Algebra I

Algebra:

Algebra is a completely different “animal” than all previous math courses. It’s much about the “unknowns.” We assign letters for unknowns and solve for them. Algebra is about thinking deeply on the nature of numbers themselves, how they relate to each other and their operations. Algebra takes you into an abstract world, but it also makes visible very real things in its application of graphing data and creating and solving equations.

Methodology:

Our method is called a mastery approach. This means we start with the simple concepts or skills to be learned, and then delve into a topic, explore all of its applications and variations, and stick with it till students understand it. In fact, on homework, students are expected to achieve 100% or very close to that given all the helps available. This mastery focus saves time, and makes math more interesting and intellectually satisfying for many students.

Another approach that is now popular among homeschoolers is an incremental or spiral approach, wherein new material is introduced incrementally and taught mainly by inference and rote. The daily review takes up most of the homework both in number and time spent. Only tiny bits of new concepts or skills taught per day. Most of one’s Math work then is drill and review each day. Some research shows that the spiral or incremental/review approach keeps students from forgetting what they have learned. But a major drawback about this method is that that for many students this approach can be very boring, and math is taught as a series of memorized steps rather than gaining deep understanding about first principles of math, and the nature of mathematical methods. Too much drill and too small an incremental learning path can detract from seeing the beauty and elegance that is inherent to mathematical principles. Also, some students need more review on one skill than another. So the extra review may just be busy work if all students are mostly doing the same exact assignments. Yes, math is beautiful because it concisely expresses concrete truths about the laws of the Divinely created universe!

The mastery approach is not opposed to drill, but at RCA review is done after each chapter and with quarterly exams. The book and the nature of the math is such that the scope and sequence is spiral or building from section to section. For instance, the needed skills from chapter two or three, are used throughout the rest of the problems in the book. Students review each week, at the end of each chapter, and quarterly, through the individualized study plan. This most of the work the student does daily is focused on exactly what that student needs in order to master the current objectives and skills. When we achieve the goal of understanding principles the student’s knowledge and ability transfers outside the text and to other subject. This is reinforced in that real world application problems are incorporated into the end of most sections each chapter has an entire section devoted to applications from science, business, and daily life.