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MAKE SURE YOU BUY AND USE THE CORRECT EDITIONS OF JOHN SAXON'S MATH BOOKS With the 2019 school year more than half through and looking towards purchasing textbooks for the 2020 school year – undoubtedly, some questions will arise about which editions of John Saxon’s math books should be used. So I thought it would be advantageous to go over with you the correct editions of his math books that I recommend you use! While there is more detail in my book, I believe the following information will help you select the correct level and edition of John Saxon’s math books from the 4th through the 12th grades. All of the textbooks listed below also include an appropriate level of introduction to basic geometry as well as a review of the geometric terms associated with geometry at the appropriate introductory grade level. As the student moves from Math 54 to Algebra 1, the repetition of these terms and concepts allows for a gradual increase in their level of difficulty. However, this geometry still remains at the introductory level and there is no formal credit for any geometry until successful completion of the Algebra 2 textbook (3rd Ed). After completing all 129 lessons of the textbook, the student has also earned a full semester credit for the first semester of a regular high school geometry course. Acquiring credit for the second semester of geometry is addressed by the link at the end of nexttolast paragraph at the end of this article. If after reading the information provided below, you feel your particular student’s situation has not been addressed, please feel free to email me at art.reed@usingsaxon.com or call me at 5802340064 (CST) before you purchase any Saxon 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 eightyfive 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 prealgebra” 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 “Prealgebra” 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, KMart, WalMart, 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 the credit for Algebra 2. I strongly recommend you not use the new fourth edition of Algebra 2 for several reasons. FIRST: The fourth edition has had all references to geometry removed from it also requiring the purchase of an additional geometry book. SECOND: The Advanced Mathematics textbook assumes the student has just successfully completed the 2nd or 3rd edition of the Saxon Algebra 2 textbook with their inclusive geometry. If the student took a separate geometry course between the fourth editions of Algebra 1 and Algebra 2, they have not had any exposure to geometry for as much as fifteen months (nine months of school plus two summer breaks). This gap will result in the student encountering extreme difficulty in the Advanced Math textbook. Advanced Mathematics (2nd Ed): Do not use the older first edition, use the 2nd Edition. Make sure you also purchase the separate solutions manual as 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 precalculus, 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 must only complete 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 at the local tech school or at a local community college – over the summer – 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.
WHAT SHOULD YOU DO WITH STUDENTS WHO CONTINUALLY MAKE Often, I receive telephone calls or emails from homeschool educators who express concern that their sons or daughters continue to make simple mistakes in computations when doing their daily work. “My son is taking Algebra 1 and constantly makes silly mistakes, like not putting the negative sign in front of his answer when his work reflects it is a negative number. He understands the concepts well but he gets a fourth or more of the problems wrong on his daily work because of these simple, careless, computational errors.” Mistakes like those described above are normal with most students working on the daily assignment preparing for the upcoming weekly test. Have you noticed that they make fewer, if any, of these same mistakes when they take a test? I like to use the phrase that “students put on their Test Hat” when taking a test, and they will not accept the same mistakes they do on their daily practice work. However, if you reward them for making these mistakes on a test by giving them partial credit, they will continue making them on the tests as well. No matter how much we try to eliminate these mistakes, some students will never stop making them, no matter how good they become at mathematics. That is why experienced engineers always check each other's work before releasing a new project for testing or production. Some years ago, I read in the daily newspaper that Spanish engineers working on a new submarine for the Spanish Navy did not do this verification check. After building a new submarine, it was found that the engineers had overlooked the erroneous placement of a decimal point in their computations. The embarrassing  and costly  result was that the Spanish Navy ended up with a new submarine so heavy that it would not surface if it were ever submerged. Most students make fewer mistakes in performing simple mental arithmetic calculations on paper than they do when pressing the wrong button on a calculator, which still constitutes a human error, although the student will try to blame the calculator! Even students looking to achieve perfection can be found guilty of “rushing” through their daily work for one reason or another. It might help to ensure students develop the habit of checking the work of the problem they just finished before moving on to the next. This process of review would enable them to find many, if not all, of these types of simple mistakes and while it may add a few minutes to the time spent on the daily assignment, it might get them to slow down a bit to avoid making them in the first place. So long as you do not reward the student for making these simple calculation errors on the weekly tests – like giving them partial credit for getting the concept right, but the answer wrong – they will eventually overcome that shortcoming. And if they do not, but their weekly test scores remain constantly at an 80 or better, I would not worry about it. Remember, the cumulative and repetitive nature of John Saxon’s math books is what creates the mastery as opposed to other math curriculums reviewing for – and teaching the test. So making a few computational errors, while maintaining a minimum score of 80 on the thirtysome weekly tests, is truly outstanding. While I fully understand that everyone considers an acceptable target grade for tests at 95 – 100, receiving an 80 on one of John Saxon’s weekly math tests is equivalent to the 95 one would receive on the periodic test using some other math curriculum that  reviews for and  teaches the test.
WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS? Over the past several decades, I have heard hundreds of homeschool educators as well as parents of my high school classroom students tell me that there was no need to finish a Saxon math book because the last twenty or so lessons of any Saxon math book are repeated in the review of the first thirty or so lessons of the next level Saxon math book.. There is a bit of truth to that observation. A few of the concepts encountered in the later lessons of a book are repeated in the early lessons of the next level book because that important concept came late in the book and did not allow sufficient time for the student to master it before reaching the end of the course. But when repeated, the reintroduction of these concepts assumes the student had encountered the concepts in a simpler format in the previous level textbook. But anyone who would attempt to skip the last twenty or so lessons of any Saxon math book under the misguided impression that all of that material is repeated in the first thirty lessons of the next math book is in for a shocking surprise. Someone may tell you their son or daughter did just that while using the Saxon Algebra 1 textbook and their child did quite well in the Saxon Algebra 2 book the following school year. While there are always exceptions that justify the rule, what most of these home educators will not tell you is that – because of this shortcut  their child struggled through the Saxon Algebra 2 course and the student either repeated the course a second year, or failed to master the required concepts  having to enroll in a no credit algebra course as a freshman in college the following year. The concept of automaticity requires the application of repetition over time and violating either one of these conditions greatly reduces the student’s chances of mastering the necessary math concepts to be successful in the next level math course. There is a third factor involved in the process of automaticity. When the student encounters a concept, works with it over several weeks and then does not encounter it again until as much as a month later, that delay in repeating – coupled with a slight change in the level of difficulty of that concept  challenges the student’s level of mastery and some students who have not quite mastered the entire concept have to review it from previous lessons before continuing. However, once mastered a second time – following the delay  the concept is more strongly imbedded in their long term memory. So after taking a break for the summer, is it not wise to start the next level Saxon math book with a small amount of review material to ensure the student retained the necessary skills to succeed in the next course? But wait, would that apply to homeschool students who do not take a summer break? The argument is that if they finish the entire Algebra 1 book, and then go straight into Algebra 2, they can easily skip the first twenty or so lessons in the Algebra 2 text. That is also a dangerous procedure to follow for at least two reasons. FIRST: Remember I said that some of the concepts introduced late in the previous textbook are repeated to allow mastery – I did not say all of them. The student will go down in flames around lesson forty or so, never having been introduced to a dozen or more concepts involving both algebra and geometry. Additionally, the Algebra 2 book assumes the students mastered their basic introduction to these new concepts in the earlier lessons (the ones the student skipped) and it now combines them with other concepts. Now students start struggling as test scores begin to fall. This is where the parent or teacher blames the book as being too difficult to use and leaves Saxon math for an easier math course. SECOND: While collegiate and professional athletes practice almost year round, they do take several months off sometime between their seasons to rest the mind as well as the body. In mathematics, it is good to take a month or so off between levels of math to allow students to refresh their thought processes. As I mentioned earlier, this break also allows them to better evaluate what concepts they have truly mastered. Once mastered a second time – following the delay  the concept is more strongly imbedded in their long term memory. I believe these are two valid reasons not to skip lessons under any circumstances.
WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS? Several decades ago, while teaching John’s Advanced Mathematics textbook my second year at the high school, I encountered a problem with my Saxon Advanced Mathematics students. The students who had received an A or B in the Saxon Algebra 2 course the previous year were now struggling with low B and C grades  and we were only in our first nine weeks of the course. I called John and explained the situation to him. He asked me if I was following the same procedure I had used in the Algebra 2 course last year (e.g. a lesson a day  all thirty problems assigned every day  and a test every Friday). I told him that we did all thirty problems every day and took a test every Friday just as we had in the Algebra 1 course as well. I went on to tell John that the students were frustrated. In Algebra 2, they had easily completed their daily work done in fortyfive to fifty minutes, but now they were spending several hours each night to complete their daily assignments – and most of them were not even getting all of the assigned homework finished in that period of time. John’s response was quick and to the point. He asked me if I had read the preface to his book, and when I told him I had not, he told me to read the preface of the book and then he hung up. This was not an unusual trait of John’s. I had known him for several decades and, like many other experienced fighter pilots I had encountered in my military service, he seldom went into any lengthy explanation when someone was not following instructions. In the preface of the Advanced Mathematics textbook, I found that John had written in detail about the textbook’s indepth coverage of trigonometry, logarithms, analytic geometry, and upperlevel algebraic concepts. He explained that the textbook could easily be broken into two 5semester hour courses at the college level. But he cautioned  that at the high school level – teachers should break the course into three or four semesters. I immediately chose the four semester option, calculating that this would allow two days for each lesson. The students could do the odd numbered problems one day and the even numbered problems the second day. By doing it this way, the students would encounter all of the concepts covered in the thirty problems both days since the concepts taught in each lesson were arranged in pairs. Also, they would not have to spend more than an hour each night on their daily assignment. Is it possible for high school students to successfully complete the entire Advanced Mathematics textbook in a single school year? Yes, but both John and I were in agreement that those students are the exception rather than the rule. In all the years that I taught using John’s math books, I have encountered only one student who completed the entire 125 lessons of the Advanced Mathematics textbook in a single year  with a test average of over 90 percent! She was a National Merit Scholar and her father taught mathematics with me at the local university. That is not to say that others could not have accomplished the same feat, but these exceptions only tend to justify the rule. The beauty of John’s Advanced Mathematics book is its flexibility that allows students to use the book at a pace comfortable to them whether that pace takes two, three or four semesters. There is no academic dishonor in a bright home school math student taking three or four semesters to complete John Saxon’s Advanced Mathematics textbook if that student needs the extra study time to take care of other tough academic subjects being taken at the same time. There is no need to bunch everything up and rush through the math just to get to calculus before the student graduates from high school. Students fail calculus in college not because of the difficulty of the calculus concepts, but because their background in algebra and trigonometry is weak. It is the student with the weak mastery of algebra and trigonometry in high school who fails the calculus course  or  perhaps the student who has mastered the algebra and trigonometry in high school, but because of this knowledge, elects not to attend the daily calculus lectures. Please watch the following short video that describes how the Advanced Mathematics course is taught and credited: The sixth and last myth to be discussed in next month’s news article is: You Do Not Have to Finish the Last Twenty or So Lessons of a Saxon Math Book.
WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS? Whether I am at a homeschool convention or browsing the online homeschool blogs, I keep hearing and seeing comments from homeschool parents that express the idea that: "You must use a separate geometry book to receive credit for geometry." More than a decade ago, I received an Examination Copy of the new fourth edition Algebra 1 book prepared by the new owners of John Saxon’s Publishing Company. They had gutted the book of all references to geometry. The index had one reference to several pages late in the textbook titled “Geometric Sequences,” but that term refers to an algebraic formula dealing with common ratios – it is not a geometry formula found in any geometry textbook. Unlike the old second or third editions of Algebra 2, their new fourth edition of Algebra 2 has also had all references to geometry removed from it. Why did the new owners do this? Well I can come up with several reasons: FIRST: The marketing people would tell you that you make more money from three books than you do from two. I learned from the Corporate Executives at the company that first bought Saxon Publishers from John’s children in 2004 that they truly believed that "A math book is a math book is a math book." In my dealings with them as they transitioned John’s Publishing Company into theirs, it was apparent that they failed to realize or accept the uniqueness of John’s math books. To them one math book was just like another. If a particular state did not buy their math book this year another state was switching from someone else’s math book to theirs. So as long as this phenomenon went on why waste profit margin selling a unique math book and explaining or defending its content. Why? Because the perception was that failure in the math program of any particular public school was never the fault of the teacher; it was always the poor quality of the math book which required switching to more “improved” math books every four to five or so years as math test scores either did not improve or fell. And the publishers would be more than happy to tout their new and improved math textbooks which they said would result in higher test scores. One book publisher even went so far as to openly advertise that since they also published the annual student state math tests and that their books were geared to ensure student success with these mandated state tests. I recall telling a high school principal several decades ago that it never ceased to amaze me that after a decade or two of schools switching math books every few years  because of low math test scores  that sooner or later school administrators would realize it might be the teachers or the poor quality of the math books responsible for the low test scores. So why not do as everyone else does and create three separate and distinct math books for the algebra one, algebra two, and geometry courses? That not only makes it easier to sell the books, but it increases the quarterly profit margins because of the requirement for the additional geometry book. SECOND: Some math teachers would tell you that students cannot learn geometry while they are trying to master the algebra. They therefore demand a separate geometry textbook. The second and third editions of John Saxon’s Algebra 2 textbooks contain the equivalent of the first semester of a regular high school geometry textbook – to include rigorous twocolumn proofs (see the December 2012 news article). But wait! Isn’t it true that students cannot handle the geometry while they are also trying to master the algebra? Not so! European students have been combining algebra geometry and trigonometry in a single math book as long as I can remember. And they consistently come out ahead of us in comparative math comprehension tests. This myth makes about as much sense as telling a high school student that they cannot take a mandatory sophomore English course while also taking a separate journalism course. So what am I getting at? Must we have a separate geometry textbook for students who cannot handle the geometry and algebra concurrently? Well, let me ask you, if students can successfully study a foreign language while also taking an English course or successfully master a computer programming course while also taking an algebra course, why can't they study algebra and geometry at the same time, as John Saxon designed it? Must the content be in two separate textbooks taken at two different times in order for the student to master their content? The geometry concepts encountered in John Saxon’s Algebra 2 textbook – whether the second or third edition – are the equivalent of the first semester material of a regular high school geometry course and that includes a rigorous amount of formal twocolumn proofs! However, if you choose to use the new fourth edition of Algebra 2, you must also purchase a separate geometry textbook to acquire geometry credit. As I previously mentioned, the new fourth editions of the revised HMHCO Algebra 1 and Algebra 2 textbooks do not contain any geometry concepts. THIRD: The new fourth editions of Algebra 1 and Algebra 2  as well as the new first edition of Geometry  do not have a responsible author, and therefore the new owners of John Saxon’s company do not have to pay any royalties! If you look at the inside cover of the new fourth editions of Algebra 1 and Algebra 2 as well as the new first edition of the new Geometry textbooks, you will not be able to find the name(s) of an author or authors of these books. Why? Because they were created by a committee hired by marketing people and the committee that constructed that edition of the algebra textbooks may or may not have had any extensive math or teaching experience. The publishers paid a onetime fee to a “committee” to create the new editions releasing them from paying future royalties to an author. So, do we blame the profit minded publishers for publishing a separate geometry textbook, or is it the fault of misguided highminded academicians who – after more than a hundred years – still demand a separate geometry text from the publishers? I am not sure, but thankfully, this decision need not yet face the homeschool educators using John Saxon’s math books. The original homeschool third editions of John Saxon’s Algebra 1 and Algebra 2 textbooks still contain geometry as well as algebra – as does the Advanced Mathematics textbook which follows the Algebra 2 textbook... Any homeschool student using John Saxon’s homeschool math textbooks who successfully completes Algebra 1, (2nd or 3rd editions), Algebra 2, (2nd or 3rd editions), and at least the first sixty lessons of the Advanced Mathematics (2nd edition) textbook, has covered the same material found in any high school Algebra 1, Algebra 2, and Geometry textbook – including twocolumn formal proofs. Their high school transcripts – as I point out in my book – can accurately reflect a full credit for completion of an Algebra 1, Algebra 2, and a separate Geometry course. NOTE: Just as you do not record “Smith’s Biology” on the student’s transcript when awarding credit for a year of biology, you should not use Saxon Algebra 1, or Saxon Algebra 2, etc., when recording Saxon math on the student’s transcript either. Just record Algebra 1, Algebra 2, etc. on the transcript. Myths that will be discussed in future News Articles: Aug  Myth 5  Advanced Mathematics Can Easily be Taken in a Single School Year! Sep  Myth 6  You Do Not Have to Finish the Last Twenty or So Lessons of a Book.
WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS? (Myth 3) Saxon Algebra 2 Does Not Contain Formal TwoColumn Proofs. When you hear someone say that if you use John Saxon’s Algebra 2 textbook, you will need a separate geometry book because “There are no twocolumn proofs in John Saxon’s Algebra 2 textbook,“ they are telling you that either (1) they have never used that textbook or (2) if they did use it, they never finished the book  they stopped before reaching lesson 124, or (3) they used the new fourth edition which has no geometry content. Whether they are using the second or third edition of John’s Algebra 2 book, students will encounter more than forty informal and formal twocolumn proof problems in the last six lessons of the textbook. The first ten or so geometry proof problems students encounter in lesson 124 of the textbook are the more informal method of outlining a proof. John felt this introduction to the informal outline would get the students better prepared for the more formal twocolumn proofs that they will encounter later. Then, from lesson 125 through lesson 129, students will be asked to solve more than thirty formal twocolumn proofs that are as challenging as any the students will encounter using any separate geometry textbook. If they proceed onto the Saxon Advanced Mathematics course the following school year, they will encounter two dozen informal proofs in the first ten or so lessons followed by more than fortysix formal twocolumn proofs in the next thirty or so lessons. They will encounter at least one formal two column proof problem in every lesson through lesson forty and then encounter them less frequently through the next twenty or so lessons of the book. When I was teaching high school math in a rural public high school, I taught both Saxon Algebra 2 as well as John’s Advanced Mathematics course. The students who took my Advanced Mathematics class came from my Algebra 2 class as well as another teacher’s Algebra 2 class. I recall the students in my Advanced Mathematics class who had taken Saxon Algebra 2 from me would comment that the twocolumn proofs in the Advanced Mathematics book were easier than those they had encountered last year in our Algebra 2 book. “Perhaps you have learned how to do twocolumn proofs” was my reply. However, the students who came from the other teacher’s Algebra 2 class moaned and groaned about how tough these twocolumn proofs were in the Advanced Mathematics book. After discussing the situation with the other teacher, I found that she knew I would cover twocolumn proofs in the early part of the Advanced Mathematics textbook so she stopped at lesson 122 in the Algebra 2 course – never covering the introduction to twocolumn proofs. The geometry concepts encountered in John Saxon’s Algebra 2 textbook – whether the second or third edition – are the equivalent of the first semester material of a regular high school geometry course and that includes a rigorous amount of formal twocolumn proofs! If you are using the new fourth edition of Algebra 2, you must also purchase a separate geometry textbook to acquire geometry credit as the new fourth editions of the revised HMHCO Algebra 1 and Algebra 2 textbooks have had the geometry content removed from them. Myths that will be discussed in future news articles:
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 masterylearning. 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 prealgebra 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 20192020 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 retake 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 art.reed@usingsaxon.com or call me at 5802340064 (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 midto 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 5802340064 (CST) and my email address is art.reed@usingsaxon.com. When Saxon students encounter difficulty in their current level math book before they reach lesson 3040 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 retaking 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 HarcourtAchieve 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 art.reed@usingsaxon.com or call me at 5802340064 (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 eightyfive 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 prealgebra” 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 “Prealgebra” 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, KMart, WalMart, 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 precalculus, 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. ***************************************************************************** 

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