WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS? (Myth 2)
Saxon Math is Just Mindless Repetition: More than a decade 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:
WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS? (Myth 1)
Saxon Math is Too Difficult: This common myth is generated by public and private schools as well as homeschool educators who place a transfer student into the wrong level of Saxon math – usually a level above the student’s ability. I recall a homeschool parent at one of the Homeschool Conventions this past summer telling me she was going to switch to Saxon Math. She wanted to buy one of my Algebra 2 DVD tutorial series. I asked her what level book her son had just completed and she said it was an Algebra 1 textbook from (you fill in the name) company.
Since she lived in the area and was coming back to the convention the next day, I asked her if she would have her son take the Saxon Algebra 1 Placement test that night and come back the next day with the results so we could make sure he was being placed into the correct level Saxon math textbook. The next day, she came by the booth and informed me that her son had failed the Saxon Algebra 1 Placement Test. When I told her that test was the final exam in the Saxon pre-algebra course, she became quite concerned. I told her that the problem was not a reflection upon her son’s intelligence.
The problem her son had encountered was that the previous textbook he had used taught the test. However, the cumulative nature of Saxon math books requires mastery of the concepts, which is why there is a weekly test. Had her son used the Saxon Algebra 2, 3rd Ed book – by the time he reached lesson twenty – he would have become painfully aware of what he and his mother would believe to be the “Difficulty” of the book. They would have blamed the Saxon book as being “Too Difficult.” They would never have realized that his difficulty in the Saxon Algebra 2 book was that the previous math book allowed him to receive good test grades through review for each test the night before, rather than requiring mastery of the concepts as Saxon books do through the weekly tests.
This parent is not alone. Every week I receive emails or telephone calls from homeschool educators who are trying to accomplish the same thing. And until they have their student take the Saxon Math Placement Test, homeschool educators do not realize that they could very well be placing the student in a Saxon math book at a level above the students’ capabilities.
The Saxon Math Placement Tests were not designed to test the students’ knowledge of mathematics; they were designed to seek out what necessary math concepts had been mastered by the student to ensure success in the next level Saxon math book. Low test results on a specific Placement Test tell us that the student has not mastered a sufficient number of necessary math concepts to be successful in that level math book.
Saxon Placement Tests should not be used at the end of a Saxon math book to evaluate the student’s progress. Classroom teachers as well as homeschool educators should use the student’s last five test scores of the course to determine their ability to be successful in the next level course. If the last five test scores are clearly eighty or better, the student will be successful in the next level Saxon math course – or anyone else’s math textbook should you elect to change curriculum.
Note: Students should be given no more than 60 minutes to complete each test of any individual Saxon math course. Each test question is awarded five points if correct. Test questions should be graded as either right or wrong with no partial credit awarded for partially correct answers.
Myths that will be discussed in future news articles:
WE'RE TAKING OUR DVD MATH TUTORIAL COURSES – ONLINE!
Don't worry – for those of you who still want - or - must use the DVDs, we will continue to manufacture and sell them until they become technically obsolete and unusable - like the old floppy disks eventually did. In all probability, I suspect that will not occur until several years from now at a minimum. By introducing the online capability our intent is to create an additional vehicle as we will continue to offer the DVD series as well.
Our current plans are to release the first of the seven Saxon math tutorial courses - the Algebra 2 series - in mid to late April of this year. If all goes well, we plan on introducing the other six math series on a weekly basis in the following order:
Our current plan is to have all seven math courses - from Math 76 through the Advanced Math series - online by late June in time for the 2019-2020 school year. We will offer a two year subscription for no more than we currently sell the DVD series for. We believe this will give the user enough flexibility to re-take part or all of the same course should they initially experience difficulty. The subscription would start from the purchase date. While we will offer the online course subscriptions direct from our website, if you have a favorite vendor like Christian Book Distributors, Rainbow Resources, Children's Books, or R.O.C.K. Solid Home School Books - and if they desire - we will continue to offer them the online course subscriptions as well as the DVD series for purchase by you.
We are announcing this new feature early to allow you to delay your purchase of the DVD series for the upcoming 2019 – 2020 school year should you desire to use the online math course subscriptions instead. If all goes as planned, you will be able to subscribe to the online math courses direct from the new website at teachingsaxon.com - or from a direct link on this website – beginning in late April of this year. You would then be able to acquire any of the online courses by late June.
With the rapid technology changes occurring in the computer industry, we felt it necessary to make learning mathematics easier for the students who use laptop computers and iPads. At the same time we wanted to also enable those homeschool families – using their Smart TVs – to use the online courses as well. Lastly, we wanted to enable our rural families to continue to use the DVDs until technology catches up to those areas as well – so we will continue to sell the DVD series until they become obsolete.
No doubt – as with any new technological endeavor – there will be some minor hiccups as we develop and install the new online math tutorial system. However, the young man whose company is setting up our new online system is extremely capable and I see few if any glitches or major delays arising - as we proceed forward with the project.
Please feel free to email me at firstname.lastname@example.org or call me at 580-234-0064 (CST) should you have any suggestions, questions - or - concerns that I have not already addressed. Upon release of the first of the series in April, we will release the necessary technical information on the website to ensure the user is aware of the simplicity of operation in using the online courses.
Please remember all of these dates and concepts are targets - and we may find a need to revise something as we move forward. However, always remember that our main objective is to support the homeschool community and provide the best and most inexpensive math tutorial program to the Saxon Math students.
WHAT TO DO WHEN A SAXON STUDENT ENCOUNTERS DIFFICULTY EARLY IN THE COURSE.
By the time the first several months of the new school year have passed, most Saxon math students are at least a fourth of the way through their respective math books and are quickly finding out that the easy review of the previous textbook's material has come to a sudden halt. They are now entering the part of the textbook that determines whether or not they have mastered sufficient material from the previous textbook to be prepared for their current course of instruction.
For students who start school in August - using the Saxon middle or high school math series from Math 76 through Algebra 2 - this generally occurs sometime in mid-to late October around lesson 35 or so. Or it can occur sometime in late November, if they started the course in September. Or, depending upon the student's schedule it may not occur until after the Christmas Holidays in January. This past school year I received a number of email and telephone calls from home school parents who had students who were experiencing difficulty after completing about forty or so lessons of the course. They were mostly upper middle school or high school students using John Saxon's Algebra ½, Algebra 1, or Algebra 2 textbooks.
The symptoms described by the home school parents were similar. The daily assignments seem to take much longer than before and the test grades appear to be erratic or on a general downward trend. The student becomes easily frustrated and starts making comments like, "Why do I have to do every problem?" - or - "There are too many of them and it takes too long." - or - "Why can't I just do the odd problems since there are two of each anyway?" They might even say things like "This book is too hard." - or - "It covers too many topics every day." Or even worse - "I hate math."
About that time, many homeschool educators do the same thing that parents of public or private school students do. They question the curriculum. They immediately look for another - easier - math curriculum so that their children can be successful. Since the students apparently did fine in the previous level book, the parents believe there must be something wrong with this textbook since their sons or daughters are no longer doing well.
Looking for an "easier" math course is like a high school football coach who has just lost his first ten high school football games. However, he assures the principal that they will definitely be successful in their next football game. "How can you be so sure that you will be successful in your next football game?" asks the principal. "Oh that's easy," says the coach. "I've scheduled the next game with an elementary school."
I do not believe the answer is to find an easier math curriculum. I believe the answer is to find out why the students are encountering difficulty in the math curriculum they are currently using, and then find a viable solution to that situation. As John Saxon often said, algebra is not difficult; it is different!
Because every child is also different, I cannot offer a single solution that will apply to every child's situation, but before I present a general solution to Saxon users, please be aware that if you call my office and leave your telephone number or if you email me, I will discuss the specifics of your children's situation and hopefully be able to assist you. My office number is 580-234-0064 (CST) and my email address is email@example.com.
When Saxon students encounter difficulty in their current level math book before they reach lesson 30-40 or so, it is generally because one or more of the following conditions contributed to their current dilemma:
There are other conditions that contribute to the students encountering difficulty early in their Saxon math book. Basically, they all point to the fact that, by taking shortcuts, the students did not master the necessary math concepts to be successful in their current level textbook. This weakness shows up around lesson 30 - 40 in every one of John's math books. The good news is that this condition - if caught early - can be isolated and the weaknesses corrected without re-taking the entirety of the previous level math book.
There is a procedure to "Find and Fill in the Existing Math Holes" that allows students to progress successfully. This procedure involves using the tests from the previous level math book to look for the "holes in the student's math" or for those concepts that they did not master. This technique can easily tell the parent whether the student needs to repeat the last third of the previous book or if they can escape that situation by just filling in the missing concepts - or holes.
If you have my book, then you already know the specifics of the solution. If you do not have my book, then you can call me or email your situation to me and I will assist you and your child. Regardless of what math book is being used, students who do not enjoy their level of mathematics are generally at a level above their capabilities.
ARE JOHN SAXON'S ORIGINAL MATH BOOKS GOING THE WAY OF THE DINOSAUR?
I am often asked by home school educators whether or not I will create my teaching DVD “videos” for the new fourth editions of Algebra 1 and Algebra 2, and the resulting new first edition of Geometry now being sold on the Saxon Homeschool website by the new owners of Saxon Publishers.
The answer is no, I will not do so. My creation of the current DVD video series for John’s math books, based upon rock solid editions created by John Saxon, was not to make money. Using my Saxon classroom teaching experiences, I wanted to create a classroom environment for home school students who wanted to master high school mathematics using John’s unique math books. However, publishing math textbooks redesigned to be like all the other math textbooks on the market are not what John intended when he created his unique style of math books.
John Saxon would not have sanctioned gutting his Algebra 1 and Algebra 2 textbooks of their geometry to create a separate geometry textbook. He believed that using a separate geometry textbook was not conducive to mastering high school mathematics. More importantly, each of John’s math books had an author - an experienced classroom mathematician - behind them. These three new editions, created under his Saxon title, do not.
When Harcourt-Achieve bought John Saxon’s dream - Saxon Publishers - from his children, I made the comment that the new owners were certainly intelligent enough to recognize the uniqueness of John’s books. I predicted that they would not change the content of John’s books. Certainly, I commented. “They would never take their prize winning bull and grind it up into hamburger” – or so I thought!
Well the new owners of Saxon Publishers appear to have done just that, and the time has come for me to apologize because they are now selling the hamburger on the Homeschool website. I have previously cautioned home school Saxon users not to use the new fourth editions of Algebra 1 and Algebra 2 then offered only on the school website because the company had gutted all geometry from them to enable them to publish a separate geometry textbook desired by the public school system. But they are now selling them on the Homeschool site as well.
Having been affiliated with one of the larger publishing companies - after Saxon Publishers was sold - I observed that the driving force in the company was not so much the education of the children, but the quarterly profit statement. And that is okay, but being around their VP’s and upper level executives showed me that to them “a book - is a book - is a book.” I still believe they have not the foggiest idea of just how unique and powerful John’s math books are when used correctly. However, I may be wrong, because they may have already observed that it is this “uniqueness” that requires special handling - and that requires special training - and that costs money – reducing quarterly profits.
I do not believe the publishing company will long suffer the expense of publishing both the third and fourth editions of Algebra 1 and Algebra 2. It is my opinion they may well stop printing and selling the third editions of Algebra 1 and Algebra 2 when current stocks run out. This will then require that home school educators using Saxon math books buy the separate geometry book also. After all, “Don’t you make more money from selling three books than you do from just selling two?”
Maybe the new owners of John Saxon's math books will not stop printing the third editions of Algebra 1 and Algebra 2 - but then I could be wrong - again! If you are serious about using John Saxon’s original math series through high school, I recommend you not buy these new fourth editions of Algebra 1 and Algebra 2. I strongly recommend you immediately acquire the home school editions of John’s math books that I discussed in my book - which include the third editions of Algebra 1 and Algebra 2.
Listed below are excerpts from my book about each edition of John’s books from Math 54 through Calculus. If after reading this, you feel your particular situation has not been addressed, please feel free to email me at firstname.lastname@example.org or call me at 580-234-0064 (CST) before you purchase any math textbooks.
Math 54 (2nd or 3rd Ed): You can use either the hard cover 2nd edition textbook or the newer soft cover 3rd edition as they have identical math content. In fact, they are almost word for word and problem for problem the same textbooks. The page numbers differ because of different graphics and changed page margins, and the newer soft cover 3rd edition homeschool packet has an added solutions manual. However, my experience with that level of mathematics is that most home school educators will not need a solutions manual until they encounter Math 76. If you can acquire a less expensive homeschool kit without the solutions manual, I would recommend acquiring that less expensive set. Calculators should not be used at this level.
Math 65 (2nd or 3rd Ed): This book is used following successful completion of the Math 54 textbook. Successful completion is defined as completing the entire Math 54 textbook, doing every problem and every lesson on a daily basis, and taking all of the required tests. To be successful in this textbook, students must have scored eighty or better on the last four or five tests in the Math 54 textbook. As with the Math 54 textbooks, the 2nd edition hard cover book and the newer soft cover 3rd edition have identical math content. The newer 3rd edition series also has a solutions manual, but if you’re on a tight budget, I do not believe that it is necessary at this level of mathematics either. Calculators should not be used at this level.
Math 76 (3rd or 4th Ed): The kingpin book in the Saxon series. This book follows successful completion of the Math 65 textbook. Again, successful completion of Math 65 means completing the entire book as well as all of the tests. To be successful in Math 76, students should have received scores no lower than an eighty on the last four or five tests in the Math 65 course. Either the hard cover 3rd edition or the newer soft cover 4th edition can be used. As with the previous two math courses, there is no difference between the math content of the hard cover 3rd edition and the softcover 4th edition textbooks. I recommend acquiring a copy of the solutions manual as this is a challenging textbook. Students who score eighty-five or better on the last five tests in this level book indicate they are ready to move to Algebra ½, 3rd edition. Student’s who encounter difficulty in the last part of Math 76, reflected by lower test scores, can easily make up their shortcomings by proceeding to Math 87 rather than Algebra ½. Calculators should not be used at this level.
Math 87 (2nd or 3rd Ed): Again, there is little if any difference between the hardcover 2nd edition and the softcover 3rd edition textbooks. Even though the older second edition does not have “with pre-algebra” printed on its cover as the 3rd edition softcover book does, the two editions are identical in math content. Students who successfully complete the entire textbook and score eighty or better on their last five or six tests can skip the Algebra ½ textbook and proceed directly to the Algebra 1, 3rd edition textbook. Both the Math 87 and the Algebra ½ textbooks get the student ready for Algebra 1; however, the Math 87 textbooks start off a bit slower with a bit more review of earlier concepts than does the Algebra ½ book. This enables students who encountered difficulty in Math 76 to review earlier concepts they had difficulty with and to be successful later in the textbook. Students who encounter difficulty in the last part of this book will find that going into Algebra ½ before they move to the Algebra 1 course will strengthen their knowledge and ability of the basics necessary to be successful in the Algebra 1 course. Their frustrations will disappear and they will return to liking mathematics when they do encounter the Algebra 1 course. Calculators should not be used at this level.
Algebra ½ (3rd Ed): This is John’s version of what other publishers title a “Pre-algebra” book. Depending upon the students earlier endeavors, this book follows successful completion of either Math 76 or Math 87 as discussed above. Use the 3rd edition textbook rather than the older 2nd edition as the 3rd edition contains the lesson concept reference numbers which refer the student back to the lesson that introduced the concept of the numbered problem they’re having trouble with. These concept lesson reference numbers save students hours of time searching through the book for a concept they need to review - but they do not know the name of what they are looking for. From this course through calculus, all of the textbooks have hard covers, and tests occur every week, preferably on a Friday. To be successful in John Saxon’s Algebra 1 course, the student must complete the entire Algebra ½ textbook, scoring eighty or better on the last five tests of the course. Students who encounter difficulty by time they reach lesson 30 indicate problems related to something that occurred earlier in either Math 76 or Math 87. Parents should seek advice and assistance before proceeding as continuing through the book will generally result in frustration and lower test scores since the material in the book becomes more and more challenging very quickly. Calculators should not be used at this level.
Algebra 1 (3rd Ed): I strongly recommend you use the academically stronger 3rd edition textbook. The new owners of the Saxon Publishers (HMHCO) have produced a new fourth edition that does not meet the Saxon methodology. The new fourth edition of Algebra 1 has had all references to geometry removed from it and using it will require also buying a separate geometry book. While the associated solutions manual is an additional expense, I strongly recommend parents acquire it at this level to assist the student when necessary. Depending upon the students earlier successes, this book follows completion of either Math 87 or Algebra ½ as discussed above. Calculators are recommended for use at this level after lesson 30. While lesson 114 of the book contains information about using a graphing calculator, one is not necessary at this level. That lesson was inserted because some state textbook adoption committees wanted math books to reflect the most advanced technology. The only calculator students need from algebra through calculus is an inexpensive scientific calculator that costs about ten dollars at one of the local discount stores. I use a Casio fx260 solar which costs about $9.95 at any Target, K-Mart, Wal-Mart, Radio Shack, etc. If the 3rd edition of Saxon Algebra 1 is used, a separate geometry textbook should not be used between Saxon Algebra 1 and Algebra 2 because the required two semesters of high school geometry concepts will be covered in Saxon Algebra 2 (1st semester) and in the first sixty lessons of the Advanced Mathematics book (2nd semester).
Algebra 2 (2nd or 3rd Ed): Either the 2nd or 3rd editions of the Saxon Algebra 2 textbooks are okay to use. Except for the addition of the lesson concept reference numbers in the newer 3rd edition, the two editions are identical. These lesson concept reference numbers save students hours of time searching through the book for a concept they need to review - but they do not know the name of what they are looking for. If you already have the older 2nd edition textbook, and need a solutions manual, you can use a copy of the 3rd edition solution manual which also has solutions to the daily practice problems not in the older 2nd edition solutions manual. Also, the 3rd edition test booklet has the lesson concept reference numbers as well as solutions to each test question – something the 2nd edition test booklet does not have. An inexpensive scientific calculator is all that is needed for this course. Upon successful completion of the entire book, students have also completed the equivalent of the first semester of a regular high school geometry course in addition to a credit for Algebra 2. I strongly recommend you not use the new fourth edition of Algebra 2 for several reasons.
Advanced Mathematics (2nd Ed): Do not use the older first edition, use the 2nd Edition. The lesson concept reference numbers are found in the solutions manual – not in the textbook! Students who attempt this book must have successfully completed all of Saxon Algebra 2 using either the 2nd or 3rd edition textbooks. Upon successful completion of just the first sixty lessons of this textbook, the student will have completed the equivalent of the second semester of a regular high school geometry course. An inexpensive scientific calculator is all that is needed for this course. For more information on how to transcript the course to receive credit for a full year of geometry as well as a semester of trigonometry and a second semester of pre-calculus, please Click Here.
Calculus: The original 1st edition is still an excellent textbook to master the basics of calculus, but the newer 2nd edition affords students the option to select whether they want to prepare for the AB or BC version of the College Boards Advanced Placement (AP) Program. To prepare for the AB version, students go through lesson 100. To prepare for the BC version, they must complete all 148 lessons of the book. While the 2nd edition reflects use of a graphing calculator, students can easily complete the course using an inexpensive scientific calculator. I recommend that students who use a graphing calculator first attend a course on how to use one before attempting upper level math as they need to concentrate on the math and not on how their fancy calculator works. It is not by accident that the book accompanying the graphing calculator is over a half inch thick.