Home Study Companion: Algebra 2 / Trigonometry
The Home Study Companion: Algebra 2 / Trig lessons, now distributed as a digital download, are based on Paul A. Foerster’s Algebra and Trigonometry: Functions and Applications. This textbook is available as part of Prentice Hall’s Classics series, or in older editions through various used book sources. The text is a true classic!
Paul A. Foerster has taught mathematics at Alamo Heights High School in San Antonio, Texas since 1961. In that same year he received his teaching certificate from Texas A&M University. His B.S. degree in Chemical Engineering and M.A. degree in Mathematics are from the University of Texas. Among many honors, he was awarded the Presidential Award for Excellence in Mathematics Teaching in 1983. He brings to his teaching and textbook writing the insights from his engineering background. His textbooks contain some of the best collections of real-world applications to be found in any algebra textbooks.
The topics covered in this course include functions and relations, systems of linear equations and inequalities, quadratic functions and relations, higher degree polynomials, complex numbers, exponential and logarithmic functions, rational algebraic functions, irrational algebraic functions, sequence and series, probability, data analysis, and trigonometry. There is a strong emphasis on real world application problems, and appropriate technology is used for visualization, graphical representation, and computer programming for problem solving.
Whether or not parents feel comfortable with this material themselves, the students would benefit by being introduced to these topics by an experienced teacher. That is what these video lessons provide. The lessons cover not only new techniques, but new levels of problem solving skills and new models for thinking about practical problems mathematically. All the topics learned in Algebra 1 are deepened and put into an expanded context. This level of material cannot simply be “presented”: it must be taught.
In this course I make use of GeoGebra for graphing and various other kinds of demonstrations. Download it (Classic Edition, Ver 5) and start getting to know it.
Students will also need to have an inexpensive hand-held scientific calculator for general problem solving. At this level pretty much any scientific calculator will do. (It needs to have the trigonometric functions, logs and exponential functions, and scientific notation. All scientific calculators I know of meet this requirement.) There are free or inexpensive scientific calculator “aps” available for smart phones or you can pick up an inexpensive scientific calculator, probably in the $10 to $20 range.
Where appropriate the text introduces computer programming problems to extend pencil and paper solutions and to better approximate real-world scale problems. The Math Without Borders course illustrates solutions of the programming problems using spreadsheet programming. Spreadsheets are a good, transparent way to lay out many kinds of programming calculations. The spreadsheet programs covered here can be created using Microsoft Excel (available commercially) or equally well using the spreadsheet component of the free, open source program suite, Libre Office. (The programming solutions shown on the disk are done in Libre Office, but saved in a format that can be opened with either Libre Office or Excel.)
The lessons for this course are based on “screen-capture video” technology. To the user they appear as “whiteboard lectures” (see screenshot below).
You will need to separately purchase a copy of Paul A. Foerster’s Algebra and Trigonometry: Functions and Applications.
ISBN10: 0131657100 / ISBN13: 9780131657106
(Prentice Hall Classics Version)
The lessons are based on the Prentice Hall Classics version, but there are only minor differences between this and earlier versions. (The 1999 and 1994 Addison Wesley editions appear to be essentially identical with the Pearson-Prentice Hall edition except for the cover.) Solution manuals are available from Pearson-Prentice Hall (also from rainbowresource.com), but you will probably not need the solution manual for this course because each lesson has a second video that demonstrates the solutions of a significant number of problems, enough to be the entire assignment. Texts may be obtained directly from Pearson-Prentice Hall. Used copies may be available from Amazon.com, Valore Books, or elsewhere.
A number of parents have asked how to pace of the class over the course of a school year. In a home schooling environment the schedule can, and probably should, be more flexible than in a standard classroom. The ultimate basis for setting the pace is the level of understanding of the student. This text is designed to be a 1-year course, but I know some people spread it out over two years. The ability and readiness of the student should be the determining factor.
Mathematics textbooks are generally structured on the assumption of covering one section per day, with extra days for testing, review, and re-teaching of the more difficult topics. The table below should help. If you typically cover 1 section per day you would have 38 extra days in a 185 day school year. I would recommend spending 2-3 days for the final word-problem section of each chapter. The problems that are worked out on the videos would be a reasonable selection of problems to assign. If more practice is needed you could select additional odd numbered problems, whose answers are in the back of the text.
I highly recommend that parents be closely involved with the students’ progress. The surest way to get behind is to allow students to “slip through” the material without demonstrating that they understand it thoroughly. When this happens early in the course, you will find them unprepared for the work later in the course.
Regarding testing and grading issues, here is an essay I published in Homeschool Magazine on that subject: Assessment and Grading for Homeschoolers. I highly recommend that you try this approach.