The intermediate position is therefore that programme implementation can be flexible as long as there is fidelity to the so-called "essential" elements of an intervention. The absence of these elements would have significant adverse effects on the capacity of an intervention to achieve its goals.
Indeed, without them it cannot meaningfully be said that an intervention has achieved high implementation fidelity. A high level of adherence or fidelity to an intervention, or its essential components, is not achieved easily. Several factors may influence or moderate the degree of fidelity with which an intervention is implemented.
Each of the potential moderators of this relationship is now considered in turn. The description of an intervention may be simple or complex, detailed or vague. Detailed or specific interventions have been found to be more likely to be implemented with high fidelity than ones that are vague. For example, a study of guidelines intended for General Practitioners GPs found that detailed and clear recommendations were almost twice as likely to be followed as vague and non-specific recommendations [ 23 ].
The specificity of these guidelines was assessed by a group of researchers and their uptake was evaluated by the GPs' self-report. In the same way, well-planned interventions, where all the key components are identified in advance, have been found to produce higher levels of adherence than less well-structured interventions [ 1 , 5 ].
Specificity enhances adherence. There is also evidence that it is easier to achieve high fidelity of simple than complex interventions [ 1 ]. This may be because there are fewer "response barriers" when the model is simple [ 18 ]. Complex interventions have greater scope for variation in their delivery, and so are more vulnerable to one or more components not being implemented as they should. This has led to calls in some quarters for improving the recording and reporting of complex interventions to identify and address potential sources of heterogeneity in implementation [ 13 , 14 , 24 ].
Overall, research suggests that simple but specific interventions are more likely to be implemented with high fidelity than overly complex or vague ones. As such, the comprehensiveness and nature of an intervention's description may influence how far the programme successfully adheres to its prescribed details when implemented.
Support strategies may be used both to optimise and to standardise implementation fidelity, i. Such strategies include the provision of manuals, guidelines, training, and monitoring and feedback for those delivering the intervention. Some studies that evaluate the implementation process have monitored the extent to which an intervention is being implemented correctly, and then have fed back these results to those delivering the intervention.
A study measuring fidelity to an exercise programme for women with hip fractures used direct observation by the designers of the intervention to monitor the intervention that was actually being delivered, and then provided feedback to the exercise trainers [ 21 ]. In this way, deviations from the intended content of the programme were addressed and corrected, and high fidelity was achieved.
It is therefore possible that these strategies, like the nature of an intervention's description, may potentially moderate the degree of fidelity achieved: the more that is done to help implementation, through monitoring, feedback, and training, the higher the potential level of implementation fidelity achieved.
The role of such strategies in optimising fidelity and standardising what is being implemented is arguably even more important in the case of complex interventions, which can be multifaceted and therefore more vulnerable to variation in their implementation [ 24 ].
Although some studies have claimed that the provision of certain facilitation strategies has positively affected implementation of an intervention, these claims are not the result of empirical research [ 13 ]. However, no study has yet measured the moderating effect of these strategies on the degree of implementation fidelity. More facilitation strategies do not necessarily mean better implementation. A simple intervention may require very little in terms of training or guidance to achieve high implementation fidelity.
A complex intervention by contrast may require extensive support strategies. There is therefore an issue of adequacy, and this may be determined by the relationship between facilitation strategies and the complexity of an intervention's description.
The relationship between these potential moderators is discussed more fully below. Empirical research has yet to demonstrate whether facilitation strategies can indeed affect how well or how badly an intervention is implemented, but this should certainly be considered as a potential moderator of implementation fidelity.
Quality of delivery is an obvious potential moderator of the relationship between an intervention and the fidelity with which it is implemented. It concerns whether an intervention is delivered in a way appropriate to achieving what was intended.
If the content of an intervention is delivered badly, then this may affect the degree to which full implementation is realised. In studies evaluating fidelity the provision of extensive training, materials and support to those delivering an intervention is an implicit acknowledgement that effort is required to optimise the quality of the delivery of the intervention being evaluated [ 3 , 26 — 28 ].
In the same way, quality assurance or improvement strategies, such as providing ongoing monitoring and feedback to those delivering the intervention, provide a more explicit acknowledgement of the importance of quality of delivery and its potential moderating effect on implementation fidelity [ 28 , 29 ].
This involved assessments by trained observers to determine whether the parent trainers applied both verbal and active teaching strategies, as required by the intervention. The scale stipulated that an "Over-reliance on verbal teaching can result in lower scores". Trained observers were also used to assess both content and process fidelity, including quality of delivery, of a life skills training program delivered by teachers in the United States [ 19 ]. However, these studies did not analyse quality of delivery as a moderator of implementation fidelity, but rather as a discrete aspect of fidelity.
If participants view an intervention as being of no relevance to them, then their non-engagement may be a major cause of its failure or low coverage, and thus implementation fidelity may be low. This idea — that the uptake of a new intervention depends on its acceptance by and acceptability to those receiving it — echoes Rogers' diffusion of innovations theory [ 30 ]. Participant responsiveness may therefore be an important moderator in any process examining implementation fidelity.
For example, it has been found that implementation fidelity of prescribed drug interventions for elderly people in the community can be low because these patients deliberately fail to comply with their prescribed regimens [ 31 — 33 ]. Reasons for this intentional non-compliance include the unpleasant side effects of the drugs, and because the therapy is only preventative or symptoms only mild, so patients feel less inclined to comply [ 31 — 33 ].
In a study of a school-based health promotion intervention, the teachers reported that they did not implement certain components of the intervention if they felt the students were not responding and were not interested [ 34 ]. In fact, participants covered by this moderator of implementation fidelity encompass not only the individuals receiving the intervention, but also those responsible for it. For example, studies examining factors associated with substance abuse prevention and health promotion programmes in schools found that teachers' beliefs concerning the intervention itself, for example whether they liked it or not, and the training and support they themselves had received, were all associated with their level of adherence to the intervention [ 34 , 35 ].
In other words, higher levels of implementation fidelity were achieved when those responsible for delivering an intervention were enthusiastic about it.
The organisation more broadly may also influence the response of those delivering a new intervention. If an organisation, as represented by senior management for example, is not committed to an intervention, then the responsiveness of individuals may be affected, too [ 2 ]. This is a key aspect of all organisational change literature [ 36 ]. Self-report is the most common means of evaluating the responsiveness of all participants to an intervention [ 30 — 34 , 37 ].
This assessment can involve several perspectives. It may evaluate how far participants fully accept the responsibilities required by an intervention [ 38 ], how far they perceive the intervention to be useful [ 26 ] and, more broadly, how responsive the environment is into which an intervention is introduced, the so-called "therapeutic milieu", which may not be conducive to a favourable response from participants [ 21 ].
In studies that have examined these dimensions of participant responsiveness, participants used logs and calendars to record and report on their response to the intervention being implemented. Participant responsiveness may even reach beyond attitudes to actual action, for example, to gauge whether a "treatment has been.
In this sense, "enactment" may be considered a potential element of participant responsiveness [ 25 ]. These moderators are not necessarily discrete elements. There may be relationships at work between two or more moderators. An obvious example is where the provision of training and guidelines on how to deliver an intervention may have a direct impact on the quality with which an intervention is actually delivered and this may in turn affect the fidelity with which an intervention is implemented.
If the amount of training provided is small, then the quality of the resulting delivery may be poor. Facilitation strategies may also influence participant responsiveness: The provision of incentives could make both providers and participants more amenable or responsive to a new intervention. Quality of delivery may function in the same way: a well-delivered intervention may make participants more enthusiastic and committed to it.
One moderator might therefore predict another. However, as noted above, these relationships are more complex than may be captured in the simple correlation of large numbers of facilitation strategies producing high quality of delivery, or by stating that small incentives produce limited participant responsiveness. One reason is the moderating role of intervention complexity: A simple intervention may not require much training or guidance to achieve high quality of delivery or participant responsiveness.
A small amount of training may suffice. In other words, there may be interaction effects between moderators, i. Participants may also be enthusiastic about new interventions because of other factors, regardless of incentives or other strategies. Thus the interaction of these moderators may further affect the relationship between an intervention and the fidelity with which it is implemented. The implication of our framework is that any evaluation must measure all the factors listed above that influence the degree of implementation fidelity, such as intervention complexity and the adequacy of facilitation strategies.
It also needs to gauge participant responsiveness or receptiveness to proposed and implemented interventions. With the exception of a few studies that do measure quality of delivery or participant responsiveness [ 8 , 20 , 38 ], most implementation fidelity research focuses solely on a fidelity score determined almost exclusively by adherence [ 3 , 6 — 8 , 21 , 22 , 27 — 29 , 38 , 39 ]. Moreover, this research rarely reports high implementation fidelity [ 8 , 29 , 40 ].
It actually often falls short of the ideal and is sometimes even very poor, yet it is only by measuring the moderators described above that potential explanations for low or inadequate implementation may be apprehended or understood. It is only by identifying and controlling for the contribution of possible barriers to implementation that such issues can be addressed and higher implementation achieved.
Achievement of high implementation fidelity is one of the best ways of replicating the success with interventions achieved by original research. Successful evidence-based practice is governed by many things [ 41 ], and implementation fidelity is one of them. This paper offers a more complete conceptual framework for implementation fidelity than proposed hitherto, and explains why and how implementation fidelity should be evaluated.
The framework is multifaceted, encompassing both the intervention and its delivery. Adherence relates to the content and dose of the intervention, i. However, the degree to which full adherence, i. This conceptualisation provides researchers with a potential framework for implementation research.
Monitoring of implementation fidelity following this framework enables better evaluation of the actual impact of an intervention on outcomes. In turn, the credibility and utility of the resulting research would be enhanced accordingly. It also offers evidence-based practitioners a guide to the processes and factors at play when implementing interventions described in research.
However, much more research is needed on this topic. Empirical research is needed to test the framework itself and to clarify the moderating impact of the components included here.
Health Educ Res. Article PubMed Google Scholar. Dane A, Schneider B: Program integrity in primary and early secondary prevention: Are implementation effects out of control. Clin Psychol Rev. Elliot D, Mihalic S: Issues in disseminating and replicating effective prevention programs. Prev Sci. Article Google Scholar. Mihalic S: The importance of implementation fidelity.
Google Scholar. Blueprints Violence Prevention Initiative. McGrew J, Griss M: Concurrent and predictive validity of two scales to assess the fidelity of implementation of supported employment.
Psychiatr Rehab J. Also stores data from intermediate steps in lists to aid in showing work. Euler's Theorem This program will solve for variables on Euler's Theorem. Euler's Method This program uses Euler's method to solve a differential equation. For a given diff eq, and initial point, you determine the number of steps you wish to take in order to approximate the y-value for a chosen x-value.
It also draws the approximations and stores them into lists 1 and 2. Expected Value This program computes the expected value and the variance of continuous functions over a finite interval. Fixed Point Algorithm This is a program for the fixed point algorithm for solving equations. It will also produce a graph of the iterates.
Slope Field v1. This program provides a variety of tools for slope fields: you can enter a differential equation, render the resultant field, edit the window settings, find the slope value at a specific x,y point, and trace an antiderivative over the field to verify that it is correct. Doors CS v4. Fourier Synthesizer V1. Version 1. A Y-axis slew value was also added. Fourier Series Calculates the coefficients of the sine and cosine terms of the Fourier series for an arbitrary function over the interval [-pi,pi].
Func Master v1. Func Master is special because it is fairly small when compared to other calculus programs that perform similar tasks. It also does not require you to install supporting applications like Symbolic or Pretty Print, so it will be ready to run as soon as you put it on your calculator! This program is highly recommended for general use and for AP Exam free response questions.
Read "help. Also note that ticalc. Function Analysis This program performs many operations with functions. In single function mode, you can differentiate, integrate, measure curve length, use the shell method, use the disk method, and analyze surface area once wrapped about the axis.
In dual function mode, you can check the area between the two curves, use the washer method, and check the moments about both the Y and X axis as well as the center point of mass centroid functions. Gamma Function Here's a short algorithm based on Lancoz approximation series for the gamma function.
Does NOT handle complex arguments though. Gamma Function solver This program solves Gamma n , which is n-1! Most efficient algorithm you will find anywhere. Gauss Legendre Quadrature This program will compute nodes, weights and the approximate integral using Gauss-Legendre quadrature method.
Please read accompanying documentation for more details. Gaussian Integration Multiple 2. Quite useful for Calculus III classes to check multiple integrals results.
Thanks to Benjamin Craig for his review. Input the derivative x any y variables , initial condition, step value, and number of steps and the Ti calculates the points!
Major time saver! Parametric Things This program will find the first and second derivative of parametric functions using symbolic and pretty print.
It will also find the arc length as well. I got lazy and when you input the variable for arc length instead of "T" it will be "X". The answer still comes out the same. I don't know how to protect source code, so feel free to use and abuse it. Hyperbola Segment This program computes the area of a hyperbola's segment. It is limited in that the hyperbola must be centered at the origin and the line must be a vertical line, so the orientation of the transverse axis is the x-axis.
Great for conic classes and calculus classes. IPMLinDrag This folder contains two files, one for ideal projectile motion and one for projectile motion when drag is considered. Great for physics or multivariate calculus students.
Improved Euler's Method v1. Same as Euler's method, but more accurate. Thus, this app should be free of this bug, allowing it to be run without any basic programs loaded and unarchived on the calculator, making it entirely portable. I thank the original author of the program, Chip Hurst. The user will receive an approximate value to the solution at a specified point and will also have the option to see the approximate solution graphed. Improved Euler Method Utilizes the Improved Euler method sometimes termed the Runge-Kutta 2 method to numerically approximate solutions to first-order differential equations.
The user enters the powers on the integrand, A and B, and the upper limit on the integral in the numerator, X. The program outputs the result. Point of inflection. This program allows you to find points of inflection on a graph. Enhanced for use with DCS6.
Integral As Accumulator Function This program will graph fint y1,x,a,x and y1 together in the same viewing window simultaneously. The area between the curve and the x-axis will be shaded and a point plotted for the value of the integral at the same value of x. You use X for the variable, and get the numerical value. Then you get an estimate with Simpson's method for intervals.
Only bytes. Integral- Area under a Curve Very simple program that easily analyzes the integral of F x between given point A and point B. Now with the fundamental theorem of calculus. Look at the screenshots. It works so that it chops up your expression into smaller bits, to give you its relevant formulas. That way you do not have to search for them. It is made to be as forgiving as possible, which of course comes with a drawback: you sometimes get more than you wanted. Do not use implicit multiplication where you want the program to give you a formula.
If you type sin x cos x , for example, you just get the formulas for sin and cos, but not the formula for how to multiply them correctly. It revolves one or two functions around any vertical or horizontal axis and will not only give the numerical answer, but the setup as well. It will also find surface area, and area between two functions. This program was written by the same mathematician who owns MathNerdShirts. Integral Area Estimation for Calculus This program allows the user to calculate the left side, right side, midpoint, trapezoidal, and Simpson's rule areas under a curve easily and at the same time.
Integration Formulas Integral Formula is pretty self-explanatory. Run the program, and you have the formulas used for integration right at your fingertips. It also lets you solve the area bound by the curve. All this has full working out in a very good text format so you can just read it right off. Also the program simplifies all fractions and everything so you won't even have to think at all!!!
Just check it out and you'll how superior its working out is!!! Integral This program solves for the definite integral between two points of a function. Can also do tables. Integrate Displays the integral of any equation. Integration This program will find the area under the curve. It has five different methods of solving for you to choose from.
Please see the text file on how to use this program. Definite Integral This program calculates the definite integral under any curve from a lower to upper limit. It also can calculate the average value for that area.
Depending on the function and limits, the answer given may be exact or a very close decimal approximation. Integral: Area Between Curves After inputing F x and G x , this program finds out the area under each curve and between them and graphs the region between them. Integral X This program is capable of finding the area under and between curves. You can choose from numerous methods of finding the area including left, right and middle, trapezoidal, solids of revolution and standard integration.
The program is easy to use, and understand, if you know the terminology. Can find definite integrals, regardless if equation is unknown, as long as co-ordinates are given. Integration Help! For those of you in Caclulus, this might help. The program shows the integrals of sin, cos, tan, sec, csc, and cot and all of them from the first through the third power!
This is just a little something to help me along in class, and it's not finished yet, eventually I will add the work to all of them plus add the arc functions. Any input would help. Integration Sums This program performs different types of summations that can be used to approximate the area under the curve.
Inverse Hyperbolic Functions This program will generate the graphs of the six inverse hyperbolic functions without using the catalog command.
The windows are set up to conform to the domain of each function. Lambert W Function This program runs Cantrell's algorithm for computing the Lambert W Function sometimes referred to the inverse to the gamma function. Limit v3. LimitMan to the rescue to save the day from evil limits!
Read the readme for more details. Calculates infinite limits too! Limits for the Ti Gives the left and right side limits of any function for a certain value of x. Delta x can also be changed. Limit Calculator This program is great for the aspiring young calculus student! Find the limit of almost any function at a given point! Does not handle functions with imaginary values like sqrt x at points near undefined points.
Linearization Complete Linearization tables are made with this program using Symbolic. Line Integrals This program computes different types of user-defined Line Integrals. I have tested everything and it works! Watch out on the 3-d one tho, the z t function needs to be put in as a function of X2t under parametric! The program can graph a StatPlot with each of the rectangles, trapezoids, or parabolas used to calculate the respective sum.
If MVT, IVT, or both need to be used to find a value of f, f-prime, or demonstrate that f-double prime is negative, zero, or positive, the program will display the set of points that need to be used with the theorems along with which theorems to use.
The program also calculates the slopes between consecutive points, and the sign of the second derivative using calculated slopes. Logistic Concavity This program will produce information about the inflection point and the intervals of concavity for logistic functions. Logistic Function Calculator - Simple A simple program that helps find important values for logistic functions.
Input a logistic function or its derivative, and the program will display its initial population, point of inflection, limit, derivative, as well as a graph. Made this for our AP Calculus class. Logistic This program works with the logistic function. It will give final amounts, rates, time spent to reach an amount, and a graph. Lower Gamma Function This program computes values for the lower gamma function.
Look at the screenshots! Maclaurin Series v1. Monty Carlo Area Under the Curve Uses a monty carlo simulation to find the area under a selected curve. Means This program will compute several kinds of means including: 1 Power harmonic, geometric, root mean-square, arithmetic are here 2 Lehmer 3 Arithmetic-Geometric 4 Harmonic-Geometric 5 Stolarsky Enjoy!
Midpoint Rule Approximates integrals using the midpoint rule. Modified Bessel This program will compute values for modified Bessel functions for non-negative order. The user inputs the order and value and the program returns the value, accurate to at least 8 decimal places.
Moving Average 2 This program is designed to compute moving averages when information is in discrete form, not in continuous form as my previous program does. Enter in the information and the spread for the interval. The program will store the averages in L3 and ask you what information you'd like plotted. Be aware that if you start your lists with a zero instead of a one, you'll have to adjust the program a little.
Moving Average This program will plot the moving average for a continuous function. It is slow though. Riemann Sums Given f x , a starting and ending point, and the number of partitions, this program will analyze the area under the curve using Riemann sums from the left, right, midpoint, and a definate integral to check accuracy.
Newtons Method This program allows the user to calculate the end value AND intermediate steps to show "work" on tests, of course of Newton's Method.
It has allowed me to brainlessly work out these problems and show that damn work that my teacher requires :- Updated June Newton's Method v1. Newton It may seem like another Newton iteration program, but I've written this one to have a few special touches to it that make it worthwhile.
First, the program displays the equation Y1 upon loading. After asking for an X value to be the starting point, the calculator tests that value. I added the pathological error aspects to this program because the typical Newton iteration program will continuously attempt iterations before the "divide by zero" error is displayed if it ever is , wasting both time and batteries. Newton's Law of Cooling A simple, efficient, and quick way of calculating the temperature of a body using initial temperature, surrounding temperature, time, and a k constant also known as Newton's Law of Cooling!
Newton's Method This program is a Newton's method root finder. It uses Y1 as f x , and shows all steps used. Newton's Method 83p This program finds the roots zeros of a function nearest a user inputed guess.
Easy to use. Newton's Method this program helps you do the tedius steps of Newton's Method and saves you lots of time. Newton's Method of Approximation Whilst sitting in calculus class, I got bored. Naturally I made a program to simplify what we were learning and share it with the class. So here it is, Jorgan Pubshire's official Newton's Method program.
This is the best Newton's Method program because not only does it approximate your zero, it also builds your entire information table through what I call a cascading table display. Also, this program can do an infinite number of iterations. There are two modes in this program: Iteration mode allows you to input a set number of iterations to be ran and Accuracy mode runs iterations until it reaches an accuracy that is set by the user.
My teacher had already made this program a couple years ago and when I gave him my program he admitted that mine was better. There literally is no way to make this program better save converting it into a fancy flash program, but since I can't do that yet, this will have to do. It will give final temp, a graph, the cooling rate and the time spent. Newton's Method AP Calculus subject: finding the root zero of an equation.
Input f x , f' x , and guess, and the program will show you all the work to do to solve the problem. This eliminates all the tedious work and mistakes when doing homework. Newton's Method Newton's Method including all work is performed using Symbolic. Newton's Method This program uses Newton's Method to find roots of a given function.
After inputing an initial guess and error, it finds a sequence of estimates and stops when the difference between estimates is less than the given error. Normal Line This program will output the slope and y-intercept of a normal line.
The user enters in the function and the x-coordinate. Great for Calc 1 students. Notes: Differential and Integral Calculus v0. The two others was more general, but this one is only on the differential and integral calculus. It is very useful for those who are studying these courses. It contains just the formulas useful for the two mathematics disciplines. There are derivative formulas, integration formulas, identities and some others. More things coming soon!
Newton-Raphson Method Visually go through the Newton-Raphson Method and understand how it the process approximates more accurately with each iteration.
It also obtains solutions for a given initial condition using Runge-Kutta. Olver's Root Finder This program uses Olver's cubically convergent method for finding roots. Diff Eq's Help - 2nd Order Nonhomogeneous ODEs Displays several formulae relevant to finding particular solutions to nonhomogeneous second-order linear differential equations. Includes formulae for the undetermined coefficients and variation of parameters methods for finding particular solutions.
Also includes relevant formulae for finding the particular steady state solutions to driven, damped spring-mass systems. Very fun to play with if Taylor series just aren't good enough for you. Parametic Curve Length This program will compute the length of a curve given in parametric form. Polar Derivatives This program will save you a ton of time when taking derivatives of polar functions. Be warned, although the function will be essentially right, it cannot simplify using trigonometric identities.
You must have Symbolic and Prettyprint installed to use this program. Polynomial Division 2. Polyroot This small program calculates the roots of a polynomial by Newton's Method, including quadratic equations. Check readme for specifics. This speed at each instant is not the same as the average calculated.
Speed is the same as the slope, which is nothing but the instantaneous rate of change of the distance over a period of time. The ratio of a small change in one quantity with a small change in another which is dependent on the first quantity is called differentiation. One of the important concepts in calculus is mainly focused on the differentiation of a function. The maximum or minimum value of a function, the velocity and acceleration of moving objects, and the tangent of a curve are determined by differentiation.
The first principle of differentiation is to compute the derivative of the function using the limits. Let us take a point P with coordinates x, f x on a curve. Now PQ is the secant to the curve. The slope of a curve at a point is the slope of the tangent line at that point. We want h to be as small as possible to get the slope of the tangent. This derivative of f x at a quantifies the change in f x with respect to x. This process of computing the derivative of a function is called differentiation.
The derivatives of the functions are found using the derivative formula as derived in the previous section. The derivatives of elementary functions are remembered as differentiation formulas. Similarly, we can derive the derivatives of other algebraic, exponential, and trigonometric functions using the fundamental principles of differentiation.
A function is differentiable in an interval [a,b] if it is differentiable at every point [a,b]. The sum, difference, product, and composite of differentiable functions, wherever they are defined, are differentiable, and the quotient of two differentiable functions is differentiable, wherever it is defined. The differentiation rules are listed as follows:. Let f x,y be a function in the form of x and y. If we cannot solve for y directly, we use implicit differentiation.
If a function is in the form of an exponent of a function over another, as in [f x ] g x then we take the logarithm of the function f x to base e and then differentiate it. We find higher-order derivatives on successive differentiation. The n th derivative of f x is f n x is used in the power series.
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