Calculus From The Ground Up

Description

This text is very well-done and would be a good follow-up to any precalculus/trigonometry course. The explanations are easy to understand and the author ties calculus concepts to real-life problems. The information is presented in a conversational tone, begins with the basics and builds to more complex concepts. This is a good traditional approach, employing the mastery approach with plenty of practice. Students should be able to manipulate equations, graph equations, analyze triangles, know the basic formulas for a line, area, quadrative, distance, Pythagorean Theorem, exponents, logarithms, etc. They should also be familiar with sin, cos, tan, inverse functions, and have an understanding of functions and how they work. There is a brief review in the first part of the book, and an appendix for reference if you need a bit of help. The Textbook is 446 uncluttered pages and is divided into 5 parts: Preliminaries, The Derivative, The Integral, Manipulating Infinity, and Appendices. The first four divisions or parts are divided into 31 chapters. The Solutions Guide offers worked solutions for the exercises found at the end of each chapter and explanations where needed.

This course is written by Jonathan Bartlett, who thinks math should be taught using a classical approach. In the grammar state students should learn to count, add, subtract, multiply, and divide. In the logic stage students should learn formulas. Calculus, in his opinion, is the gateway to the rhetoric stage and allows students to be creative. This is the time for students to create their own formulas and understand them and their origins. The focus of Calculus from the Ground Up is how math is invented, and how students can learn to be part of the creative process.

Each chapter is divided into sections (ex. 3.1, 3.2, etc.), offering explanations for each concept. New terms are printed in bold and a review that covers the topics of the chapter is included at the end of each. After the review section, students are provided wuth exercises for that chapter. Once a concept is taught with a thorough explanation, the explanation becomes less the next time the student sees that concept. By the third time a student sees that concept, it is assumed that they are familiar with it, and there is no explanation. Appendices are full of helpful information that students can use as a reference while working through the text.

The text is written to be taught over a one-year period of about 30 weeks – one high school credit. The author offers a suggested teaching schedule in Appendix A. ~ Donna

Teaching Method
Traditional
Teacher-centered curriculum commonly used in classrooms that may include a text, teacher manual, tests, etc.
Charlotte Mason
A methodology based on the work of a 19th century educator who maintained that children learn best from literature (Living Books), not textbooks.
Classical
A methodology based on the Latin Trivium (three stages of learning), including the grammar stage (memorization and facts), logic stage (critical thinking), and rhetoric stage (developing/defending ideas).
Unit Study
A thematic or topical approach centered around one topic that integrates multiple subject areas.
Montessori (Discovery)
A methodology based on the work of a 20th century educator that emphasizes student and sensory-driven discovery learning and real-life applications.
Other
Other methodologies
Religious Content
Secular
Contains content contrary to common Christian beliefs (i.e. evolution).
Neutral
Avoids religious or theoretical topics or presents multiple viewpoints without preference.
Christian/Religious
Faith-based or including instructional religious content.
Learning Modality
Auditory
Learns through listening, talking out loud or reading out loud.
Visual
Learns through seeing, prefers written instructions and visual materials.
Kinesthetic/Tactile (Hands-On)
Learns through moving, doing and touching.
Multi-Sensory
Curriculum that employ a variety of activities/components.
Presentation
Sequential
Curriculum progresses through well-defined learning objectives. Emphasizes mastery before moving to the next topic.
Spiral
Topics and concepts are repeated from level to level, adding more depth at each pass and connecting with review.
Conceptual/Topical
Focus is on the “why,” often with a unifying concept as well as specific skills; coverage may be broader.
Teacher Involvement
Low Teacher Involvement
Student-led materials; parent acts as a facilitator.
Medium Teacher Involvement
A mix of teacher-led time and independent student work.
High Teacher Involvement
Teacher-led lessons; may utilize discussions, hands-on activities and working together.
Additional Materials Required
No other materials needed
Everything you need is included.
Other Materials Required
There are additional required resources that are a separate purchase.
Other Materials Optional
There are additional resources mentioned or recommended but are not absolutely necessary.
Consumable
Consumable
Designed to be written in; not reusable.
Non-Consumable
Not designed to be written in; reusable.