Initial Calculus Essentials
Initial Calculus Essentials was built to help anyone learning calculus for the first time. Many institutions don't set aside substantial course time for "initial" skill development or review of concepts that should have been addressed in a standard precalculus course.
This app was built for our Back-End project at DigitalCrafts.
Acknowledgement : The creation of this application was inspired by the Ready. . . Set. . . CALCULUS document (here forth referred to simply as RSC) prepared by the faculty of the Department of Mathematical Sciences at Rensselaer Polytechnic Institute, a document prepared “in the interest of enriching the Freshman Calculus experience.” Similarly, Initial Calculus Essentials (here forth referred to simply as ICE) has been prepared in the interest of not only college freshmen but also everyone learning calculus for the first time.
Main Difference: The content of ICE is largely based on the RSC document but differs in a significant way. ICE has worked out solutions and answers to all of the problems whereas RSC only has answers. Although simple answers should be enough for students to piece together solutions to all of the problems, ice takes the stance that answers and solutions are fundamentally different and that students would likely benefit from seeing both instead of just the former. In particular, even if a student obtains the correct answer to a problem, simply reading over the provided solution(s) may provide a new perspective on how to approach a particular problem or highlight a much more efficient method of attack.
Purpose: Experience by a multitude of beginning and veteran calculus teachers shows that calculus students who begin their study with substantial “initial” mathematical skills are better able to gain a mastery of the subject. Calculus classes (really any class) invariably have students with a wide range of mathematical experiences,and there is no panacea when it comes to ensuring that all students have the “initial” skills they need when undertaking their study of calculus. This application has been prepared by compiling a variety of questions (mostly from rsc) that explicitly deal with“initial” skills. These questions are meant for students to self-assess their individual strengths.
Review at Course Beginning: Many institutions do not set aside substantial course time for “initial” skill development or review of concepts that should have been addressed in a standard pre-calculus course. Many courses will often begin with a cursory review and then plunge into new material, but occasionally the syllabus does not afford such a luxury for starting-from-scratch skill development (even if it is only a week).
Student self-assessment: It is believed that nearly every student beginning his or her study of calculus will find at least one topic (if not more) addressed in ice in which skills can be enhanced. While a number of skills will no doubt be developed and sharpened while the calculus course is in progress, it is strongly believed that students would benefit from improving their “initial” skills in advance as opposed to trying to make up lost ground once the course begins.
Importance of "initial" skills: Taking a calculus course can be a daunting experience,especially if a number of requisite skills are shaky or completely missing. It is believed that a student taking calculus for the first time should expend the majority of his or her effort in contemplating many of the new concepts broached in such a dynamic field of study instead of laboriously developing skills that are necessary for any study of calculus to be worthwhile. For example, when a student first encounters the limit definition of a derivative, the student’s effort should be focused on what the limit of the difference quotient means as opposed to uncomfortably fumbling around with the algebra to make things work out nicely.
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