Section 5 The Structure of Each Section
The core structure of each section is the following:
Learning Objectives: Each section has 1 to 4 learning objectives. This gives a brief summary of the core concepts in the section.
Main Content with Examples: Students are expected to read the text and complete the "Try It" examples. If students are reading the text, they should be able to do these problems. And if they can't do these problems, that's a signal to them that they need to contact the instructor (or campus tutoring services, if available) to get help. The solutions to these examples are provided in the text.
Worksheets: The worksheets are extra problems that are sometimes similar to the "Try It" examples, but they also sometimes diverge into a deeper look at familiar ideas. Those problems are where students are being asked to think mathematically. Given what they know, can they push deeper and make a new connection? We encourage students to approach these as group explorations because the act of talking through ideas (communication) is important to the primary learning outcomes. The worksheets are intentionally short to allow for these types of conversations to happen relatively quickly, rather than having them first do dozens of rote exercises before sharing their ideas with each other.
Deliberate Practice: Most sections will have a short collection of exercises to allow students a bit of additional practice. This is called "deliberate practice" because students are given a number of ideas to focus on while they do these problems. These are supplements to provide students with further opportunities to practice the skills that they've developed (thinking, presenting, explaining, and executing) by doing standard manipulations. If you are looking to just dump a bunch of problems on students, you're much better off using a different textbook. These sections are intentionally kept short to discourage instructors from just assigning students to do rote exercises.
Closing Ideas: Each section has a brief discussion that summarizes the ideas that are found in the section and the worksheets. The purpose of this is to redirect the focus towards the horizon. As students work their way through each section, it's easy to get fully absorbed in executing the calculations and lose track of how this fits into the bigger picture.
Going Deeper: Many sections will have an additional topic that pushes students deeper. These sections exist to better illuminate the ways that the ideas from the section link to higher levels of mathematics and other applications of the ideas in each section. These additional topics can all be skipped without losing any of the core content of the book, but some instructors may find some of the topics to be helpful for use in just-in-time remediation. For example, there is a series of sections that focus on manipulating rational expressions that a precalculus course may want to cover. Other sections are there simply as fodder for discussion and to broaden students' mathematical perspective.