Preface To the Instructor¶
This book is a collection of activities — a digital workbook — that replaces traditional textbook reading with an interactive, guided-lesson approach to learning. The workbook covers common topics of precalculus that are otherwise delivered as passive reading assignments or lectures.
We hope this book will feel very natural to use. Each chapter begins with activities which introduce students to the basics of a topic. Activities use WeBWorK, an open-source online homework system, to give students immediate feedback on their learning. Many exercises include dynamic GeoGebra graphs for students to manipulate.
These activities mimic what has traditionally been done in discovery-based classroom work, to be completed by students as “homework”. Having completed the activities, students come to class ready to engage in further discussion and application of the material. Since WeBWorK gives students immediate feedback, they get basic questions answered as they actively read.
Following the activities, each chapter has a Gist section which resembles the expository content in a traditional textbook, though it still has interactive components such as found in the activities.
Why Another Math Book.
Many mathematics textbooks begin with the assertion that they deliver a new or unique approach to learning. This book is different, at least in that regard, in that the authors concede there is really nothing new in our approach. What follows is a presentation of learning that already happens in mathematics classrooms worldwide — students actively engaged in the learning process: experimenting, observing, discovering and applying.
Current technology in education software is used mostly in the assessment of homework. On the other hand, reading material in the form of an e-book is relatively static — it is an electronic version of the text that remains a passive reading experience for the student. The result is that students often skip the reading altogether and go directly to the homework section where they hope to learn their skills through repetition or by “reverse engineering” the solutions. While homework remains a key aspect in student learning, it is currently used at the “back end” of the learning process. This text was created with the belief that an active, discovery-based approach in knowledge development contributes to longer knowledge retention and is linked to a deeper understanding of the material.
Therefore with this book, we hope that the active learning process used so well in college classrooms can be brought to the reading experience. This is nothing new to mathematics, though perhaps it is somewhat new to the textbook.