Precalculus

Precalculus - Three Distinct Series

Students have different goals, learning styles, and levels of preparation. Instructors have different teaching philosophies, styles, and techniques. Rather than write one series to fit all, the Sullivans have written three distinct series. All share the same goal—to develop a high level of mathematical understanding and an appreciation for the way mathematics can describe the world around us. The manner of reaching that goal, however, differs from series to series.

Contemporary Series 11e

The Contemporary Series is the most traditional in approach yet modern in its treatment of precalculus mathematics. Graphing utility coverage is optional and can be included or excluded at the discretion of the instructor.

Enhanced with Graphing Utilities Series 7e (New Edition Coming January, 2020)

This series provides a thorough integration of graphing utilities into topics, allowing students to explore mathematical concepts and encounter ideas usually studied in later courses. Using technology, the approach to solving certain problems differs from the Contemporary Series, while the emphasis on understanding concepts and building strong skills does not.

Concepts through Functions Series 4e

This series differs from the others, utilizing a functions approach that serves as the organizing principle tying concepts together. Functions are introduced early in various formats. This approach supports the Rule of Four, which states that functions are represented symbolically, numerically, graphically, and verbally. Each chapter introduces a new type of function and then develops all concepts pertaining to that particular function. The solutions of equations and inequalities, instead of being developed as stand-alone topics, are developed in the context of the underlying functions. Graphing utility coverage is optional and can be included or excluded at the discretion of the instructor.

CoRequisite Support for College Algebra/Precalculus

The Sullivan CoRequisite solution for College Algebra is based on the Sullivan/Sullivan College Algebra through Concepts 4e title  The Sullivan CoRequisite solution for Precalculus offers either a unit circle appraoch or right triangle approach to trigonometry.  The Precalculus courses are based on either the Sullivan/Sullivan Precalculus Concepts through Functions: A Unit Circle Approach to Trigonometry 4e or Precalculus Concepts through Functions: A Right Triangle Approach to Trigonometry 4e.

All three titles corequisite support material is based on the Sullivan/Struve/Bernards/Fresh Intermediate Algebra 4e title.

Michael Sullivan, III is currently teaching Corequisite Precalculus using the Unit Circle text at Joliet Junior College.  Feel free to copy his MyLab course.  The courseID is

sullivan-pearson07201

In the Corequisite portion of the course, we provide students with the material necessary to be successful in the corresponding material in the College Algebra course.

The learning path for students in a corequisite course is something that each individual instructor must decide upon.  However, the course downloaded from Pearson has been developed by the authors and comes with the following learning path:

  1. For Chapter R, Elementary Algebra Review.
    1. Student takes a diagnostic quiz on Sections R.1 through R.4. The material in these sections qualifies as an arithmetic quiz.  If the student passes, the student then moves to taking a diagnostic quiz on Sections R.5 through R.10, which represents an Elementary Algebra quiz.
    2. If the student does not pass the R.1-R.4 diagnostic quiz, then the student takes a quiz corresponding to each section (R.1, R.2, R.3, R.4). For each section, if the student passes the quiz, the student moves to the next section.  If the student does not pass, the student works a personalized homework which focuses on those objectives for which the student did not demonstrate mastery.  Upon completion of the personalized homework, the student retakes the section-level quiz until mastery is achieved.
    3. Once the student completes the arithmetic sections (R.1 to R.4), the student takes a diagnostic quiz on Sections R.5 to R.10 (Elementary Algebra). If the student passes the quiz, the student may move to Preparing for Chapter F.  If the student does not pass the R.5-R.10 diagnostic quiz, then the student takes a quiz corresponding to each section (R.5, R.6, …, R.10).  For each section, if the student passes the quiz, the student moves to the next section.  If the student does not pass, the student works a personalized homework which focuses on those objectives for which the student did not demonstrate mastery.  Upon completion of the personalized homework, the student retakes the section-level quiz until mastery is achieved.
  2. Student works through an assignment for each section of Preparing for Chapter F.
  3. Student works through an assignment for each section of Preparing for Chapter 1.
  4. And so on.

Each assignment in the Preparing for chapters has two MyLabMath assignments.

  • The first assignment is a multimedia assignment that incorporates the Author in Action lecture videos, the new applet discovery exercises, “How To” guided exercises, and the Quick Check exercises from the text. Recall, the Quick Check exercises follow many of the examples in the text. To assist students in utilizing the text, the Textbook learning aid for each Quick Check exercise will link directly to the corresponding example in the text. All learning aids, with the exception of “View an Example”, will be available for this portion of the homework. Our experience as instructors has been that too many students rely on this learning aid while doing homework, thereby reducing the effect of homework as students simply mimic the View an Example content.
  • The second assignment is based on the Skill Building and Mixed Practice exercises from the text. Skill building exercises are tied to objectives within the text, so the Textbook learning aid will link directly to the objective within the section. The idea is to reduce the amount of guidance provided to the student (compared with Quick Check exercises) so they are more responsible for identifying the problem type. The Mixed Practice exercises are based on multiple concepts learned within the section or text, so the Textbook learning aid is linked to the section. The student must determine the problem type based on Quick Check and Skill Building exercise experience. The “View an Example” learning aid is disabled for this exercise set as well. Because this text has Skill Builder available in MyLabMath, you may consider reducing the number of exercises in the second assignment. By checking the Skill Builder box, the assignments will adapt to provide support exercises personalized to each student’s needs.

Note:  If you are using a mastery-based learning model, you will need to build quizzes (at either the chapter or section level to assess mastery of skills for each Preparing for chapter).

Study Skills

In our experience as corequisite instructors, one of the main impediments to success for our students has been their lack of study skills.  In fact, data based on Tennessee corequisite students compiled by the Tennessee Board of Regents showed that students who failed both their corequisite course and college-level course also only earned roughly 20% of all attempted college credits for all their courses, while students who passed both courses also earned roughly 85% of all attempted credits for all their courses.  What does this suggest?  It suggests that students who are not successful in corequisite courses tend not to be successful in any of their courses.  These students can be described as not being college-ready (as opposed to academically ready). Therefore, corequisite courses must develop quality study skills in students.  To address this, Jessica Bernards and Wendy Fresh developed innovative study skills videos.  The following skills are addressed in the videos and there is one MyLab multiple choice question and one MyLab free response question for each skill.

  1. How Learning Math Is Different
  2. Grit and Growth Mindset in Math
  3. Resources Available for Help
  4. Time Management
  5. How to be an Effective Listener and How to Take Notes
  6. How to Do Math Homework the Right Way
  7. How to Study for a Math Exam
  8. Overcoming Math and Test Anxiety

Course Dependencies

Teaching a corequisite course is a delicate balancing act.  The instructor must be sure the students have mastery of the corequisite content while also making sure the integrity of the corresponding college algebra course is maintained (and the course content is completed).  Therefore, it is likely necessary for an instructor to begin some college algebra material even though the corresponding corequisite content is not complete.  The table below lists sections in the corequisite course that should be mastered prior to introducing the corresponding college algebra material.   A detailed table of contents for both the college algebra text and corequisite support text follows.

Co-Requisite Section Completed before… …College Algebra/Precalculus  Section
Chapter P Elementary Algebra Review Any College Algebra material
Section PF.1 Section F.1
Sections PF.2 through PF.4 Section F.2
Section PF.5 Section F.4
Section P1.1 Section 1.1
Section P1.2 Section 1.3
Section P1.3 Section 1.7
Sections P2.1 through P2.3 Section 2.3
Section P2.4 Section 2.7
Section P2.5 Section 2.8
Sections P3.1 and P3.2 Section 3.2
Section P3.3 Section 3.4
Sections P3.4 through P3.6 Section 3.5
Sections P4.1 and P4.2 Section 4.3
Section P4.3 Section 4.6
Sections P4.4 and P4.5 are optional and included for completeness of the discussion of radicals