What is Differentiating: Definition and 269 Discussions
Differentiated instruction and assessment, also known as differentiated learning or, in education, simply, differentiation, is a framework or philosophy for effective teaching that involves providing all students within their diverse classroom community of learners a range of different avenues for understanding new information (often in the same classroom) in terms of: acquiring content; processing, constructing, or making sense of ideas; and developing teaching materials and assessment measures so that all students within a classroom can learn effectively, regardless of differences in their ability. Students vary in culture, socioeconomic status, language, gender, motivation, ability/disability, learning styles, personal interests and more, and teachers must be aware of these varieties as they plan in accordance with the curricula. By considering varied learning needs, teachers can develop personalized instruction so that all children in the classroom can learn effectively. Differentiated classrooms have also been described as ones that respond to student variety in readiness levels, interests, and learning profiles. It is a classroom that includes and allows all students to be successful. To do this, a teacher sets different expectations for task completion for students, specifically based upon their individual needs.Differentiated instruction, according to Carol Ann Tomlinson, is the process of "ensuring that what a student learns, how he or she learns it, and how the student demonstrates what he or she has learned is a match for that student's readiness level, interests, and preferred mode of learning." Teachers can differentiate in four ways: 1) through content, 2) process, 3) product, and 4) learning environment based on the individual learner. Differentiation stems from beliefs about differences among learners, how they learn, learning preferences, and individual interests (Algozzine & Anderson, 2007). Therefore, differentiation is an organized, yet flexible way of proactively adjusting teaching and learning methods to accommodate each child's learning needs and preferences to achieve maximum growth as a learner. To understand how students learn and what they know, pre-assessment and ongoing assessment are essential. This provides feedback for both teacher and student, with the ultimate goal of improving student learning. Delivery of instruction in the past often followed a "one size fits all" approach. In contrast, differentiation is individually student centered, with a focus on appropriate instructional and assessment tools that are fair, flexible, challenging, and engage students in the curriculum in meaningful ways.
Planck's radiation law:
I(\lambda)=\frac{2\pi hc^2}{\lambda^5(e^{\frac{hc}{\lambda kT}}-1)}
I'm trying to calculate the peak of a graph, so setting the derivative equal to 0, I've gotten it down to
\frac{\lambda(e^{\frac{\alpha}{\lambda}}-1)}{e^{\frac{\alpha}{\lambda}}}=\frac{\alpha}{5}...
In equation 5.8 in this document
http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf
I am trying to derive this Hamiltonian. I find
H= \pi \dot{\psi} - L = i \psi^\dagger \dot{\psi} - \bar{\psi} ( i \gamma^\mu \partial_\mu - m ) \psi = i \bar{\psi} \gamma^0 \partial_0 \psi - i \bar{\psi}...
Differentiating an equation!
Homework Statement
How do I differentiate this
V(x) = 300x * sqrt(1296-x^2)
The Attempt at a Solution
I tried using the product rule but that didnt work at all
PLease help
Thank you so much!
I'm in real analysis classes but my calculus is shaky when I hit things that aren't plug and chug. How do you evaluate this integral and why can you ignore the dx differential?
The more theoretical details, it smells like some flavor of the Fundamental Theorem of Calculus or Leibniz's Rule...
According to Kant's synthetic a priori what differences would lie between intelligent design AND certain interpretations of physical principles such as, but not limited to, multiple universe ideas? and
Does Kant's reasoning even hold water when comparing the two?
IMO, it does apply and no...
Homework Statement
(2x-10+e)^(y+8)=e^(x-6)
value of dy/dx at the point, (5,-9)
Homework Equations
The Attempt at a Solution
(y+8)ln(2x-10+e)=x-6
y' ln(2x-10+e)+(y+8)(2+e)/(2x-10+e)=1
ln(2*5-10+e)=1
y'+(-9+8)(2+e)/e=1
y'-(2+e)/e=1
y'=1+(2+e)/e
but the answer is (2+e)/e, I don't know where i...
Homework Statement
z = cr^2
Homework Equations
The Attempt at a Solution
I have a pretty simple question. What is the second derivative of the z equation.
I know that z' = 2crr'.
Am I correct to say that z'' = 2cr'^2 or is it something else?
Hopefully my question...
Homework Statement
I need to differentiate uxe^-x in order to do a reduction order question.
Homework Equations
d/dxf(x)g(x) = f(x)g'(x) + g(x)f'(x) <--- that's the product rule about 2 variable
The Attempt at a Solution
I would assume
y' = -uxe^-x + u'xe^-x
I was told...
Hi
So this is pretty basic but how would you differentiate u = (a^2 + b^2 + c^2) please where a, b and c are three separate, independent variables. Please.
would it be (2a+b^2+c^2)+(2b+a^2=c^2)+(2c+a^2+b^2)?
Thanks
Hi so I am new to calculus and need help with differentiation
The question is:
Differentiate the following function:
sqrt(x^2-8x+20)
So far I have gotten
=(x^2-8x+20)^(1/2)
=(1/2)(x^2-8x+20)^(-1/2) * 2x-8
I am unsure where to go from here
I know we are supposed to use the chain...
Homework Statement
integral 0 to infinite (x^3)(e^-8)(cos(5x)) dx
Homework Equations
integral by part?
The Attempt at a Solution
should I use integral by part?
I was reading on a textbook and came across a step and I had no idea how the author got the next step from it. This was basically differentiation of a definite integral.
So here it is.
\frac{\partial}{\partial t}{\int_0^t}{\int_0^1}u_t^2(x,s)dx ds
So I figured that u_t=\frac{\partial...
If you differentiate the formula for the volume of a solid sphere, 4/3 \pir3, you get 4\pir2, the formula for the surface area. This seems to make sense, as, onion-like, the sphere is made up of successive surface areas, so the rate of change will be the surface area for any given r. If you...
Homework Statement
\int_{2}^{y(x)}e^{t^2+1}dt + \int_{x^2+3x}^{0}\frac{e^z}{1+z}=0
I need so find y'(0).
The Attempt at a Solution
\frac{d}{dx}\int_{2}^{y(x)}e^{t^2+1}dt =y'(x) \cdot e^{y(x)^2+1}
\frac{d}{dx}\int_{x^2+3x}^{0}\frac{e^z}{1+z}=-\frac{e^{x^2+3x}}{x^2+3x+1}\cdot...
Homework Statement
For the function y= |x2-4x+3|
a. Sketch the function
b. Is the function continuous? Explain.
c. Is the function differentiable everywhere? explain
d. find gradient of curve at the point where x = 3/2
Homework Equations
chain rule, differentiating...
The...
Hi,
First: Hello, Physics Forums (this is my first post)!
Now to business.
I am trying to enter the Distance Forumula:
m = sqrt([x2-x1] + [x2-x1])
into the Equation Solver on the HP-50g. However, I cannot find a way to subscript variables. Of course, I could just enter,
m= sqrt ([A2-B1] +...
Ok so i was wondering if what i am doing is correct, But it gets the wrong minimum point?
So my function is y=|x+4|
1) y^2=x+4
2)2y(dy/dx)=1
3)dy/dx = 1/2y
4)dy/dx = 1/2|x+4|
I set that 0 and get
0=1/(2(|x+4|))
Am i write in thinking this cannot be solved? or missing something...
okay we know that velocity is in meters per second and that acceleration is in
m/(s^2) , so if I take the derivative of velocity with respect to time i get acceleration .
but just looking at the units , if i start with velocity m/s (ms^-1) this might sound crazy but can i just take...
Homework Statement
Differentiate the following:
y = e4x/x2+1
2. The attempt at a solution
I know you have to use quotient rule here.
so I wrote out (x2+1)* d/dx e4x) - d/dx (x2+1)* e4x all over (x2 + 1) 2
I have no idea how to continue on from here...how would you...
Homework Statement
Find dy/dx, given
y = sin( 3 x ) cos( 6 x )
Homework Equations
product rule= f'g+g'f
The Attempt at a Solution
I used the product rule and got this, but its supposedly wrong, what have i done wrong?((3*cos(x))*(6*cos(x)))+((6*sin(-x))*(3*sin(x)))
1. Differentiate cosh(x) using first principles
2. cosh(x) = (e^x+e^-x)/2
From previous exercises, I know the answer will be sinh(x)= (e^x-e^-x)/2 but I cannot get to the answer.
I seem to be left with the equation: lim h ---> 0 (e^2x*e^2h +1-e^h*2e^x +e^h)/(2h*e^x*e^h)
But when...
Homework Statement
Given: f is integrable on [a,b] and has a jump discontinuity at c in (a,b) (meaning that both one-sided limits exist as x approaches c from the right and from the left but that Lim(x->c-)[f] is not equal to Lim(x->c+)[f]).
Show that F(x) = Integrate[f,{a,x}] is not...
Again, I'm not sure whether this is the best place to post this question but its to do with gauge transformations, etc.
The question itself is rather stupid...
If we have a matrix U(g) (a Lie Group) and a vector φ in C (which is a scalar in spacetime) - does it make sense to use the chain...
Hello,
First of all, I am not trying to "spam" subforums. I found out that my thread shouldn't be posted under homework. Anyways, here it is.
Integration
Let say there's a polynomial, 5x+6 and you want to integrate from 0 to 3 respect to x, how do you input in MATLAB? (I guess you can't...
Homework Statement
we have been doing some error analysis in school, but they were very straight forward for example. centripetal acceleration : Fc = 4pi^2 m R / T^2
however, for my project i must find the uncertainty in the angle that i measured.
the angle is formed by a cardboard...
Homework Statement
we have been doing some error analysis in school, but they were very straight forward for example. Centripetal Acceleration : Fc = 4pi^2 m R / T^2
however, for my project i must find the uncertainty in the angle that i measured.
the angle is formed by a cardboard...
Homework Statement
Don't really know what to do with this one, any help welcome
If A, B and α are constants, independent of x, and
y= Acosαx + Bsinαx
Evaluate the derivates
y'=dy/dx
y^n=d^2y/dx^2
Determine values of A, B and α such that y satisfies
y^n+y=0 and y(0)=0, y'(0)=1...
Homework Statement
Say f(z) = Σ(z^n), with sum from 0 to infinity
Then we can say f'(z) = Σn(z^n-1), with sum from 0 to infinity (i)
= Σn(z^n-1), with sum from 1 to infinity (as the zero-th term is 0)...
Optimization problem -- Trouble differentiating function
Homework Statement
The efficiency of a screw, E, is given by
E=\frac{(\Theta - \mu\Theta^{2})}{\mu + \Theta} , \Theta > 0
where \Theta is the angle of pitch of the thread and \mu is the coefficient of friction of the material, a...
Homework Statement Homework Statement [/b]
Hello. I'm trying to solve a non-linear problem and I have been working through the notes on this pdf to try and understand the method before I use it but I get stuck at one of the steps. The pdf is here:
http://www.nrbook.com/a/bookfpdf/f9-7.pdf
I...
Homework Statement
Consider
I = \int^{1}_{0} \frac{t-1}{ln t}
(No, the problem does not contain a dt at the end of the integral, but I'll assume its a typo)
Think of the t in t-1 as the a=1 limit of t^a. Let I(a) be the corresponding integral. Take the a derivative of both sides...
Hey everyone, I'm new to using the Maxima software and I'm having some trouble. When I enter the following formula to be evaluated:
diff(1-exp^(-t/R*C),t);
I get the following output:
\frac{log\left( exp\right) \,C}{{exp}^{\frac{t\,C}{R}}\,R}
This doesn't look right, even if I...
Hello. I have the following query. Consider a continuous function f(x). We want to know whether this function ever gets zero or not. So we make the assumption that it does. If (e.g) we have f(x)=x^2 + 4x + 2 - cosx
we'll assume that f(x)=0 (=) x^2 + 4x + 2 -cosx =0
now we differentiate with...
a particle moves along the curve xy=10, x=2 and dy/dt=3, what is the value of dx/dt?
i tried product rule and got x*y*dy/dt + y*x*dx/dt = 0 and the answer that i get doesn't appear on the multiple choice answers
a)-5/2 b)-6/5 c) 0 d) 4/5 e) 6/5
i don't know what I am...
Homework Statement
L(t)=15(0.5^(t/26))
Find the rate of L, when t=60
Homework Equations
The Attempt at a Solution
L'(t) = (15/26)(1/2)^(t/26)ln(1/2)
L'(60)=(15/26)(1/2)^(60/26)ln(1/2)
= -0.08
Did I do this right? If I did it wrong, please say where, I am having great...
Hey all, I'm really having a hard time figuring out a couple of problems in which I have to differentiate:
1: \frac{e^3^x}{\ln x}
I just don't know how to put it together... I know that e^3^x is 3e^3^x, and I know that you can't different \ln x, so I don't know what to do from there...
Homework Statement
Differentiate sin x - 1/3 sin^3 (x) + 7
The attempt at a solution
sin x becomes cos x, and 7 becomes 0.
Using the product rule on (1/3) sin^3 (x) + 7 I get:
(0) sin^3 x + (1/3) [derivative of sin^3 (x)]
Getting the derivative of sin^3(x) is the tricky part I'm...
Homework Statement
does anyone know how i can differentiate a strong acid from a weak acid and likewise for a strong base and a weak base based on its chemical formula?
Homework Equations
The Attempt at a Solution
Homework Statement
Hi all.
I have a time-dependent variable called x. I wish to differentiate x2 with respect to the time t, and this is what I have done:
\frac{d}{dt}x^2 = \frac{d}{dx}x^2\frac{dx}{dt} = \frac{d}{dx}x^2\dot x.
where the dot over x denotes differentiation with...
Homework Statement
\int\sqrt{49-4x^2}
I have done the integration to the best of my ability. My teacher requires that I differentiate the answer to get back to the original integrand. Can someone please check my work and help me along with the differentiation?
Homework Equations
U...
Why does the derivative of (sin(x* theta))/(2x-1) equal [(-2sin(x*theta))/(2x-1)^2]?
I'm an undergraduate physics student with a shaky math background, who's enrolled in an advanced Physics math class for which I lack prerequisites. I'm working an infinite series where the general term comes...
Homework Statement
d/dx (\int^{x}_{0} x2t2dt)
So the problem is to solve the derivative of the integral \int x2t2dt from 0 to x.
Homework Equations
d/dx (\int^{x}_{a} f(t)dt) = f(x)
The Attempt at a Solution
I'm really unsure of how this should be computed but this was my guess...
Homework Statement
Differentiate the identity sin2x = 2sinxcosx to develop the identity for cos2x, in terms on sin x and cos x
Homework Equations
The Attempt at a Solution
Im not sure where to start with this one. Should I find the derivative of both sides of the equation, and...
Hey guys,
I've just recently started calculus, and just trying to get to grips with it.
I'll use an example for my question; if y=e^x, then the source suggests rearranging to \ln y=x, the differentiating with respect to x yields \frac{\delta}{\delta{x}} (ln\ y)=1.
I understand that for my...
How would I go about finding the derivative of x2 + y2 = 36.
I know it is a circle with radius 6. Is there a better way to find the derivative then:
y2 = 36 - x2
y = (36 - x2)1/2
y = 1/2(36 - x2)-1/2(-2x)
y' = -x/(36-x2)1/2
Struggling with these two questions, any ideas?
A
Homework Statement
Differentiate with respect to x
sin-1 2x - 4 cos-1\frac{x}{2}
Homework Equations
The equations I have in my notes are identical to those derived here...
Homework Statement
I'm having trouble factoring this to its simplest term. I'm not very good at factoring, but I'm working on it. I was hoping that someone might be able to help me here.
Homework Equations
Find the critical points for f(t) = t * sqrt(4 -(t^2)) on the closed interval [1...