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December 2017


                                            COMMON CORE REQUIREMENTS  -  and  -  SAXON MATH

As I write this article, there are seven states that have already voted to drop the Federal Common Core Requirements - with several more states in the process of passing legislation to do the same. Actually, there are hundreds of thousands of students who have individually opted out of the program. In the state of New York alone here are more than 200,000 students whose parents have legally opted out of the Federally Mandated Common Core Program.

You should also know that if you use John Saxon’s math books correctly – and you do not want to opt out of the program - you do not have to worry about whether or not your state has adopted the Federal Common Core Requirements. Because of the depth of John’s textbooks, your child will be parallel to or ahead of those standards. Certainly do not listen to the textbook publisher’s propaganda as their primary mission is not to educate, but to ensure satisfactory quarterly profit margins.

I recall when Oklahoma passed their state mandated math tests called the PASS test almost two decades ago. The test was designed to ensure that all students who completed an algebra one course in high school could pass the state mandated PASS test which was nothing more than a test of one’s knowledge of algebra one concepts. The test was given in mid-March of that year and it was advertised as an “End of Course” test – yet we were only two thirds of the way through the algebra one textbook - anticipating finishing the textbook by the end of school in late May.

I argued with the high school principal that this was not an honest or fair test to give the Algebra 1 students as we had not completed the book and therefore the students were not prepared for an “End of Course” test. In no uncertain words, he informed me that I would administer the test and that I was to make sure they passed it. He made it clear that, during the three weeks leading up to the test day, I was to teach those concepts that had not yet been reached. As I thought about it that evening, I decided to take a more honest approach.

When the test results came back that fall, our high school had one of the four highest PASS results in the entire state (I cannot remember if we were second, third or fourth). If that principal is reading this news article, it will come as a surprise to him to learn that I had my Saxon Algebra 2 students take the state mandated “End of Course Algebra 1 PASS Test,” since - unlike the algebra one students who had not yet finished the book - these students had and they were therefore most capable – and legally eligible – to take the “End of Course” PASS test mandated by the state.

So, how does all this affect you and your homeschool student in meeting the mandated Common Core requirements for mathematics?

I realize that the founders of these requirements tout the fact that they are mandating teaching students how to solve problems rather than just learning rote memory of math facts, but as John Saxon often said, “Understanding should follow doing rather than preceding it. If you are going to teach someone how to drive an automobile, don’t lecture them on the theory of the internal-combustion engine. Get them to drive the car around the block.”

The professional tree company that sent a man out to my house several years to estimate how much it would cost to spray my Elm tree against a specific disease had to send someone who knew something about the formula needed to calculate the surface area of the 40 – 50 foot high tree trunk - and thereby estimate the amount of liquid to use to spray the tree trunk – and also calculate how much to charge me?

Because you cannot change or hope to change those foolish enough to demand compliance with the Common Core - or similar “fuzzy” math standards - you can either opt out of taking the test, or you can make sure that your son or daughter is prepared to meet the challenge created by them. You can ensure that your sons and daughters are adequately prepared for these tests.

I will make you a promise. If you will follow the schedule I have outlined below, and in doing so ensure that the student truly masters each course as I have often described what “mastery” is defined as – that student will pass any fair and honest Core Curriculum Requirement in mathematics at any level. The key is to use the correct editions of John Saxon’s math books, and to not take any short cuts or allow deviations from what is required – such as weekly testing. And to make sure the student enters the Saxon Math curriculum no later than the sixth or seventh grade.

Here is the schedule:

6th Grade - Saxon Math 76, 4th Ed (You can also use the 3rd Ed textbook. However, there is no Solutions Manual for that edition). The 3rd Ed is a hard cover textbook.

7th Grade - Math 87, 2nd or 3rd Ed or Algebra ½, 3rd Ed. Entry into one or the other is dependent upon how well a student does on the last five tests in Math 76. The 2nd and 3rd editions of Math 87 are identical except that the 2nd Ed is a hard cover textbook – while the 3rd Ed is a soft cover.

8th Grade - Algebra 1, 3rd Ed (I recommend not using the 4th Ed as the new owners have removed all references to geometry from that edition).

9th Grade - Algebra 2, 2nd or 3rd Ed (I recommend not using the 4th Ed as they have also removed all references to geometry from that edition.) The 2nd and 3rd editions are identical except that the older 2nd Ed does not have the concept lesson reference numbers like the 3rd Ed does.

10th Grade - Advanced Mathematics, 2nd Ed (Part 1). Course is titled “Geometry, with Advanced Algebra.” Note that the concept lesson reference numbers are found in the Solutions Manual.

11th Grade - Advanced Mathematics, 2nd Ed (Part 2). Course is titled “Trigonometry and Pre-Calculus.” Note that the concept lesson reference numbers are found in in the Solutions Manual.

12th Grade – Calculus taken at a local university or college under “Concurrent” or “Dual Enrollment.” Or - the student can take a college algebra/trig course at a local college or university under “Concurrent” or “Dual Enrollment – or – the students can finish John Saxon’s Calculus, 2nd Ed textbook.

NOTE: To better explain how a full year’s geometry credit is awarded - and how to correctly pace the student using the very rigorous Advanced Mathematics textbook - take a moment and review this short seven minute video that describes how the courses are structured and recorded: Problem solving only takes place when the problem solver knows the “how” in solving them. In teaching students how to program a computer I would explain to them that the thought process was identical to what they had encountered in the two-column proofs they had encountered in their Saxon Algebra 2 and the Saxon Advanced Mathematics books.

The principle used to find a solution in either course is identical.

                                            “You cannot walk through a door until you have opened it.

                                             And you cannot open it, until you have walked to it. And

                                             you cannot walk to it, until you have identified it as the door

                                             you need to walk through.”

Every child is different and some students may be able to be successful in these courses a year or two earlier than the schedule reflects, while some may fall a year behind this schedule. However, if a student encounters difficulty along the way and never gets to calculus his senior year of high school, that is okay. Students fail college calculus because they are weak in algebra – not because they do not understand the calculus.

Some students may need both Math 87 and Algebra ½ before they are successful in the Saxon Algebra 1 course and that is okay as they are building a solid base before entering the upper level math courses. Any student who masters the entirety of John Saxon’s Algebra 1, 3rd Ed will be successful in the Algebra 2, 2nd or 3rd Ed course as well.

Please feel free to call me if you have any questions - or - email me your number and I will call you as my office has unlimited long distance calling anywhere in the US or its territories. My office telephone number is: 580-234-0064 (CST)

A SIDE NOTE: I recently saw a copy of a sample Common Core test taken by a group of fourth grade students. On one of the questions, the students were told to add several numbers and record their answer. The next question then asked them “What procedure did you use to find the answer to the previous question?”

To which one bright young fourth grader had boldly written Math as his answer.

    "May you have a Merry and Blessed Christmas"



November 2017



Over the last twenty-some years, I have heard just about every story told by public and private school classroom teachers, school administrators, and home school educators about how difficult John Saxon’s math books are. I believe that home school educators who speak poorly about John Saxon’s math books are like the classroom teachers and administrators I encountered who always blamed the math book for students’ poor showing. They never became aware that misusing John Saxon’s math books was a major contributing factor to the student’s difficulty. They never received or asked for any special training on how to correctly use John Saxon’s math books. Why should they? After all, isn’t one math textbook just like another?

Several decades ago, while briefing the superintendent of a large school district in Colorado I related to him - from my observations - that the vast majority of the district’s math teachers were not properly using John Saxon’s math books. His district had been using (rather misusing) John’s books for more than five years and the students’ math scores were getting worse, not better! I told him that it was not the books, but rather this misuse of the books that accounted for the district’s failing math scores.

The greatest mistake a classroom teacher or a home school educator can make in establishing a grading system for a mathematics course is to put too much weight upon the daily grade as this does not reflect mastery of the material. Teachers have little or no idea how students acquired the answers to the daily work unless they stand over the students as they do their work – which is not a recommended course of action.

In the middle of my briefing, he stopped me and said, “What I hear you saying Art, is that we bought a new car, and since we already knew how to drive, we saw no reason to read the owner’s manual – wouldn’t you agree?” To which I replied “It’s worse than that, sir! You all thought you had purchased a car with an automatic transmission, but Saxon is a stick shift! It is critical that certain procedures be followed, just as well as some are dropped, or you will strip the gears!” I went on to tell him that while I was not the owner of the company, if John Saxon were here today, standing up here addressing them under these circumstances, he would tell them to either use his books correctly or get rid of them, and blame someone else’s textbooks for the failing grades. They ultimately followed my advice and the students’ scores - as well as everyone’s spirits – increased.

On another occasion while briefing administrators at a school district in the state of Missouri - whose math teachers were guilty of the same misuse - I promised their superintendent the same results I had promised the superintendent in Colorado – that if they would make some adjustments and use the books correctly, they would develop a successful math program and their students’ math scores would go up. The district decided to implement the changes I had recommended. About eighteen months later, I received a letter from the superintendent. She wrote that their middle school students had scored the highest of any middle school in the state on their end-of-year math exams.

During these past several decades of advising and assisting homeschool parents about curriculum choices for their children, I noticed many of their calls and email to me are the result of them having received inaccurate or inadequate – sometimes downright erroneous – advice. This erroneous advice comes from other home school parents, discussion groups, well-meaning but uninformed or inexperienced publishing company employees, or from well meaning, but inexperienced employees of homeschool textbook distributors.

With all the new math books and supplemental math products on the market today – and textbook publishers promising every home school parent that if you use their books, your sons and daughters will score well on the ACT or SAT tests or pass the Common Core exams − I thought it appropriate to take this opportunity to defend John’s math books for the benefit of the home school educators and their students. I do not sell John Saxon’s math books – I never have! But I firmly believe that John’s math books remain the best math textbooks on the market today. I also believe that some of these new book fads – openly advertising how their product makes math fun - will ultimately leave your child short of mastering the requisite fundamentals of mathematics necessary to succeed in the collegiate realm of engineering, architecture, science, medicine, et al.

Students fail calculus – not because they do not understand the calculus – but because they never mastered the fundamentals of algebra, and they will fail a basic algebra course if they have not mastered the concepts of decimals, fractions and percents. John Saxon’s math books were designed to create mastery of mathematics at all levels, and the infusion of repetition over time (referred to by Dr. Benjamin Bloom as “automaticity”) creates this mastery at every level for every student who uses John Saxon’s math books properly.

While home school students have a great deal more academic flexibility than the public or private classroom students do, they can just as easily fall prey to the same difficulties in mathematics as the public classroom students if they are using one of John Saxon’s math books incorrectly. Parents of home school students who have displayed poor progress while using John Saxon’s math books, generally have unknowingly contributed to the student’s poor performance by taking shortcuts and preventing the student from receiving the full benefit of John Saxon’s methods.

Earlier this year, in my July and August news articles, I went over the essential Do’s and Don’t’s together with my comments and recommendations on how to correct them and have your child enjoy mathematics and realize mastery of the material using the best mathematics curriculum on the market today – John Saxon’s math books!

If you need to discuss a special situation concerning your son or daughter’s math progression or difficulty, please do not hesitate to either email or call me at:

Email: Telephone: 580-234-0064 (CST)

“Do not worry about your difficulties in mathematics; I can assure you that mine are far greater”

Albert Einstein




October 2017


            Does The Student's Grade in the Course Reflect the Student's Understanding of the Concepts?

Recently I read a math teacher’s syllabus that stated how their seventh grade Saxon math class would be graded. The syllabus stated that the grading scale would be the standard 90-100 A; 80-89 B; 70-79 C; 60-69 D; 59 and below was failing. The syllabus then explained that 10% of the student’s grade would be awarded for class participation and timely submission of the daily work. Accuracy of the daily work comprised another 40% of the student’s grade, and test grades comprised the remaining 50% of the student’s overall grade.

What this means is that a student who does not understand the material, reflected by weekly test grades in the 50’s, but who has enough initiative to copy his friend’s homework paper via the telephone, email, or other means – and who then receives a daily homework grade of 100 – will receive an overall math grade of a 75 (a good solid ‘C) reflecting he understands the work – which he clearly does not! How did I arrive at that passing grade? Easy. Fifty percent of a homework grade of one hundred is 50. Fifty percent of a test grade of only fifty is 25. Adding them together, you can easily see how the student quickly calculates the critical value of the daily assignment grades.

The greatest mistake a classroom teacher or a home school educator can make in establishing a grading system for a mathematics course is to put too much weight upon the daily grade as this does not reflect mastery of the material. Teachers have little or no idea how students acquired the answers to the daily work unless they stand over the students as they do their work – which is not a recommended course of action.

The beauty of the Saxon math curriculum is the weekly tests which tell the parent or teacher how the student is progressing. The daily work is nothing more than practice for that weekly test as the 20 test questions come from the 150 questions the student encounters in the previous five days of daily work. However, unlike students using some textbooks which provide a “test review” section, the Saxon students have no idea which of the 150 problems will be on the upcoming test. The Saxon students cannot memorize the concepts they encounter. They must understand them.

Oh yes, I almost forgot. The syllabus went on to explain to the parents and students that “after every test, students will be given the opportunity to retake a similar test, after more practice, and be given full credit.” A sure way to ensure students will pass the course - whether they understood the concepts or not. Have you ever known any student to receive a lower grade on a re-take of the same test? I say re-take because the Saxon classroom test booklet has an A and a B version of each test. Both versions are identical in content except the numbers are changed resulting in different numerical answers. The two versions were designed – not for re-takes – but for make-up tests to ensure the student taking the make-up test on Monday, did not receive the answers from another student who took the test on Friday.

John Saxon’s math books are the only math books on the market today (that I am aware of) that require a weekly test to determine how well the student is progressing. That means that in a school year of about nine months, the student takes about 30 tests. My grandson has been in his sophomore high school math class for over eight weeks now and he just took his first test. He passed it with a 94, but what if he had received a 60? How do you review material covered in over two months of instruction? In a Saxon math curriculum, if the teacher or parent never looked at the student’s homework - and the student never asked for help - the teacher or parent would know on a weekly basis how the student is progressing, allowing sufficient time for review and remediation if necessary.

The two scenarios I have discussed above are what I would define as the difference between “Memorizing” and “Mastering.” Both reflect “knowledge”, but the mastery reflects what the student has placed in long term memory as opposed to what the student has memorized for the short term benefit of a good test grade. In a Saxon curriculum, the mastery enables the student to effortlessly move from middle school math (the foundation for upper level math) to the challenges of upper level algebra, trigonometry and geometry, pre-calculus and calculus should they so desire.

Grades in the Saxon curriculum (after K – 3) are based upon test scores. It is the test scores that determine mastery or acquisition of knowledge – not the daily assignment grades.




September 2017



Some of you may remember that more than a decade ago—in the summer of 2004—the Saxon family sold Saxon Publishers to Harcourt Achieve. Just to put everything in perspective, Harcourt Achieve, Inc. was then owned by the Harcourt Corporation which in turn was later acquired by the multi-billion dollar conglomerate Reed-Elsevier who then sold Harcourt, Inc. to Houghton Mifflin creating the current company (that owns Saxon Publishers) which is now the Houghton-Mifflin Harcourt Company also known as HMHCO. It all reminds me of when the Savings and Loan Companies got the nickname “Velcro banks” because they changed names so often before they disappeared the way of the dinosaurs.

When I published my June 2007 news article, I told readers “Not to worry!” As I had said earlier when Harcourt acquired John Saxon’s publishing company in 2004, the new sale should not affect the quality of John’s books. I asked the obvious question, “Why would anyone buy someone’s prize-winning ‘Blue Ribbon Bull’ to make hamburger with?” I did not believe that this new sale would change John’s books much either, and I told the readers that if these changes became more than just cosmetics, I would certainly keep them informed.

Well, it is time to mention that some of the changes are no longer cosmetic. Some of the new editions are not what John Saxon had intended for his books. These new editions are vastly different, and both home school educators as well as classroom teachers must be aware of these changes and be selective about what editions and titles they should and should not use if they desire to continue with John Saxon’s methods and standards.

Initially, these revised new editions were offered only to the public and private schools and not to the home school community. However, introduction of their new geometry textbook to the home school educators tells me that it may not be long before the new fourth editions of Algebra 1 and Algebra 2 replace the current third editions now offered on their website.

I could be wrong. Perhaps they added the geometry textbook to the home school website because some home school parents were unaware that a full year of high school geometry was already offered within the Algebra 2 textbook (first semester of geometry) and the first sixty lessons of the Advanced Mathematics textbook (second semester of geometry). Additionally, placing the geometry course in between the Saxon Algebra 1 and Saxon Algebra 2 textbooks is a sure formula for student frustration in Saxon Algebra 2 since the new geometry book does not contain algebra content. The only reference to “Geometry” in the new fourth edition of Saxon Algebra 1 is a reference in the index to “Geometric Sequences” found in lesson 105. That term is not related to geometry. It is the title given to an algebraic formula dealing with a sequence of numbers that have a common ratio between the consecutive terms. If you desire a more detailed analysis of this situation, please read my September 2015 news article.

It would be my hope that the senior executives at HMHCO would recognize the uniqueness and value of the current editions of John Saxon’s math books that continue his methods and standards. However, to ensure you have the correct editions of John Saxon’s math books, as he published them, you can go to my September 2016 news article where I list the correct editions to use from Math 54 through Calculus. The editions I referenced in that article will be good for many more decades.





August 2017



In last month's news article we discussed the Essential Do's when using John Saxon's math books. This month we will go over the Essential Don'ts that will help Home School Educators ensure a student's success when using John Saxon's math books.

Don't Skip the First 30 - 35 Lessons in the Book. Many home school parents still believe that because the first thirty or so lessons in every Saxon math book appear to be a review of material in the last part of the previous textbook, they can skip them. Let's review the two elements of automaticity. The two critical elements are: repetition - over time!

Yes, some of the early problems in the textbook appear similar to the problems found in the last part of the previous textbook. They have, however, been changed from the previous textbook to ensure that the student has mastered the concept. Remember, part of the concept of mastery involves leaving the material for a period of time and then returning to it. Students are supposed to have sixty to ninety days off in the summer to rest their thought processes. They need this review to reinstate that thought process! Additionally, while the first lessons in the books do contain some review, they also contain new material as well.

I would add you the same question I have asked thousands of classroom teachers and Home School Educators these past nine years. "Must students always have to do something they do not know how to do? Why can't they do something they already know how to do? What is wrong with building or reinforcing their confidence in mathematics through review?"

Don’t Skip Textbooks. Skipping a book in Saxon is like tearing out the middle pages of your piano sheet music and then attempting to play the entire piece while still providing a meaningful musical presentation. In my book, under the specific textbook descriptions, I discuss any legitimate textbook elimination based upon specific abilities of the individual students. However, these recommendations vary from student to student depending upon their background and ability.

Don’t Skip Lessons. Incremental Development literally means introducing complicated math concepts to the students in small increments, rather than having them tackle the entire concept all at once. It is essential that students do a lesson a day and take a test every four to five lessons, depending on what book they are using. So what happens when you skip an easy lesson or two? Very simply, the student cannot process the new material satisfactorily without having had a chance to read about it, and to understand its characteristics. Some students attempt to fix this shortcoming by then working on several lessons in a single day, to catch up to where they should be in the book. This technique is also not recommended.

As I have told my classroom students on numerous occasions, "The only way to eat an elephant is one bite at a time."

Don’t Skip Problems in the Daily Assignments. When students complain that the daily workload of thirty problems is too much, it is generally the result of one of the following conditions:

  • Students are so involved in a multitude of activities that they cannot spend the thirty minutes to an hour each day required for Saxon mathematics.
  • Students are at a level above their capabilities and unable to adequately process the required concepts in the allotted time because of this difficulty.
  • The student is either a dawdler or just lazy!
  • Doing just the odd or just the even numbered problems in a Saxon math book is not the solution to those difficulties. As I mention in one of the early chapters in my book, there are two of each type of problem for several reasons - and doing just the odd or even is not one of those reasons!

Don't Let Students use the Solutions Manual to do their Daily Assignments. Why not? When I attended Homeschool Conferences, I often spoke at seminars and one of the analogies I would use is that of the honey bee. If you cut the bee out of the beeswax cell - to save it the struggle it must take to remove itself and speed its departure from the hive - the bee will not be able to fly because while struggling to get through the beeswax, it strengthens itself - and – in making it "easier" by removing the beeswax, you took away that advantage. The same goes with a math student who follows along every day with what someone else has laid out as the solution to every problem in their daily assignment. That encourages memorizing – it does not foster mastery.

Don't Grade the Student's Daily Work. In all the years I taught John Saxon’s math at the high school, I never graded a single homework paper. I did monitor the student's daily work to ensure it was done and I would speak with students whose test grades were falling below the acceptable minimum of eighty percent. I can assure you that having the student do every problem over - that he failed to do on his daily assignments - does not have anywhere near the benefit of going over the problems missed on the weekly tests because the weekly tests reveal mastery – or lack thereof - while the daily homework only reveals their daily memory! If you have not already read the Feb 2017 news article, please do so as it goes into more detail about why there is no need to grade the daily work.

While my book goes into more detail, I believe these few simple rules about what TO DO and what NOT TO DO to ensure success when using John's math books will benefit home school educators who use, or are contemplating using, Saxon math books. So long as you use the books and editions I referenced in my book, and later re-iterated in my Sept 2016 news article, you will find that Saxon math books remain the best math books on the market today - if used correctly! Those referenced books and editions will be good for your child’s math education - from fourth grade through their senior year in high school - for several more decades – or longer! And the proper use of them will more than adequately prepare that same math student for any of the current state or federal "Common Core" math requirements."





July 2017



The unique incremental development process used in John Saxon’s math textbooks - coupled with the cumulative nature of the daily work - make them excellent textbooks for use in either a classroom or home school environment. If the textbooks are not used correctly, however, they will eventually present problems for the students.

Some years ago, I was asked to help a school district in the Midwest recover from falling test scores and an increased failure rate in their middle and high school math programs. The teachers in the district had been using - actually misusing - their Saxon math books for several years. After I had a chance to tell the group of school administrators and teachers some of the reasons for their difficulties, the district superintendent commented. “What I hear you saying Art, is that we bought a new car, and since we already knew how to drive, we saw no reason to read the owner’s manual – wouldn’t you agree?” To which I replied, “It’s worse than that, sir! You all thought you had purchased a car with an automatic transmission, but Saxon is a stick shift! It is critical that certain procedures be followed - just as well as some should be dropped - or you will strip the gears!”

The uniqueness of John Saxon’s method of incremental development, coupled with the cumulative nature of the daily work in every Saxon math textbook, requires a few specific rules be followed to reduce failure and frustration and to ensure success – and ultimately mastery! If properly used at the correct levels, students will not have any trouble with what has been recently introduced into the educational system as “Common Core” requirements.

In the next several news articles, we will discuss the ESSENTIAL DO’S and DON’T’S when using John Saxon’s math books.

This month I will discuss the ESSENTIAL DO’S that should be followed when using John Saxon’s math books.

Do Place the Student in the Correct Level Math Book. Probably the vast majority of families who dislike John Saxon’s math books do so because the student is using a math book above his or her capability. Since all of John’s math books were written at the appropriate reading level of the student (or a grade level below), the problem is not one of students not being able to read the material presented to them, but their not being able to comprehend the math concepts being presented to them. This frustration is then interpreted as being created by the book and not by incorrect placement of the student.

Do Always Use the Correct Edition. Using the wrong edition of a Saxon math book can quickly lead to insurmountable problems. For example, moving from the first or second edition of Math 76 to the second or third edition of Math 87, or the third edition of Algebra ½ would be like moving from Math 65 to Algebra ½ in the current editions. For more information on which editions of John’s books are still valid, read the earlier published April 2013 Newsletter, or read pages 15 – 18 in my book.

Do Finish The Entire Book. Finishing the entire textbook is critical to success in the next level book. I know, parents and teachers often ask me, “Why finish the last twenty or so lessons when much of that same material is presented in the first thirty or so lessons of the next level textbook?” While the first twenty or so lessons of the next level Saxon book may appear to cover the same concepts as the last thirty or so lessons in the previous book, the new textbook presents the review concepts in different and more challenging ways. Additionally, there are new concepts mixed in with them. The review is used to enable a review of necessary concepts while building the student’s confidence back up after a few months off during the summer. Then comes the argument from some home school educators, “But we do not take any break between books – we go year round, so the review is not necessary.”

My only reply to that is “Why must students always do something they do not know how to do? Can’t they sometimes just review to build their confidence by doing something they already know how to do? If they are continuing year round, and already know how to do some of the early concepts in the next textbook, then it won’t take them long to do their daily assignment. I once had a public school superintendant ask me “Which is more important, mastery or completing the book?” To which I replied, “They are synonymous.”

Do All of the Problems - Every Day. There is a reason the problems come in pairs, and it is not so the student can do just the odd or even problems. The two problems are different from each other to keep the student from memorizing the procedure, as opposed to mastering the concept. Students who cannot complete the thirty problems each day in about an hour are either dawdling, or are at a level of mathematics above their capabilities, based upon their previous math experiences.

Do Follow the Order of the Lessons. I am often asked by parents at workshops and in email “Why study both lessons seventeen and eighteen? After all, they both cover the same concept?” Why not just skip lesson eighteen and go straight to lesson nineteen?” Why do both lessons? Well, because the author took an extremely difficult math concept and separated it into two different lessons. This allowed the student to more readily comprehend the entire concept, a concept which will be presented again in a more challenging way later in lesson twenty-seven of that book!

Do Give All of the Scheduled Tests – On Time. In every test booklet, in front of the printed Test 1 is a schedule for the required tests. Not testing is not an option! I have often heard home school parents say, “He does so well on his daily work; why test him?” To which I reply, “The results of the daily work reflect memory – the results of the weekly tests reflect mastery!” The results of the last five tests in every book give an indication of whether or not the student is prepared for the next level math book. Scores of eighty or better on any test reflect minimal mastery achieved. Scores of eighty or better on the last five tests in the series tell you the student is prepared to advance to the next level.

In next month’s news article, I will discuss the ESSENTIAL DON’T’S to follow when using John Saxon’s math books.





June 2017


                                                   TRANSCRIPTION OF MATH CREDITS – TWO BOOKS, FOUR YEARS

The first year I started teaching high school mathematics, I encountered freshman students who, while having passed an eighth grade pre-algebra course, could not manage John Saxon’s Algebra 1 textbook. The frustration and failure rate was incredible and many upper level students were shying away from any math course above Algebra 1.

I soon became aware of the distinct difference between receiving good grades and mastery of the concepts. That summer I developed an alternate curriculum using John’s Algebra 1 and Algebra 2 books. The plan would allow students the ability to accept the challenge of algebra without having to accept failure. I went to Oklahoma City and briefed the Director of Curriculum for the Oklahoma State Department of Education on my plan.

After my briefing, he sat quietly for a few seconds then said to me, “Mr. Reed, I wish that my daughter would have had the opportunity to use your plan when she was struggling with algebra in high school.” He then went on to explain that anything can be entered on a student’s transcript so long as it is an honest evaluation of what was being taught in the classroom. He approved the plan and we implemented it that following fall at the high school.

In the following three years, our ACT average math scores went from 13.4 to over 21.9 (above both the state and national averages). In that same time period, we had over ninety percent of our high school students enrolled in math courses above Algebra 1 and the number of students taking the ACT test tripled.

The plan is simple. The student has to complete the entire algebra one textbook. However, the student who struggles through John Saxon’s Algebra 1, 3rd Ed textbook - and receives an overall second semester test average of 50 – 60 (a D or F) - can receive credit for a “lesser inclusive course.” The title of “Basic Algebra,” “Pre-Algebra,” or “Introduction to Algebra 1” can be used on the transcript and the grade recorded as a “C. The student then retakes the same course the next year and should receive an average test grade of 80 or better. The course is recorded on the transcript the second year as “Algebra 1.” Since the students have now mastered the material they previously missed the first time through the book.

Ninety percent of these students only needed the “lesser inclusive course” assist in Algebra 1. However, a small percent needed the same assist in Algebra 2, so we came up with “Introduction to Algebra 2” for the first attempt and “Algebra 2” for the second attempt. Thus the title of the program, “Four Years – Two Books.”

The difficulty many students encounter in John Saxon’s Algebra 1 or Algebra 2 books generally stems from their having had a weak math background in previous math courses. Some students need a second chance to master this material because of this weaker math background. Or, they might have moved through several different math curriculums in the past few years and developed holes in their math background. They hit a brick wall because they now encounter advance math concepts they never saw before at the introductory level.

What makes this concept work so well is that John Saxon’s Algebra 1 and Algebra 2 textbooks are really tough, no-nonsense, cumulative math textbooks. Using this system, we have shown that any student who truly masters the content of these two textbooks in four years of high school will successfully pass any college level algebra course at any university.

There is considerably more detail in my book, but if you have a question or situation that requires immediate assistance, please feel free to email me at - and include your telephone number so I can call you. Or – if you prefer - you can reach me at my office any week-day between 9:00 am and 4:00 pm at 580-234-0064 (CST).

My experience in assisting homeschool educators is that a telephone conversation allows an immediate exchange of ideas not readily afforded in lengthy email sent back and forth over several days. A few minutes spent on the telephone will be less frustrating to the homeschool educator and will more often result in a successful solution for both the student and the homeschool educator.

I realize that every student is different, and what works for one may not work for another. However, my experience these past twenty years is that there is a solution for your son or daughter – we just need to find the right one!





May 2017


                                                   THE COLLEGE LEVEL EXAMINATION PROGRAM (CLEP)

Over the years, I have had parents ask about the advantages of having their child take a test under the College Level Examination Program (CLEP) - or as some of my students would say "CLEP out of a Course." For those not familiar with the program, the 90-minute CLEP tests are administered by The College Board at any of their more than 1800 test centers or at one of the 2900 colleges or universities that accept them.

The College Board states it is a not-for-profit membership association whose mission is to connect students to college success and opportunity. It was founded in 1900, and the association has a membership of more than 5,600 schools, colleges, universities and other educational organizations. Each year, the College Board serves more than seven million students through major programs and services in college readiness, college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. While most homeschool educators are more familiar with the College Board's SAT and AP programs, their CLEP Program can also save students considerable course fees if they can pass the appropriate tests. For a fee of $80.00 per course, students can take CLEP tests in any of the more than 33 subjects in the areas of Literature, Foreign Languages, History and Social Studies, Science and Mathematics, and Business.

One word of caution - the College Board advises students that:

          "Before you take a CLEP exam, learn about your college's CLEP policy. Most colleges  and

            universities grant credit for CLEP exams, but not all. There are 2,900 institutions that grant

            credit for CLEP and each of them sets its own CLEP policy; in other words, each institution

            determines for which exams credit is awarded, the scores required and how much credit will

            be granted. Therefore, before you take a CLEP exam, check directly with the college or

           university you plan to attend to make sure that it grants credit for CLEP and review the

           specifics of its policy."

Not every university or college may accept every College Board CLEP test score, and not all have the same scoring levels for credit. For example, while one university may award three credit hours for a score of 55 on the college algebra CLEP test, another may require a higher score, while still a third university may not accept the College Board CLEP results for that particular test at all. It may require that students take their individual university CLEP test for a particular subject.

In the area of mathematics, parents also need to know what levels of high school math courses correspond to what level CLEP test. For example, the student who takes the college algebra CLEP test before mastering John Saxon’s Algebra 2 course will, in all likelihood receive a failing grade. Each of the CLEP math tests indicate the subject matter included in the tests. Following the math book's index will give you a pretty good idea of whether or not the student can handle that particular test.

I will say this about John Saxon's second edition of Advanced Mathematics. All students who have mastered the first ninety lessons in that book should easily pass the College Board's CLEP test for College Algebra and College Mathematics. If they have mastered the entire Advanced Mathematics book and also finished the first 25 lessons of calculus, they can easily pass not only those same two course tests, but the College Board pre-calculus CLEP test as well.

I recall that when I was teaching in the high school, one of my calculus students went down to the OU campus and took the calculus CLEP test and passed it. While in my senior calculus class, he was happy with just a "C" because he was going to study "Communications" at OU and openly admitted that he did not really need the math. He never took another math course in his life. When I asked him why he did not just take the college algebra CLEP test, he smiled and said, "I just wanted to be able to tell people that I had passed college calculus at OU." The College Board tests are a great way to get a few basic courses out of the way and save mounting college tuition costs, but if the students are going into engineering or research science, I would recommend they not use the CLEP tests to replace core courses in their field. They need to revisit these courses at the collegiate level.





April 2017



I was online at a popular website for home school educators a while back and I noticed some back and forth traffic about the benefits and drawbacks of John Saxon’s math books. One of the homeschool parents had just commented about the benefits of John’s books. As she saw them - through their use of continuous repetition throughout the books - she thought the process contributed to mastery as opposed to just memorizing the math concepts in each lesson for the upcoming test.

One reader replied to her comment with the following:

“Or, one can use a math program that makes the mathematical reasoning clear from the outset as a matter of course rather than believing that a child will grasp the mathematical concepts by repeating procedures ad nauseam. I think the Saxon method is flawed.”

This reminds me of one of John’s favorite sayings when challenged with similar logic. John’s reply would be to the effect that “If you are setting about to teach a young man how to drive an automobile, you do not try to first have him understand the workings of the combustion engine; you put him behind the wheel and have him drive around the block several times.”

I recall when teaching incoming freshman the Saxon Algebra 1 course that I would first present students with several conditions such as having them all stand up and then asking if they were standing on a flat surface or a curve. Then I explained to them that an ant moving around on the side of the concrete curve of the quarter mile track at the high school would think he was moving in a straight line and he would never realize that, because of his minute size when compared to the enormity of the curve, he thought the curve to be a straight line.

I would then go on to explain that – like the ant’s experience in his world - they were standing on an infinitesimal piece of another curve which appears to be a flat surface to them. I would continue by telling the students that in “Spatial Geometry” there are more than 180 degrees in a triangle. It never failed, but about this time someone would put up their hand and – as one young lady did - say “Mr. Reed, I am getting a headache, could we get on with Algebra 1?”

It was a different story when presenting the same conditions to seniors in the calculus class. They would excitedly begin discussing how to evaluate or calculate them. And telling them there were no parallel lines in space did not seem to upset them either. Could it be because the seniors in calculus were all well grounded in the basic math concepts, and they understood the difference between the effects of these conditions in “Flat Land” as opposed to their “Spatial Application?”

Perhaps John and I are old fashioned, but both of us thought it was the purpose of the high school to create a solid educational foundation - a foundation upon which the young collegiate mind would then advance into the reasoning and theory aspects of collegiate academics. Both John and I had encountered what I referred to as “At Risk Adults” while teaching mathematics at the collegiate level. These students could not fathom a common denominator, or exponential growth. They were incapable of doing college level mathematics because they had never mastered the basics in high school.

Students fail algebra because they have not mastered fractions, decimals and percents. They fail calculus - not because of the calculus, for that is not difficult - they fail calculus because they have not mastered the basics of algebra and trigonometry. I recall my calculus professor after he had completed a lengthy calculus problem on the blackboard - filling the entire blackboard with the problem. Striking the board with the chalk he turned and said “The rest is just algebra.” I saw many of my freshman contemporaries with quizzical looks upon their faces. Being the “old man” in the class, I quickly said “But sir that appears to be what they do not understand. Could you go over those steps?” Without batting an eye, he replied “This is a calculus class Mr. Reed, not an algebra class.”

I firmly believe that what causes individuals to so strongly dislike John Saxon’s math books is, not from their having “used” the books, and suffering frustration or failure, but from their having “misused” the books. Or—more importantly—from having entered the Saxon curriculum at the wrong math level assuming the previous math curriculum adequately prepared the student for this level Saxon math book—when in reality it had not!

So when home school parents place the student into the wrong level Saxon math book—and the student quickly falters in that book—it stands to reason they would blame the curriculum, when in reality, their student was not prepared for the requirements at that level.

Why? Because Saxon math books do not teach the test, they require mastery of concepts introduced in previous levels of math to enable the student to proceed successfully at every level of the curriculum.

Taking the Saxon Placement Test before entering a Saxon math book from Math 54 through Algebra 2, will ensure the student and parent can adequately evaluate the student’s ability to proceed at a certain level with success based upon what they have previously mastered.

The Placement Tests can be found on this website at the link shown below:





March 2017


                                                                           WHY USE SAXON MATH BOOKS?

The title of today’s news article was the title of my seminar at Homeschool Conventions when I travelled the Homeschool Convention circuit several years ago. What I wanted to convey to homeschool educators at these seminars was factual information on why John Saxon’s math books – when properly used – remain the best math curriculum for mastery of mathematics on the market today.

Why did I emphasize “when properly used”? The reason is because improper use of Saxon math books is one of their major weaknesses. The vast majority of students who encounter difficulties in a Saxon math textbook do so, not because the book is “tough” or “difficult”, but because they either entered the Saxon curriculum at the wrong math level or because they skipped books and have not properly advanced through the series. Or - for one reason or another - they had been switching back and forth between different math curriculums. Because of switching curriculums, the students had all developed “holes” in their basic math concepts, concepts critical for future success in the math book they were now using. In John Saxon’s math books these “math holes” created frustration and failure for the students who were returning to the Saxon curriculum in the upper level math books.

At every convention, there were always a half dozen or more homeschool parents who came to the booth - all facing the same dilemma! Their sons or daughters had recently completed or were currently completing another curriculum of instruction in algebra, and while they said they were happy with the curriculum they were using, they expressed concern that their son or daughter was not mastering sufficient math concepts to score well on the upcoming ACT or SAT tests. I asked each of them to have their student take the on-line Saxon algebra one placement test which consisted of fifty math questions. The test was actually the final exam in the Saxon pre-algebra book (Algebra ½, 3rd Ed).

In almost every case, regardless of which math curriculum the students were using, the answer was always the same. Not one of the students passed the test. It was not a matter of receiving a low passing grade on the test. The vast majority of them failed to attain fifty percent or better. The curriculums the students were using were not bad curriculums. They correctly taught students the necessary math concepts in a variety of ways. But unlike John Saxon’s method of introducing incremental development coupled with his application of “automaticity” to create mastery of the necessary math skills, none of these curriculums enabled students to master these concepts. They taught the test!

In those cases where the parents asked for my advice after learning about the failed pre-algebra test, we worked out a successful plan of action to ensure that the failed concepts were mastered and the “math holes” were filled. The plan enabled each of the students to successfully move to an advanced algebra course later in their academic schedule.

Now to address another topic that arose during the seminars. Several attendees asked whether or not they should use the new fourth editions of algebra one and algebra two textbooks as well as the new separate geometry textbook. I told the audience that the new fourth editions were initially created for the public school system together with the company’s creation of a new geometry textbook. After all, don’t you make more money from selling three math books than you do from selling just two?

I explained that the daily geometry review content as well as the individual geometry lessons had been gutted from the third editions of John’s original Algebra one and Algebra two to create the new fourth editions of those books In my professional opinion, I replied to the homeschool educators that they should stay with the current third editions of John’s original Algebra one and Algebra 2 two books and not fall into the century old trap of using a separate geometry text in-between the algebra one and algebra two courses.

One homeschool parent commented that I was mistaken because she had called the company customer service desk and they told her there was geometry in the new fourth edition of their Saxon Algebra 1 book. I have a copy of that edition. It was designed to be sold to the public schools along with the company’s new geometry textbook, and it does not integrate geometry into the content of the book’s one hundred twenty lessons as John’s third edition of Algebra one does.

Here are the facts regarding the geometry content in the two books. I will let you draw your own conclusions:

1. In the index of the third edition of John Saxon’s Algebra 1 textbook, there are seventeen references dealing with the calculation of total area, lateral surface area, and volume of spheres, cones, cylinders, etc. In the new fourth edition index, there are only four references to area and volume and they are not geometric references. They deal with determining correct unit conversions of measure and the application of ratios and proportions in their solution, all of which are algebraic not geometric functions.

2. In the index of the third edition of John’s Algebra 1 book there are nine references to the word “angles.” In the index of the fourth edition, there are none. The reference term “angles” does not appear.

3. In the third edition index of John’s Algebra 1 book, there are three references to “Geometric Solids.” In the fourth edition index, the word “Geometric Solids” does not appear.

4. The only reference to the word “geometry” in the fourth edition index is the phrase “Geometric Sequences” and that term is not a geometry term. It refers to an algebraic pattern determined through the use of a specific algebraic formula.

5. Geometry references, terms, concepts and daily problems dealing with them are found throughout John’s third edition of Algebra one. This does not occur in the fourth edition of algebra one created by HMHCO - the new owners of Saxon Publishers.

So why was the homeschool educator told there was geometry in the new fourth edition of algebra one?

Well, let me see if I can explain what I believe the marketing people came up with. I say marketing people because several of us have tried for several years to find out who authored the new fourth edition and no one at the company could – or would – tell us who the author is. Someone commented that it was given to a textbook committee to create the new fourth editions of algebra one and two as well as the new geometry textbook.

At the back of the new fourth edition of algebra one, just before the index, is a short section of thirty-two pages referred to as the “Skills Bank.” Within these thirty-two pages are thirty-one separate topics of which only twelve deal with geometric functions and concepts. Each of the concepts is about a half page in length and covers just a few practice problems dealing with the concepts themselves. Since they are not presented or practiced throughout the book, I believe it makes it difficult if not impossible for the student to master any of these concepts encountering them this late in the book – if they are encountered at all.

Here are several examples of how these geometry concepts are presented in the “Skills Bank” of the new fourth edition of algebra one:.

1. Skills Bank Lesson 14: Contains two short sentences explaining how to classify a quadrilateral. The student is then given only three practice problems on the concept.

2. Skills Bank Lesson 16: Contains two short explanatory sentences describing congruency followed by only two practice problems.

3. Skills Bank Lesson 19: Contains five brief statements describing the various terms used to describe a circle and its component parts, immediately followed by two problems asking the students to identify all of these parts.

The “Skills Bank” concept is fine as far as using a brief addendum to define what those geometric terms mean. But when does the student get to work these concepts so that the review creates “mastery” as John‘s original books were designed? “The “frequent, cumulative assessment” of John Saxon’s math program is referenced by the company on page 5 of their new textbook as one of the key elements of the new book. However, those attributes are never developed for the geometry concepts. Additionally, the company’s use of colored “Distributive Strands” reflecting the distribution of functions and relations throughout the textbook does not list any geometry functions or relation strands showing up anywhere in the book – at least not in the book they sent me.

The new algebra one fourth edition textbook created by HMHCO - under the Saxon name – may be a good algebra textbook. However, it does not contain geometry concepts on a daily basis as John’s third edition of algebra one does. Before you make a decision to use a separate geometry textbook along with the new fourth edition of algebra one and two, please read my September 2015 news article. If you need to discuss the issue further, please do not hesitate to call or email me.





February 2017


                                             SHOULD YOU GRADE THE DAILY SAXON MATH ASSIGNMENTS?

I continue to see comments on familiar blogs about correcting – or grading – the daily work of Saxon math students. That is a process contrary to what John Saxon intended when he developed his math books. Unlike any other math book on the market today, John’s math books were designed to test the student’s knowledge every week. Why would you want to have students suffer the pains of getting 100 on their daily work when the weekly test will easily tell you if they are doing well?

I always tell homeschool educators that grading the daily work, when there is a test every Friday, amounts to a form of academic harassment to the student. Like everything else in life, we tend to apply our best when it is absolutely necessary. Students will accept minor mistakes and errors when performing their daily “practice” of math problems. They know when they make a mistake and rather than redo the entire problem, they recognize the correction necessary to fix the error and move on without correcting it. They have a sense when they know or do not know how to do a certain math problem; however, when they encounter that all important test every Friday, – as I like to describe it – they put on their “Test Hat” to do their very best to make sure they do not repeat the same error!

In sports, daily practice ensures the individual will perform well at the weekly game, for without the practice, the game would end in disaster. The same concept applies to daily piano practice. While the young concert pianist does not set out to make mistakes during the daily practice for the upcoming piano recital, he quickly learns from his mistakes. Built into John Saxon’s methodology are weekly tests (every four lessons from Algebra ½ through Calculus) to ensure that classroom as well as homeschool educators can quickly identify and correct these mistakes before too much time has elapsed.

In other words, the homeschool educator as well as the classroom teacher is only four days away from finding out what the student has or has not mastered during the past week’s daily work. I know of no other math textbook that allows the homeschool educator or the classroom teacher this repetitive check and balance to enable swift and certain correction of the mistakes to ensure they do not continue. Yes, you can check daily work to see if your students are still having trouble with a particular concept, particularly one they missed on their last weekly test, which can be correlated to their latest daily assignment. However, as one home school educator stated recently on one of the blogs “Yes, they must get 100 percent on every paper or they do not move on.” While this may be necessary in other math curriculums that do not have 30 or more weekly tests, it is a bit restrictive and punitive in a Saxon environment.

John Saxon realized that not all students would master every new math concept on the day it is introduced, which accounts for the delay allowing more than a full week’s practice of the new concepts before being tested on them. He also realized that some students might need still another week of practice for some concepts which accounts for his using a test score of eighty percent as reflecting mastery. Generally, when a student receives a score of eighty on a weekly test, it results from the student not yet having mastered one or two of the new concepts as well as perhaps having skipped a review of an old concept that appeared in the assignment several days before the test. When the students see the old concept in the daily work, they think they can skip that “golden oldie” because they already know how to do it! The reason they get it wrong on the test is that the test problem had the same unusual twist to it that the problem had that the student skipped while doing the daily assignment.

In all the years I taught John Saxon’s math at the high school, I never graded a single homework paper. I did monitor the daily work to ensure it was done and I would speak with students whose test grades were falling below the acceptable minimum of eighty percent. I can assure you that having the student do every problem over that he failed to do on his daily assignments does not have anywhere near the benefit of going over the problems missed on the weekly tests because the weekly tests reveal mastery – or lack thereof - while the daily homework only reveals their daily memory!

NOTE: The upper level Saxon math textbooks from algebra ½ through calculus have a test every four lessons, making it easy to standardize the tests always on a Friday - with a weekend free of math homework. However, from Math 54 through Math 87, the tests are taken after every five lessons which either require a Saturday test or place the test day on a rotating schedule. You can easily remedy this by having the student do the fifth lesson in the test series on Friday morning, then later that day, have them take the weekly test leaving them to concentrate on resolving the one’s they missed on the test - with no week-end homework. This places them on the same Friday test schedule as the upper level Saxon math students.

January 2017


                                             SHOULD HOMESCHOOL STUDENTS TAKE CALCULUS?

Calculus is not difficult! Students fail calculus not because the calculus is difficult - it is not - but because they never mastered the required algebraic concepts necessary for success in a calculus course. However, not everyone who is good at algebra needs to take a calculus course.

A number of the students I taught in high school never got to calculus their senior year because they could not complete the advanced mathematics textbook by the end of their junior year. They ended up finishing their senior year with the second course from the advanced math book titled "Trigonometry and Pre-calculus" and then taking calculus at the university level. This worked out just fine for them as they were more than adequately prepared and had an opportunity to share the challenge with likeminded contemporaries on campus.

Some of my students advanced no further than completing Saxon Algebra 2 by the end of their senior year in high school. They were able to take a less challenging math course their first year of college by taking the basic college freshman algebra course required for most non-engineering or non-mathematics students. These students would never have to take another math course again - unless of course they switched majors requiring a higher level of mathematics. And, if they did, they would be adequately prepared for the challenge.

I believe the answer for homeschool students in these same situations is what we in Oklahoma call "concurrent enrollment." In other words, don't take a calculus course at home by yourself. Under the guidelines of "concurrent" or "dual" enrollment - or whatever your state calls it - take the course at a local college or university and share the experience with likeminded contemporaries. If your state has such a program a high school student can also receive both high school and college credit for the course. I would not recommend taking calculus under "concurrent" or "dual" enrollment at a local community college unless you first verified that the college or university your child was going to attend will accept that level credit for the course. Many of them will accept those credits but only as electives and not as required courses in the student's major field of studies. Check with the head of the mathematics department or the registrar's office before you enroll in the local community college.

The concept of "concurrent" or "dual" enrollment was just beginning to take hold in the field of education when I was teaching and there were not many high school students taking these college courses enabling them to receive both a high school and college math credit for their efforts. As we gained experience with the new program, we learned that our high school juniors and seniors who had truly mastered John Saxon's Algebra 2 course could easily enroll at the local university in the freshman college algebra course and could - provided they went to class - easily pass the course. And, if they were English or Art majors, they would never have to take another math course if they so desired.

Students who were eligible and wanted to take a calculus course their senior year looked forward to taking it at the local university and receiving "concurrent" or "dual" credit for the course. Many of these same students went on to become research technicians in the field of bio-chemistry and physics. However, several of them never took another math course in their college careers because they were English or Art History majors. They took the college freshman calculus course because they wanted to prove they could pass the course. They wanted to be able to say "I took college calculus my senior year of high school."

So, what does all this mean? Home school students whose major will require calculus at the college level should adjust their math sequence to complete John Saxon's advanced mathematics textbook (2nd Ed) by the end of their junior year of high school, and then take calculus the first semester of their senior year at a local college or university. Not only will this enable them to receive "concurrent" or "dual" - unless their state prohibits it - but they will enjoy the camaraderie of other likeminded college students taking the course with them. There is a final serendipity to all of this. When enrolling at most universities, honors freshman and freshman with college credits enroll before the "masses" of other freshman students. This would virtually guarantee the student with college credits the courses and schedule they desire - not to mention the potential for scholarship offers with high ACT or SAT scores and earned college credits in a course titled "Calculus I" recorded on their high school transcript.



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