Over their combined 81 years of teaching experience, Gary Taylor and another Davis High School math teacher, J. Michael Shaw spearheaded the development of one of the most successful AP™ Calculus programs in the Intermountain West at Davis High School in Kaysville, Utah. Along with a dedicated and talented math department, they developed a teaching method of carefully selected content, constant review, and increasing difficulty. This method achieved a pass rate average of about 95% and over one-third of the school’s student population took AP™ Calculus before graduation.
Gary and Mike became greatly frustrated with the textbooks available to support their method as they were all designed for college-level Calculus.The problem sets were heavy on mathematical symbol manipulation, short on meaningful applications, filled with problems that were either too easy or too difficult, and consisted mainly of problems incorporating one concept only with no built-in review. The answers given in the texts frequently involved obscure, inaccessible forms of the correct answers and there was seldom any direction about calculator usage. This meant some students overused a calculator instead of learning Calculus concepts. Meanwhile other students never learned how to use a calculator at all. Perhaps most significantly, the textbooks simply did not include AP-type questions.
After gradually supplementing existing texts more and more, the two instructors decided to develop a textbook with a significantly different format. This involved two years of intense work and about ten years of refinement.
While the resulting texts allowed the Davis High School AP™ Calculus program to flourish and continues to be used by each of its nearly 300 students each year, the greatest benefit of the texts is that the authors’ success can be exported to other teachers and other schools. They are now used by many schools in the US and Canada, providing teachers and students with an invaluable resource that supports a rigorous and thorough understanding of AP™ Calculus.
A recent survey of teachers using The Essentials of Calculus and/or Calculus Extended with 1755 student scores reported showed the following results on the May 2017 AP Calculus exam:
AB results:
30% earned a 5 (19% globally)
78% earned a 3, 4, or 5 (58% globally)
average score 3.5
BC results:
52% earned a 5 (42% globally)
87% earned a 3, 4, or 5 (81% globally)
average score 4.1