WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON’S MATH BOOKS?
(Myth 2)
Saxon Math is Just Mindless Repetition
More than thirty years ago, at a National Council of Teachers of Mathematics (NCTM) Convention, John and I encountered a couple of teachers manning their registration booth. When John introduced himself, they made a point to tell him that they did not use his math books because they felt the books were just “mindless repetition.”
John laughed and then in a serious note told the two teachers that in his opinion it was the NCTM that had denigrated the idea of thoughtful, considered repetition. He quickly corrected them by reminding them that the correct use of daily practice results in what Dr. Benjamin Bloom of the University of Chicago had termed “Automaticity.” Dr. Bloom was an American educational psychologist who had made significant contributions to the classification of educational objectives and to the theory of mastery-learning.
Years earlier, John Saxon had taken his Algebra 1 manuscript to Dr. Bloom to evaluate his manuscript’s methodology. John wanted to find out if there was a term that described the way his math book was constructed. Dr. Bloom informed John that he had not created a new teaching method. He himself had named this same methodology in the early 1930’s
Dr. Bloom referred to this method of mastery – the same one contained in John’s manuscript – as “Automaticity. He described it as the ability of the human mind to accomplish two things simultaneously so long as one of them had been overlearned (or mastered). He went on to explain to John that the two critical elements of this phenomenon were repetition and time. John had never heard this term used before, but while in military service, he had encountered military training techniques that used this concept of repetition over extended periods of time, and he had found them extremely successful.
If you think about it, professional sports players practice the basics of their sport until they can perform them flawlessly in a game without thinking about them. By “Automating” the basics, they allow their minds to concentrate on what is occurring as the game progresses. Basketball players do not concentrate on dribbling the basketball, they concentrate on how their opponents and fellow players are moving as each play develops and they move down the floor to the basket while automatically dribbling the basketball.
Baseball players perfect their batting stance and grip of the bat by practicing hitting a baseball for hours every day so that they do not waste time concentrating on their stance or their grip at the plate each time they come up to bat. Their full concentration is on the pitcher and the split second timing of each pitch coming at them at eighty or ninety miles an hour.
How then does applying the concept of “Automaticity” in a math book differentiate that math book from being just “mindless repetition?” John Saxon’s math books apply daily practice over an extended period of time. They enable a student to master the basic skills of mathematics necessary for success in more advanced math and science courses. As I mentioned earlier, the two necessary and critical elements of “Automaticity” are repetition over time. If one attempts to take a short cut and eliminate either one of these components, mastery will not occur. You cannot review for a test the day before the test and call that process “Automaticity.” Nor can you say that textbook provides mastery through review.
Just as you cannot eat all of your weekly meals on a Saturday or Sunday – to save time preparing meals and washing dishes daily – you cannot do twenty factoring problems one day and not do any of them again until the test without having to create a review of these concepts just before the test. When a math textbook uses this methodology, it does not promote mastery; it promotes memory of the concepts specifically for the test. That procedure would best be described as “Teaching the Test.”
John Saxon’s method of doing two problems of a newly introduced concept each day for fifteen to twenty days, then dropping that concept from the homework for a week or so, then returning to see it again, strengthens the process of mastery of the concept in the long term memory of the student. Saxon math books are using this process of thoughtful, considered repetition over time to create mastery!
Myths that will be discussed in future news articles:
July – Myth 3 – Saxon Algebra 2 does not Contain Two-Column Proofs.
Aug – Myth 4 – You Must Use the New Saxon Geometry Textbook to Receive Geometry Credit.
Sept –Myth 5 – Advanced Mathematics Can be Taken Easily in a Single School Year!
Oct – Myth 6 -You Do Not Have to Finish the Last Twenty or So Lessons in any Saxon Math Book