mathematicalthinking thus helping in the understanding of the crucial concepts aswell as mathematical structures.
Visualrepresentations are excellent manners for learners to access generalmath aspects. Drawing a scenario, graphing the lists of informationand putting numbers on a number line assist in bringing a situation,charting the lists of information and putting numbers on a numberline assists in developing the conceptual aspects that invokeunderstanding in students. Adopting this strategy early offers thestudents with tools and manners of thinking that they can utilize asthey progress their studies of more specific concepts. Thus, the bestselection of instructional materials could help to retain thealertness as well as the interests of learners during the classperiod. Integration of visual representations alongside with othermodes generates significant studying improvements for students inmathematics.
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