Keith always enjoyed tutoring students in a variety of school subjects. But it was math that always stood above the rest. The excitement of math stemmed from its use in thousands of inventions and scientific discoveries.

Keith earned graduate degrees in engineering and business from leading universities. He has also worked in numerous technical positions, including Undergraduate teacher, Software Engineer, Hardware Engineer, Product Manager and senior business leader in a number of organizations such as University of Colorado, Texas Instruments, Intel, and Qualcomm. His work experience highlights the practical importance of understanding math, which is used in diverse functions such as marketing, engineering, operations, and finance.

Keith continues to help teach others in a variety of subjects. He currently lives in San Diego, CA with his wife and three beautiful children, ages 5, 8, and 10.

History of Understanding Mathematics: From Counting to Calculus

Several family friends expressed the common concern that their homeschooled children were entering grades with math levels outside of their parent's comfort zone. Other family friends had students in public and private schools who were simply struggling with math. Based on their requests for help, Keith wrote a number of informal papers to more clearly explain subjects such as Fractions, Algebra and Trigonometry. These informal papers quickly grew in scope and audience. Based on feedback, Keith thought about writing a more comprehensive math book, which could help a greater number of students, families, and adults.

But before writing yet another math book, it was important to better understand why students and families had such trouble with existing resources. After all, there was no shortage of existing math curriculum, texts, and help books. By talking to students/families and taking a personal survey of many available math books, Keith gained much better understanding of the problem. Many "made simple" books simply abbreviated explanation, rather than providing more clarity. Many other books focused on helping students primarily through the use of sample problems and lacked added explanation and understanding. It was also clear that math experts, instead of frustrated parents and students, had reviewed most texts. Finally, there was added confusion created by different writing styles, notation and difficulty when moving across authors and math subject levels.

Using this survey information, Keith set five key criteria before writing Understanding Mathematics:

• Provide a single comprehensive book covering all major math topics (K-12)
• Write in an easy-to-read, informal style so anyone could read every subject without difficulty
• Prioritize building the reader's understanding, math intuition and confidence.
• Use a format that enabled it to be used as either a reference book or as a core curriculum
• Keep it as inexpensive as possible so it could help working parents and adults

The first criteria seemed the most difficult. After all, how do you fit 12 years of math education into a single non-intimidating book? There were two keys to accomplishing this feat. First, most math texts contain introductory chapters that cover past subjects and advanced sections that are beyond the scope of the primary subject being taught. So, a single comprehensive book could be written very efficiently, eliminating unnecessary repetition. The second key was that most math books were filled primarily with problems for the reader to work on his/her own. By keeping examples that supported the explanation, but by eliminating problem sets for the student to work on his/her own at the end of every chapter, a reasonably sized, yet comprehensive book was possible. (Note that based on reader requests for targeted problems and solution sets for each section, a companion book was later written. In 2008 Keith teamed up with David Scheinker, a math PhD student at UCSD, to write the Math Problems and Solutions Guide. This companion book contains 1000s of problems & solutions, together with math tips & tricks.)

While writing, Keith gathered first hand feedback from many students, families, and teachers at all skill levels. Keith used this first hand feedback extensively to ensure the book was easy-to-read and informal, yet provided readers needed understanding, intuition and confidence.

Since publication, Understanding Mathematics: From Counting to Calculus has been used by thousands of students of all levels, parents, homeschoolers, working professionals, charter schools, math clubs, libraries, tutors and more.