Using John Saxon's Math Books - How homeschool parents can use them

Newsletters

June 2023

WHICH SAXON HIGH SCHOOL MATH COURSES CAN BE TRANSCRIPTED AS HONORS COURSES?

Several years ago – I believe in March of 2021 – I wrote an article about how to transcribe your student's courses in Algebra 2 and the Advanced Math book as well. I did not include the Algebra one textbook because I thought it did not quite meet the standards for describing an Honors Course – although it still is an excellent algebra textbook.

I am going to retransmit that article because I did not include it in my book and I felt that the readers needed to be reminded as they prepared their student's transcripts for them attending college this fall.

Almost two decades ago – when I wrote the book on how to use John Saxon's Math books – I did not include a chapter on honors courses because I mistakenly thought that by then everyone knew about them. My apologies, but the subject should have been included in the book. Since it was not, I thought I would publish the subject in the monthly news articles and make it available for homeschool educators to print a copy as an addendum to the book. (Click Here for a printable copy)

I would like to say that all of John Saxon's Math Books are honors courses. The contents of John's math books are no-nonsense, straightforward, rigorous, challenging, and conceptually sound. These outstanding math books enable mastery of the concepts, not just memorization; however – I would be stretching the accepted definition of honors courses. Generally, the title of honors course when applied to math classes is reserved for the higher-level math courses that cover more material and are therefore more rigorous and challenging than regular courses.

Yes, the term "honors course" can be applied to non-math courses as well; however, in this article, I will restrict use of the term to just mathematics courses – and more specifically – to John Saxon's math courses.

Unless your State Board of Education has created its own standards regarding who can certify an honors curricula, the classroom mathematics teacher can authorize an honors course. There are no official rules or standards that list what defines an honors course. However; the term is generally applied to high school courses considered to be more rigorous and therefore more academically challenging. With some exceptions, a student must acquire the classroom teacher's approval to enroll in an honors course along with an overall grade average of a B or higher in prerequisite math courses.

I am a qualified State certified secondary mathematics teacher with more than twelve years' experience teaching high school mathematics while using John Saxon's math books from algebra through calculus.

There is no doubt in my mind that the courses in John Saxon's high school math curriculum that qualify for honors courses are the Saxon Algebra 2 (only the 2^nd or 3^rd Ed), Saxon Advanced Mathematics (2nd Ed. – whether taught in a single year or in three or four semesters) and the Saxon Calculus textbook (1^st or 2^nd Ed). Let me briefly state why each of these qualify for the title of "Honors Course."

Algebra 2, 2^nd or 3^rd. Why not the new 4^th Edition? In my opinion, the new fourth edition of this book will not allow the student to satisfactorily enter the Advanced Math textbook – nor would it qualify for the title of "Honors Course." This new edition was not created by John Saxon. It was created by a publishing company that stripped all references to geometry from the fourth edition textbook. You can read more detail about the potential problems with using this non-Saxon edition in my Nov 2019 News Article. The challenges and rigorous nature of John Saxon's Algebra 2, 2nd or 3rd Ed. textbook have been reduced to a standard high school algebra 2 textbook in this new non-Saxon 4th Ed. version.

Now, what is it that makes the 2^nd or 3^rd editions of John's Algebra 2 textbook qualify as an honors course? When using the 2^nd or 3^rd Ed. of John's Algebra 2 textbook, students have 30 problems to tackle every day through all 129 lessons as well as a weekly test to determine their mastery of the material. Unlike a regular algebra 2 course, students must not only master the daily menu of some very rigorous algebra 2 concepts, but they must also master the rigorous geometry concepts found in the first semester of a high school geometry course – plus the introduction of trigonometric functions midway in the book as well.

It is acceptable to use Algebra 2 w/Geom (1 credit) on the student's HS transcript and in an appropriate place indicate honors credit for that course. Don't forget when a student takes an honors course, the GPA is scored differently: An A is worth 5 pts, a B is worth 4 pts, a C is worth 3 pts, and a D is 2 points, The grade of F is still 0.

I recall at a homeschool convention several years ago, a homeschool parent told me that she was told by a homeschool friend you could not award a semester of HS geometry because there were no two-column proofs in the Saxon Algebra 2 (2^nd or 3^rd Ed) textbooks. My reply was "Your friend did not finish the book, he probably stopped at lesson 122 ("Venn Diagrams"), because there are more than 15 rigorous two-column proofs in the six lessons between lesson 123 and 129 (the end of the book).

As I promised my students and their parents – and I will promise you – if students get no further than successful mastery of the Saxon Algebra 2 textbook (2^nd or 3^rd Ed) when they graduate from high school, they will be able to pass any freshman college algebra course from MIT to Stanford – provided they attend class every day, pay attention, complete assignments, and do not sleep in class. Oh, and – one more minor requirement – show up on test days!

Advanced Mathematics, 2^nd Ed: John designed this course to be taken in three, or four semesters. I taught the textbook as a four semester (2 year) course. If you would go to this link on my website, you can watch a short seven minute video on why and how you transcript the course:
https://usingsaxon.com/flvplayer.html

Unless textbooks have drastically changed in the field of collegiate freshman mathematics, this textbook is tougher than any collegiate freshman algebra textbook I have seen or previewed. Students who complete the entirety of the textbook and successfully master the material presented will score in the 90^th – or higher – percentile on either the ACT or SAT math score. As described in the referenced video, both of the course titles described in the four semester use of the book definitely qualify as honors courses.

Calculus (1^st or 2^nd Ed.): Either calculus textbook would qualify as an honors course in a high school environment. And, while successful completion of all 117 lessons of the older 1^st edition textbook prepares students for the AB portion of the College Board's Advanced Placement (AP) program for calculus, I recommend you use the newer 2^nd edition. That edition prepares students for both the AB (through lesson 102) – and the BC (all 148 lessons) portions of the College Board's Advanced Placement (AP) program for calculus. The 2^nd Ed. Of John's Calculus textbook contains 31 more lessons than the older 1^st Ed.

Lastly, the new 2^nd Ed. Of John's Calculus textbook has the added feature of the lesson reference numbers which appear in parenthesis under each problem number as used earlier in the third editions of Saxon's Algebra 1 and Algebra 2 textbooks. They direct students to the lesson that introduced the concept of that problem they may need to revisit. It saves the student wasted hours of valuable time trying to find the lesson that introduced the concept without knowing the correct terminology of what it is they are looking for.

May 2023

HOW TO SUCCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 THROUGH CALCULUS

(Part III)

Here is the final article in the three part series describing situations I have encountered these past three decades while teaching Saxon in a rural high school as well as providing curriculum advice to homeschool educators for John Saxon. As with the previous two parts of the series, I have added my thoughts about why you want to avoid them:

ATTEMPTING THE ADVANCED MATHEMATICS TEXTBOOK IN A SINGLE YEAR: Since there are only 125 lessons in the textbook, it seems reasonable to assume this is possible.

RATIONALE: "My son had absolutely no trouble in the Algebra 2 book and I believe he will have no trouble in this book either. The book has fewer lessons than the Agebra 2 book has. Besides, he is a junior this year and we want him to be in calculus before he graduates from high school."

FACTS:The second edition of John Saxon's advanced mathematics textbook is tougher than any college algebra textbook I have ever encountered. The daily assignments in this book are not impossible, but they are time consuming and can take most math students more than several hours each evening to complete the thirty problems. This generally results in students doing just doing the odd or even numbered problems to get through the lessons. I must have said this a thousand times "Calculus is easy; students fail calculus because they do not understand the algebra." Speeding through the advanced mathematics textbook by taking shortcuts does not allow the student the ability to master the advanced concepts of algebra and trigonometry to be successful in calculus. And if the only argument is that the student will not take calculus in high school, then what is the rush?

The DVD tutorial series for the second edition of John's Advanced Mathematics book that I have prepared allows students three different choices based upon their needs and capabilities.

They can follow my advice and take the course in two years (doing a lesson every two days). Thereby gaining credit for the first academic year of "Geometry w/Advanced Algebra," with a first semester credit for Trigonometry and a second semester credit for Pre-calculus in their second academic year.

- Or -

They can take the course in three semesters. Their first semester credit would be titled Geometry, followed by a second semester credit for Trigonometry w/Advanced Algebra; ending with a third semester credit for Pre-calculus.

- Or -

While not recommended — they can take the entire 125 lessons in the Advanced Mathematics book in a single school year gaining credit for a full year of Geometry along with a semester credit for Trigonometry w/Advanced Algebra. In all the years that I taught the subject, I only had one student complete the entire Advanced Math course of 125 lessons in a single school year – with a test average above ninety percent - and she was a National Merit Scholar whose father taught mathematics with me at the local university.

The specific details of how the transcript is recorded are covered in my book, but if you have any questions regarding your son or daughter's high school transcript, please feel free to send me an email (Include your phone number as I may need to ask you some questions to ensure an accurate recommendation).

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IS IT CRITICAL FOR STUDENTS TO TAKE CALCULUS IN HIGH SCHOOL? Students lacking a solid base in algebra and a basic knowledge of trigonometry will find taking calculus at any level difficult, if not impossible.

RATIONALE: "I want our son to take calculus his senior year in high school. The only way we can accomplish that is to have him speed through the Saxon Algebra 2 and Advanced Mathematics book to finish them by the end of his junior year. He may even have to use the summer months for math as well."

FACTS: Even if students successfully complete a calculus course their senior year in high school, whether at home or at a local community college, I would strongly recommend that they enroll in "Calc I" as a freshman at the university or college they choose to attend for several reasons.

First: If they truly understand enough of their calculus I course (usually encompassing derivatives) they can enjoy a solid five hours of "A" on their transcript for their first five hours of math as a freshman. They can also make some nice extra money tutoring their less fortunate classmates.

Second: While they think they understand everything there is about calculus, they will see much more as they sit back and "understand" what the professor is talking about. They might even learn something they never fathomed in the high school textbook they went through.

Third: Their solid "A" the first semester in a calculus I class lets the professors know what kind of student they are. That perception by the professor makes a big difference should they encounter difficulties later in their second semester of calculus II (usually through integrals). Finishing John Saxon's second edition of Advanced Mathematics at a pace that allows the student to grasp all of the material in that textbook, without being frustrated or discouraged, is paramount to their success in calculus at the university or college level.

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DO HIGH SCHOOL STUDENTS NEED A SEPARATE GEOMETRY TEXTBOOK? To reflect that a student has received a well-rounded math background, states that require three or more math courses require that geometry be recorded on a student's high school transcript, along with algebra 1, algebra 2, trigonometry, etc.

RATIONALE: "It is too difficult for high school students to learn both algebra and geometry at the same time." My son did just fine in the Saxon Algebra 1 textbook. However, he is only on lesson 35 in the Saxon Algebra 2 book, and he is already struggling." - or - their rationale is – "I have been told by other home school parents that there are no two-column proofs in John Saxon's Algebra 2 textbook."

FACTS: Many of my top students' worst test in the Saxon Algebra 2 course was their very first test. This happened because they did not realize the book covered so much geometry review from the algebra 1 text, as well as several key new concepts taught early in the Algebra 2 text. They quickly recovered and went on to master both the algebra and the geometry concepts. From my experiences, most students who encountered difficulty early in John Saxon's Algebra 2 textbook did so - not because they did not understand the geometry being introduced - but because their previous experiences with the Saxon Algebra 1 course did not result in mastery of the math concepts necessary to handle the more complicated algebra concepts introduced early in the Algebra 2 textbook. I would not recommend students attempt John Saxon's Algebra 2 math book if they have done any one or more of the following:
1. Never finished all of the lessons in the Saxon Algebra 1 textbook.
2. Hurried through the Saxon Algebra 1 textbook doing two lessons a day and then only did the odd or even numbered problems from each lesson.
3. Received multiple test scores of less than seventy-five on their last four or five tests in the Algebra 1 textbook (Not counting partial credit).
What about the students who never took the tests, because parents used the students' daily homework grades to determine their grade average? What does that reveal about the students' ability? Establishing a students' grade average based upon their daily work reflects what they have "memorized." The weekly tests determine what they have "mastered."
The successful completion of John Saxon's Algebra 2 textbook (2nd or 3rd Editions) gives students an additional equivalent of the first semester of a high school geometry course (including two-column proofs). Successful completion of the first sixty lessons of the Saxon Advanced Mathematics textbook (2nd Ed) ensures they receive the equivalent of the second semester of high school geometry, in addition to the advanced algebra and trigonometry concepts they also receive in the latter half of the book.

But what about the lack of two-column proofs in the Saxon Algebra 2 book (2nd or 3rd Ed)? Whenever I hear Homeschool Educators make the comment that "John Saxon's Algebra 2 book does not have any two-column proofs," I immediately know they stopped before reaching lesson 124 of the book which is where two-column proofs are introduced. The last six lessons of the Saxon Algebra 2 textbook (2nd or 3rd editions) contain thirty-one different problems dealing with two-column proofs. The following year, in the first half of the Advanced Mathematics textbook, they not only encounter some heavy duty algebra concepts, but they will also complete the equivalent of the second semester of a regular high school geometry course. The first thirty of these sixty lessons contain more than forty different problems dealing with two-column proofs.

So why then did John Saxon not want to publish a separate geometry textbook? As I mentioned in my April newsletter earlier this year, a group of professors who taught mathematics and science at the University of Chicago bemoaned the fact that educators continued to place a geometry course between basic algebra (Algebra 1) and the advanced algebra course (Algebra 2) to the detriment of the student. AND THEY WROTE THIS 108 YEARS AGO!

In the preface to their book titled "Geometric Exercises for Algebraic Solution," published in 1907, the professors explained that it is this lengthy "void" between the two algebra courses that prevents students from retaining the necessary basic algebra concepts learned in basic algebra (algebra 1) to be successful when encountering the rigors of advanced algebra (algebra 2).

Then apparently aware of this situation, and knowing John Saxon's position on the subject, why did HMHCO (the current owners of John's books) go ahead and create and publish the new fourth editions of Saxon Algebra 1, Algebra 2, and a separate first edition Saxon Geometry textbook? I do not know why they did, but I do know that three textbooks will make more money for a publisher than two textbooks will. I also know that the new books – while initially sold only to the schools on the company's school website, are now offered to Homeschool Educators as well. Having to decide between the two different editions of algebra makes the selection process more confusing; however, I would not recommend any student go from the fourth edition of Saxon Algebra 2 to John Saxon's Advanced Mathematics textbook.

If you stick with the editions of John Saxon's math books that I listed in my April 2022 Newsletter, you will have the best math books on the market today – good for several more decades to come.

As I mentioned last month, there will always be exceptions that justify the rule. However, just because one parent tells you their child did any one or all of the above, and had no trouble with the Advanced Math course does not mean you should also attempt it with your child. Those parents might not have told you that one or more of the following occurred.
1. Their children encountered extreme difficulty when they reached Saxon Algebra 2, and even more difficulty and frustration or even failure with the Saxon Advanced Mathematics or Calculus courses.
2. They had switched curriculum after experiencing difficulty in Saxon Algebra 1.
3. Their son or daughter had to take remedial (no credit) college algebra because that received low scores on the universities mathematics entrance exam.
For those readers who do not have a copy of my book, please don't forget to take a minute and read that April 2022 news article for information that will help you select the correct level and edition of John Saxon's math books. As I said earlier, these editions will remain excellent math textbooks for many more decades.

If your child is already experiencing difficulty in one of the Saxon series math books, and you need to find a workable solution, please email me at: art.reed@usingsaxon.com (Don't forget to include your telephone number as I may some questions generated by your comments). Or feel free to call me at my office using (580) 234-0064 (CST).

HAVE A GREAT SUMMER – HOWEVER, IF YOU DO SCHOOL WORK THROUGH THE SUMMER – MAKE SURE YOU GIVE STUDENTS AT LEAST A MONTH OFF BEFORE STARTING INTO THE FALL SEMESTER TO RELAX AND GIVE THEIR BRAIN A REST!

April 2023

HOW TO SUCCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 THROUGH CALCULUS

(Part II)

As I promised last month here are several more of the common misuses I have encountered during the past three decades of teaching and providing curriculum advice to homeschool educators. I have added my thoughts about why you want to avoid them:

1) THE EFFECTS OF DOING JUST THE ODD OR EVEN PROBLEMS: Allowing the student to do just the odd or even problems in each daily lesson may appear to save time, but it creates a false sense of mastery of the concepts.

RATIONALE: "Each lesson shows two of each of the different problems, and it saves us valuable time by doing just one of the pair. Besides, since they both cover the same concept, why take the extra time doing both of them?"

FACT: The reason there are pairs of each of the fifteen or so concepts found in the daily assignments is because each of the problems in each pair is different from the other. While both problems in each pair address the same concept, they are different in their approach to presenting that concept. One goes about presenting the concept one way while the second one approaches the concept from a totally different perspective. Doing both of them gives the student a broader basis for understanding the concept and prevents the student from memorizing a particular procedure rather than mastering the concept based upon solving the two different formats or procedures.

Whenever I receive an email from a homeschool educator or student, and they need help with solving a particular problem on one of the tests remarking that they never saw this test question in any of their daily work, I can tell that they have been doing either the "odds" or the "evens" in their daily work because this test question resembled an approach to the concept that was contained in the set they never did. Additionally, doing only half of the daily assignment restricts the student's ability to more quickly and easily master the concepts. Doing two a day for fourteen days increases the student's ability to more quickly master those concepts than doing just one a day for that same period of time.

The "A" or "B" student who has mastered the material should take no more than fifty minutes to complete the daily assignment of thirty problems if their grade is based upon their weekly test scores and not upon their daily homework. The "C" student should complete the daily assignment of thirty problems in about ninety minutes. The additional time above the normal fifty minutes is usually the result of the "C" student having to look up formulas or concepts that might not have yet been mastered. This is why I recommend using "formula cards."

Use of the formula cards saves students many hours of time flipping through the book looking for a formula to make sure they have it correctly recorded. The details on how to implement using these cards is explained in detail on page 94 of my book. If you have not yet acquired that book, you can find information on how to make and use them in my February 2022 Newsletter.

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2) THE EFFECTS OF DOING MORE THAN ONE LESSON A DAY: Permitting the students to do two or three lessons a day believing this will allow them to complete the course faster.

RATIONALE: "My son wants to finish the Saxon Calculus course by the end of his junior year. The only way he can do that is to finish the Algebra 2 book in six rather than nine months. Besides, he told me that he already knows how to do most of the material from the previous Algebra 1 book."

FACT: To those who feel it necessary to "speed" through a Saxon math book, I would use the analogy of eating one's daily meals. Why not just eat once or twice a week to save time preparing and eating three meals each day? Not to mention the time saved doing all those dishes. The best way I know to answer both of these questions is to remind the reader that our bodies will not allow us to implement such a time saving methodology any more than our brains will allow us to absorb the new math concepts by doing multiple lessons at one sitting.

I have heard just about every reason to support doing multiple lessons, skipping tests to allow another lesson to be taken, or taking a lesson on a test day. All of these processes were attempted solely to speed up completing the textbook. Students who failed calculus did so, not because they did not understand the language and concepts of calculus, but because they did not sufficiently master the algebra.

Why must students always be doing something they do not know? What is wrong with students doing something they are familiar with to allow mastery as well as confidence to take over? Why should they become frustrated with their current material because they "rushed" through the previous prerequisite math course?

The two components of "automaticity" are time and repetition and violating either one of them in an attempt to speed through the textbook (any math book) results in frustration or failure as the student progresses through the higher levels of mathematics. I recall my college calculus professor filling the blackboard with a calculus problem and at the end, he struck the board with the chalk, turned and said "And the rest is just algebra." To the dismay of the vast majority of students in the classroom - that was the part they did not understand and could not perform. When I took calculus in college, more than half of my class dropped out of their first semester of calculus within weeks of starting the course, because their algebra backgrounds were weak.

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3) ENTERING THE SAXON MATH CURRICULUM AFTER MATH 76: Switching to Saxon Algebra 1 or Algebra 2 because you have found the curriculum you were previously using was not preparing your child for the ACT or SAT and you wanted them to be more challenged.

RATIONALE: "We were having trouble with math because the curriculum we were using, while excellent in the lower grades, did not adequately prepare our son and daughter for the more advanced math concepts. We needed a stronger more challenging math curriculum, so we switched to Saxon algebra 1."

FACT: Switching math curriculums is always a dangerous process because each math curriculum attempts to bring different math concepts into their curriculum at different levels. Constantly moving from one math curriculum to another - looking for the perfect math book - creates "mathematical holes" in the students' math background. It also creates a higher level of frustration for these students because, rather than concentrating on learning the mathematics, they must concentrate on what the new textbook's system of presentation is and spend valuable time trying to analyze the new format, method of presentation, test schedule, etc.

If you intend to use Saxon in the middle and upper level math courses because of its excellence at these levels of mathematics, I would strongly recommend that you start with the Math 76, 3rd or 4th Ed textbook. The cumulative nature of the Saxon Math textbooks requires a solid background in the basics of fractions, decimals and percentages. All of these basics, together with the necessary prerequisites for success in pre- algebra or algebra 1 are covered in Saxon's Math 76, 3rd or 4th Edition textbook. This math textbook is what I refer to as the "HINGE TEXTBOOK" in the Saxon math curriculum.

Successful completion of this book will take care of any "Math Holes" that might have developed from the math curriculum you were using in grades K – 5. Successful completion of this book can allow the student to move successfully to the Saxon algebra ½ textbook (a pre-algebra course). Should students encounter difficulty in the latter part of the Math 76 text, they can move to the Saxon Math 87, 2nd or 3rd Ed and, upon successful completion of that book, move either to the Algebra ½ or the Algebra 1 course depending on how strong their last 4 or 5 test scores were. Yes, some students have been successful entering the Saxon curriculum at either the Algebra 1 or the Algebra 2 levels, but the number of failures because of weak math backgrounds from using other curriculums, roughly exceeds the number of successes by hundreds!

As I mentioned last month, there will always be exceptions that justify the rule. However, just because one parent tells you their child did any one or all of the above, and had no trouble with their advanced math course, does not mean you should also attempt it with your child. That parent might not have told you that:
1. Their child encountered extreme difficulty when they reached Saxon Algebra 2, and even more difficulty and frustration or failure with the Saxon Advanced Mathematics course, or –
2. They had switched curriculum after experiencing difficulty in Saxon Algebra 1, or –
3. Their child had to take remedial college algebra when they enrolled at a university, because they had received a low score on the university's math entrance exam.
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For those readers who do not have a copy of my book, please read my April 2022 news article for information that will help you select the correct level and edition of John Saxon's math books. These editions will remain excellent math textbooks for many more decades.

If your child is already experiencing difficulty in one of the Saxon series math books from Math 76 to Advanced Mathematics, and you need to find a workable solution, please email me at: art.reed@usingsaxon.com. Include your telephone number as it helps provide a quicker solution to your dilemma. In next month's issue, I will cover:
1. ATTEMPTING THE ADVANCED MATH TEXTBOOK IN A SINGLE YEAR:
2. IS IT CRITICAL FOR STUDENTS TO TAKE CALCULUS IN HIGH SCHOOL?
3. DO HIGH SCHOOL STUDENTS NEED A SEPARATE GEOMETRY TEXTBOOK?
March 2023

HOW TO SUCCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 THROUGH CALCULUS AND PHYSICS (Part 1)

Both homeschool educators as well as public and private school administrators often ask me "Why do John Saxon's math books require special handling? Another question I am also frequently asked is "If John Saxon's math books require special instructions to use them successfully, why would we want to use them"? Before the end of this newsletter, I hope to be able to answer both of these questions to your satisfaction.

There is nothing "magic" about John Saxon's math books. They were published as a series of math textbooks to be taken sequentially. Math 54 followed by Math 65, and then Math 76, followed by either Math 87 or Algebra ½, and then algebra 1, etc. While other publishers were "dumbing-down" the content of their new math books, John Saxon was publishing his new editions with stronger, more challenging content. Homeschool families, attempting to save money by buying older used Saxon Math books and inter-mingling them with the newer editions were unaware that the older out-of-print editions were often incompatible with these newer, more challenging editions. The same problem developed in the public and private school sector adding to the confusion about the difficulty of John's math books.

For example, a student using the old first or second edition of Math 76 would experience difficulty entering the newer second or third editions of Math 87 because the content in the outdated first or second editions of Math 76 was about the same as that of the material covered in the newer editions of Math 65 (the book following Math 54 and preceding Math 76). Jumping from the outdated older edition of Math 76 to the newer editions of either Math 87 or Algebra ½ would ultimately result in frustration or even failure for most, if not all, of the students who attempted this.

Many homeschool educators and administrators were also unaware that – when finishing a Saxon math book, they were not to use the Saxon placement test to determine the student's next book in the Saxon series. The Saxon placement test was designed to assist in initially placing non-Saxon math students into the correct entry level Saxon math book. The test was not designed to show parents what the student already knew, it was designed to find out what the student did not know. Students taking the placement test, who are already using a Saxon math book, receive unusually high "false" placement test scores. These test results may erroneously recommend a book one or even two levels higher than the level book being used by the student (e.g. from their current Math 65 textbook to the Math 87 textbook – skipping the Math 76 textbook).

By far, the problems homeschool educators as well as classroom teachers encounter using – or shall I say misusing – John's math books are not all that difficult to correct. However, when these "short-cuts" are taken, the resulting repercussions are not at first easily noticed. Later in the course, when the student begins to encounter difficulty with their daily assignments – in any level of Saxon math books, the parent or teacher assumes the student is unable to handle the work and determines that the student is not learning because the book is too difficult for the student.

Here are some of the most common misuses I have encountered literally hundreds of times during these past several decades of teaching and providing curriculum advice to home school educators:
1. NOT FINISHING THE ENTIRETY OF THE TEXTBOOK: Not requiring the student to finish the entirety of one book before moving on to the next book in the sequence.
  
  RATIONALE: "But the beginning twenty or so lessons of the new book covers the same material as in the last lessons of the book we just finished, so why repeat it"?
  
  FACT: The student does encounter review of this material in the next book. However, because the student has not done sufficient work on these concepts in the previous book to "master" them in the short time left in the school year, their review in the new book is essential to later success in the new book. Skipping the last twenty or so lessons in the previous level textbook means the students are encountering these concepts for the first time. This does not initially appear to create a problem until the student gets to about lesson thirty or so in the book, and by then both the parent and the student have gotten so far into the new book that they do not attribute the student's problem to be the result of not finishing the previous textbook. They start to think the material is too difficult to process correctly and do not see the error of their having skipped the last twenty to thirty or so lessons in the previous book. They now fault the excessive difficulty of the current textbook as the reason the student is failing.
  
  Always finish the entirety of every Saxon math textbook! Because all students are not alike, if as you're reading this article you have already encountered this particular phenomenon with your child, there are several steps you can take to satisfactorily solve the problem without harming the child's progress or self-esteem. So that we can find the correct solution, please email me – and include your telephone number – and I will call you with a solution for your child's particular situation that same day.
2. MISUSE OF THE SAXON PLACEMENT TEST: Skipping one of the books in the sequence (e.g. going from Math 54 to Math 76) because the "Saxon Placement Test" results clearly showed the student could easily handle the Math 76 material.
  
  RATIONALE: "He even got some of the Math 87 level questions correct. Besides, we had him look at the material in the Math 65 book and he said that he already knew that material, so why bother doing the same concepts again."
  
  FACT: First, as I wrote earlier, the Saxon Placement Test was designed to place non-Saxon math students into the correct level math book. It was designed to see what the child had not encountered or mastered, not what he already knew. Saxon math students who take the Saxon placement test receive unusually high "false" test scores. The only way to determine if the student is ready for the next math book is to evaluate their last four or five tests in their current Saxon math book to determine whether or not they have mastered the required concepts to be successful in the next level book. The brain of young students cannot decipher the difference between recognizing something and being able to provide solutions to the problems dealing with those concepts. So when they thumb through a book and say "I know how to do this" what they really mean is "I recognize this." Recognition of a concept or process does not reflect mastery.
3. USING DAILY HOMEWORK TO DETERMINE A STUDENT'S GRADE: Skipping the weekly tests and using the student's daily assignments to determine their grade for the course reflects memory rather than mastery of the material.
  
  RATIONALE: I cannot count the number of times I have been told by a parent "He does not test well, so I use the daily assignment grades to determine his course grade. He knows what he is doing because he gets ninety's or hundreds on his daily work."
  
  FACT: Just like practicing the piano, violin, or soccer, the student is not under the same pressure as when they have to perform in a restricted time frame for a musical solo or a big game. The weekly tests determine what a student has mastered through daily practice. The daily homework only reflects what they have temporarily memorized as they have access to information in the book not available on tests. Answers are provided for the odd numbered problems and some students quickly learn to "back-peddle." This phenomenon occurs when the student looks at a problem and does not have the foggiest idea of how to work the problem. So they go to the answers and after seeing the answer to that particular problem, suddenly recall how to solve the problem. However, later, when they take the test, there are no answers to look up preventing them from "back-peddling" through to the correct solution.
As with anything, there are always exceptions that justify the rule. However, just because one parent says their child did any one or all of the above, and had no trouble with their math, does not mean you should also attempt it with your child. That parent might not have told you that (1) their child encountered extreme difficulty when they reached Saxon Algebra 2, and even more difficulty with the Saxon Advanced Mathematics textbook, or (2) they had switched curriculum after experiencing difficulty in Saxon Algebra 1, or (3) their child had to take remedial college algebra when they enrolled at the university because they had received a low score on the university's math entrance exam.

If your child is already experiencing trouble in one of the Saxon series math books, and you need to find a workable solution, please email me at: art.reed@usingsaxon.com. Include our telephone number as it helps provide a quicker solution to your dilemma..

In next month's issue, I will cover:
1. THE EFFECTS OF DOING JUST THE ODD OR EVEN PROBLEMS:
2. THE EFFECTS OF DOING MORE THAN ONE LESSON A DAY:
3. ENTERING THE SAXON MATH CURRICULUM AFTER MATH 76:
February 2023

THAT OLD "GEOMETRY BEAR" KEEPS RAISING ITS UGLY HEAD

Home School Educators frequently ask me about students taking a non-Saxon geometry course between algebra 1 and algebra 2, as most public schools do. They also ask if they should buy the new geometry textbook recently released to homeschool educators by HMHCO (the new owners of Saxon). As I mentioned in a previous newsletter late last year, a group of professors who taught mathematics and science at the University of Chicago bemoaned the fact that educators continued to place a geometry course between basic algebra (Algebra 1) and the advanced algebra course (Algebra 2) to the detriment of the student. AND THIS WAS MORE THAN 110 YEARS AGO!

The danger of using a separate geometry textbook as described by these professors more than one hundred and ten years ago - still exists today! Placing a nine month geometry course between the Algebra 1 and Algebra 2 courses creates a void of some fifteen months between the two algebra courses. How did I arrive at fifteen months? In addition to the nine month geometry course, you must also add the additional six months of summer between the two courses when no math is taken. The professors went on to explain in their book that it was this "lengthy void" that prevented most students from retaining the necessary basic algebra concepts from the basic algebra (Algebra 1) to be successful when encountering the rigors of the Algebra 2 concepts.

Home school educators also asked about using the new fourth editions of Saxon Algebra 1 and Algebra 2 recently released by HMHCO (the new Saxon owners) together with their new separate geometry textbook now offered for homeschool use. To create the new fourth editions of both the Algebra 1 and Algebra 2 textbooks, all the geometry was gutted from the previous third editions of both Algebra 1 and Algebra 2. Using the new fourth editions of their revised Saxon Algebra 1 and Algebra 2 now requires also purchasing their new Saxon Geometry book to receive any credit for geometry. That makes sense, if you consider that publishers make more money from selling three books than they do from selling just two. Regardless of which editions you finally choose to use, I would add a word of caution. If you intend to use John's Advanced Mathematics, 2nd Ed textbook, do not use the new fourth editions of Algebra 1 or Algebra 2.

So what Saxon math books should you use? The editions of John Saxon's math books from fourth through twelfth grades that should be used today appears on page 15 of my book. These editions remain the best math books on the market today, and they will remain so for decades to come.

If you desire more information about the pros and cons of using a separate Geometry textbook, please read my January 2022 Newsletter. Should you still have questions or reservations, feel free to email me at art.reed@usingsaxon.com or call my office any week-day at 580-234-0064 (CST).



January 2023

The Infallible Professor

As we start a new year, I thought I would share a quick story about an experience I had while a student in college decades ago, an experience I am certain many of your sons and daughters encounter in their classrooms as well.

More than 50 years ago while attending a university in the South – as an active duty member of the armed forces – I encountered a rather single minded professor in a sociology class who – in his own words – "Did not want to hear any student's thoughts or opinions." Needless to say – having grown up in Chicago – I violated his edict and was ejected from his class when I questioned some rather obvious misinformation he was putting out about large cities – obvious at least to anyone who had the opportunity to live in these cities. There were about twenty young men and women in the class all from rural areas of the state and it was clear that none of them had yet – except for perhaps a vacation – traveled outside the state or came from a large city he was referring to.

Later in the afternoon, I went to his office to discuss why he had ejected me from his class. He was still quite openly angry with me and quite adamant about me accepting a "C" with the added stipulation that I was not to return to his class. I reminded him that I had earned an "A" in his class at that point. He would not budge from his position, so I left his office. That evening I wrote the following poem and had it published in the school newspaper several days later.

The Infallible Professor

"With my professor I must agree.
Not he with me, but me with he!
How then am I to learn what's true
And pass on to you the knowledge
Of mankind – when my thoughts are
thoughts of a professor's mind?"

The day after it was published, the professor contacted me and after a sometimes heated discussion, we both agreed upon some ground rules. He would allow me to return to class with the grade I had earned to that point. And I would not be penalized again for questioning anything he brought up in class. While we tangled in class a bit over other items he brought up – he never again lost his temper. And I passed his class with my earned grade of an "A"!

What had angered me most at that time was that my question was brought up in a respectful way. I gave several actual existing locations in the city of Chicago that made his statement of fact untrue – that all large cities were not identical in their physical layouts. Rather than asking me to explain in detail what I had just stated was fact – contradicting his premise – he immediately took on the aura of a dictator and attempted to shut me down by loudly and angrily shouting at me to "shut up" and loudly and angrily shouting that this was his classroom and if he wanted my opinion he would have asked for it.

I wanted to tell him that it was my money paying him to teach us — not to dictate to us. I wanted to tell him that we lived in a free democracy and that all ideas are open for meaningful and polite discussion. I wanted to remind him that is what my uncles and cousins — and my father — had fought and died for during two World Wars. But somehow I also realized that this was not the time or place for that discussion and I quietly picked up my notes and book and left his room.

I realize that his persona lives on in some college professor that your son or daughter may encounter. And I thought the poem I wrote more than half a century ago (change "he" to "she" if necessary) may be used again by any student if it brings the same peace of mind to that young student that it brought to me that night.

I promise to get back to mathematics next month.

           Have a Blessed, Safe, and Happy New Year!

HAVE A GREAT SUMMER – HOWEVER, IF YOU DO SCHOOL WORK THROUGH THE SUMMER – MAKE SURE YOU GIVE STUDENTS AT LEAST A MONTH OFF BEFORE STARTING INTO THE FALL SEMESTER TO RELAX AND GIVE THEIR BRAIN A REST!