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Newsletters
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.
I Hope you had a Blessed Christmas and that you
will also experience a Blessed and a Happy New Year!
MASTERY - vs - MEMORY
More than two decades ago, at one of the annual mathematics conventions of the National Council of Teachers of Mathematics (NCTM), John Saxon and I were walking the floor looking at the various book publisher's exhibits, when we encountered a couple of teachers manning the registration booth of the NCTM. When I introduced John to them, they instantly recognized him as the creator of the Saxon Math books and, after gleefully mentioning that they did not use his math books, they proceeded to tell him that they felt his math books were nothing more than mindless repetition.
John laughed and then in a serious note told the two teachers that in his opinion it was the NCTM that had denigrated the idea of thoughtful considered repetition. He quickly corrected them by reminding them that the correct use of daily practice over time results in what Dr. Benjamin Bloom of the University of Chicago had described as "Automaticity." Dr. Bloom was an American educational psychologist who made contributions to the classification of educational objectives and to the theory of mastery-learning.
Years earlier, John Saxon had taken his Algebra 1 manuscript to Dr. Benjamin Bloom (known for Bloom's Taxonomy) at the University of Chicago. John wanted to find out if there was a term that described the way his math book was constructed. Dr. Bloom examined the book's content and then told John that the technique used in his book was called "automaticity." which describes the ability of the human mind to do two things simultaneously - so long as one of them was overlearned.
If you think about it, every professional sports player practices the basics of his sport until he can perform them flawlessly in a game without thinking about them. By "automating" the basics, players allow their thoughts to concentrate on what is occurring as the game progresses. Basketball players do not concentrate on their dribbling the basketball as they move down the floor towards the basket. They have overlearned the basics of dribbling a basketball and they concentrate on how their opponents and fellow players are moving on the floor as the play develops.
The great baseball players practice hitting a baseball for hours every day so that they do not spend any time concentrating on their stance or their grip on the bat at the plate each time they come up to bat. Their full concentration is on the movements of the pitcher and the split second timing of each pitch coming at them at eighty or ninety miles an hour. How then does the term "automaticity" change John's math books from being called "mindless repetition" to math books that - through daily practice over time - enable a student to master the basic skills of mathematics necessary for success?
The two necessary elements of "automaticity" are "repetition over time." If one attempts to take a short cut and eliminate or shorten either one of these components, mastery will not occur. Just as you cannot eat all of your weekly meals only on Saturday or Sunday - to save time preparing meals and washing dishes every day - you cannot do twenty factoring problems one day and not do any of them again until the test in five weeks without having to review just before the test.
Both John and I taught mathematics at the university level. And we both encountered freshman students who could not handle the freshman algebra course. These students had failed the entrance math exam and were forced to take a "no-credit" algebra course before they were allowed to enroll in the freshman algebra course for credit. In my book, I refer to them as "at risk adults." I tell about asking for and receiving permission from the university to use John's high school Algebra 2 textbook for this "no-credit" course and adjusting the instruction to enable covering the entire book in a college semester.
The results were astounding. More than 90% of those who received a "C" or higher passed their freshman algebra course the following semester.
They had all taken an Algebra 2 course in high school and they had all passed the course. They could not understand why they had failed the math entrance requirement. The day John and I had encountered the NCTM teachers at the registration booth, I would have given anything to have had some of these "at risk adults" tell those teachers just what they thought of their teaching the test, rather than requiring them to master the concepts. They would also have given them a piece of their mind about their teachers using "fuzzy" grading practices that allowed them to pass a high school Algebra 2 course while failing the university's basic entrance exam several weeks later. They would have also given these NCTM representatives an earful about the difference between being taught the test and receiving a warm fuzzy passing grade and mastering the necessary math concepts to be successful in math at the collegiate level.
There are some new math curriculums out there today using the word "mastery" in their advertisements - attempting to show that their "fun" curriculum is as good if not better than John"s - but to date, I know of none of them that use a cumulative review of the math concepts coupled with weekly tests to reflect mastery by the student rather than re-packaging what my "at risk adults" encountered more than a quarter of a century ago.
WHICH SAXON HIGH SCHOOL MATH COURSES CAN BE TRANSCRIPTED AS HONORS COURSES?
Almost two decades ago – when I wrote the book on how to use John Saxon’s Math books – I did not include a chapter on honors courses because I mistakenly thought that by then everyone knew about them. My apologies, but the subject should have been included in the book. Since it was not, I thought I would publish the subject in the monthly news articles and make it available for homeschool educators to print a copy as an addendum to the book. (Click Here for a printable copy)
I would like to say that all of John Saxon’s math books are honors courses. The contents of John’s math books are no-nonsense, straightforward, rigorous, challenging, and conceptually sound. These outstanding math books enable mastery of the concepts, not just memorization; however – I would be stretching the accepted definition of honors courses. Generally, the title of honors course when applied to math courses is reserved for the higher-level math courses that cover more material and are therefore more rigorous and challenging than regular courses.
Yes, the term honors course can be applied to non-math courses as well; however, in this article, I will restrict use of the term to just mathematics – and more specifically – to John Saxon’s math courses.
Unless your State Board of Education has created its own standards regarding who can certify an honors curricula, the classroom mathematics teacher can authorize an honors course. There are no official rules or standards that list what defines an honors course. However; the term is generally applied to high school courses considered to be more rigorous and therefore more academically challenging. With some exceptions, a student must acquire the classroom teacher’s approval to enroll in an honors course along with an overall grade average of a B or higher in prerequisite math courses.
I am a qualified state certified secondary mathematics teacher with more than twelve years’ experience teaching high school mathematics while using John Saxon’s math books from algebra through calculus. There is no doubt in my mind that the courses in John Saxon’s high school math curriculum that qualify for honors courses are the Saxon Algebra 2 (only the 2nd or 3rd Ed), Saxon Advanced Mathematics (2nd Ed. – whether taught in a single year or in three or four semesters) and the Saxon Calculus textbook (1st or 2nd Ed). Let me briefly state why each of these qualify as honors courses.
Algebra 2, 2nd or 3rd Ed. Why not the new 4th Edition? In my opinion, the new fourth edition of this book will not allow the student to satisfactorily enter the Advanced Math textbook – nor would it qualify for the title of “Honors Course.” This new edition was not created by John Saxon. It was created by a publishing company that stripped all references to geometry from the fourth edition textbook. You can read more detail about the potential problems with using this non-Saxon edition in my Apr 2022 News Article. The challenges and rigorous nature of John Saxon’s Algebra 2, 2nd or 3rd Ed. textbook have been reduced to a standard high school algebra 2 textbook in this new non-Saxon 4th Ed. version.
Now, what is it that makes the 2nd or 3rd editions of John’s Algebra 2 textbook qualify as honors courses? When using the 2nd or 3rd Ed. of John’s Algebra 2 textbook, students have 30 problems to tackle every day through all 129 lessons as well as a weekly test to determine their mastery of the material. Unlike a regular algebra 2 course, students must not only master the daily menu of some very rigorous algebra 2 concepts, but they must also master the rigorous geometry concepts found in the first semester of a high school geometry course – plus the introduction of trigonometric functions midway in the book as well.
It is acceptable to use Algebra 2 w/Geom (1 credit) on the student’s HS transcript and in an appropriate place indicate honors credit for that course. Don’t forget when a student takes an honors course, the GPA is scored differently: an A is worth 5 pts, a B is worth 4 pts, a C is worth 3 pts, and a D is 2 pts – the grade of F is still 0.
I recall at a homeschool convention several years ago, a homeschool parent told me that she was told by a homeschool friend you could not award a semester of HS geometry because there were no two-column proofs in the Saxon Algebra 2 (2nd or 3rd Ed) textbooks. My reply was “Your friend did not finish the book, he probably stopped at lesson 122 (“Venn Diagrams”), because there are more than 15 rigorous two-column proofs in the six lessons between lesson 123 and 129 (the end of the book).
As I promised my students and their parents – and I will promise you – if students get no further than successful mastery of the Saxon Algebra 2 textbook (2nd or 3rd Ed) when they graduate from high school, they will be able to pass any freshman college algebra course from MIT to Stanford – provided they attend class every day, pay attention, complete assignments, and do not sleep in class. Oh, and – one more minor requirement – show up on test days!
Advanced Mathematics, 2nd Ed: John designed this course to be taken in three, or four semesters. I taught the textbook as a four semester (2 year) course. If you would go to this link on my website, you can watch a short seven minute video on why and how you transcript the course: https://usingsaxon.com/flvplayer.html
Unless textbooks have drastically changed in the field of collegiate freshman mathematics, this textbook is tougher than any collegiate freshman algebra textbook I have seen or previewed. Students who complete the entirety of the textbook and successfully master the material presented will score in the 90th – or higher – percentile on either the ACT or SAT math score. As described in the referenced video, both of the course titles described in the four semester use of the book qualify as honors courses.
Calculus (1st or 2nd Ed.): Both calculus textbooks qualify as honors courses in a high school environment. And, while successful completion of all 117 lessons of the older 1st edition textbook prepares students for the AB portion of the College Board’s Advanced Placement (AP) program for calculus, I recommend you use the newer 2nd edition. That edition prepares students for both the AB (through lesson 102) – and the BC (all 148 lessons) portions of the College Board’s Advanced Placement (AP) program for calculus. The 2nd Ed. of John’s Calculus textbook contains 31 more lessons than the older 1st Ed.
Lastly, the new 2nd Ed. of John’s Calculus textbook has the added feature of the lesson reference numbers which appear in parenthesis under each problem number as used earlier in the third editions of Saxon’s Algebra 1 and Algebra 2 textbooks. They direct students to the lesson that introduced the concept of that problem they may need to revisit. It saves the student wasted hours of valuable time trying to find the lesson that introduced the concept without knowing the correct terminology of what it is they are looking for.
SHOULD STUDENTS TAKE CALCULUS AT HOME?
- OR -
SHOULD THEY USE “CONCURRENT” OR “DUAL” ENROLLMENT?
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.
DOES THE STUDENT'S GRADE IN THE COURSE REFLECT THE STUDENT'S UNDERSTANDING OF THE CONCEPTS?
Some years ago 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 youngest grandson was in his sophomore high school math class for over eight weeks before he 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.
REASONS FOR STUDENT FRUSTRATION OR FAILURE WHEN USING JOHN SAXON'S MATH BOOKS - (PART 2)
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 ask 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! In the upcoming January 2021 newsletter, I will go into more detail on how to treat the daily practice work and why I believe it is the better way.
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 November 2019 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.”
REASONS FOR STUDENT FRUSTRATION OR FAILURE WHEN USING JOHN SAXON'S MATH BOOKS - (PART 1)
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 Nov 2019 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.
Fuzzy Mathematics
If you’re not old enough to remember the old "Ma and Pa Kettle" movies, you will have to ask grandma or grandpa about them. Their movies were among the best of the funny classic black and white movies made back then. The kind of movie the entire family could watch and laugh together over.
My brother and I often went to see the same movie more than once.
Today’s news item is from one of their movies. I just saw it on the internet and could not resist sharing it with you and your students as we start the new school year.
To watch this unbelievable short 2 minute episode of “Fuzzy Math” click here.
Next month, I will get back to the academic world of mathematics.
Are the New Saxon Math Books Better Than the Older Editions?
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 mentioned 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.
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. - will be good for many more decades.
JOHN SAXON'S LEGACY
John Saxon was, among other things, a teacher, a leader, a graduate of West Point, and a great storyteller. I first met John and his wife Mary Esther in the late 1960’s in my mother-in-law’s kitchen in Enid, Oklahoma, while I was on leave preparing to go to Germany. While his mother-in-law and mine had been members of the same sewing club and also the same Presbyterian Church for almost forty years, our military careers took us our separate ways, and I never had a chance to know him very well until I started teaching several years after he had already published his first algebra book in 1981.
That night in the kitchen, John told the story about when he flew the supply route from Japan to Korea – in between B-26 bombing runs – during the Korean War. He said he had not had much sleep in the preceding five days, and he was concerned that he would doze off while piloting the aircraft, so he instructed his enlisted crew chief to make sure he stayed awake. “I told him that whatever it took, keep me awake! I woke up the next morning and I could barely move my right arm, the pain was so intense. I looked at my right shoulder and it was a dark purple color,” John said. “I learned later that day that the crew chief kept punching my shoulder every time I started to doze off - all the way from Japan to Korea! I told him, Chief, you almost broke my shoulder. So he says to me, ‘Kept you awake, Sir!’”
The high school where I had done my student teaching had been using John’s math books for several years. I liked using them, so when I started my first job as a high school math teacher, I asked for and received approval to buy his math books for two of my three math courses. The first year I taught, I finished all the lessons in John Saxon’s first Algebra 2 book. When school was out, I drove to Norman to visit with John. When I bragged to him that we had finished his book, he smiled and, pitching me his new second edition, said, “Here. Try this new edition. It’s seven lessons longer.” John and his finance officer loaded seventy of the new second edition Algebra 2 books into the trunk of my car. As I drove home later that evening, I wondered what I would say to the highway patrolman if I were stopped and he looked in the trunk. John had given me the books, and I did not have a paid invoice for them.
I remember in the early days of his company, John had a personal policy that if a student found an error in one of his math books and wrote to him about it, John would send him five dollars for each error he found. That fall, when we started using these brand new first printings of the new second edition of Algebra 2, one of the students had found four problems - with wrong answers.
Checking the answers, I verified that the student was indeed correct. The four answers were wrong! The young man then asked about the twenty dollars that I had mentioned he would receive. So using my classroom telephone, I called John at his office. I had placed the telephone on the speakerphone, so the class could hear the conversation. They appeared excited that they were actually sitting in their classroom, talking to the author and owner of the publishing company that had published their math book! John asked me if I had verified that the answers were indeed in error, and I told him the student was correct, that the answers were in fact wrong. Without hesitation, John immediately asked the young man his name and congratulated him for finding them.
I reminded John about his “five dollar” policy. He agreed that the young man deserved the twenty dollars and that he should not have to wait around for the money. Then John, in a loud and clear voice said, “Art, you pay him,” and hung up! A warm summer evening in June and a free trunk load of seventy Algebra 2 books flashed before my eyes as I gave the young man my only twenty-dollar bill.
John was both a mathematician and an engineer. After retiring from military service, while teaching mathematics at Rose State College in Oklahoma City, he was appalled to see that the incoming college students could not handle simple math concepts. So John decided to write his own math books to correct this. I soon learned what John meant by “at-risk adults” when, some twenty years later, I also encountered college students who still did not understand fractions, percents or decimals. They were failing their basic algebra course at the local university where I taught mathematics.
Throughout John’s years of publishing his math textbooks, he always used the words “students,” “educators,” and “responsibility” when speaking about his books. He had designed them to teach the basic concepts of mathematics. They were not designed to teach just “critical thinking” or “higher-order thinking” at the expense of this critical subject matter, as many books still do today to meet requirements of textbook selection committees.
One of John’s favorite analogies of what was wrong with this idea was instances when he would tell his audience, most often teachers and administrators, "Understanding should follow doing, rather than precede it. If you’re going to teach someone how to drive an automobile, don’t lecture him on the theory of the internal-combustion engine. Get him to drive the car around the block."
John was always aware of and deeply concerned about our high school students as they continued to fall behind in their understanding of the basic concepts necessary to be successful in mathematics and science. He believed so strongly in what he was doing that, in 1980, so that he could publish his first math book (an Algebra 1 textbook), he borrowed money from his children, from his bank, mortgaged his house, and also borrowed against the value of his future military retirement pay!
More than twenty-five years later, we all know John and his company were a tremendous success! And we all know the legacy that John Saxon has left the field of mathematics – especially for homeschool families. In July of 1993, in an open letter to then - President Clinton, John Saxon warned of the pending disaster in the areas of mathematics and science. He was concerned that educators were advocating teaching critical thinking when they should be teaching basic math concepts.
He complimented the President on the fact that, while still Governor of Arkansas, he had supported a bill in the Arkansas Legislature that returned control of textbook selection to the local school boards. Local control was something John felt would keep the “unknowing” at the state level from being able to control the local school boards and administrators, and allow them to solve these problems locally.
John Saxon passed away on October 17, 1996. His children continued management of Saxon Publishers until it was finally sold to Harcourt Achieve in the fall of 2004. I remember the warm sunny day in 2004 when John Saxon’s children announced the acquisition of Saxon Publishers by Harcourt Achieve at the newly constructed Saxon Headquarters in Norman, Oklahoma.
Just a few minutes after the children had made their announcement, dark ominous clouds swept in, and in the midst of a torrential downpour, one of the biggest electrical storms in Norman’s history knocked out all the electrical power and telephone lines to the Saxon Corporate headquarters after lightning had struck the building.
I told you John was a great storyteller. It appears, again, that he had the last word that day!
DO YOU REALLY HAVE TO DO THE DAILY “WARM-UP” BOX AND “PRACTICE PROBLEMS”?
(For the Math 54 through Math 87 Textbooks)
I receive several emails each week about the excessive amount of time some home school students spend on their math assignments each day. In almost every case, the students have spent between thirty minutes and an hour on the “Warm-Up” box and the six to eight “Practice Problems” before they even get started on the thirty problems of the Daily Assignment.
It has been a little more than a decade since I have been in a public classroom, and I am not sure if public school middle school math teachers still lean on what they used to call a math “Warm-Up” at the start of each class. The purpose of the “Warm-Up” was to settle their students down and get them ready for the math regimen of the day.
Using the “Warm-Up” box at the beginning of each lesson in the Saxon Math 54 through Math 87 textbooks can become quite frustrating to students who do not have the advantage of a seasoned classroom math teacher gently guiding them in the direction of the correct solution for the problem of the day – knowing that problem might come from a concept not yet introduced to the students.
But what about the “Daily Math Facts Practice” and the “Mental Math”; how will students receive training in those areas? While these two areas are essential to the student becoming well-grounded in the old pen and pencil format of adding, subtracting, multiplying and dividing, graded by the teacher, that format has been improved with a computer model. Using the computer format allows the students to instantly know whether their answers are right or wrong. Additionally, while the home educators can easily spot the results tallied on the computer as the student moves along, it saves them the time spent manually grading the documents. I have placed a link to a wonderful Math Facts site on my website. Readers can find it by going to my home page, and from the list on the left side of the home page, click on “Useful Links.” When the new window appears, select the second link from the top labeled “On-Line Math Facts Practice.”
That link takes you to a math facts practice site that allows the student to select from seven different levels of difficulty in adding, subtracting, multiplying and dividing. Five to ten minutes on this site every day at the appropriate level for the student to be challenged without being frustrated is just as good as the mental math or facts practice found in the “Warm-Up” box. While the Math 87 book still reflects the same “Warm-Up” box that the previous three math textbooks do, a student should have mastered the facts practice by this time. If this is the case, skipping the entire box is acceptable – unless – the student particularly enjoys the challenge of the “Problem Solving” exercise.
Now let’s see if I can explain why I am recommending you stop having the student take time to do the six to eight practice problems at the front of each of the mixed practices (the daily assignments). The original purpose of these practice problems was for the classroom teacher to use all or some of them in explaining the concept on the board so that the teacher did not have to make up their own or use the homework problems. Sometimes teachers would use some of them to have students come to the board to show their understanding of the new concept.
My experience in teaching John’s method of mastering math has shown me that there are basically two possibilities that can exist after the student has read and/or had the concept of the daily lesson explained to them.
Possibility 1: The student understands the concept and after doing the two homework problems dealing with that new concept, completely understands what to do and has no trouble doing them. Mastery of this concept will occur over the next five to six days as the student does several more each of these for the next few days. If this is a critical concept linked to other steps in the math sequence, they will keep seeing this concept periodically throughout the rest of the book.
Possibility 2: When students encounter the two homework problems that deal with the new concept, they have difficulty doing them. So, on their own, should they go back to these practice problems and get another six to eight more problems wrong? If they did the practice problems before they started their daily work, would anything have changed? If they cannot do the two homework problems because they do not understand the new concept, why give them another six to eight problems dealing with the new concept to also get wrong? This approach ultimately leads to more frustration on the part of the student. Students will have spent thirty minutes or more on these additional six to eight practice problems and still not understand the new concept. Not every student completely grasps a new concept on the day it is introduced which is why John’s books do not test a new concept until the student has had five to ten days to practice that concept.
Those practice problems were not placed there to give the student more problems to do in addition to the thirty they are assigned every day. They were placed there for the classroom teacher to use on the blackboard to teach the new concept so they did not have to develop their own or use the student’s homework problems. There is nothing wrong with a home school educator asking a student to do one or two of them to show them the student does understand the new concept; however, doing more than that could be a waste of time and effort in either possibility.
Not every child is the same and I realize that because of a particular child’s temperament, there may be some instances where the parent has to go over more than one or two of the practice problems with the child – and this is okay – but for most students this is not necessary. If the student really enjoys the challenge of the daily “Problem Solving:” that is okay – except parents should make sure that the student does not spend an excessive amount of time on that individual challenge and allow the real goal of completing the thirty problems of the Daily Assignment to become a secondary goal – and later a bother to the student.
DO MATH SUPPLEMENTS REALLY HELP STRUGGLING STUDENTS?
- or -
CAN YOU TEACH A DROWNING CHILD HOW TO SWIM WHILE HE IS DROWNING?
Before addressing that question directly, let me first relate a story about a man walking across a bridge spanning a river. As he looked down at the water, he noticed a boy who had fallen into the swift current. It was apparent from the boy’s struggle that he could not swim. The man realized he had only two alternatives. He could shout instructions to the boy on how to overcome the swift current and perhaps enable him to dog paddle to safety on the shore, or he could dive into the water and rescue him. Without hesitating, the man dived into the water and immediately swam to the side of the struggling boy. Now the man had to face another dilemma. Should he pull the struggling boy to safety or should he immediately try to teach him how to swim?
Everyone would agree that when people are drowning, that is not the time to try to teach them how to swim. All one can do at that time is try to get them to a place of safety where they can overcome the swift current of the river. So it is with mathematics. In any of John Saxon’s math textbooks from Math 54 through Calculus, if student’s begin struggling before reaching lesson thirty or sooner, it is a sign that they will drown in the later lessons of the book unless they are taken to a place of safety where they can better manage and learn the concepts that they are now unfamiliar with. Concepts that are dragging them into deep water! It should become apparent that they are not prepared for the book they are in, and no amount of supplemental material or expensive tutors will overcome those shortcomings.
Mathematics is like the swift current that challenged the drowning boy. Like the river, upper level mathematics is challenging and can easily become unforgiving. Looking for a slower moving or shallower river may create a temporary solution, but eventually that water will again become swifter and deeper and unless one is prepared, all the advice and assistance given at the time of the struggle will come too late.
While it is a noble goal for students to strive towards taking a calculus course in their senior year of high school, it is critical that they first master the algebra. The calculus is easy! It is the challenge of the algebra and to a lesser degree the trigonometry that causes students to fail calculus. Any student with a solid algebra background, entering any college or university, will pass that school’s math entrance exam and will be successful in a calculus course should they choose to do so.
When classroom teachers or home school educators take shortcuts with one of John Saxon’s math books, they are not adequately preparing the student for the deeper water ahead. More than a quarter of a century of experience with Saxon Math textbooks has shown me that classroom teachers and parents who take shortcuts with his curriculum (instead of going slowly and deliberately through as John intended) cause students to “flounder” as they encounter the “deeper” water. At this point, they find it easier to blame the book – and they look to switch to an easier math course!
The classroom instructions contained within my “video” tutorial series – as well as the online lessons – are not math supplements. They contain actual classroom instruction on each concept in the book. Like the book, the classroom instruction is designed for the homeschool student who is in the appropriate level math book. The instruction enhances the written word they have already read from the textbook. Many of the lessons present a different explanation by an experienced Saxon math teacher that helps the student through the difficult reading of the lesson.
However, regardless of who creates them, neither the CD white-board presentations nor my video classroom tutorials – or online lessons – will help students who are taking a course they are ill prepared for. They will eventually find themselves frustrated and floundering in the “deeper water” of a math course they are not prepared for!
Have a Blessed and Happy New Year
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