WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS?
MYTH 4: You Must Use the New Saxon Geometry Textbook to Receive Geometry Credit.
Whether I am at a homeschool convention or browsing the online homeschool blogs, I keep hearing and seeing comments from homeschool parents that express the idea that: "You must use a separate geometry book to receive credit for geometry."
A little over three years ago, I received an Examination Copy of the new fourth edition Algebra 1 book prepared by the new owners of John Saxon's Publishing Company. They had gutted the book of all references to geometry. The index had one reference to several pages late in the textbook titled "Geometric Sequences," but that term refers to an algebraic formula dealing with common ratios - it is not a geometry formula found in any geometry textbook.
Unlike the old second or third editions of Algebra 2, their new fourth edition of Algebra 2 has also had all references to geometry removed from it. Why did the new owners do this? Well I can come up with several reasons:
FIRST: Marketing people would tell you that you make more money from three books than you do from two. Almost a decade ago, I learned from the Corporate Executives at the company that first bought Saxon Publishers from John's children in 2004 that they truly believed that "A math book is a math book is a math book." In my dealings with them as they transitioned John's Publishing Company into theirs, it was apparent that they failed to realize or accept the uniqueness of John's math books. To them one math book was just like another. If a particular state did not buy their math book this year another state was switching from someone else's math book to theirs. So as long as this phenomenon went on why waste profit margin selling a unique math book and explaining or defending its content.
Why? Because the perception was that failure in the math program of any particular public school was never the fault of the teacher; it was always the poor quality of the math book which required switching to more "improved" math books every four to five or so years as math test scores either did not improve or fell. And the publishers would be more than happy to tout their new and improved math textbooks which they said would result in higher test scores.
One book publisher even went so far as to openly advertise to administrators and teachers that since their company published the annual student state math tests that their math books were geared to ensure student success with these mandated state tests. So why not do as every other publisher does and create three separate and distinct math books for the algebra one, algebra two, and geometry courses? That not only makes it easier to sell the books, but it increases the quarterly profit margins because of the requirement for the additional geometry book.
SECOND: Some math teachers would tell you that students cannot learn geometry while they are trying to master the algebra. They therefore demand a separate geometry textbook. The second and third editions of John Saxon's Algebra 2 textbooks contain the equivalent of the first semester of a regular high school geometry textbook - to include rigorous two-column proofs (take a look at the Dec-2012 news article). But wait! Isn't it true that students cannot handle the geometry while they are also trying to master the algebra? Not so! This myth makes about as much sense as telling high school students that they cannot take a mandatory sophomore English course while also taking a separate journalism course. European students have been combining algebra, geometry, and trigonometry in a single math book as long as I can remember. And they have consistently come out ahead of us in comparative math comprehension tests.
So what am I getting at? Must we have a separate geometry textbook for students who cannot handle the geometry and algebra concurrently? Well, let me ask you. If students can successfully study a foreign language while also taking an English course or successfully master a computer programming course while also taking an algebra course, why can't they study algebra and geometry at the same time? Must the content of these two subjects be in two separate textbooks taken at two different times in order for the student to master both subjects?
The geometry concepts encountered in John Saxon's Algebra 2 textbook - whether the second or third edition - are the equivalent of the first semester material of a regular high school geometry course and that includes a rigorous amount of formal two-column proofs! However, if you choose to use the new fourth edition of Algebra 2, you must also purchase a separate geometry textbook to acquire geometry credit. As I previously mentioned, the new fourth editions of the revised HMHCO Algebra 1 and Algebra 2 textbooks do not contain any geometry concepts.
THIRD: The new fourth editions of Algebra 1 and Algebra 2 - as well as the new first edition of Geometry - do not have a responsible author, and therefore the new owners of John Saxon's company do not have to pay any royalties! If you look at the inside cover of the new fourth editions of Algebra 1 and Algebra 2 as well as the new first edition of the new Geometry textbooks, you will not be able to find the name(s) of an author or authors of these books. Why? Because they were created by a committee hired by marketing people and the committee that constructed that edition of the algebra textbooks may or may not have had any extensive math or teaching experience. The publishers paid a one-time fee to a "committee" to create the new editions releasing them from paying future royalties to an author.
So, do we blame the profit minded publishers for publishing a separate geometry textbook, or is it the fault of misguided high-minded academicians who - after more than a hundred years - still demand a separate geometry text from the publishers? I am not sure, but thankfully, this decision need not yet face the homeschool educators using John Saxon's math books. The original homeschool third editions of John Saxon's Algebra 1 and Algebra 2 textbooks still contain geometry as well as algebra - as does the Advanced Mathematics textbook which follows the Algebra 2 textbook.
Any homeschool student using John Saxon's homeschool math textbooks who successfully completes Saxon Algebra 1 (3rd Ed), Algebra 2, (2nd or 3rd editions), and at least the first sixty lessons of the Advanced Mathematics (2nd edition) textbook, has covered the same material found in any high school Algebra 1, Algebra 2, and Geometry textbook - including two-column formal proofs. Their high school transcripts - as I point out in my book - should accurately reflect a full credit for completion of an Algebra 1, Algebra 2, and a separate Geometry course. For a more detailed explaination Click Here.
NOTE: Just as you do not record "Smith's Biology" on the student's transcript when awarding credit for a year of biology, you should not use Saxon Algebra 1, or Saxon Algebra 2, etc., when recording Saxon math on the student's transcript either. Just record Algebra 1, Algebra 2, Geometry, etc.
Myths that will be discussed in future News Articles:
- Advanced Mathematics Can Easily be Taken in a Single School Year.
- You Do Not Have to Finish the Last Twenty or So Lessons of a Book.
HAVE A VERY HAPPY, HEALTHY, AND BLESSED NEW YEAR!
WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS?
MYTH 5: Advanced Mathematics Can Easily be Taken in a Single School Year.
Several decades ago, while teaching John's Advanced Mathematics textbook my second year at the high school, I encountered a problem with my Saxon Advanced Mathematics students. The students who had received an A or B in the Saxon Algebra 2 course the previous year were now struggling with low B and C grades - and we were only in our first nine weeks of the course.
I called John and explained the situation to him. He asked me if I was following the same procedure I had used in the Algebra 2 course last year (e.g. a lesson a day - all thirty problems assigned every day - and a test every Friday). I told him that we did all thirty problems every day and took a test every Friday just as we had in the Algebra 1 course as well. I went on to tell John that the students were frustrated. In Algebra 2, they had easily completed their daily work done in forty-five to fifty minutes, but now they were spending several hours each night to complete their daily assignments - and most of them were not even getting all of the assigned homework finished in that period of time.
John's response was quick and to the point. He asked me if I had read the preface to his book, and when I told him I had not, he told me to read the preface of the book and then he hung up. This was not an unusual trait of John's. I had known him for several decades and, like many other experienced fighter pilots I had encountered in my military service, he seldom went into any lengthy explanation when someone was not following instructions.
In the preface of the Advanced Mathematics textbook, I found that John had written in detail about the textbook's in-depth coverage of trigonometry, logarithms, analytic geometry, and upper-level algebraic concepts. He explained that the textbook could easily be broken into two 5-semester hour courses at the college level. But he cautioned - that at the high school level teachers should break the course into three or four semesters.
I immediately chose the four semester option, calculating that this would allow two days for each lesson. The students could do the odd numbered problems one day and the even numbered problems the second day. By doing it this way, the students would encounter all of the concepts covered in the thirty problems both days since the concepts taught in each lesson were arranged in pairs. Also, they would not have to spend more than an hour each night on their daily assignment.
Is it possible for high school students to successfully complete the entire Advanced Mathematics textbook in a single school year? Yes, but both John and I were in agreement that those students are the exception rather than the rule. In all the years that I taught using John's math books, I have encountered only one student who completed the entire 125 lessons of the Advanced Mathematics textbook in a single year - with a test average of over 90 percent! She was a National Merit Scholar and her father taught mathematics with me at the local university.
That is not to say that others could not have accomplished the same feat, but these exceptions only tend to justify the rule. The beauty of John's Advanced Mathematics book is its flexibility that allows students to use the book at a pace comfortable to them whether that pace takes two, three or four semesters. There is no academic dishonor in a bright home school math student taking three or four semesters to complete John Saxon's Advanced Mathematics textbook if that student needs the extra study time to take care of other tough academic subjects being taken at the same time. There is no need to bunch everything up and rush through the math just to get to the calculus before the student graduates from high school.
Students fail calculus in college not because of the difficulty of the calculus concepts, but because their background in algebra and trigonometry is weak. It is the student with the weak mastery of algebra and trigonometry in high school who fails the calculus course - or - perhaps the student who has mastered the algebra and trigonometry in high school, but because of this knowledge, elects not to attend the daily calculus lectures.
Please Click Here to watch a short video that describes how the Advanced Mathematics course is taught and credited.
The sixth and last myth to be discussed in next month's news article is:
You Do Not Have to Finish the Last Twenty or So Lessons of a Saxon Math Book.
WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON's MATH BOOKS?
MYTH 6: You Do Not Have to Finish the Last Twenty or So Lessons of a Saxon Math Book.
Over the past several decades, I have heard hundreds of homeschool educators as well as parents of my high school classroom students tell me that there was no need to finish a Saxon math book because the last twenty or so lessons of any Saxon math book are repeated in the review of the first thirty or so lessons of the next level Saxon math book.
There is a bit of truth to that observation. A few of the concepts encountered in the later lessons of a book are repeated in the early lessons of the next level book because that important concept came late in the book and did not allow sufficient time for the student to master it before reaching the end of the course. But when repeated, the re-introduction of these concepts assumes the student had encountered the concepts in a simpler format in the previous level textbook.
But anyone who would attempt to skip the last twenty or so lessons of any Saxon math book under the misguided impression that all of that material is repeated in the first thirty lessons of the next math book is in for a shocking surprise. Someone may tell you their son or daughter did just that while using the Saxon Algebra 1 textbook and their child did quite well in the Saxon Algebra 2 book the following school year.
While there are always exceptions that justify the rule, what most of these home educators will not tell you is that - because of this shortcut - their child struggled through the Saxon Algebra 2 course and either repeated the course a second year, or failed to master the required concepts, having to enroll in a no credit algebra course as a freshman in college the following year. The concept of automaticity requires the application of repetition over time and violating either one of these conditions greatly reduces the student's chances of mastering the necessary math concepts to be successful in the next level math course.
There is a third factor involved in the process of automaticity. When students encounter a concept, work with it over several weeks and then do not encounter it again until as much as a month later, that delay in repeating - coupled with a slight change in the level of difficulty of that concept - challenges their level of mastery. Some students who have not quite mastered the entire concept have to review it from previous lessons before continuing. However, once mastered a second time - following the delay - the concept is more strongly imbedded in their long term memory.
So after taking a break for the summer, would it not be better to start the next level Saxon math book with a small amount of review material to ensure students retain the necessary skills for success in the new course?
But wait, would that apply to homeschool students who do not take a summer break? The argument is that if they finish the entire Algebra 1 book, and then go straight into Algebra 2, they can easily skip the first twenty or so lessons in the Algebra 2 text. That is also a dangerous procedure to follow for at least two reasons.
FIRST: Remember I said that some of the concepts introduced late in the previous textbook are repeated to allow mastery. I did not say all of them. The student will go down in flames around lesson forty or so, never having been introduced to a dozen or more concepts involving both algebra and geometry.
Additionally, the Algebra 2 book assumes the students mastered the basic introduction to these new concepts in the earlier lessons (the ones the student skipped) and it now combines them with other concepts. Now students start struggling as test scores begin to fall. This is where the parent or teacher blames the book as being too difficult to use and leaves Saxon math for an easier math course.
SECOND: While collegiate and professional athletes practice almost year round, they do take several months off sometime between their seasons to rest the mind as well as the body. In mathematics, it is good to take a month or so off between levels of math to allow students to refresh their thought processes. As I mentioned earlier, this break also allows them to better evaluate what concepts they have truly mastered. Once mastered a second time - following the delay - the concept is more strongly imbedded in their long term memory.
I believe these are two valid reasons not to skip lessons under any circumstances.
NOTE: I am not sure just what next months article will be about. I believe I will take a month off and see what surfaces in my thought process.
MAKE SURE YOU BUY AND USE THE CORRECT EDITIONS OF JOHN SAXON'S MATH BOOKS
As we approach textbook purchasing time for homeschool educators I thought it would be advantageous to go over with you the correct editions of John Saxon's math books to use, and also to provide you with some recommendations on how to use the textbooks correctly and reduce students' frustration with mathematics. While there is more detail in my book, I believe the following information will help you select the correct level and edition of one of John Saxon's math books.********************************************************************************************
Math 54 (2nd or 3rd Ed):
All of the textbooks listed below also include an introduction to basic geometry as well as a review of the geometric terms associated with geometry at the introductory level. As the student moves from Math 54 to Algebra 1, the repetition of these terms and concepts allows for a gradual increase in their level of difficulty. However, this geometry remains at the introductory level and there is no formal credit for any geometry until successful completion of the Algebra 2 textbook (2nd or 3rd Ed) where the student also earns a full credit for the first semester of a regular high school geometry course.
If after reading this newsletter, you feel your particular situation has not been addressed, please feel free to email me at firstname.lastname@example.org or call me at 580-234-0064 (CST) before you purchase any math textbooks.
You can use either the hard cover 2nd edition textbook or the newer soft cover 3rd edition as they have identical math content. In fact, they are almost word for word and problem for problem the same textbooks. The page numbers differ because of different graphics and changed page margins, and the newer soft cover 3rd edition homeschool packet has an added solutions manual. However, my experience with that level of mathematics is that most home school educators will not need a solutions manual until they encounter Math 76. If you can acquire a less expensive homeschool kit without the solutions manual, I would recommend acquiring that less expensive set. Calculators should not be used at this level.
Math 65 (2nd or 3rd Ed):
This book is used following successful completion of the Math 54 textbook. Successful completion is defined as completing the entire Math 54 textbook, doing every problem and every lesson on a daily basis, and taking all of the required tests. To be successful in this textbook, students must have scored eighty or better on the last four or five tests in the Math 54 textbook. As with the Math 54 textbooks, the 2nd edition hard cover book and the newer soft cover 3rd edition have identical math content. The newer 3rd edition series also has a solutions manual, but if you're on a tight budget, I do not believe that it is necessary at this level of mathematics either. Calculators should not be used at this level.
Math 76 (3rd or 4th Ed):
The kingpin book in the Saxon series. This book follows successful completion of the Math 65 textbook. Again, successful completion of Math 65 means completing the entire book as well as all of the tests. To be successful in Math 76, students should have received scores no lower than an eighty on the last four or five tests in the Math 65 course. Either the hard cover 3rd edition or the newer soft cover 4th edition can be used. As with the previous two math courses, there is no difference between the math content of the hard cover 3rd edition and the softcover 4th edition textbooks. I recommend acquiring a copy of the solutions manual as this is a challenging textbook. Students who score eighty-five or better on the last five tests in this level book indicate they are ready to move to Algebra 1/2, 3rd edition. Student's who encounter difficulty in the last part of Math 76, reflected by lower test scores, can easily make up their shortcomings by proceeding to Math 87 rather than Algebra 1/2. Calculators should not be used at this level.
Math 87 (2nd or 3rd Ed):
Again, there is little if any difference between the hardcover 2nd edition and the softcover 3rd edition textbooks. Even though the older second edition does not have "with pre-algebra" printed on its cover as the 3rd edition softcover book does, the two editions are identical in math content. Students who successfully complete the entire textbook and score eighty or better on their last five or six tests can skip the Algebra 1/2 textbook and proceed directly to the Algebra 1, 3rd edition textbook. Both the Math 87 and the Algebra 1/2 textbooks get the student ready for Algebra 1; however, the Math 87 textbooks start off a bit slower with a bit more review of earlier concepts than does the Algebra 1/2 book. This enables students who encountered difficulty in Math 76 to review earlier concepts they had difficulty with and to be successful later in the textbook. Students who encounter difficulty in the last part of this book will find that going into Algebra 1/2 before they move to the Algebra 1 course will strengthen their knowledge and ability of the basics necessary to be successful in the Algebra 1 course. Their frustrations will disappear and they will return to liking mathematics when they do encounter the Algebra 1 course. Calculators should not be used at this level.
Algebra 1/2 (3rd Ed):
This is John's version of what other publishers title a "Pre-algebra" book. Depending upon the students earlier endeavors, this book follows successful completion of either Math 76 or Math 87 as discussed above. Use the 3rd edition textbook rather than the older 2nd edition as the 3rd edition contains the lesson concept reference numbers which refer the student back to the lesson that introduced the concept of the numbered problem they're having trouble with. These concept lesson reference numbers save students hours of time searching through the book for a concept they need to review - but they do not know the name of what they are looking for. From this course through calculus, all of the textbooks have hard covers, and tests occur every week, preferably on a Friday. To be successful in John Saxon's Algebra 1 course, the student must complete the entire Algebra 1/2 textbook, scoring eighty or better on the last five tests of the course. Students who encounter difficulty by time they reach lesson 30 indicate problems related to something that occurred earlier in either Math 76 or Math 87. Parents should seek advice and assistance before proceeding as continuing through the book will generally result in frustration and lower test scores since the material in the book becomes more and more challenging very quickly. Calculators should not be used at this level.
Algebra 1 (3rd Ed):
I strongly recommend you use the academically stronger 3rd edition textbook. The new owners of the Saxon Publishers (HMHCO) have produced a new fourth edition that does not meet the Saxon methodology. The new fourth edition of Algebra 1 has had all references to geometry removed from it and using it will require also buying a separate geometry book. While the associated solutions manual is an additional expense, I strongly recommend parents acquire it at this level to assist the student when necessary. Depending upon the students earlier successes, this book follows completion of either Math 87 or Algebra 1/2 as discussed above. Calculators are recommended for use at this level after lesson 30. While lesson 114 of the book contains information about using a graphing calculator, one is not necessary at this level. That lesson was inserted because some state textbook adoption committees wanted math books to reflect the most advanced technology. The only calculator students need from algebra through calculus is an inexpensive scientific calculator that costs about ten dollars at one of the local discount stores. I use a Casio fx260 solar
which costs about $9.95 at any Target, K-Mart, Wal-Mart, Radio Shack, etc. If the 3rd edition of Saxon Algebra 1 is used, a separate geometry textbook should not be used between Saxon Algebra 1 and Algebra 2 because the required two semesters of high school geometry concepts will be covered in Saxon Algebra 2 (1st semester) and in the first sixty lessons of the Advanced Mathematics book (2nd semester). Because they have removed all references to geometry from the new 4th edition, I do not recommend using the 4th edition of Algebra 1.
Algebra 2 (2nd or 3rd Ed):
Either the 2nd or 3rd editions of the Saxon Algebra 2 textbooks are okay to use. Except for the addition of the lesson concept reference numbers in the newer 3rd edition, the two editions are identical. These lesson concept reference numbers save students hours of time searching through the book for a concept they need to review - but they do not know the name of what they are looking for. If you already have the older 2nd edition textbook, and need a solutions manual, you can use a copy of the 3rd edition solution manual which also has solutions to the daily practice problems not in the older 2nd edition solutions manual. Also, the 3rd edition test booklet has the lesson concept reference numbers as well as solutions to each test question - something the 2nd edition test booklet does not have. An inexpensive scientific calculator is all that is needed for this course. Upon successful completion of the entire book, students have also completed the equivalent of the first semester of a regular high school geometry course in addition to the credit for Algebra 2. I strongly recommend you not use the new fourth edition of Algebra 2 for several reasons. FIRST:
The fourth edition has had all references to geometry removed from it requiring the purchase of an additional geometry book. SECOND: The Advanced Mathematics textbook assumes the student has just successfully completed the 2nd or 3rd edition of the Saxon Algebra 2 textbook with their inclusive geometry. If the student took a separate geometry course
between the fourth editions of algebra 1 and Algebra 2, theywill not have had any exposure to geometry for as much as fifteen months (nine months of school plus two summer breaks). This gap will result in the student encountering extreme difficulty in the Advanced Math textbook.
Advanced Mathematics (2nd Ed): Do not use the older 1st edition, use the 2nd edition. The lesson concept reference numbers are found in the solutions manual - not in the textbook! Students who attempt this book must have successfully completed all of Saxon Algebra 2 using either the 2nd or 3rd edition textbooks. Upon successful completion of just the first sixty lessons of this textbook, the student will have completed the equivalent of the second semester of a regular high school geometry course. An inexpensive scientific calculator is all that is needed for this course. For more information on how to transcript the course to receive credit for a full year of geometry as well as a semester of trigonometry and a second semester of pre-calculus, please Click Here.
Calculus: The original 1st edition is still an excellent textbook to master the basics of calculus, but the newer 2nd edition affords students the option to select whether they want to prepare for the AB or BC version of the College Boards Advanced Placement (AP) Program. To prepare for the AB version, students go through lesson 100. To prepare for the BC version, they must complete all 148 lessons of the book. While the 2nd edition reflects use of a graphing calculator, students can easily complete the course using an inexpensive scientific calculator. I recommend that students who use a graphing calculator first attend a course on how to use one before attempting upper level math as they need to concentrate on the math and not on how their fancy calculator works. It is not by accident that the book accompanying the graphing calculator is over a half inch thick.
DO MATH SUPPLEMENTS REALLY HELP STRUGGLING STUDENTS?
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 for an easier math course!
The classroom instructions contained within my DVD "video" tutorial series 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 DVD classroom tutorials will help students who are taking a course they are ill prepared for - and they find themselves frustrated and floundering in "deep" water.
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 "Calc I" the first semester of their senior year at a local college or university. Not only will this enable them to receive "concurrent" or "dual" credit - 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" recorded on their high school transcript.
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 last year. 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 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. (See the August - 2012 news article).
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:
- 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.
- 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.
- 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.
- 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.
- 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:
- 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.
- Skills Bank Lesson 16: Contains two short explanatory sentences describing congruency followed by only two practice problems.
- 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 August - 2012
news article. If you need to discuss the issue further, please do not hesitate to call or email me.
THE NEW OWNERS OF SAXON PUBLISHERS (HMHCO) HAVE CHANGED THEIR WEBSITE
The current owner of John Saxon's Publishing Company, the old Saxon Publishers is the Houghton Mifflin Harcourt Company (HMHCO). While many of the older Saxon curriculum users are familiar with the old HMHCO website and the ease in finding the original Saxon Publisher's Homeschool logo, catalog, related homeschool educational materials and Placement Tests, it is not that easy anymore when navigating the new HMHCO website.
Saxon math books are only one of the nine or more textbook curriculums sponsored or sold by HMHCO. Their new website recently launched is not that easy to navigate to find the older traditional editions of John's math books. The new website may create confusion for homeschool Saxon users attempting to find the true Saxon curriculum designed and published by John Saxon through his publishing company Saxon Publishers.
While most of the original changes to John's books were only cosmetic changes made by marketing people of the new owners, there have been several conceptual changes that have changed John's original curriculum presentation. Unless you have kept abreast of these changes, you could very well purchase the wrong editions of Saxon homeschool materials using the new HMHCO website without realizing it. For a descriptive analysis of these Saxon editions, go to the Apr - 2013 news article elsewhere on this website.
I believe the reader can do better purchasing John Saxon's Math books directly from one of the resellers of Saxon Math, such as www.rainbowresource.com or www.christianbooks.com. The price of their Saxon books and materials is considerably less than buying directly from the HMHCO catalog of Saxon materials. However, if you feel you must peruse their catalog remember that it is not as easy to find as before. It would appear they are concentrating their marketing efforts on the larger school markets and assume homeschool educators will buy directly from resellers such as the two I mentioned above. While I have heard from a reliable source that HMHCO will continue to sell previous editions of Saxon math books through resellers - home budget allowing - I would acquire them now rather than later.
I spent a good twenty minutes trying to find the "Saxon Homeschool Catalog" on their website, and - I can assure you that it is not easy to find! However, if you do feel you must review the material in HMHCO's Saxon Homeschool Catalog, you will notice that of the catalog's 65 pages, only 25 pages are devoted to information about John Saxon's original math curriculum, and they no longer offer the Saxon Physics textbook. The remainder of the catalog discusses books unrelated to Saxon Math such as Singapore Math, On Core Mathematics, Houghton Mifflin Science, Holt McDougal Biology, History and Physics, etc.
Another problem I encountered on their new website is the apparent absence of the Saxon Placement Tests. Several days ago, I discovered that the link from my website no longer went to the Saxon Placement Tests on the new HMHCO website. I spent the better part of an hour attempting to locate them on the new HMHCO website - to no avail. I finally removed the link to the HMHCO website from my website and changed the link so that it now takes the reader to the Saxon Placement Test files located on my website.
I have no idea why they no longer afford homeschool educators easy access to the Saxon Placement Tests. Any homeschool educator who has had a student frustrated by the difficulty of a Saxon Math course knows that these tests are critical in the proper placement of a student new to Saxon Math. Proper placement prevents frustration and potential failure when entering the Saxon curriculum at a course level above the student's ability or math background. Using these placement tests assists in the proper placement and greatly reduces if not eliminates the possibility of frustration or failure.
If you have any problem deciding which editions or level of math book to use, or need assistance in deciding how to interpret the results of the Saxon Placement Test, please feel free to either email me at email@example.com or call my office any weekday at 580-234-0064 (CST). If you email me your telephone number, I will call you at my expense as I have unlimited long distance calling anywhere in the US.
NOTE: To locate and print copies of the original Saxon Math Placement
Tests from this website [ Click Here ]
WHAT SHOULD YOU DO WITH STUDENTS WHO CONTINUALLY MAKE SIMPLE MISTAKES ON THEIR DAILY WORK?
Often, I receive telephone calls or emails from homeschool educators who express concern that their sons or daughters continue to make simple mistakes in computations when doing their daily work.
As one homeschool parent recently stated:
"My son is taking Algebra 1 and constantly makes silly mistakes, like not putting the negative sign in front of his answer when his work reflects it is a negative number. He understands the concepts well but he gets a fourth or more of the problems wrong on his daily work because of these simple, careless, computational errors."
Mistakes like those described above are normal with most students working on the daily assignment preparing for the upcoming weekly test. Have you noticed that they make fewer, if any, of these same mistakes when they take a test? I like to use the phrase that "students put on their Test Hat" when taking a test, and they will not accept the same mistakes they do on their daily practice work. However, if you reward them for making these mistakes on a test by giving them partial credit, they will continue making them on the tests as well.
No matter how much we try to eliminate these mistakes, some students will never stop making them, no matter how good they become at mathematics. That is why experienced engineers always check each other's work before releasing a new project for testing or production. I recently read in the daily newspaper that Spanish engineers working on a new submarine for the Spanish Navy did not do this verification check. After building a new submarine, it was found that the engineers had overlooked the erroneous placement of a decimal point in their computations. The embarrassing - and costly - result was that the Spanish Navy ended up with a new submarine so heavy that it would not surface if it were ever submerged.
Most students make fewer mistakes in performing simple mental arithmetic calculations on paper than they do when pressing the wrong button on a calculator, which still constitutes a human error, although the student will try to blame the calculator!
Even students looking to achieve perfection can be found guilty of "rushing" through their daily work for one reason or another. It might help to ensure students develop the habit of checking the work of the problem they just finished before moving on to the next. This process of review would enable them to find many, if not all, of these types of simple mistakes and while it may add a few minutes to the time spent on the daily assignment, it might get them to slow down a bit to avoid making them in the first place.
So long as you do not reward the student for making these simple calculation errors on the weekly tests - like giving them partial credit for getting the concept right, but the answer wrong - they will eventually overcome that shortcoming.
And if they do not, but their weekly test scores remain constantly at an 80 or better, I would not worry about it. Remember, the cumulative and repetitive nature of John Saxon's math books is what creates the mastery as opposed to other math curriculums reviewing for - and teaching the test.
So making a few computational errors, while maintaining a minimum score of 80 on the thirty-some weekly tests, is truly outstanding. While I fully understand that everyone considers an acceptable target grade for tests at 95 - 100, receiving an 80 on one of John Saxon's weekly math tests is equivalent to the 95 one would receive on the periodic test using some other math curriculum that teaches the test.
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 just 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 a 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 that reflect mastery by the student rather than re-packaging what my "at risk adults" encountered more than a quarter of a century ago.
THIS MONTH'S NEWS ARTICLE IS NOT ABOUT MATHEMATICS.
IT IS ABOUT A VETERAN OF WORLD WAR I - A DOUGHBOY - MY FATHER!
Each year on the 11th of November our country celebrates Veteran's Day. This is the day our nation has set aside to recognize military veterans of all branches of service for the sacrifices they have made throughout our country's history; Sacrifices that have ensured our continued freedom. This day of recognition in November of each year originated from the date of the signing of the armistice at the end of World War I.
The armistice was signed in a railroad car in the forest near the French village of Compiegne. The document was signed exactly at the eleventh hour of the eleventh day in the eleventh month in the year 1918. There are no more living veterans of WWI, but if you know or meet a veteran of any armed conflict from WWII to the Gulf War, Iraq or Afghanistan, and you get the chance this coming Veteran's Day, shake their hand and thank them for their service - and tell them "Welcome Home!"
Private John William Reed, Infantryman
Company F, 358th Infantry
90th Infantry Division
(Wounded at St. Mihiel, France on September 12, 1918)
My father was twenty-two years old when he received his induction notice from the local draft board in Minneapolis, Minnesota on April 22, 1918 (Order # 651, Serial # 356, Division #4). He was ordered to report to the draft board one week later on April 29, 1918 for immediate induction into the United States Army. Immediately after his induction, he was shipped to Camp Davis, Texas for training and deployment with the 358th Infantry of the 90th Infantry Division. In less than two months, he would be on a troop ship headed overseas for the War in France. In less than five months from the day he was inducted, he would find himself in battle near the small French village of St. Mihiel.
The 90th Infantry Division was activated on August 25, 1917 at Camp Travis, Texas. It was nicknamed the "Alamo Division" and sometimes referred to by the enlisted men as the "Tough Ombres" (for Texas and Oklahoma). Initial members of the 90th Division came from Texas and Oklahoma; however, just before the division deployed to France in the summer of 1918, it received a large number of new recruits from other states like Minnesota. The division began its embarkation from Hoboken, New Jersey in early June of 1918, and by June 30th all of the units of the 90th Infantry Division had sailed from Hoboken. The division initially landed in England where, on July 4th, 1918, the 358th Infantry (including my father) paraded before the Lord Mayor of Liverpool. That evening, the entire 358th Infantry was hosted at a banquet given by the city of Liverpool, England.
The 358th Infantry arrived in France shortly thereafter and was stationed at Minot, France. In early September, the unit was moved about 192 km NE to a small village east of Paris in the northeast part of France. The name of the village was "Villers - en - Haye." It had a population then of only 96 people. In 2007, the population of "Villers - en - Haye." was still only 167).
Their first engagement with the German army came on September 12, 1918, at a town called St. Mihiel. The town was much larger than "Villers - en - Haye" having a population in 1918 of slightly more than 2000 residents. It was located 42 km from "Villers - en - Haye" on the edge of the Meuse River. The town had grown around a Benedictine abbey founded in 709 A.D. At the time of the battle, there were still several Abbey buildings in the town constructed in the 17th and 18th century. The town church had a door that dated back to Roman times. Both the church and the Abby buildings are still there today, undamaged by the fierce fighting that occurred there more than ninety-five years earlier. In 2008, the population of St. Mihiel had increased to 4,816.
The World War I battle that took place at St. Mihiel on September 12 - 14, 1918, was the first major American military offensive of the war. The campaign against the German fortifications at St. Mihiel involved 550,000 men of the U.S. First Army commanded by Gen. John J. "Black Jack" Pershing. The 90th Infantry Division (including the 358th Infantry Regiment) was part of that force. The three-day campaign led by the U.S. First Army was successful. They forced the Germans to relinquish a military fortification held by the Germans since 1914.
In those first three days of battle in mid-September of 1918, the 90th Infantry Division suffered a total of 37 officers and 1,042 enlisted men killed in action and another 266 officers and 8,022 enlisted men wounded and mustard gassed during the battle with the German units. In just three days, the division had lost more than half of its men! Private John William Reed, Company F, 358th Infantry, was among those wounded and mustard gassed by the Germans that first day of battle, on September 12, 1918. Today, more than 4,150 American soldiers, killed in that September offensive, are buried in the American Military Cemetery at St. Mihiel.
Now the "Rest of the Story.....!"
More than half a century later, while I was stationed with the U.S. Army in Heidelberg, Germany, my wife and I were visiting the nearby town of Schwetzingen, Germany located several kilometers from Heidelberg. My wife wanted to visit the world famous historical doll maker Ilse Ludecke. While she visited with the doll maker, I practiced my German by conversing with Ilse's older sister. After I mentioned that my father had fought in France during World War I, she smiled and commented that I was too young to have a father who was in the First World War. "Mein Vater diente im Ersten Weltkrieg" - "My father served in the First World War,"
she said. "Sie sind gerade ein Baby. Sie sind zu jung, um einen Vater zu haben, der in diesem Krieg war." - "You are just a baby. You are too young to have a father who was in that war.
I then told her that my father had fought near Verdun at St. Mihiel, France in September of 1918 and that he was wounded and mustard gassed by the opposing German forces in that battle. She stared at me and momentarily looked somewhat confused, and then she excused herself and went upstairs, returning shortly clutching a scroll. She handed me the scroll and asked me to read it. As I unrolled the scroll and began reading it (mentally translating the German words into English), I could not believe what I was reading. It was a certificate addressed to Oberst (Colonel) Ludecke, Kommandant (Commander) of the 81st Chemical Brigade for a special mission against the American 90th Infantry Division in September of 1918. It was signed by Kaiser Wilhelm II, and dated in 1918.
Without thinking, I turned to her and said "Your father killed my father!"
She turned pale and appeared weak-kneed. I quickly put my arm around her shoulders and, realizing the ramifications of what I had just blurted out, I said to her "But he knew enough to marry my mother who was German."
I then told her that my mother's parents were born in the small town of Mohringen just on the outskirts of Stuttgart. She looked at me and laughed. "Sie sind nicht deutsch, Sie sind Swaibish" - "You are not German, you are Swaibish,"
she said. It should be noted that the Swaibish are known as a hard headed (or bull headed) clan of Germans living in the Stuttgart area of Germany.
She said something to her sister Ilse and they laughed about the "Swaibish" revelation. Then the two of them invited my wife and me to accompany them upstairs to their home above the store. I learned later that day when speaking with one of the neighbors that Ilse Ludecke and her sister had never before invited Americans upstairs to their home. As we came up the stairway and entered the large living room, I noticed there were paintings of military officers lining the walls. Judging by the uniforms worn by each of the men in the paintings, most of them dated back before World War I. The older sister pointed to the painting of her father and grandfather as well as one of her great-grandfather telling me that all were once officers in the Prussian Army. She explained that when the American soldiers came through their town during WWII, she and her sister would take the military paintings down and hide them in the closet. When the American soldiers left, they would return the paintings to the wall.
Frau Ludecke walked over to a closet behind a beautiful ornate wood burning stove and returned with a small brown cardboard box. She opened the box and showed me a large piece of shrapnel from a WWI mustard gas shell. The shell fragment was about nine inches in length. She explained that her father did not want to be in the military, that he always wanted to be an artist. He had brought home this painting he had made depicting a battle scene near Verdun. Painted on the side of this large piece of shrapnel was a scene from one of the small French villages that her father's unit had shelled. She explained that while the mustard gas had eventually killed my father from his wounds on the battlefield that day in France, her father also died of cancer just a few short years after returning from the war.
She believed her father's cancer had developed from him mixing the chemicals and handling the mustard gas mortar rounds just as sure as she believed those mustard gas shells that her father had fired upon the American soldiers during the St. Mihiel campaign had caused them to later die of cancer as well. We talked for awhile longer and as we left, Ilse's sister gave me a hug and whispered in my ear, "Ihr Vater machte eine kluge Wahl, welcher feiner Sohn, den er hat." - "Your father made a wise choice, what a fine son he has."
Two weeks later, my family and I left Germany for stateside, and several months later the handmade dolls my wife had ordered arrived at our home. I thought one of the doll boxes was a bit heavy for just the doll and after opening the box and removing the doll, I noticed a second small brown cardboard box at the bottom. Upon opening the box, I noticed the note on top. It read "Besser haben Sie das als wir" - "Better you have this than us."
Inside was the piece of shrapnel she had showed me that day. It was the one her father had picked up on the battlefield and upon which he had painted a portrait of the French village he had shelled and where my father was wounded that September day in 1918.
Here is a photo of that mustard gas shell fragment painted by Frau Ludecke's father:
Below is a photo of my father taken just after he was released from a military hospital in December of 1918. He was medically discharged from the U.S. Army in January of 1919. He spent the next several decades going from one VA hospital to another, courageously fighting against the debilitating effects of the cancer caused by the mustard gas. Dad died in 1945 at the Hines VA Hospital, located just outside Chicago in Hines, Illinois.
Private John William Reed, January 1919
Why do Some Homeschool Educators Either Strongly Like or Dislike
John Saxon's Math Books?
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 mathematical
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.
May Each of You have a Very Merry and Blessed Christmas,
and a Prosperous and Happy New Year!