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.
when differentiating
e^(at) * (cos(bt) + isin(bt))
are you able to use product rule to find the derivative considering (cos(bt) + sin(bt)) as one function??
why??
and what does d/dt exactly mean?? (they get multiplied to a function that needs to be differentiated and I wanted to...
Here's what I have so far:
std::string CalculusWizard::derivative(std::string& fx, const char & x, unsigned & n = 1)
{
if (n == 0)
{
return fx;
}
else if (n > 1)
{
while (n-- > 1)
fx = derivative(fx, x);
}
// If here, find and return the derivative of fx ...
Marxian economics: Differentiating the "Rate of Profit Equation"
While watching a recent Youtube video on Marxian crisis theory and the Tendency Of The Rate Of Profit To Fall, I decided to apply calculus to the equations to see what I got.
The rate of profit is defined as ∏ = S / (C...
Homework Statement
I have the functionu(x,t)=\frac{1}{2c}\int^{x+ct}_{x-ct}g(\xi)d\xiwhere g is continuously differentiable and c is a constant. I need to verify that this is a solution to the wave equation.
Homework Equations
My prof gave me the...
Suppose I have something like \frac{-2(t - 1)}{9t^5}
I know I just plug in two points to check its concavity...But How do I know what to choose between what and what? Like would I just choose between 0 and 1? And how do I know ?
Also suppose I have something like
- \frac{1}{4t^3}
would I...
Homework Statement
In oppgave 1 a) I am supposed to show that the given equality is true (namely that the isoterm compressibility coefficient partial-differentiated with regards to temperature = isobar coefficient differentiated with regards to pressure multiplied by minus one)...
Hi,
I figured out the only redundancy to my problem is this:
I'll start off with a simple case, where w1,w2 are the displacements at intervals of one third along a beam.
w = 3w1/L.x (Note, x is in the numerator for all cases)
To differentiate this with respect to time, I use the...
In my high school Calculus course, I've encountered several optimization problems involving the area of a circle and I noticed the obvious fact that if you differentiate the area of a circle you obtain the expression for its circumference. This implies that the rate of change of a circle's area...
So the question is…Evaluate the following…
\frac{d}{dx} \left(\int _1^{x^2} \cos(t^2) \, dt \right)
I thought i could use the FTC on this because it states…
\frac{d}{dx} \left(\int_0^x f(t)\, dt \right)=f(x)
but i can't correct? because in my question it starts at 1…is there some way to apply...
I have to solve a bunch of exercises related to function series and in some of them they ask me whether a particular series converges uniformly if one differentiates it term by term. So here I came up with a doubt: When ##\sum_0^{\infty} f_n(x)## can be differentiated term by term? What...
Say I have a simple series like
\Sigma^{∞}_{n=0} X^{n}
When I differentiate this series the first term goes to 0 because it's a constant. Does that mean that I have to adjust the index of the series from n=0 to n=1? If I don't do it, the first term still goes to zero as n(x^(n-1)) when n=0...
Sorry, I did not know where to post this as it is sort of a "philosophy of physics" question that I am not sure has an answer and was curious if anyone had any thoughts not grounded in pseudoscience. How can a set of particles interacting in quantum fashion (perhaps a bose einstein condensate...
something I often see without justification in my physics books. What is the justification for the following convolution property (pulling the derivative inside the integral)
(f*g)^\prime = \frac{d}{dx} \int f(x) g(x-u) dx = \int f(x) \frac{d}{dx} g(x-u) dx = f(x) * g(x)^\prime
Dear all,
I just wondered whether there was any standard identity to help me solve this equation:
$$ \int \delta(f(x))^{\prime\prime}g(x) dx $$
Thanks in advance for your help.
Hi...
I was looking at the problem of a particle in a Coulomb field in three dimensions. Time-translation invariance and spherical symmetry ensures that the energy and angular momentum are conserved, allowing us to write the action as
A = -εt + L ∅ +f(r)
The form of f(r) in terms of ε...
Hi.
So I have this vector function which I need to differentiate, it is however very tricky to do by hand, so I'm doing it in Mathematica.
\hat{u}=\left\langle\bar{u}+\bar{r}\frac{(1+\gamma)}{r(r+\bar{u}\cdot \bar{r})}\right\rangle
(The brackets denote normalisation)
I want to do this...
Spectral redshift is currently understood to be of a variety of sources, velocity / doppler redshift, gravitational redshift, cosmological redshift, etc.
Is there any ability to tell,purely from the spectral analysis of the light itself, without knowing what the source of the light is, what...
Homework Statement
I need to differentiate the pressure P(r) equation directly below, for the case where the density is constant (i.e. ρ(r) = ρc), to show that it is of the same form as the dP/dr equation further below:
Homework Equations
P(r) = rhoc×c2×( (√(1-2βr2/R2) -...
Homework Statement
A small commuter plane has 30 seats. The probability that any particular passenger will not show up
for a flight is 0.10, independent of other passengers. The airline sells 32 tickets for the flight. Calculate the probability that more passengers show up for the flight...
I came across this simple expression while doing some maths.
If \frac{d}{dx}f(x)=g(x)
Then \frac{d}{dx}f(-x)=-g(-x)
Is this correct? How do we prove it?
I am attempting to work my way through the product rule for inner products, using the properties of linearity and symmetry. I am wondering if the following step is allowed, exploiting the bilinear property:
f(t) = \left\langle{\alpha}(t),{\beta}(t)\right\rangle \rightarrow f'(t) = \lim_{h \to...
Homework Statement
Sin(tan(2x))
With respect to x
Homework Equations
Differentiation
The Attempt at a Solution
My question is whether I can simply use d/dx (Tan x) = Sec^2(X) to extrapolate that to d/dx(tan 2x) = Sec^2(2x) ?
Or do I have to convert to sine/cosine and go from...
How do i derivate e^e^x (I don't know how to type it on latex but here you can se what i mean e^e^x - Wolfram|Alpha Results basicly don't know how I shall think
Homework Statement
Obtain an expression for the potiential energy between to particles in an ionic bond at radius r0 Homework Equations
Coloumb's laws: F = (-k * q1 * q2)/r-1The Attempt at a Solution
I think that if i do U = r0∫0 F(r)dr = [k * q1 * q2 * r-1]r00 = k * q1 * q2 * r0-1, Then that's...
Homework Statement
I have a problem where I have a mass suspended in a system of springs. I need to differentiate the equation wrt time so I can can show equivalence with Newton's second law.
The mass and springs are vertically aligned so the motion is in one dimension. The actual problem has...
A particle of mass m is moving along the x-axis and experiences a force F(x), also along the x-axis, given by F(x) = -kx. Deduce an expression for the potiential energy of the particle.
I tried intergrating both side (just to see if it gave me anything helpful). I got ∫F(x)dx=mv for the...
Here was my thinking for differentiation (which, by the way, is wrong):
By the definition of the function, the following equations are equal:
$$W(xe^x)=x$$
By the chain rule and product rule:
$$\frac{dW}{dx}( e^x+xe^x ) =1$$
$$\frac{dW}{dx}=(e^x+xe^x)^{-1}$$
What is the error here? What is...
Hello everyone!
I've came across this problem: differentiate $\int _S f \ln f$ with respect to $f$. From previous explanation, I believe $\int _S f \ln f$ means $\int _S f(x) \ln f(x)dx$.
The answer is $\ln f(x)$... Could anyone indicate how they reached this answer?
Thanks!
Homework Statement
Differentiate:
v = 3t^2 - 14t + 8The Attempt at a Solution
I am not sure if you do anything with the constant "+ 8" is it ignored when differentiating?
if its ignored then the answer is:
a = \frac{dv}{dt} = 6t - 14
I don't have a ton of experience in numerical methods, so I'm hoping someone can help me out. Suppose I have a sequence of position data points for a car, but they've been truncated to integer values. I want to find the speed (derivative), but for speeds which are low relative to the time...
Homework Statement
Differentiate V0 - iR - q/C = 0 to prove that di/dt = -i/RC.
Homework Equations
V0 - iR - q/C = 0
^ derived from previous question for a circuit that had one battery with emf V0, a resistor of resistance R and a capacitor of capacitance C (all in series).
di/dt =...
Let's say we have an object falling through an accelerated field from r to s. I would say a gravitational field, as it is by the same process as gravity, but I will be applying a different constant of motion within the field.
If the constant of motion is something like (1 - b / r) = (1 -...
Suppose I have a really simple first order linear ODE like:$$\dot{\omega} = -k\omega$$ where k is some constant, ω(t) is a function of time that I want to solve for, and the overdot denotes the derivative w.r.t. time. This is really easy to solve, and we all know that with the initial condition...
I know how to differentiate the dot and cross products of two vectors, is the differentiation of a vector sum done like this:
d/dt (u+t) = u' + t + u + t'
Or simply add them and then differentiate?
Thanks
Hi, I am having some trouble understanding what I have done here, or if it makes any sense at all.
Recall that
\frac{d^a}{dx^a}x^k = \frac{\Gamma(k+1)}{\Gamma(k-a+1)}x^{k-a}
We can extend this to complex numbers if we let a be of the form p + qi, where p and q are real, and i is the imaginary...
Hello!
The picture says a thousand words:
http://www.hot.ee/jaaniussikesed/v6rrand.jpg
In the last member under the square root, there is the error. For some reason I am not able to differentiate with an array index, ts1 is a single column 5 row matrix. How to solve this? The error says...
What are rules for differentiating a Fourier series?
For example, given
$$
f = \frac{4}{\pi}\sum_{n=1}^{\infty}\frac{\sin(2n-1)\theta}{2n-1} = \begin{cases} 1, & 0 < \theta < \pi\\
0, & \theta = 0, \pm\pi\\
-1, & -\pi < \theta < 0
\end{cases}
$$
Can this be differentiating term wise? If so...
differentiating to find one unknown function out of three??
Homework Statement
Hi everyone
I need some help with a question that i have solved yet i find it hard to understand.
I have three given functions in the picture attached. All three consist of one single graph. And they give me...
What is the difference? I always see differentiate a function but never an equation, a lot of exercises have y=blahblah which is an equation. Does it just mean that when you're asked to differentiate the equation (without using implicit), that it is satisfies the conditions for a function?
Differentiating y=x^x
x=ln(y)
I changed the base to e
x=\frac{ln(y)}{ln(x)}
xln(x) = ln(y)
e^{xln(x)} = y
e^{xln(x)}(1+ln(x) = \frac{dy}{dx}
The answer the calculator got was x^{x(1+ln(x))} so I noticed that since y=x^x and e^{xln(x)} = y, then I could replace it with x^x in the final answer...
Somebody want to help with this derivative:
y = (7.75x3 + 2250) / 750x
I differentiate it with the quotient rule and get:
dy/dx = 31x / 1500 - 3 / x2
But that's wrong. It's got a zero around 5 - 6 and the original function has its minimum at (4.03, 1.12). Not sure what I did wrong.
Differentiating the term:
(x2-1)u' n+1 times gives (according to my book):
(x2-1)u(n+2) + 2x(n+1)u(n+1) + n(n+1)u(n)
Now I see how the first two parts arise. However, I don't really understand the last one - or more specifically I don't understand how you find that un appears exactly...
So, when you differentiate a function, specifically an explicit function, where y is a function of x, you are differentiating each term with respect with x. Well, when you differentiate x with respect with x, does that mean you are trying to find out how x changes with x? What does that mean...
They give a differential equation: x' = f_a(x) = ax(1-x) . In determining if the equilibrium points are sources or sinks, they say: We may also determine this information analytically. We have f'_a(x) = a - 2ax
How can they differentiate with respect to x? x is a function, it doesn't...
Homework Statement
Find the derivative of (x^2)(sinx)(tanx)
Homework Equations
f(x+y)(d/dx)=(x)(y)d/dx+(y)(x)d/dx
That's for differentiating with 2 terms. With 3, I haven't done it yet.
The Attempt at a Solution
x^2(sinx)(sec^2x)+tanx(sinx)2x+x^2(tanx)(cosx)...
Homework Statement
(See attached figure) I need to find V0 in terms of R1, R2, R3 and C.Homework Equations
V0 = -RC (dVs/dt) for a differentiatorThe Attempt at a Solution
I understand I have to apply KCL at the node between C and R1, and I've also determined that R1 and R2 are in series (not...