Calculus II includes many interactive opportunities where you can strengthen your knowledge and practice using the concepts taught in the course. Research has shown that this type of learn-by-doing approach has a significant positive impact on learning. We encourage you to utilize as many resources in this course as possible to deepen your understanding over time. Since this course can feel daunting with all of its components, we’ve compiled some helpful tips and bits of information about the structure of the course to assist you as you navigate through.
- Every module begins and ends with a “Why It Matters” page and a “Putting It Together” page. The Why It Matters page presents a real-world example of a calculus concept to be taught in the module. Then the problem is restated, solved, and explained on the Putting It Together page once the module is completed.
- Each module is proceeded by a “Prerequisite Material” module and followed by a “Supplemental Content” module. The Prerequisite Material pages present skills needed for the upcoming module that you should be review from earlier math classes. The Supplemental Content pages contain the problems sets, discussions, etc. that specifically focus on the concepts presented in the prior module.
- Every module is divided into sections; each section begins with an “Introduction to” page and ends with a “Summary of” page.
Colored Emphasis Boxes
The objective is for you to master the concepts and skills stated below. Mastery takes time, effort, practice, and application. Reading the content on the page is only one step in the learning process.
- Learning Outcome 1
- Learning Outcome 2
The complete Learning Outcome spreadsheet can be used if a specific “LO” is referenced anywhere in the course, i.e. “LO 4.1.3”
These problems are usually the first demonstration of how to apply the content you just read about. The solutions are usually detailed and outline each step of the process. Solutions are hidden so that you can attempt them first on your own and then compare.
These problems are your chance to independently apply what you just saw in the previous example problem. Usually the only part of the solution shown is the answer, but there are sometimes hints to help if you don’t know where to begin. If the problem is regenerative you can try multiple versions of the same question.
OHM Embedded Practice Questions
- Practice questions appear on most pages in the course, embedded in the main text of the page. The purpose of these questions is different than the questions on homework or quizzes, which are designed to assess mastery of learning outcomes. Instead, practice questions allow you to learn-by-doing, immediately after seeing similar example problems in the text. These questions can be attempted multiple times with different values since they are algorithmically generated. Click the “Try Another Version of This Question” to see a new version of the question as many times as you want. You can use this feedback to inform your study choices after learning a new concept and verifying a basic understanding or continued confusion.
REcall or Strategy
The information in these red boxes will help you recall mathematical concepts that will be needed as a foundation for the next idea or problem presented in the text. These should be familiar to you; if not, you may need to review and practice these skills more before moving on (i.e. if you cannot remember how to count, it would be very difficult to learn how to add). The other information given in these red boxes are problem-solving strategies to help you breakdown the steps to complex questions.
The purple boxes usually contain a link that leads to an interactive feature. These allow you to explore concepts in a more hands-on way or see how they relate to real-world situations.
- We highly recommend trying to solve the example problems in the videos at your own speed while playing and pausing the video every couple steps to check your work.
- Double-click any video in the course to open in full-screen viewing mode.
- Transcript text is linked below each video and clicking the YouTube button on the video will open the video with a closed caption option.
- When you see a [T] next to a question in the problem sets, it means that this question is technology-based and a graphing calculator or graphing utility can be used to help solve it.
- Try to solve the problems with answers fully before clicking “Show Solution” to unhide the answer.
- In addition to practice questions, the course contains select opportunities for additional learning by doing in the form of more extensive interactive activities. These often occur at places in the course where instructors report that students tend to struggle, or where data shows that students need extra support.