This series targets students sixth grade and above, but it uses a mastery learning approach that might work especially well for students who have struggled with math or who have learning gaps.

Courses are offered in two formats—textbook or online--with one exception: *Pre-Calculus* is only available online. For each course you also need the companion Parent's Guide that is essential to each course. This is true for both text and online versions.

You begin with the placement test in the Parent's Guide. Student's can then begin studying chapters that teach concepts they have not yet mastered rather than completing every lesson. The placement test answer key indicates which chapters cover which problems. At the beginning of each chapter is a list of "Chapter Objectives" that might also be used as a pre test to help identify which units within a chapter a student should complete if you suspect your student already knows much of the material.

Lessons are presented quite differently than in traditional texts. There is no introductory lesson with sample problems. Instead, each lesson begins with only a brief highlighting of key terms for the lesson. The lesson itself is presented in two columns. A wide column (about 2/3 of the page) on the left presents information in the form of statements and questions broken down into small nuggets, each one numbered. For example, p. 86 of *Beginning Algebra*, number 4 reads "The fact that xy is equivalent to yx is the **Commutative Law of Multiplication**. According to the Commutative Law of Multiplication, 5 · 8 is equivalent to _____."

Immediately to the right in the smaller column is the answer "8 · 5."

Number 5 continues to develop the topic giving an example using "rs is equivalent to sr because of the _________ Law of Multiplication." The correct answer would be "Commutative." The lesson continues with a number of similar "paragraphs" (as they are called in these courses) to be completed such as number 9, "The expression w · 7 may be replaced by ____ by the Commutative Law of Multiplication." This format provides a great deal of reinforcement and explanation of each concept.

Students should be covering answers and attempting to answer correctly on their own before looking at them. Online courses have a question mark that students click to reveal each answer. The courses suggest that students write answers on paper, then compare to the book or computer. However, I suspect that many students will skip this step with many of the simple answers to save time.

This type of instruction continually elicits responses to keep students tuned in and thinking about what they are learning. Occasionally, students will need to use paper and pencil to work out steps in a problem before arriving at a correct answer.

Sometimes, the format changes to accommodate different types of problems/skills. For example, some "Applications" sections of *Beginning Algebra* deal with word problems. They present word problems then expand the answer sections greatly to provide detailed explanations of how to arrive at the correct solutions. (I think this text would benefit from even more of these word problems.) A similar approach is used for solving multi-step equations.

Visually, these courses are quite plain. There are no illustrations other than those required for problem solving. Answers are printed in a different color. Some perceive this positively as "no distractions" and "no fluff" while others miss the visual stimulation. The latter might find the computer version more appealing since the computer screens are more colorful and visually interesting.

Courses are arranged in chapters, with from 7 to 14 chapters each. Each chapter is broken down into units. A unit typically, but not always, has 50 or more of these numbered explanation/problems, each requiring a response.

At the end of each unit in the books is a "Feedback Unit." In the online version, these are called "Unit Exercises." Think of these as comparable to problem sets for a lesson in a traditional textbook. Students work through these problems. Then either student or parent can check the answers in the back of the book or against the online answer key. Online courses require paper and pencil responses for all unit quizzes, but multiple-choice chapter tests are completed online by students then automatically scored by the computer. A student must score 90% or higher to move on to the next unit. If not, they need to go back and review the material. The publisher provides free assistance via email or fax if a student gets stuck.

Chapter Mastery Tests at the end of each chapter work the same way. If a student scores 90% or better, he or she is ready to take the Chapter Test that is provided in the Parent's Guide. Chapter Tests from the Parent's Guide are used with both textbook and online courses. Up to this point, the student might be working totally independent, checking and scoring his or her own work. So the parent administered Chapter Test with answers available only in the Parent's Guide helps to keep students honest. The Parent's Guide has three alternative Chapter Mastery Tests plus answer keys in case students do not pass the first time.

Online College Prep has six courses available. *Arithmetic: An Individualized Approach* is for students sixth grade and above who either need to review basic concepts or fill gaps. It assumes basic instruction in whole numbers, operations, fractions, and decimals has already been presented, but it does review at a very basic level (e.g., adding 2 + 9). It also serves as a pre-algebra course in that it covers signed numbers and order of operations. However, it is not as comprehensive as most pre-algebra courses.

The next course is *Beginning Algebra: An Individualized Approach.* This course also reviews at very basic levels such as simple addition, moving on into the first part of what would be considered a high school algebra course. This is not a complete algebra 1 course, but it can be treated as the first semester of such a course. *Elementary Algebra: An Individualized Approach* serves as the second semester of algebra 1. The design of these algebra courses make them particularly suitable for remedial situations, but they can also be used for other students since the placement tests and also the chapter objectives show students which chapters and units they need to study. While advanced or very bright students can skip topics they've already mastered, I suspect that some of them would find these courses a bit frustrating since so much space is devoted to review and reinforcement that such students don't need.

This series continues with *Intermediate Algebra, Trigonometry,* and *Pre-Calculus*. While I have not reviewed these upper level books individually, they appear to follow a similar format with less challenging content than some other texts for the same courses.

What makes these courses particularly appropriate for homeschoolers is their design for independent study. Parents need only administer chapter, cumulative, and final tests. Courses do not require parental teaching, and assistance is available from the publisher if needed.

The publisher says that students should plan to spend about one hour per unit in the lower level course, although I suspect that some students will breeze through some units much more quickly than that. The number of units varies, with 69, 58, 75, 69, 33, and 52 units respectively in *Arithmetic, Beginning Algebra, Elementary Algebra, Intermediate Algebra, Trigonometry*, and *Pre-Calculus*. While *Trigonometry *has about half as many units as the other courses, each one has far more time-consuming problems. These units should not be tackled in one sitting.

Online versions are web-based courses, so you'll need an internet connection. The online versions are not significantly different from the textbook versions since students will work the same way with either format. With online courses, they enter answers into the computer only for chapter tests. However, parents are the ones most likely to appreciate this time-saving option. Parents can enter the administrative area at their convenience to view student scores on these tests. Online versions are quite easy to navigate and use for both student and teacher.

It's a toss up as to which type course to choose. Since textbooks are not designed for students to write in them, they are not consumable. You might be able to reuse a textbook for additional students. With any subsequent students using a text, you might need to buy another Parent's Guide if you need more versions of the Chapter Tests since they are not reproducible. This all means that you might save with the textbook versions if you think you have a younger student who will eventually use the same course. Computer and internet access might also be significant factors in your decision.