HOW TO SUCCESSFULLY USE JOHN SAXON’S MATH BOOKS FROM MATH 54 THROUGH CALCULUS AND PHYSICS (Part 2)
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:
- 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 –
- They had switched curriculum after experiencing difficulty in Saxon Algebra 1, or –
- 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@teachingsaxon.com. Include your telephone number as it helps provide a quicker solution to your dilemma. In next month’s issue, I will cover:
- ATTEMPTING THE ADVANCED MATH TEXTBOOK IN A SINGLE YEAR:
- IS IT CRITICAL FOR STUDENTS TO TAKE CALCULUS IN HIGH SCHOOL?
- DO HIGH SCHOOL STUDENTS NEED A SEPARATE GEOMETRY TEXTBOOK?