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 about a fourth of the way through their respective math books and are quickly finding out that the easy review of the previous textbook’s material has come to a sudden halt. They are now entering the part of the textbook that determines whether or not they have mastered sufficient material from the previous textbook to be prepared for their current course of instruction.
For students who start school in August - using the Saxon middle or high school math series from Math 76 through Algebra 2 - this generally occurs sometime in mid-October around lesson 35 or so. Or it can occur sometime in late November, if they started the course in September. 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 thirty or so lessons of the course. They were mostly upper middle school or high school students using John Saxon’s Algebra ½, Algebra 1, or Algebra 2 textbooks.
The symptoms described by the home school parents were similar. The daily assignments seem to take much longer than before and the test grades appear to be erratic or on a general downward trend. The student becomes easily frustrated and starts making comments like, “Why do I have to do every problem?” – or - “There are too many of them and it takes too long.” – or – “Why can’t I just do the odd problems since there are two of each anyway?” They might even say things like “This book is too hard.” – or - “It covers too many topics every day.” Or even worse - “I hate math.”
About that time, many homeschool educators do the same thing that parents of public or private school students do. They question the curriculum. They immediately look for another – easier – math curriculum so that their children can be successful. Since the students apparently did fine in the previous level book, the parents believe there must be something wrong with this textbook since their sons or daughters are no longer doing well.
Looking for an “easier” math course is like a high school football coach who has just lost his first ten high school football games. However, he assures the principal that they will definitely be successful in their next football game. “How can you be so sure that you will be successful in your next football game?” asks the principal. “Oh that’s easy,” says the coach. “I’ve scheduled the next game with an elementary school.”
I do not believe the answer is to find an easier math curriculum. I believe the answer is to find out why the students are encountering difficulty in the math curriculum they are currently using, and then find a viable solution to that situation. As John Saxon often said, algebra is not difficult; it is different!
Because every child is also different, I cannot offer a single solution that will apply to every child’s situation, but before I present a general solution to Saxon users, please be aware that if you call my office and leave your telephone number or if you email me, I will discuss the specifics of your children’s situation and hopefully be able to assist you. My office number is 580-234-0064 (CST) and my email address is firstname.lastname@example.org.
When Saxon students encounter difficulty in their current level math book before they reach lesson 30-40 or so, it is generally because one or more of the following conditions contributed to their current dilemma:
1) They did not finish the previous level book because someone told them they did not have to since the first 30 or so lessons in the next book contained the same material anyway.
2) In the previous level math book, when students complained the daily work took too long the parents allowed them to do only the odd problems. Doing this negates the built-in automaticity of John Saxon’s math program.
3) In the previous level math book, to hasten course completion, the parents allowed the students to combine easy lessons, sometimes doing two lessons a day, but only one lesson’s assignment.
4) The students did not take the weekly tests in the previous courses. Their grades were predicated upon their daily homework. NOTE: The daily homework grade reflects memory. The weekly test grade reflects mastery.
There are other conditions that contribute to the students encountering difficulty early in their Saxon math book. Basically, they all point to the fact that, by taking shortcuts, the students did not master the necessary math concepts to be successful in their current level textbook. This weakness shows up around lesson 30 – 40 in every one of John’s math books. The good news is that this condition – if caught early - can be isolated and the weaknesses corrected without re-taking the entirety of the previous level math book.
There is a procedure to “Find and Fill in the Existing Math Holes” that allows students to progress successfully. This procedure involves using the tests from the previous level math book to look for the “holes in the student’s math” or for those concepts that they did not master. This technique can easily tell the parent whether the student needs to repeat the last third of the previous book or if they can escape that situation by just filling in the missing concepts – or holes.
If you have my book, then you already know the specifics of the solution. If you do not have my book, then you can call me or email your situation to me and I will assist you and your child. Regardless of what math book is being used, students who do not enjoy their level of mathematics are generally at a level above their capabilities.
WHAT DETERMINES THE DIFFERENCE BETWEEN MASTERY AND MEMORY?
Think back to your days in high school and your math classes. Do you recall having your math teacher hand out a review sheet a few days before the big test? So what did you do with this review sheet? Right! You memorized it knowing that most of the questions would appear on the test in some form or other.
We are the only industrialized nation in the world that I know of where parents proudly announce “Oh, I was never very good at math.” Not hard to explain considering you probably memorized the material for a passing test grade, and then after the test was over, quickly forgot the material.
I still see students in the local public school receiving a passing math grade using the “review” sheet technique, even though their test grades never get above a sixty. How can this happen? Easy! The student‘s grades are based upon a grading system that ensures success even though the student cannot pass a single test (unless you consider a sixty a passing grade).
Many students‘ overall average grades are computed based upon fifty percent of their grade coming from the homework (easily copied by them) and another fifty percent determined from their test scores (following the review sheet). So the student who receives hundreds on the daily homework grades and fifties or sixties on the tests is cruising along with an overall grade average of a high “C” or a low “B.” Yet, that student cannot explain half of the material in the book.
I have often explained to parents of students who were struggling in my math classes that their struggle was akin to the honey bee struggling its way through the wax seal of the comb. It is that struggle that strengthens the bee‘s wings and enables it to immediately fly upon its exit from the hive. Cut the wax away for the young bee and it will die because its wings are too weak to allow it to fly. Yes, there is a difference between struggling and frustration! The home educator as well as the classroom teacher must be ever vigilant to recognize the difference.
While we all would like the student to master the new concept on the day it is introduced, that does not always happen. Not every math student completely understands every math concept on the day it is introduced. It is because of this that John Saxon developed his incremental approach to mathematics. When John‘s incremental development is coupled with a constant review of these concepts, “mastery” occurs.
Mastery occurs through a process referred to by Dr. Benjamin Bloom as “automaticity.” The term was coined by Dr. Bloom, of “Bloom‘s Taxonomy,” while at the University of Chicago in the mid 1950‘s. He described this phenomenon as the ability of the human mind to accomplish two things simultaneously so long as one of them was over-learned (or mastered). The two critical components for mastery are repetition over time.
Automaticity is another way to describe the placing of information or data into long term memory. The process requires that its two components–repetition over time–be used simultaneously. It is this process in John Saxon‘s math books that creates the proper atmosphere for mastery of the math concepts. Violating either one of the two components negates the process. In other words, you cannot speed up the process by taking two lessons a day or doing just the odd or even numbered problems in each lesson.
Trying to take shortcuts with mathematics would be like trying to save meal preparation time every day. Why not just eat all the meals on weekends and save the valuable time spent preparing meals Monday through Friday. Just as your body will not permit this “short-cut,” your mind will not allow mastery of material squeezed into a short time frame for the sake of speeding up the process by reducing the amount of time spent on the individual math concepts.
In a single school year of nine months, the student using John Saxon‘s math books will have taken more than twenty-five weekly tests. Since all the tests are cumulative in content, passing these tests with a minimum grade of “80” reflects “mastery” of the required concepts - not just memory!
While a student may periodically struggle with an individual test or two throughout the entire range of the tests, it is not their test “average” that tells how prepared they are for the next level math course, nor is it the individual test scores (good or bad) they received on the early tests that matter. What is important in a Saxon math book is the individual test scores the student receives on the last five tests in the course. It is these last five test scores that reflect whether or not the student is ready for the next level math course. Students who receive individual test scores of 80 or higher–first time tested–on their last five tests in any of John Saxon‘s math books are well prepared for the next level math course. They have mastered the concepts necessary for success.
WHICH BOOK SHOULD BE USED AFTER MATH 76? MATH 87 OR ALGEBRA ½?
How Can Students Overcome Their Difficulty With Algebra?
When John Saxon published his original series of math textbooks, they were designed to be taken in order from Math 54 to Math 65, followed by Math 76, then Math 87, then Algebra ½, on to Algebra 1, then Algebra 2, followed by Advanced Mathematics (which, coupled with Algebra 2, gave the high school geometry and trigonometry credits) culminating with the calculus textbook for some students.
The books were not originally intended to be “grade” oriented textbooks, but were intended to be taken in sequential order based upon a student‘s knowledge and capabilities without regard to the student‘s grade level. But schools and homeschool educators quickly assigned Math 54 to the fourth grade level, Math 65 to the fifth grade level, Math 76 to the sixth grade, and Math 87 to the seventh grade level to be followed by the pre-algebra course titled Algebra 1/2. When the new third edition of Math 76 came out in the summer of 1997, it was much stronger academically than its predecessor, the older second edition textbook. It did not take long for confusion to develop around which textbooks were now the correct editions to be used and what the correct sequencing would be.
In the thousands of telephone calls I received over the years I served as Saxon Publishers‘ Curriculum Director for Math 76 through calculus, the question that arose most often among classroom teachers as well as homeschool educators was whether the student should go from the new stronger Math 76 book to Math 87 or to Algebra ½ as both the Math 87 and the Algebra ½ textbooks appeared to contain basically the same material. Adding to the confusion, after John Saxon‘s death, was the fact that the new soft cover third edition of Math 87 had the title changed to read Math 8/7 ‘with pre-algebra.‘
So what Saxon math book does a student who has completed Math 76 use? Well, that depends upon how well the student did in the Math 76 book. The key word is “successfully completed,” not just “completed” Math 76. If a student completed the entirety of the Math 76 textbook and his last five tests in that book were eighty or better, he would have “successfully completed” Math 76 and he could move on to the Algebra ½ book. However, if the student‘s last five test grades were all less than seventy-five, that student has indicated that he will in all likelihood experience difficulty in the Algebra ½ materials and should therefore proceed first through the Math 87 textbook.
While both the Math 87 and the Algebra ½ textbooks prepare the student for any Algebra 1 course, the Math 87 book starts off a bit slower with more review, allowing the student to “catch up.” The student who then moves successfully through the Math 87 textbook, receiving eighties or better on the last five tests, can then skip the Algebra ½ book and move directly to an Algebra 1 textbook.
However, if the student finishes the Math 87 book and the last five test grades reflect difficulty with the material, that student should then be moved into the Algebra ½ book to receive another – but different – look at “pre-algebra” before attempting the Algebra 1 course. Students fail algebra because they do not understand fractions, decimals and percents; they fail calculus because they do not understand the basics of algebra. Attempting to “fast track” a student who had weak Math 76 test scores - into Algebra ½ - then on to Algebra 1, will most certainly result in frustration if not failure in either Algebra ½, or Algebra 1 – or cause the homeschool educator to seek an “easier” math curriculum..
So what have we been talking about? If students have to take all three courses (Math 76, Math 87 and Algebra ½), how will they ever get through algebra? When I taught Saxon math in a public high school, we established three math tracks for the students. Fast, Average, and Slower math tracks to accommodate the difference in learning styles and backgrounds of the students. Listed below are the recommended three math tracks. Please note there are no grade levels associated with these courses, but Math 76 was generally taught in the 6th grade at the middle school.
The course titled “Introduction to Algebra 2” was the student‘s first attempt at the Algebra 2 course which resulted in low test scores, so the course was titled as an “Introduction to Algebra 2” and the student repeated the entirety of the same book the following year.
Over ninety-five percent of all these students received an “A” or “B” their second year through the Algebra 2 course. In the ten years we used the system, I only had one student who received a “D” in the course and he did so because he did little or no studying the second year and still passed the course with a 65 percent test average.
I will make you the same promise I made to the parents of my former students. If students can accomplish no more than “mastering” John Saxon‘s Algebra 2 course by the time they are seniors in high school, they will pass any collegiate freshman algebra/trig course from MIT to Stanford (provided they go to class). Remember, they can still take calculus at the university if they have changed their mind and need the course in their new major field of study. And because they now have a strong algebra background, they will be successful!
FAST MATH TRACK: Math 76 – Algebra ½ – Algebra 1 – Algebra 2 – Geometry with Advanced Algebra – Trigonometry and Pre-Calculus – Calculus. NOTE: The Saxon Advanced Mathematics textbook was used over a two year period allowing the above underlined two math credits after completing Saxon Algebra 2. (TOTAL Possible High School Math Credits: 4)
AVERAGE MATH TRACK: Math 76 – Math 87 – Algebra ½ – Algebra 1 – Algebra 2 – Geometry with Advanced Algebra – Trigonometry and Pre-Calculus. (TOTAL Possible High School Math Credits: 4)
SLOWER MATH TRACK: Math 76 – Math 87 – Algebra ½ – Algebra 1 – Introduction to Algebra 2 – Algebra 2 – Geometry with Advanced Algebra. (TOTAL Possible High School Math Credits: 4)
NOTE 1: You should use the following editions as they are academically stronger than the earlier editions are. Using the older editions will result in frustration or failure for the students.
Calculus: Either the 1st or 2nd Edition will work just fine. If you use my DVD tutorials, you will need the 2d Ed textbook.
NOTE 2: When recording course titles on the transcript, use the following titles:
Algebra 1: Self Explainatory.
Algebra 2: Self Explanatory.
Advanced Mathematics: Use Trigonometry w/Pre-Calculus (1 Credit) after they have completed lessons 61 - 125.
Calculus: Self explanatory.
Under no circumstances should you record “Advanced Mathematics” on the student‘s high school transcript because
colleges or universities will not know what math this course contains. They will ask you for a course syllabus.
Each child is unique and what works for one will not always work for another. Whatever track you use, you must decide early to allow students sufficient time to overcome any hurdles they might encounter in their math journey. If you have any questions, please feel free to email me at email@example.com or call me at (580) 234-0064 (CST) and leave your telephone number and I will return your call.
THAT OLD "GEOMETRY BEAR" KEEPS RAISING HIS 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 108 YEARS AGO!
The danger of using a separate geometry textbook as described by these professors more than a hundred 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 are listed at the end of my April 2013 Newsletter. This same list 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 feel free to either email me at firstname.lastname@example.org or call my office any week-day at 580-234-0064 (CST).
HOW TO SUCCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 TO CALCULUS
Here is the final 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:
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.”
FACT: 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 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.
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.”
FACT: 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.
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.”
FACT: 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:
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 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 2013 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.
For those readers who do not have a copy of my book, please don‘t forget to take a minute and read that April 2013 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: email@example.com. Or feel free to call me at (580) 234-0064 (CST).
HOW TO SUCCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 TO CALCULUS
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:
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 September 2014 Newsletter.
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.
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:
For those readers who do not have a copy of my book, please read my April 2013 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 several 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: firstname.lastname@example.org. Or feel free to call me at (580) 234-0064 (CST).
In (Part III) of next month‘s issue, I will cover:
HOW TO SUCCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 TO CALCULUS
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 a great deal of 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 twenty years of teaching and providing curriculum advice to home school educators:
RATIONALE: “But the beginning of the new book covers the same material as that in the last lessons of the book we just finished, so why repeat it”?
FACT: The student encounters some review of this material in the next book, but this review assumes the student has already encountered the simpler version in the previous text. The review concepts in the new book are more challenging than the introductory one‘s they skipped in the previous book. 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 that same day – on my dime!
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 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.
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: email@example.com.
In Part II of next month‘s issue, I will cover:
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 HMHCO - the new owners of Saxon Publishers.
JOHN WAS RIGHT! - SOME THINGS HAVEN'T CHANGED - EVEN AFTER MORE THAN A HUNDRED YEARS!
Homeschool educators are constantly faced with the dilemma of deciding whether or not their son or daughter needs to take a separate high school geometry course because some academic institution wants to see geometry on the high school transcript. Or, because the publishers offer it as a separate math textbook in their curriculum - implying it is to be taken as a separate course. Remembering, of course, that selling three different math textbooks books brings in thirty-three percent more revenue than selling just two.
algebra by dropping it for a whole year after barely starting it, are numerous and strong . . . With no
other subject of the curriculum does a loss of continuity and connectiveness work so great a havoc
as with mathematics . . . To attain high educational results from any body of mathematical truths, once
grasped, it is profoundly important that subsequent work be so planned and executed as to lead the
learner to see their value and to feel their power through manifold uses."
How Much Time Should Students Spend on Math Each Day?
One of several arguments advanced by home school educators regarding the efficiency of the Saxon math curriculum is that from Math 54 through Advanced Mathematics the courses require too much time to complete the daily assignment of thirty problems. Their solution to this often takes one of two approaches. Either they allow the student to take shortcuts to reduce the time spent on daily assignments, or they find another math curriculum that takes less time (you know) you've heard them say, "We found another math curriculum that is more fun, easier, and it does not require so much time."
Remember, John Saxon's math books are the only books I am aware of that use weekly tests to evaluate a student's progress. There are a minimum of twenty or more weekly tests in every one of John's math books from Math 54 on.
Too Much Time is Spent on The Warm Up Box: From Math 54 through Math 87, there is what used to be called a "Warm Up" box at the top of the first page of every lesson. I recall watching a sixth grade teacher waste almost thirty minutes of class time while three boys took turns giving different opinions as to how the "Problem of The Day" was to be solved — and arguing as to which had the better approach. After class, I reminded the teacher that the original purpose of the box was to get the students settled down and "focused" on math right after the second bell rang. I said to her, "Why not immediately review a couple of the problems from yesterday's lesson at the start of class for the few who perhaps did not grasp the concept yesterday? Then move immediately to the new lesson." This process would take about 10 to 20 minutes and would leave students with about 40 minutes of remaining class time to work on their new homework assignment.
NOTE: In any of John Saxon's math books from Math 54 through Algebra 2, the "A" and "B" students will get their 30 problems done in less than 40-50 minutes. The "C" students will require more than an hour.
The Student is Required to Do All of The Daily Practice Problems: The daily practice problems were created for teachers to use on the blackboard when teaching the lesson's concept so they did not have to create their own or use the homework problems for demonstrating that concept. Many of the lessons from Math 54 through Math 87 have as many as six or more such problems and if the student understands the concept, they are not necessary. If the student has not yet grasped the concept, having the student do six or more additional practice problems of the same concept will only further frustrate him. Remember, not every student grasps every concept on the day it is introduced. The five minutes spent on review each day is essential to many students.
The Student is a Dawdler or a Dreamer: There is nothing wrong with being a "Dreamer," but some students just look for something to keep them from doing what they should be doing. I call these students "Dawdlers." I recall the first year I taught. I had to constantly tell some students in every class to stop gazing out the window at the cattle grazing in the field outside our classroom and get on their homework. That summer, I replaced the clear glass window and frame with a frosted glass block window - and in the following eleven years I had absolutely no problem with my "Dawdlers."
The Student is Slowed by Distractions: Is the student working on the daily assignment in a room filled with activity and younger siblings who are creating all sorts of distractions? Even the strongest math student will be distracted by excessive noise or by constantly being interrupted by younger siblings seeking attention. Did you leave the student alone in his room only to find he was on his cell phone talking or texting with friends or listening to the radio? Or worse, does he have a television or computer in his room and does he use the computer to search the internet for a solution to his math problems or engage in something equally less distracting by watching the television?
Please do not misinterpret what I have discussed here. If you desire to do all of the above and the student takes two hours to complete a daily assignment-and both you and the student are satisfied-then that is acceptable. But if you are using this excessive time as an excuse for your child's frustration-and as an argument against John Saxon's textbooks-I would remind you of what John once told a school district that did everything John had asked them not to do. They were now blaming John's math books for their district's low math test scores.
John told them "If you want to continue your current practices, get rid of my books and buy someone else's book to blame."
WHY IS THERE A "LOVE - HATE" RELATIONSHIP WITH SAXON MATH BOOKS?
Over the past twenty-five years, I have noticed that parents, students, and educators I have spoken to, either strongly like or, just as strongly, dislike John Saxon's math books. During my workshops at home school conventions, I am often asked the question about why this paradigm exists. Or, as one home school educator put it, "Why is there this Love - Hate relationship with Saxon math books?" It is easy to understand why educators like John's math books. They offer continuous review while presenting challenging concepts in increments rather than overwhelming the student with the entire process in a single lesson. They allow for mastery of the fundamentals of mathematics.
JUST WHAT IS THE DIFFERENCE BETWEEN MATH 87 AND ALGEBRA 1/2?
There appear to be varying explanations regarding whether a student should use Math 87 or Algebra ½ after completing the third or fourth edition of John Saxon's Math 76 textbook. Let me see if I can shed some light on the best way to determine which one, or when both, should be used.