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Differentiated Instruction or Literacy across Content Areas
Differentiated Instruction/Literacy across Content Areas
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Differentiated Instruction/Literacy across Content Areas
Differentiated instruction learning also known as diverse learning refers to a learning program where the instructors ensure the lessons are structured to meet the needs of all students. To achieve this system instructors are required to adjust concepts, amount of work, period of learning, instructional strategies and besides product demonstrated learning. This is because students are different and so is their level and speed of understanding. Therefore, to be able to achieve good results in learning, instructors should take time to understand their students and this should be practiced by all instructors and in all subject areas (Levine, 2002)..
Differentiated learning can be incorporated in different ways in the classroom and the teacher is left with the responsibility of identifying the most applicable ways to teach the entire group of students. The system requires the teacher to incorporate both individual mode of instruction and group based instruction, thus ensuring all students’ needs are meet. The system also requires continuous assessment so that the learning process does not yield work quantity but quality. Multiple approaches are incorporate in learning to accommodate different intelligences that are all student centered. Student in this model will be required to actively participate since lessons are in most cases interesting, active and relevant to them. In that light, differentiated learning method can be incorporated in any learning discipline since it’s expected to be organized and planned.
Planning a learning lesson requires an instructor to take an adaptive approach that will incorporate the needs of all students. Students’ learning preferences differ; some prefer hands on approach (tactile), more active approach (kinaesthetic) or visual approach which requires use of maps and charts. Whichever approach a child prefers a classroom lesson should be able to incorporate all these needs in learning. Literacy across content or differentiation is the best model to incorporate these needs because it embraces the main stages of learning; brain based learning, pre- assessment, ongoing assessment, content and process. This learning system is currently facing severe criticisms on the grounds that it is chaotic since it’s not pre-structured, only applicable to individualized instructions and call for more work for students it still has several benefits (Gardner, 1983).
Strengths of differentiated learning are noted in different curriculums since it addresses individual needs of students and adjusts to them. The system is structured through analyzing and understanding the skills and experience level a specific classroom, thus providing students with an opportunity to dictate how they will participate in a learning lesson. Students are more excited and interested feel the need to participate in a classroom if the learning process is structured to meet their desired topics. For instance, including outside classroom activities in learning enhances meaning to what the students learn in class. When students take ownership of the learning process they incorporate essential elements in learning such as interaction. They further find the desire to improve learning styles by accessing additional information over the internet and demonstrate what they learn in class.
Application of literacy or differentiated approach in learning can be used in any subject; be it science, literature, art or mathematics. It can be applied in different stages of learning, for example teachers can incorporate it when laying down curriculum, developing models, making writing activities and in student evaluation. During application the system dictates whether learning in a specific classroom should be learner responsive or teacher facilitated, however, all these structures are dictated by student desires. Bottom line, differentiated instruction approach proves that students even those in a diverse classroom can succeed using their own individualized approach (Levine, 2002).
References
Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. New York: BasicBooks
Levine, Mel (2002). A Mind at a Time. New York: Simon & Schuster.
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Hamlet and Fortinbras
Hamlet
Name
Institution
Question1: Hamlet and Fortinbras
One similarity between Hamlet and Fortinbras as sons is that they have both lost their fathers through murder. Hamlet is the prince of Denmark, while Fortinbras is the prince of Norway. The two had difficulty in ascending to the throne that they were the rightful heirs. Hamlet is a thoughtful and mercurial individual, whereas Fortinbras is an all action kind of man. Fortinbras fights for what he believes in whereas Hamlet does not. In act IV, scene IV, line 18, Fortinbras leads a pack of army to fight for a plot of land that they claim to own, Hamlet, on the other hand, is afraid avenging his father’s death.
Question2: Ophelia and her songs
There is a sense in Ophelia’s sudden madness. She is emotionally distraught by the event of things. In act IV, scene v, lines 23-26, Ophelia expresses her disappointment in her lovers action. She laments that it is difficult to know if one is truly in love. She explains how Hamlet took her virginity, and later left her. In line 29 of the same scene, she mourns the death of her father. She further proclaims that her father was innocent as evidenced in line 35 where she refers to him as a white shroud.
Question3: Hamlet’s attitude towards death
Hamlet’s mindset towards death changes after an encounter with the captain. In Act IV, scene IV, lines 25-28, he wonders why the army was risking their lives in a battle, for an unworthy cause. He refers to a piece of land as: “a straw that twenty thousand men could not discuss but risk dying.” According to him, death was “an affair that was inevitable at any cost.” He further supports this comment in line 62 of the same act and scene when he says that the army was going to their graves like beds, to fight for a plot.
Based on the foregoing, Hamlet says in line 66 of act IV, scene IV, that his thoughts henceforth will be bloody and nothing else. From his speech, he, therefore, strives to be violent in the remainder of the play. He hopes to revenge on Claudius, who murdered his father.
Differential Calculus
Differential Calculus
Name
Institution
Tutor
Date
Differentiation is about determining the rate of change of a certain quantity compared to another one. Differentiation is useful when the rate of change is unvarying. Economists and business analysts use it to select rational course of action, forecast the effects of diverse business policies and to describe what is happening in the business world. They also use it to find optimal solutions. For example to minimize the costs of production, or to minimize the amount of material used in packaging. Other than in business world, calculus is applied in the analysis of crash data and it is also used in motor industry to improve the safety of motor vehicles. Also, differential calculus is significant in civil engineering. Engineers in designing dams, they do this by first determining the force of water from the surface area of the reservoirs. And to assess the suspension system of dump trucks (trucks are used to clear unused material from the construction sites) (Lebedev, 2012).
One significant application of derivatives is optimization. That is finding the situation in which a minimum or maximum will occur. Optimisation is important in engineering (minimum cost, maximum strength) and business (profit increase, cost reduction).
In using mathematical functions to model the things that happen in the physical world, the physical quantity under study if often referred to as the variable. An engineer is only interested in the turning point of a function, minimum and maximum values, and its ups and downs. They then draw the graph of the function using either a computer or graphical calculator. However, to locate the exact position of the points, differential calculus is used.
Differentiation is used to find the displacement of dumper trucks as well as its displacement. It is always recommended that the suspension systems of the dump trucks are assessed especially when large masses of waste material are loaded on it from a high point. This is because the truck bed undergoes velocity, displacement as well as acceleration.
To model this velocity, displacement and acceleration, a mathematical function is used. The function is used to get the acceleration and maximum displacement of the truck at a certain point.
This is the equation: Y=0.26066E-εωt sin (ωdt)
Where; ε is about 5 radians per second, Ω is about 0.18 and Ω is about 4.85 radians per second
To get the maximum displacement of the dumper truck; we first get the derivative of y with respect to time t.
That is QUOTE = QUOTE .v + QUOTE .u
And to get the first derivative, that is QUOTE , product rule is used. In product rule, the first function in the equation is multiplied by the derivative of the second function plus twice the derivative of the first function (Narayan 2005).
For example, given the function g(x) = f(x). H(x)
The first derivative g’(x) = f(x). h’(x) + h’(x). f’(x).
U= 0.26066 e-εωt
QUOTE = -εωt 0.26066e-εωt
v=sin (wdt)
QUOTE = wd cos (wdt)
To get the minimum or maximum velocity (v)
QUOTE = 0.261 e-εωt [-εωsin (wdt) +ωd cos (ωdt)] =0
Which implies that ωd cos (ωdt) – -εωsin (ωdt)
Therefore, εωsin (ωdt) = ωd cos (ωdt)
Εωtsn (ωdt) =ωd
Thus 0.9 tan (4.85t) = 4.85
Thus t= 0.3 seconds
Therefore when time t is 0.3 second, the displacement is approximately 0.2 meters. This is obtained by substituting time t with 0.3 seconds.
Acceleration of the track is determined by getting the second derivative of the equation.
From equation one, QUOTE = v= 0.27e-εωt [ωd cos (wdt) –εωsin (ωdt)]
Therefore acceleration a = QUOTE = QUOTE .v = QUOTE .u
Thus u= 0.27e-εωt
QUOTE =-εω0.3e-εωt
V=-εωsin (ωdt) +ωd cos (ωdt)
QUOTE =-ω2dsin(ωdt) -εωωd cos (ωdt)
Thus QUOTE = -εω 0.27e-εωt (-εωsin (ωdt) + ωd cos (ωdt)) + 0.27e-εωt (-εωωd cos (ωdt) – ω2d sin (ωdt))
0.27e-εωt [ε2ω2 sin (ωdt) -εωωd cos (ωdt) –εωωd cos (ωdt) – ω2d sin (ωdt)]
0.27 e-εωt [ε2ω2sin (ωdt) –εωωd cos (ωdt) –εωωd cos (ωdt) – ω2d sin (ωdt)]
0.27 e-εωt [(ε2ω2 – ω2d) sin (ωdt) – 2εωωd cos (ωdt)]
0.27 e -0.88t [ – 22.7 sin ( 4.9 t) – 8.5 cos(4.9t)
Since t=0.3, QUOTE = -4.9 metres per square second.
Thus after the maximum displacement at 0.3 seconds, the acceleration of the dump truck is about 5 meters per square second downwards.
For trigonometric functions; cos bx differentiates to –bsin bx and Sin bx differentiates to bcos bx.
Differentiation is used to get the stationary points namely minimum, maximum and the point of inflection. That is when the first derivative is equal to zero. The second derivative is used to classify the stationary points (Narayan 2005).
In graphical analysis, the derivative gives information on the slope or the gradient of a graph of a given function. Additionally, the point where the gradient is zero in a graph can be located using differentiation. This is done by first determining the points where the vertical axis crosses the horizontal axis. Also, find out what happens when x tends to infinity on both sides (Ayres 2000).
References
Ayres, F., Hademenos, G. J., Ayres, F., & Mendelson, E. (2000). Calculus: Based on Schaum’s
outline of differential and integral calculus. New York: McGraw-Hill.
Lebedev, L. P., Cloud, M. J., & Eremeyev, V. A. (2012). Advanced engineering analysis: The
calculus of variations and functional analysis with applications in mechanics. Singapore: World Scientific Pub. Co.
Narayan, S. (2005). Differential calculus. S.l.: Dk Agencies Ltd.