HOW TO SUCCESSFULLY USE JOHN SAXON’S MATH BOOKS FROM MATH 54 THROUGH CALCULUS AND PHYSICS (Part 3)
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.
A) 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 –
B) 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 –
C) 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:
A. Never finished all of the lessons in the Saxon Algebra 1 textbook.
B. 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.
C. 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 February 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.
- 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.
- They had switched curriculum after experiencing difficulty in Saxon Algebra 1.
- 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@teachingsaxon.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).