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How Do I Prepare My Child for AP Calculus?
Susan Gilleran, 6/27/2010

Susan Gilleran will be leading AP Calculus with PA Homeschoolers for her 5th year, and her classes always get rave reviews from students. She earned a BS and secondary teaching certificate in Mathematics from Wayne State University, and an MBA from Lawrence Technological University. She taught high school mathematics before moving to the business world at Ford Motor Company for 30 years where she was an Information Technology Manager.

This will be my fifth year teaching the AP Calculus course for PA Homeschoolers. I have also completed two five day College Board summer institutes. One of the institutes was dedicated to teaching AP Calculus AB and the other addressed AP Calculus BC.

I am often asked the question “How do I prepare my son or daughter for AP Calculus?” It’s an excellent question and a common dilemma. I decided to use two of the most well prepared students, a brother and sister, who took my BC class as an example of a path to follow from first grade through pre-calculus. Then I’ll give some extra suggestions for pre-calculus alternatives.

I asked the brother and sister’s mother if she would share the choices she made for her son and daughter’s math classes. Here’s what she had to say:

“During our children's elementary years, they did Miquon math during grades 1, 2, and 3 and Singapore math during grades 4 and 5.  I think both programs do a great job of allowing younger students to discover and explore math concepts on their own. I did need to supplement the Miquon program with extra practice problems.  We started pre-algebra in 6th grade. Specifically, our course sequence is as follows: pre-algebra in sixth grade, algebra I in seventh grade, geometry in eighth grade, advanced algebra with some trigonometry in ninth grade, pre-calculus in tenth grade, AP Calculus in eleventh grade, and AP Statistics in twelfth grade.

For all of the algebra classes, we used the University of Chicago School of Mathematics Project's textbooks: Transition Mathematics, Algebra, and Advanced Algebra.  I have a high opinion of these textbooks as they are generally well-written, colorful and engaging for the student, and fairly self-explanatory.  They contain a good amount of easier and more challenging problems (including "real life" situations) and review previous concepts in each section (though not to the degree that Saxon does).  In order to expose the kids to different textbook authors, we switch to Harold Jacobs's Geometry for geometry. I do like the text, and it stresses proofs which I consider important.  Some of the problem sets are meant to encourage discovery of concepts, but a few of the questions just leave the student perplexed and unsure of what the question is asking.  For pre-calculus, I purposefully chose what I thought was a challenging text with many practice problems: Precalculus (Graphical, Numerical, Algebraic) by Demana, Waits, Foley, and Kennedy.    

I do have some experience with the Saxon program as I used it for some homeschool math co-op classes (specifically Algebra II and Advanced Mathematics) I taught a few years ago.  My initial reason for using Saxon was that it was the program that the children in the class had used for several years. Since geometry is not its own course in Saxon (which I personally do not like), I had to continue the Saxon program so that the students would be able to complete their high school geometry education.  That said, I found that Saxon certainly gets the job done - those students did well on the math section of the ACT.  On the negative side, I found the Saxon text to be a bit boring and repetitive, especially for talented math students.  On the positive side, the text's repetitiveness is what helps the average math student truly learn the concepts.  I do believe the Saxon program is a great choice for homeschooled students who have to do more self-teaching than the usual student.   

           Wasn’t that a great summary of her children’s math history? I want to thank their mother for her time and effort in sharing the wealth of experience she’s gained over the years of schooling her children.

            Now for the extra alternatives for pre-calculus alternatives that I promised – another excellent pre-calculus text book that my well prepared students have used is by Paul Foerester. He’s a very highly regarded author amongst math teachers. And lastly there’s an excellent pre-calculus text by Larson and Hostetler.

            As you can see there are several options to choose from when selecting a pre-calculus text. As to when to take AP Calculus and whether to take AB or BC I’ll leave that decision to my next article so stay tuned.


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