John Harold Saxon Jr. (December 10, 1923 – October 17, 1996) was an American mathematics educator who authored or co-authored and self-published a series of textbooks, collectively using an incremental teaching style which became known as Saxon math.
Saxon was born in Georgia and graduated from high school in Athens, Georgia. He earned a bachelor's degree in Engineering from West Point in 1949 and his master's degree in electrical engineering in 1961. He became an officer in the U.S. Air Force, achieving the rank of Lieutenant Colonel, and flew 55 missions in a B-26 Night Intruder during the Korean War. Saxon also taught engineering at the United States Air Force Academy for five years. After his retirement from the Air Force in the 1970s, he settled in Norman, Oklahoma. He taught algebra part-time at Rose State College in Midwest City, Oklahoma.
Throughout the 1980s and 1990s, John Saxon spoke out against mathematics education reform efforts that he believed would lead to a disaster in math and science education. He wrote or co-wrote a series of nine mathematics textbooks for kindergarten through high school which use an incremental teaching method often called "Saxon math". According to Saxon in media interviews in the 1980s and early 1990s and documentation coming with the high-school level textbooks, the inclusion of specialised and/or somewhat uncommon words such as "sciolist" in the story problems is intended as a vocabulary builder in preparation for the verbal section of the SAT and similar tests.
The basic philosophy of his approach was incremental development and continuous review. Incremental development meant that larger concepts were broken down into smaller, more easily understood pieces that were introduced over time; continuous review refers to the practice of concepts in cumulative problem sets once they were introduced. As a student completed a new concept, a brief review of the previous chapters and concepts were also tested.