Half a Hundred Acre Wood

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I recently mentioned something I would have done differently if I could turn back time and homeschool our oldest two sons through high school once again. There’s another thing I would have done differently, especially because they both ended up as STEM majors in college. Neither were math whizzes, but surprisingly, one decided to major in chemistry and the other decided to major in electrical engineering. Both enrolled in calculus their first semester in college but would have benefited from an introduction to calculus beforehand.

At the time, I was not aware of a course in calculus which could be taken without precalculus, trigonometry, or even Algebra 2. In fact, the only prerequisite for this course is a basic understanding of Algebra 1. That course? Calculus for Everyone.

So… how can a course in calculus be taken before Algebra 2? In Calculus for Everyone, the concepts of calculus are presented using functions that are introduced in Algebra 1 (polynomials). By setting aside the more advanced trigonometric, exponential, and logarithmic functions introduced in later math classes, students can master the concepts and practical applications of calculus as a tool for STEM. Further, this foundational understanding of calculus will provide a context for learning more advanced math in other classes.

Calculus for Everyone not only teaches the core concepts of calculus, but it also introduces the history of calculus and its importance to physics — and why calculus was invented in the first place. The course consists of a textbook, exercise solutions, and a video course. The textbook includes hundreds of hand-drawn illustrations with detailed explanations of each concept.

One of the goals of this course is for students to establish the habit of reading a math textbook (something students should do in any math class).  Because this textbook is more engaging and appealing to read than most, it’s a great resource for learning this important yet often overlooked skill for success in mathematics. (Other important skills often overlooked in mathematics are repetition, neatness, and organization. This textbook also encourages students to work problems repeatedly and to keep their work neat and organized.)

The course is divided into 25 chapters (plus the introduction and epilogue) with each chapter/lesson consisting of four parts:

  • 28 video lectures (30-60 minutes long) that walk students through background and step-by-step examples
  • textbook reading
  • study questions
  • exercises

Calculus for Everyone can be taken in a single semester or a full academic year and provides a strong foundation for a more conventional calculus course in the future. Course content includes:

  • The Problem Of Change
  • Space, Time, And Numbers
  • The Paradox Of Speed
  • The Platonic-Pythagorean Project
  • The Scientific Revolution And The Need For Calculus
  • Newton And Calculus
  • Variables, Functions, And Graphs
  • The Limit
  • The Method Of Approximation
  • Using The Method Of Increments
  • Derivatives
  • Using The Power Rule To Find Derivatives
  • Graphs And Slopes
  • Slopes And The Problem Of Change
  • Graphs Of Free Fall
  • The Antiderivative
  • Defining The Integral
  • Using The Method Of Summation
  • The Fundamental Theorem Of Calculus
  • Interpreting Areas
  • More about the Problem of Change

As indicated on the course website, students learn:

  • the need for calculus and its historical development.
  • the general concept of function and its applications to real-world situations.
  • to work with algebraic functions and their applications in applied problems.
  • the concepts of the derivative and its underlying concepts.
  • to calculate derivative for various type of functions using definition and rules.
  • the concept of derivative to completely analyze graph of a function.
  • about various applications of the derivative
  • about anti-derivative and the Fundamental Theorem of Calculus and its applications.
  • to use concept of integration to evaluate geometric area and solve other applied problems.

To test drive the curriculum, you can watch “How to Use This Course” and “Chapter 5: The Scientific Revolution and the Need for Calculus” by clicking on the “Sample Lessons” tab at this link.  You can also preview a large sample of the textbook by clicking on “Sample Textbook.” MyCompassClassroom also provides free access to the Preface & Introduction (14 min video) and Chapter 1: The Problem of Change.

Our family recommends Calculus for Everyone — not just for STEM majors but for any student — because it provides foundational concepts for understanding the answer to the oft asked questions, “Why am I learning this?” and “What will I use this for?” (In fact, our third son who is opting for trade school, is planning to take this course in conjunction with Discover Physics next year because of its practical application in heavy equipment operation and mechatronics.)

Math is a practical tool, and sometimes we miss the forest for the trees. This course gives the broad overview that is often missing in conventional math classes.


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