Pre-algebra focuses on introductory algebra concepts. It is designed to transition the student from concrete arithmetic to the abstract logic of algebra. The goal of mathematics is to teach students how to quantify the world around them, analyze it, and give it value—in other words, how to logically understand their world. Algebra uses the simplicity of numbers and their operations to define a logical process for that evaluation. In algebra students learn to apply a series of logical processes to a numeric problem which develops within them problem solving skills for the greater problems of life.
The repetition found in the problem sets is not busy work. Instead, the student is practicing concepts to make each step second nature. Things that are different become familiar only after some time of exposure. Having them internalize and master the steps gives them a well of perspective from which to view a problem and determine how to solve it.
Algebra 1 moves away from the basic algebraic logic using foundational arithmetic and adds complexity and new concepts. It takes the student into a more logically abstract view of mathematics, while still maintaining the previous concepts and rules of pre algebra. It peppers in more complex geometry and builds the applied geometry understanding. It also begins to introduce topics like probability and statistics, logarithms, and data analysis.
Algebra 2 continues the study of algebra and geometry while adding trigonometry concepts, geometric proofs, and more probability. It prepares the student for pre-calculus, trigonometry, and advanced mathematics. Concepts are applied continuously to master them and show their relationships to one another. Each mathematical rule is relative to every other and should be continually considered. Due to the interspersing of geometry over a three-year period from Algebra 1/2 through Algebra 2, students learn all of the applied geometry necessary for a typical high school geometry credit by completing Saxon’s Algebra 2 3rd edition. The fourth edition of Saxon’s algebra courses removes geometry and makes it a separate textbook focusing on theorems, postulates, and proofs placing minor emphasis on the calculations of geometry. This geometric calculation rigor is why I prefer the third edition. John Saxon included geometry in his final publications of algebra to keep geometry from being a separate subject. The publisher, not John Saxon, separated it into a separate textbook in the fourth editions to appease public and private school systems who wanted geometry as a separate course.
In most homeschool-friendly states, the parent is the determiner of the needs of the student and the credits they earn. the parent may choose to teach geometry as a separate topic to ensure the credit, but in doing so will find that most of the geometry curriculum out there will be redundant to what the student has learned throughout the Saxon Algebra 3rd edition trilogy. Still, it is always up to the parent to choose the rigor of the curriculum. For most in this situation, eliminating a separate geometry course is beneficial to retention between algebra years one and two. It is expeditious in students who have neglected mathematics studies while still providing all the rigor necessary for the mastery required of an essential geometry credit. Should you choose to teach a geometry course in addition to the algebra trilogy it is recommended to teach it after algebra 2, not before. Based on the rigor of the Saxon methodology and material, my recommendation is that the student receive a standard unweighted credit for geometry without taking a separate course and an honors credit if they do.
A more thorough examination of the scope and sequence of the Saxon Algebra trilogy may be found in the below document.