|
Pre-Algebra: Pre-Algebra is about using all the arithmetic operations with all types of numbers which students should have learned from about 1-7th grade. I. It is also about learning self-discipline of daily work, meeting deadlines, learning to be self-motivated. In this course, the further application of the math is done with extensive types of real world “word problems”. In the second half , of the course we introduce simple ratio, percent, and many types of simple linear equations to solve using elementary algebra. Learning to use order of operations with number sentences marks the course apart from the review and mastery seventh grade math course. This is why mastery of regular arithmetic is needed. This is and a foundation of conceptual knowledge so that Algebra will not be a completely foreign course.
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. Page through this site to get all the info about this course.
A quick comment on the text: A college math book for thirteen year olds? Am I serious? Yes. Most eight grade students can comfortably use this book. Don’t let the work “college” in the book scare you. This is a remedial text book that is meant to help beginning college students who somehow didn’t get their math and to prepare them for Algebra in a no nonsense, very logical way. An advanced 6th graded ready for pre-algebra could also use it, and I had two such students finish the course with “A’s” in past years. If you have a “math-phobic” middle school or high school student, or one “behind” in math, this book can be a great esteem builder. Instead of being “behind”, they are now using a “college” text! The reason we use Lial's College Mathematics series is because the mathematical explanations behind the problem solving are excellent. The explanations help develop sound mathematical reasoning from the beginning, in preparation for higher mathematics. In this series, emphasis is placed on the solution process, understanding how to solve the problem, rather than just finding the correct answer. Enough problems are offered to allow a student to master math concepts, yet there are not so many problems that a student becomes bored. Also the student is continually encouraged to completely understand a section before moving to the next section. Emphasis is also placed on vocabulary (definitions) - understanding the language of math. Read more details on the page about the text. |
|
Regina Coeli Academy Pre-Algebra |
|
The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. --Aristotle |
