Textbook

The first-semester calculus curriculum has been reorganized into chapters, each of which is a study of particular types of functions and associated applications. By the end of each chapter, you will have had the opportunity to gain an understanding of the graphical, algebraic, and numerical nature of the featured functions. The curriculum develops early and reinforces often the main ideas from both differential and integral calculus in the context of each function type and associated applications. Relevant precalculus topics are reviewed as necessary.

The organization of the textbook is intended to promote focus and efficiency. Each lesson consists of one page of lesson notes, one page of examples, and two or more pages of class activities. The lesson notes may seem brief but this is so that only small bits of information are covered in each lesson and that only the relevant and necessary content is included. Convince yourself that the presented information is all that is needed to complete the quizzes and activities.

Each chapter of the textbook contains a set of review problems. An individualized version of the review set may also be assigned to each student on WeBWorK. (See below for more information on WeBWorK.) These problems may be assigned for hand-in, depending on teacher preference.

Lesson and Examples Videos

Traditional classroom lectures and examples have been replaced with ones that match the textbook, condensed, and recorded to video. Lesson and examples videos average 5:43 and 10:33, respectively. The video lessons do not simulate full lectures, but rather they are compact and strategic bursts of information focusing on specific topics. The accompanying examples provide demonstrations on how to solve problems related to the topics. Even though detailed notes for each lesson are included in the text, you are strongly encouraged to take your own notes as if you were sitting in class. You must also fill in the solutions to the examples while watching the video, as they have been omitted from the text. Write down the questions you have so that your teacher can answer them through email or during the class meeting. You will have plenty of time to get on track so that you can complete the homework assignment.

Set aside dedicated time for watching videos and studying. Bergmann and Sams “encourage students to eliminate distractions. They shouldn’t try to watch the video with Facebook open and the iPod in the ear while simultaneously texting and making dinner” (Bergmann, 79). They also note that “because the vast majority of the direct instruction is delivered through videos, students who do not watch them are not prepared for class… [and] will totally miss important content. It is as if they skipped the class in a traditional classroom” (Bergmann, 98).

The videos are intended to match the textbook as closely as possible. Lectures for many classes (even non-math classes) are verbatim from the text. Anything not covered is typically the responsibility of the student. We avoid this by giving to you all the information necessary and in two different media. In addition, some of the burden of reading a section of the textbook prior to coming to class has been minimized by providing the option of listening to and watching the text rather than reading it. We have condensed and simplified the course content so that it takes an average of about 17 minutes to cover a lesson the day before the class meeting. This is arguably much less time than it would take to read a section of a traditional text.

It is impossible to show examples of every different type of problem you will encounter. Traditional texts seemingly attempt to do this, but it is the reason an exercise set from a section of a traditional text sometimes contains almost 100 problems. We chose basic examples that follow immediately from the lesson so that fundamental concepts and applications are enforced. You will have the opportunity to experience more complicated problems in the in-class activities and in the homework assignments.

We understand that it may take time for some of you to become comfortable with watching and learning from the videos. If this is the case, then maybe you can learn simply by reading and working from the textbook. In any case, please feel free to browse the internet for additional information and support. There exist dozens of websites and thousands of videos intended to provide support for students of calculus. Ask your teacher for some suggestions and references. It is your ultimate goal and responsibility, however, to walk into the classroom prepared for the day’s lesson. The good news is that you have some control in how you reach this goal.

WeBWorK Quizzes and Homework

Your basic understanding of the content of the lesson is assessed through quizzes and homework using the WeBWorK homework system. WeBWorK is designed to give instant feedback so that you can self-assess your understanding and correct errors immediately after they occur.

A lesson quiz opens in WeBWorK the morning that the lesson videos are assigned and closes at a date and time set by your teacher, usually prior to the next class meeting. The intentions of the quizzes are to track whether or not you watched the videos and studied the lesson, and to reinforce immediately the concepts that you learned from the lesson. It is crucial for the learning process that you try your best to understand the concepts from each lesson and quiz so that you are well-prepared for the class meeting, but this may not always be the case. It is your responsibility to email your teacher, ask questions during class, consult with your classmates, and visit office hours. Try watching the assigned videos a day early, generate and print the PDF of the quiz when it opens in the morning, and work on it during the day so that you have time to ask questions. Bring the hardcopy quiz and your work to class and office hours so that your teacher can see your version of the problem as well as the progress you have made.

A homework assignment may open in WeBWorK the same time as the quiz, but the due date is usually set by your teacher to occur after the in-class activity is completed. Homework sets are typically more challenging and comprehensive than the quizzes. They may count for a grade or may be used as extra practice, depending on teacher preference.

In general, WeBWorK requires that you be precise with typing in your answers, but you must develop this skill early in your college career. Every discipline requires precision in both computation and communication. One suggestion is to generate and print PDF hardcopies of the quiz and homework sets and work the problems carefully on paper. All of the work should be completed as soon as possible so that you have time to get help if you need it.

Classroom Activities

Many research studies have documented the positive benefits of an active learning environment compared to the traditional lecture format. The activities contain a variety of exercises including drill sets, applications of prior knowledge, previews of upcoming concepts, and investigations using technology. Almost every activity begins with one or more “For Discussion” questions. If your teacher decides to implement this section of the activity, then be prepared to contribute to the class discussion. This may be a good time to ask a question that you wrote down the night before. The main body of the activity consists of a problem set intended to help you transition from the basic questions asked in the quiz to the more challenging questions asked in the homework assignment. This is a great time to assess your understanding and to get help if you need it. Sections marked “Optional” are intended for those students who have finished the required problems and who are interested in some of the more theoretical and deeper aspects of calculus. Most lessons have optional supplemental exercises for extra practice, and these can be found in Appendix C.

How the Course Works

1. On the date when the lesson and examples videos are assigned, navigate to the AUCI website (http://people.alfred.edu/~calculusinitiative/).
2. Watch and pay attention to the lesson and example videos. Follow along with the textbook, take notes as if you are sitting in class, and record any questions that arise.
3. Immediately take the self-assessment quiz through WeBWorK. If you are instructed to do so, email your teacher with any questions or problems.
4. Attend the next class meeting and complete the corresponding activity in class. Ask your teacher about any questions or problems that arose the night before.
5. Complete the hand-in or WeBWorK homework assignment. If you are instructed to do so, email your teacher with any questions or problems.

Additional Advice

We have based this course on years of sound research and successful techniques and trends in STEM education, but it is a two-way street. Bergmann and Sams assert that “in order to succeed, the students must take responsibility for their own learning… [which] is no longer an imposition on their freedom but rather a challenge to be unpacked and explored. As the teacher gives up control of the learning process, the students take the reins, and the educational process becomes their own” (Bergmann, 60). Here is a list of things to keep in mind:

• Keep track of the daily schedule so you do not miss an assigned lesson.
• Keep track of the opening and closing dates and times for the quizzes and homework.
• Watch the videos and read the text as many times as needed.
• Find additional online support, if necessary.
• Take plenty of notes and write down your questions and problems.
• Get help as soon as you need it either by email, in class, or during office hours.
• Generate and print PDF copies of the quiz and homework sets and carry them with you.
• Work quiz and homework problems carefully on paper before submitting answers online.
• Create your own study guides and form a study group.

Reference

Bergmann, Jonathan, and Aaron Sams. "Flip Your Classroom: Reach Every Student in Every Class Every Day." Eugene, Oregon: ISTE, 2012.