The problem with trying to teach advanced math at home is often that the teacher (or parent) doesn't know the material themself. Dr. Dale Callahan has attempted to alleviate this problem by offering video courses that present existing math texts lesson by lesson. He is a professor of engineering at the University of Alabama and brings his expertise to bear in explaining as clearly as possible the complex world of algebra, geometry, trigonometry and calculus. This series of DVDs is especially useful for students who intend to pursue math studies in college and need to be sure their math foundations are secure.
Dr. Callahan's DVDs cover algebra, geometry, college algebra with trigonometry, and calculus. For algebra and geometry he uses the Harold Jacobs texts; for college alegbra with trigonometry he uses the McGraw-Hill text; and for calculus he uses the Brooks/Cole text by James Stewart. All lessons are taught by Dr. Callahan except those for the algebra course, which are taught by his daughter Cassidy (who is a classical school teacher and quite entertaining).
Each lesson on the DVDs corresponds to a lesson in the text, and features Dr. Callahan in front of a white board explaining the material and working through the examples. It is important that you have the texts, since the video lessons are meant as supplements, not a complete, independent program. Callahan's explanations are detailed and thorough, if not entirely entertaining. Students should read the appropriate chapter in the text before watching the lesson, and probably again afterward to ensure they've really grasped each concept.
Cassidy Callahan takes a different approach from her father. She offers possibly the world's most energetic and enthusiastic presentation of algebra, and even incorporates editing and multimedia elements (as opposed to a single sustained direct shot). While not as "professorial" as her father, she will probably get even reluctant math students to enjoy algebra. (Not that Dr. Callahan will necessarily turn kids off from math, but anyone studying calculus or trig probably doesn't need much encouragement anymore.)
College Algebra with Trigonometry is a McGraw-Hill text. Definitely a college-level book, chapters are long with extended text and examples and surprisingly protracted problem sets (most with over 60 exercises). There are no illustrations or any other attempt to make the material entertaining. This is serious math, and if your student doesn't take it seriously at first, by the end of a year he will. The solutions manual includes fully worked solutions and answers for all in-text review problems, and for all odd-numbered problem set exercises.
Single Variable Calculus is very similar in approach to the college algebra program, except harder. This is very difficult math, and for most students (especially those without much instructional help) it would be impossible without Dr. Callahan's guidance. The solutions manual offers fully worked solutions for all odd-numbered problem set exercises. Students really only need to complete this course if they plan on a career or college education in a math-intensive field. One of the benefits of Callahan's comments on this text is that he manages to point out many practical applications of the equations and concepts being studied, so students understand they aren't learning purely theoretical and abstract material.
Each DVD set comes with a teacher's guide disc compatible with most PC or Mac computers. It contains tests and test answer keys, as well as a syllabus and outline for teaching the course. If you want your student to pursue advanced math education but can't or won't teach him yourself, these DVDs are what you need. By reading the text and watching each lesson, students will have virtually the experience of sitting in a classroom, except they won't be able to ask questions directly. The DVD format allows them to pause the lesson when necessary to keep up with the information or work an example for themselves.
If your student wants more math instruction than you can give him, these may be what you're looking for. The Harold Jacobs texts are some of the best available, and while the college algebra and calculus books aren't as entertaining they are excellent straightforward presentations of complex material. Dr. Callahan's teaching style may be lost on some students, but for the most part he is easy to follow and takes the mystery out of seemingly impossible problems. This would be a good series to start after completing the VideoTextInteractive algebra course.