Scott Pauls Department of Mathematics Dartmouth College Math 3, Fall 2014 Scott Pauls Department of Mathematics Dartmouth College Lecture 1 - 9/15/2014

Contact Information Scott Pauls 303 Kemeny Hall 603-646-1047 scott.pauls@dartmouth.edu (but, mail through canvas is preferred) I’ll announce office hours later in the week. Lecture 1 - 9/15/2014

Introduction to the course Administration and course repository: canvas.dartmouth.edu Text: Stewart’s Calculus 7th Edition Supplemental Material: Khan Academy videos (khanacademy.org) Homework: Khan Academy practice problems Exams: Two midterms (October xx, November x) Final Exam (November xx) Lecture 1 - 9/15/2014

Logistics: Preparing for class Class preparation will take most of your time outside of class. It includes reading, watching short video lectures, and doing practice problems and occasional quizzes. Lecture 1 - 9/15/2014

Logistics: In-class Brief lecture – recap of main points, focus on pieces that you are having difficulty with. Work on focus areas Recap and launch into next class Lecture 1 - 9/15/2014

Logistics: After class After class, students review materials, practice problems again. Concurrently, students prepare for the next class period. Lecture 1 - 9/15/2014

Problems -> Mastery Class Time Prep: Reading Videos Problems Prep: Reading Videos Problems Review: Reading/Videos/ Notes Problems -> Mastery Class Time Review: Reading/Videos/ Notes Problems -> Mastery Class Time Lecture 1 - 9/15/2014

Course Grading Scheme Percentage KA practice problems and quick quizzes 5% Mastery of KA exercises by the end of term 15% Midterm 1 25% Midterm 2 Final Exam 30% Total 100% Lecture 1 - 9/15/2014

Mastery and Final Grades Level 2 Level 1 Lecture 1 - 9/15/2014

Outcomes There are two major learning outcomes for the course: Students will be able to generate solutions to unfamiliar problems. Students will be able to identify areas in mathematics and other fields where Calculus is useful. Lecture 1 - 9/15/2014

Generating solutions to unfamiliar problems Three levels – low, medium, and high. Low level pieces are basic definitions, concepts, and techniques. These are the fundamental pieces that we spend most of our time learning, discussing, and applying. Lecture 1 - 9/15/2014

Generating solutions to unfamiliar problems Lower level objectives: Define terms Describe techniques Apply these to simple applications Content mastery: by the end of the course, achieve mastery in all Khan Academy skills associated with the course. Lecture 1 - 9/15/2014

Generating solutions to unfamiliar problems Mid-level objectives: Students will be able to decompose problems into more easily approachable components. Students will be able to match problems with effective techniques of solution. Students will be able to combine different techniques to solve complex problems. Lecture 1 - 9/15/2014

Generating solutions to unfamiliar problems Higher-level objectives: Students will be able to discriminate between competing methods of solution. Students will be able to evaluate the effectiveness of methods, techniques, and algorithms in different contexts. Students will be able to explain and interpret the results of techniques in the context of the problem they are trying to solve. Lecture 1 - 9/15/2014

Applications of Calculus Throughout the course, we will explore different applications of the ideas and techniques we learn. From these examples, students will learn how to recognize problems in other fields where calculus might be an appropriate tool. Lecture 1 - 9/15/2014

Adequate scores on exams: Grade Description A Excellent mastery of course material Student performance indicates a very high degree of originality, creativity, or both Excellent performance in analysis, synthesis, and critical expression, oral or written Student works independently with unusual effectiveness B Good mastery of course material Student performance demonstrates a high degree of originality, creativity, or both Good performance in analysis, synthesis, and critical expression, oral or written Student works well independently C Acceptable mastery of course material Student demonstrates some degree of originality, creativity, or both Acceptable performance in analysis, synthesis, and critical expression, oral or written Student works independently at an acceptable level D Deficient in mastery of course material Originality, creativity, or both apparently absent from performance Deficient performance in analysis, synthesis, and critical expression, oral or written Ability to work independently deficient E Serious deficiency in mastery of course material Originality, creativity, or both clearly lacking Seriously deficient performance in analysis, synthesis, and critical expression, oral or written Cannot work independently Prerequisite: C students must have an average of Level 1 mastery on problems by the end of the course. Adequate scores on exams: C students demonstrate the ability to replicate straightforward problems similar to those in the problems sets. Lecture 1 - 9/15/2014

Grade Description A Excellent mastery of course material Student performance indicates a very high degree of originality, creativity, or both Excellent performance in analysis, synthesis, and critical expression, oral or written Student works independently with unusual effectiveness B Good mastery of course material Student performance demonstrates a high degree of originality, creativity, or both Good performance in analysis, synthesis, and critical expression, oral or written Student works well independently C Acceptable mastery of course material Student demonstrates some degree of originality, creativity, or both Acceptable performance in analysis, synthesis, and critical expression, oral or written Student works independently at an acceptable level D Deficient in mastery of course material Originality, creativity, or both apparently absent from performance Deficient performance in analysis, synthesis, and critical expression, oral or written Ability to work independently deficient E Serious deficiency in mastery of course material Originality, creativity, or both clearly lacking Seriously deficient performance in analysis, synthesis, and critical expression, oral or written Cannot work independently Prerequisite: B students must have an average of Level 2 mastery on problems by the end of the course. Good scores on exams: B students demonstrate the ability to replicate straightforward problems similar to those in the problems sets as well as problems which combine techniques in novel but relatively simple ways. Lecture 1 - 9/15/2014

Excellent scores on exams: Grade Description A Excellent mastery of course material Student performance indicates a very high degree of originality, creativity, or both Excellent performance in analysis, synthesis, and critical expression, oral or written Student works independently with unusual effectiveness B Good mastery of course material Student performance demonstrates a high degree of originality, creativity, or both Good performance in analysis, synthesis, and critical expression, oral or written Student works well independently C Acceptable mastery of course material Student demonstrates some degree of originality, creativity, or both Acceptable performance in analysis, synthesis, and critical expression, oral or written Student works independently at an acceptable level D Deficient in mastery of course material Originality, creativity, or both apparently absent from performance Deficient performance in analysis, synthesis, and critical expression, oral or written Ability to work independently deficient E Serious deficiency in mastery of course material Originality, creativity, or both clearly lacking Seriously deficient performance in analysis, synthesis, and critical expression, oral or written Cannot work independently Prerequisite: A students must have an average of complete mastery on problems by the end of the course. Excellent scores on exams: A students demonstrate the ability to replicate straightforward problems similar to those in the problems sets, problems which combine techniques in novel but relatively simple ways, and, most importantly, truly novel problems which require application of known techniques in new combinations. Lecture 1 - 9/15/2014

Evaluation of the course Does this course structure work better than a course with “traditional” lectures? So far, the evidence points to a fairly strong yes - Freeman et al., PNAS 2014 Math 3 from the fall of last year We will continue to evaluate our results in the context of past versions of math 3. To that end, we will occasionally collect data from you concerning your progress in and attitudes towards the course. Lecture 1 - 9/15/2014

Next Steps Sign up for Khan Academy with your Dartmouth ID as your user id. Add two coaches with codes W6E8E7 and 8GN3PJ. In tomorrow’s xhour, I’ll give an introduction to the Khan Academy platform. Take the diagnostic exam on canvas by Sunday. Fill out the background survey on canvas by Sunday. Do class preparation assignment #1 by Thursday at 6pm. This first assignment is light on the KA work so our first class time will be mostly Q&A – if you have questions that arise, please mail them to me from within Canvas. Lecture 1 - 9/15/2014