If you are wondering whether to skip from Algebra 2 directly to Calculus or whether to take Precalculus first, the answer (almost always) is to take Precalculus first. Gaining depth is more important than racing ahead, and the depth offered through this course is tremendous. Recording this course has been a remarkable experience for me, personally. I have grown in my appreciation for Foerster’s work in the process. Through my career I have taught out of several other Precalculus textbooks, but none of them is in the same league with Foerster when it comes to teaching problem solving and real-world applications.
I am using the 3rd edition of Foerster’s Precalculus with Trigonometry, available from Kendall Hunt, which recently took over its publication from Key Curriculum Press. (Follow the link and use the order form on the right side of the web page.) The DVD course makes heavy use of computational tools, primarily scientific calculator, spreadsheet programming, Geogebra, and Sage.
I have been working a lot with the new software tool, Geogebra and am using it heavily in lieu of “graphing calculators.” Download it and start playing with it even now.) Graphing calculators are severely limited by their clumsy user interface and small screen size. All students using these DVDs are using computers, so software on a larger platform makes sense.
One step I am taking in this course is to introduce RPN calculators, the system developed for scientific calculators by Hewlett-Packard. A pocket calculator should be optimized to be able to evaluate expressions fluently and reliably. RPN logic takes some learning at first, but it is wonderful for its fluency and reliability. I describe my HP calculator as an “extension of my brain.” (I highly recommend students at this level invest in an HP-35s calculator, in the $50 range.) The on-screen calculator Calc98, which Math Without Borders students have seen since Algebra 1, has the ability to switch into RPN mode. Download it and try it out! Students are free to use any calculator they have in any mode they like, but in this course I will be doing the on-screen calculations in RPN.
(Make Your Calculator an Extension of your Brain)
Another even more powerful computational tool introduced in the last quarter of Precalculus, is called Sage, available to use online or download from http://www.sagemath.org. Sage is useful all the way from high school math through university and professional level mathematics. Many of the tutorials available online are aimed at university level mathematics and might overwhelm Precalculus mathematics students. I have therefore recorded a short introduction to Sage that covers most of the needs of this course and posted it to YouTube. You can watch it here.
For practice you can access the Sage file shown in the video and interact with it directly here: Zip file containing a Sage sws file. Download this file, then unzip it to your desktop, then start Sage, then upload the sws file from your desktop into Sage.
Also check out the YouTube “channel” http://www.youtube.com/user/sagemath. Linda Fahlberg-Stojanovska has created a number of Sage video tutorials at a simple level that are relevant to a number of the topics in this course.