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November 2024

WOULD YOU LIKE TO LIVE UNDER COMMUNISM?

I fully realize that is a very strange title for a mathematician's monthly news article. However, as a retired army officer with more than 27 years of active military service - and having visited four separate Communist countries during those 27 years of service - I am deeply concerned that we could very well wake up on November 6th and find that we had elected a Marxist Communist.

Understand, I am not trying to tell you who to vote for. I am trying to tell you that Kamala Harris is a Marxist Communist who was raised by Marxist parents - and I would ask you not to vote for a Communist.

She is not a liberal, or a socialist. She is a Communist and if you doubt my description, go to CPUSA.ORG and read what they believe in. I worked with the FBI over sixty years ago tracking the speeches and lectures of a Communist (Dr. Apthecker) and I can assure you Kamala Harris sounds just like him.

I apologize for publishing the article, but I do not apologize for its content.

May God keep you in the palm of his hand.

November 25th

Again, I apologize for not covering math this month, but I copied part of a small chapter from my book - "Until We Meet Again Old Friend -Tales of an old Soldier." The chapter briefly deals with how the German citizens living in occupied Eastern Germany (occupied by Soviet Russia) reacted under Communist rule immediately after WWII.

The Berlin Encounter

I had left Rome, by train for Frankfurt, that Sunday afternoon in 1963, hoping that when I got to Frankfurt, the weather would then be clear.. With clear weather, I thought I could get a military hop to West Berlin--which at that time was only the Western half of the city of Berlin occupied by the Allied Forces immediately after the surrender of the Third Reich in WWII The Soviet Communists occupied the Eastern half of the city. This division - approved by The Marshall Plan - was the reason for how the titles East and West Berlin, and also East and West Germany came about.

The Western half of the city of Berlin was divided by the victorious Allies into three parts—the French, British and American Sectors. These three sectors were adjacent to the Soviet controlled Eastern half of the city. What made access to the city even more difficult, was the fact that the entire city of Berlin was surrounded by what was then known as the Soviet Communist Zone - often referred to as East Germany.

To stop what the communists called the illegal emigration of East Berlin citizens to West Berlin, the Soviets had erected a huge concrete wall across the eastern border of West Berlin—clearly dividing the Eastern Soviet Sector from the American, British and French Sectors of West Berlin. What came to be known as the "Berlin Wall" had been completed several years earlier, but there was still a chance I could get to see East Berlin—still occupied by the Russians—because the Allied Forces had just opened a new checkpoint.

The new checkpoint was located at Friedrichstrasse in West Berlin, at the wall on the border with East Berlin. The checkpoint was named Checkpoint Charlie. It was added as the third crossing point into East Berlin from the American Sector. However, there was one major restriction. German civilians could not cross into East Berlin through that checkpoint. It was for use only by Allied military, and State Department personnel. The other two crossings for West Berliners (Checkpoints Alpha and Bravo) had just reopened — several days earlier — allowing West Berlin citizens to again visit East Berlin for the first time since August of 1961.

Arriving in Frankfurt, I was informed by the army specialist at the standby flight desk that the only way I could catch a hop into West Berlin was to sign on as a classified courier. There was a daily C-47 flight into West Berlin early every morning and they always needed a classified courier. I had a Top-Secret clearance that could easily be validated by a telephone call to the Special Forces Security Office back at Fort Bragg.

My clearance was authenticated that afternoon by a priority military TWX (today's equivalent of an email). I was handed a classified instruction manual to read and authenticate before I was certified as a courier. I read the manual explaining the emergency procedures for handling and disposing of classified material should the plane go down over Russian-occupied East German territory.

Among the detailed instructions, the procedures required that I be the last person to board the plane after the classified materials were loaded into the cargo hold. I was also to be the first to disembark from the aircraft when it landed at Tempelhof Airport in West Berlin to ensure no one had access to the documents while the plane was on the ground.

If the airplane were forced down by enemy aircraft and required to land in Communist occupied East Germany, my instructions were clear—I was to immediately exit the aircraft and destroy the classified documents using the thermite grenades I would be given.This could only occur I thought, if I were not shot by the Russians as I left the aircraft. The instructions were specific. The two mail bags containing the classified documents would be placed in the cargo hold of the aircraft under us, inaccessible from inside the aircraft. At the time, I remember also reading there would be U.S. Air Force jet fighters accompanying us along the flight corridor while we were flying over occupied East Germany. The primary mission of these fighter aircraft was to drop aluminum foil ahead and behind our courier flight to confuse the enemy radar below us on the ground. Their secondary mission was to provide us with air cover should we be forced to land in East German territory.

The next morning, as instructed, I appeared at the terminal several hours before the scheduled departure time. I was introduced to the Army major in charge of the handling and processing the classified documents. I have no recollection of his name, but years later, in watching an episode of M*A*S*H, I thought I had seen his twin brother when I first laid eyes on Major Burns—old "Ferret Face." This Major's idiotic mannerisms and facial expressions were identical to those of Major Burns "Old Ferret Face."

The Major instructed me there would be two mail bags of classified documents put on board the aircraft by his people after everyone had boarded the aircraft and it had taxied out on the edge of the runway. After the bags were loaded into the cargo hold of the C-47 (under the fuselage), I would board the aircraft and keep my eye on the cargo door under the aircraft until the aircraft started moving down the runway. I was then to swing back into the aircraft and, with the assistance of the crew chief, close the door located behind the wing, forward of the tail section.

The Major became noticeably irritated when I questioned this procedure. I asked him why he could not just drive down the runway in his sedan alongside or behind the aircraft and watch the door from his moving vehicle. I went on to tell him that I could not envision anyone running after a moving C-47 and attempting to steal several heavy bags of mail from it. "These procedures are to be followed to the letter!" he barked. "There will be no deviation!"

He then had me sign for two sealed, serial-numbered bags of classified documents. I asked to verify the inventory of the contents and—you guessed it—the procedures did not require an inventory of the bags' contents.The major then had me sign for the .45 caliber pistol, a holster and belt, and four thermite grenades. As I boarded the aircraft, I noticed that there were about a dozen military passengers—and they were all field grade officers, mostly full colonels. There were also several men in civilian clothes who I assumed were either State Department or CIA.

The plane began taxiing towards the runway. I put down my duffle bag and briefcase and turned towards the open door of the aircraft. My paratrooper experience helped me survive the somewhat strange experience that followed. The airplane was now on the runway and beginning to pick up speed as it started its take-off run. Before sticking my head out the door, I had removed my beret, tie, and khaki shirt knowing the blast from the propellers would rip off my beret, parachute wings, military ribbons—and anything else that would catch the prop blast. As the airplane lifted off the runway I closed and latched the door.

The instructions stated that after the plane had leveled off and began its flight down the corridor, I was to brief the passengers. So, I put my beret, shirt and tie back on, picked up the intercom mike and addressed the passengers. I asked them who had eaten a large breakfast. They all looked at me like I was crazy! Two or three raised their hands. I explained to them that if we were forced down in Russian occupied territory, they would all be required to eat some of the Top-Secret documents. They immediately all started laughing. One of the colonels said something about my solution made more sense than the instructions he had read on disposing of the documents. He was an Air Force Colonel, and later when I sat down next to him, he told me that I was lucky it was not raining when they took off. He said the propellers would have blown most of the runway water into my face and on my clothing as I hung outside the door. Spotting my Master Parachute badge, he then added "But then you already knew that."

The flight to West Berlin was uneventful. Several times along the corridor, I looked out the window and saw the accompanying jet fighter aircraft pass by us. It was a strange feeling. We were flying over Communist East Germany.

After we landed at Tempelhof Airbase in West Berlin, I signed over the bags of classified documents, turned in the pistol, belt, and four thermite grenades and was officially relieved of my courier duties. I headed for a nice clean, quiet hotel—and a good German restaurant.

The next morning, I got up, put on my uniform and beret and went down to Checkpoint Charlie. It was not a very inspiring sight. Checkpoint Charlie was a small wooden shanty that was painted white. It looked like a portable hamburger stand l had seen outside Wrigley Field or Comisky Park as a kid. The white wooden shack was surrounded by sandbags and as you approached it, you could see the East German police (Volkspolizie or VOLPOs for short) just yards away from the building on the Communist controlled East Berlin side. I approached the open window of the shack and asked if I could visit East Berlin. The army corporal said, "Yessir" and then asked to see my ID card and my travel orders. To visit East Berlin, my travel orders had to authorize me to be in East Berlin. I gave him a copy of my leave and travel orders and my ID card, and he handed me a briefing document that among other things told me I had to return through this same checkpoint.

The document also warned me not to throw gum wrappers, cigarette butts, or paper on the ground or to spit on the street or sidewalk while in East Berlin. It also told informed me I could exchange and spend no more than twenty dollars in U.S. currency for East Berlin Deutsche Marks, which was not a recognized currency in West Germany.

The corporal handed back my ID card, and my leave and travel orders, and asked me to sign my name, rank, and serial number—and the time of entry into East Berlin—on the register affixed to the clipboard he handed me. I asked the guard why we had to record the time. He told me if I did not sign back out through the Checkpoint Charlie within four hours, they would come looking for me. "Great," I thought, as I proceeded towards the East Berlin wall. "How would they know where to look for me?"

As I walked towards the East German VOLPOs, a black sedan with several passengers in civilian clothing inside drove slowly passed me and proceeded through what resembled a rat maze of street barriers designed to prevent any vehicle from speeding through the checkpoint from either side! The VOLPOs stopped the car, checked the occupants' ID cards and then waived them on. As I approached the VOLPOs, I remembered the briefing booklet had cautioned me that I was not to show them any ID card if they asked. I was to state that I was an American military officer.

I did not speak to them, and they did not salute me. I was aware that the VOLPOs were not military soldiers; they were East German police—and as such they were civilians, and not required to salute an officer of any army. By now the black sedan had already cleared the Russian checkpoint just ahead. I kept walking towards the next barrier, which was manned by two armed Russian soldiers. They stood ramrod straight and saluted me as I approached them. I returned their salute and in impeccable English they asked to see my ID card. I replied that I was an American military officer and did not need to show any ID while in uniform. They then handed me a clipboard and said I had to sign in. Again, I repeated that as an American military officer, I did not need to do so.

They waived me on and saluted me again. I returned their salute and walked into East Berlin. As I passed the two Russian soldiers and entered East Berlin itself, I noticed a short—somewhat frumpy-looking woman—about fifty years old.

She was wearing a black skirt that went almost to her ankles and a thick brown wool sweater. Her shoes resembled the kind of white shoes worn by hospital nurses back then—the ones with the wide toe and thick heels—except these shoes were black.

She was carrying a large black bag on her left shoulder and as I passed her, she looked straight at me, but I appeared to not even notice her as I walked by her. As I walked along the street, I stopped in several shop windows and noticed in the reflection of the glass that she was right behind me. As I proceeded down the main street further into East Berlin, she remained always about ed always about twenty to thirty feet behind me. "How strange," I thought, "I'm being followed."

Looking around, I noticed the distinct difference between what I had seen in the free sector of West Berlin and this Russian, communist occupied sector of East Berlin. East Berliners wore drab, dark clothing. They did not look up as they walked hunched over as they looked at the ground ahead of them. They all appeared as though they were carrying a heavy weight upon their shoulders. They all - every man, women, and child would not look me in the eye -- they always glanced away as I approached them. They did not appear to be very happy at all. And unlike the West Berlin streets, there was little or no automobile traffic on the streets in the communist controlled East Berlin.. Recalling that as I had walked in the West Berlin sector and as I passed the people of West Berlin on the street, unlike the drab, dark clothing worn by the East Berliners these Germans wore bright colors, and the street traffic was like downtown Chicago. The people on the street would smile and greet you as you passed them. They would look at you—and smile they were happy—and it showed!

Something else caught my eye as I proceeded down the street further and further into occupied East Berlin. The two East German VOLPOs at the first checkpoint were short and squatty looking, and they had no weapons. But the Russian soldiers I passed were all armed with AK-47 automatic rifles—with fixed bayonets. And they were all six feet or taller—and sharply dressed.

They walked the streets or drove jeeps riding in pairs—you never saw a Russian soldier by himself. They saluted me smartly as I approached them. And yes—I returned their salute just as smartly as I passed them. I turned around once and observed they had kept on walking. They did not turn to look at me.

I spotted a German bank and went in to exchange my twenty-dollar bill for some unknown amount of East German Deutsche Marks. My lady friend followed me into the bank and went to another line in front of another teller's cage. There were three or four people in front of me, so I had to stand in line for a few minutes. No one looked at me or spoke to me.

As I approached the metal bars on the teller's cage, I said in my best German that I wanted to exchange twenty dollars in American money for East German Deutsche Marks. The teller answered me in fluent English. Looking through the bars on the teller's cage waiting for her to make the exchange, my peripheral vision caught two men coming up alongside of me—one on each side—and the one on the right slid something in front of me on the teller's counter at the window. All my intelligence training suddenly came into focus. "If you look down it may say follow me, you're under arrest," I thought. So, I kept my head ramrod straight and looked straight forward straining my peripheral vision until I could make out a tall, white-haired man on my right with a goatee and a short, dark-haired man with a mustache and goatee to my left, both dressed like college professors in the States.

I strained my eyes to look down without moving my head and saw part of a news clipping that the man on the right had slipped in front of me. I could read the large print of the headline. It was printed in English. It announced that President Kennedy had been assassinated. The man standing to my right—in fluent English—said, "This is such a sad time for all Germans!" He paused. "We are all so sorry to hear this."

I had read in the Army newspaper, the Stars and Stripes, and heard on the U.S. Radio Station in Frankfurt that President Kennedy had been assassinated a week earlier in Dallas. Suddenly, I remembered that President Kennedy had just visited West Berlin a few months earlier in June.

Perhaps these two men were genuine in their expression of sympathy. But then, perhaps this was a setup! Hundreds of young East Berliners had lost their lives attempting to get past the 20 or so feet of mined land and then get over the twenty-some feet of stone wall only to face another twenty feet or so of mined land on the other side of the wall.

For decades East Berliners had gone over and even tunneled under the wall to escape to "Freedom" in the Western Sector of Berlin. It was not until 9 November of 1989, more than two decades later, that the President of the United States - Ronald Reagan - finally got the Russian President - Mr. Gorbachev - to take down the wall.

November 26th

I hope this has not removed anyone from reading about math. I feel very strongly about our leaders of this Great Nation. And whether you are a Democrat, a Republican, or an Independent, I felt that one month out of a year of math was not too drastic.

May God continue to Bless you and your loved ones over this coming Thanksgiving Holiday!

 

 

                    

September 2024

SHOULD YOU GRADE THE DAILY SAXON MATH ASSIGNMENTS?

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

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

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

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

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

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

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

 

 

                    

August 2024

 

WHAT TO DO WHEN A SAXON STUDENT ENCOUNTERS DIFFICULTY EARLY IN THE COURSE.

By the time the first several months of the new school year have passed, most Saxon math students are at least a fourth of the way through their respective math books and are quickly finding out that the easy review of the previous textbook's material has come to a sudden halt. They are now entering the part of the textbook that determines whether or not they have mastered sufficient material from the previous textbook to be prepared for their current course of instruction.

For students who start school in August - using the Saxon middle or high school math series from Math 76 through Algebra 2 - this generally occurs sometime in mid-to late October around lesson 35 or so. Or it can occur sometime in late November, if they started the course in September. Or, depending upon the student's schedule it may not occur until after the Christmas Holidays in January. This past school year I received a number of email and telephone calls from home school parents who had students who were experiencing difficulty after completing about forty or so lessons of the course. They were mostly upper middle school or high school students using John Saxon's Algebra ½, Algebra 1, or Algebra 2 textbooks.

The symptoms described by the home school parents were similar. The daily assignments seem to take much longer than before and the test grades appear to be erratic or on a general downward trend. The student becomes easily frustrated and starts making comments like, "Why do I have to do every problem?" - or - "There are too many of them and it takes too long." - or - "Why can't I just do the odd problems since there are two of each anyway?" They might even say things like "This book is too hard." - or - "It covers too many topics every day." Or even worse - "I hate math."

About that time, many homeschool educators do the same thing that parents of public or private school students do. They question the curriculum. They immediately look for another - easier - math curriculum so that their children can be successful. Since the students apparently did fine in the previous level book, the parents believe there must be something wrong with this textbook since their sons or daughters are no longer doing well.

Looking for an "easier" math course is like a high school football coach who has just lost his first ten high school football games. However, he assures the principal that they will definitely be successful in their next football game. "How can you be so sure that you will be successful in your next football game?" asks the principal. "Oh that's easy," says the coach. "I've scheduled the next game with an elementary school."

I do not believe the answer is to find an easier math curriculum. I believe the answer is to find out why the students are encountering difficulty in the math curriculum they are currently using, and then find a viable solution to that situation. As John Saxon often said, algebra is not difficult; it is different!

Because every child is also different, I cannot offer a single solution that will apply to every child's situation, but before I present a general solution to Saxon users, please be aware that if you call my office and leave your telephone number or if you email me, I will discuss the specifics of your children's situation and hopefully be able to assist you. My office number is 580-234-0064 (CST) and my email address is art.reed@usingsaxon.com.

When Saxon students encounter difficulty in their current level math book before they reach lesson 30-40 or so, it is generally because one or more of the following conditions contributed to their current dilemma:

1) They did not finish the previous level book because someone told them they did not have to since the first 30 or so lessons in the next book contained the same material anyway.

2) In the previous level math book, when students complained the daily work took too long the parents allowed them to do only the odd problems. Doing this negates the built-in automaticity of John Saxon's math program.

3) In the previous level math book, to hasten course completion, the parents allowed the students to combine easy lessons, sometimes doing two lessons a day, but only one lesson's assignment.

4) The students did not take the weekly tests in the previous courses. Their grades were predicated upon their daily homework. NOTE: The daily homework grade reflects memory. The weekly test grade reflects mastery.

There are other conditions that contribute to the students encountering difficulty early in their Saxon math book. Basically, they all point to the fact that, by taking shortcuts, the students did not master the necessary math concepts to be successful in their current level textbook. This weakness shows up around lesson 30 - 40 in every one of John's math books. The good news is that this condition - if caught early - can be isolated and the weaknesses corrected without re-taking the entirety of the previous level math book.

There is a procedure to "Find and Fill in the Existing Math Holes" that allows students to progress successfully. This procedure involves using the tests from the previous level math book to look for the "holes in the student's math" or for those concepts that they did not master. This technique can easily tell the parent whether the student needs to repeat the last third of the previous book or if they can escape that situation by just filling in the missing concepts - or holes.

If you have my book, then you already know the specifics of the solution. If you do not have my book, then you can call me or email your situation to me and I will assist you and your child. Regardless of what math book is being used, students who do not enjoy their level of mathematics are generally at a level above their capabilities.

 

 

 

July 2024

ARE JOHN SAXON'S ORIGINAL MATH BOOKS GOING THE WAY OF THE DINOSAUR?

I am often asked by home school educators whether or not I will create my teaching DVD “videos” for the new fourth editions of Algebra 1 and Algebra 2, and the resulting new first edition of Geometry now being sold on the Saxon Homeschool website by the new owners of Saxon Publishers.

The answer is no, I will not do so. My creation of the current DVD video series for John’s math books, based upon rock solid editions created by John Saxon, was not to make money.  Using my Saxon classroom teaching experiences, I wanted to create a classroom environment for home school students who wanted to master high school mathematics using John’s unique math books. However, publishing math textbooks redesigned to be like all the other math textbooks on the market are not what John intended when he created his unique style of math books.

John Saxon would not have sanctioned gutting his Algebra 1 and Algebra 2 textbooks of their geometry to create a separate geometry textbook.  He believed that using a separate geometry textbook was not conducive to mastering high school mathematics.  More importantly, each of John’s math books had an author - an experienced classroom mathematician - behind them. These three new editions, created under his Saxon title, do not.

When Harcourt-Achieve bought John Saxon’s dream - Saxon Publishers - from his children, I made the comment that the new owners were certainly intelligent enough to recognize the uniqueness of John’s books. I predicted that they would not change the content of John’s books. Certainly, I commented. “They would never take their prize winning bull and grind it up into hamburger” – or so I thought!

Well the new owners of Saxon Publishers appear to have done just that, and the time has come for me to apologize because they are now selling the hamburger on the Homeschool website. I have previously cautioned home school Saxon users not to use the new fourth editions of Algebra 1 and Algebra 2 then offered only on the school website because the company had gutted all geometry from them to enable them to publish a separate geometry textbook desired by the public school system. But they are now selling them on the Homeschool site as well.

Having been affiliated with one of the larger publishing companies - after Saxon Publishers was sold - I observed that the driving force in the company was not so much the education of the children, but the quarterly profit statement. And that is okay, but being around their VP’s and upper level executives showed me that to them “a book - is a book - is a book.” I still believe they have not the foggiest idea of just how unique and powerful John’s math books are when used correctly. However, I may be wrong, because they may have already observed that it is this “uniqueness” that requires special handling - and that requires special training - and that costs money – reducing quarterly profits.

I do not believe the publishing company will long suffer the expense of publishing both the third and fourth editions of Algebra 1 and Algebra 2. It is my opinion they may well stop printing and selling the third editions of Algebra 1 and Algebra 2 when current stocks run out. This will then require that home school educators using Saxon math books buy the separate geometry book also. After all, “Don’t you make more money from selling three books than you do from just selling two?”

Maybe the new owners of John Saxon's math books will not stop printing the third editions of Algebra 1 and Algebra 2 - but then I could be wrong - again!  If you are serious about using John Saxon’s original math series through high school, I recommend you not buy these new fourth editions of Algebra 1 and Algebra 2. I strongly recommend you immediately acquire the home school editions of John’s math books that I discussed in my book - which include the third editions of Algebra 1 and Algebra 2. 

Listed below are excerpts from my book about each edition of John’s books from Math 54 through Calculus. If after reading this, you feel your particular situation has not been addressed, please feel free to email me at art.reed@usingsaxon.com or call me at 580-234-0064 (CST) before you purchase any math textbooks.

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Math 54 (2nd or 3rd Ed):  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 ½, 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 ½. 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 ½ textbook and proceed directly to the Algebra 1, 3rd edition textbook.  Both the Math 87 and the Algebra ½ 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 ½ 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 ½ 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 ½ (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 ½ 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 ½ 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).

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 a 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 also 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, they have not 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 first 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.

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June 2024

BLOCK SCHEDULING

For Use With
Saxon Algebra ½ – through – Algebra 2

The concept of "block scheduling or "flex scheduling" (looked at by homeschool educators as a way to speed-up the process by going through the books at a faster pace) while not advocated by John Saxon or the author, can be successfully utilized for these Saxon textbooks, if the procedures discussed in this information booklet are followed.

John Saxon believed that children learn more efficiently and effectively when they are exposed to mathematical concepts in small, easily understandable concepts.  This is what John referred to as "incremental learning" or "incremental development." We also believe, and research supports this view, that new concepts and skills should be reviewed continually.  However, if you must use block scheduling – while teaching from any one of the three textbooks mentioned above, we recommend you follow these guidelines.

The author of this article is a retired high school math teacher who has taught the Saxon textbooks from Algebra ½ through Calculus for more than a decade.  The concepts reflected here were implemented at a local university over thirty years ago when incoming freshman with low ACT scores were required to take a non-credit introductory algebra course to prepare them for college algebra.

The author (as an adjunct professor) used the Saxon Algebra 2, (3^rd Ed) textbook and, because of the ninety-minute class every other night, he adapted the instructional methods used during the day in his high school classes. Over ninety-percent of the college freshman in his evening no-credit math class successfully passed their college algebra course on their first attempt the following semester.

Successful implementation of these procedures will allow a student who – for whatever reason -needs to complete one of the three courses listed above in a single semester, rather than a full nine month school year. As with any new procedures, there are always variations that may or may not work; however, it is recommended these procedures not be altered until you have followed them for at least one full academic semester. 

There are 123 lessons in the Algebra ½ textbook, 120 lessons in the Algebra 1 textbook, and 129 lessons in the Algebra 2 textbook. So, basically, you need to commit a minimal time span of at least six months to acquire a minimum of 130 useable days.  Using three days per week to accomplish six lessons and one test per week, you could easily cover the 129 lessons in the Algebra 2 textbook.

What we have not covered is what to do with the student who, after going through the six months' Block Scheduling course ends up with a "D" or worse an "F"? Please read the December 2023 News Article and follow the advice given there.

If questions regarding these instructions or situations arise that create conflict with these procedures, or if additional information is needed, please feel free to call the author at (580) 234-0064 (CDT).

ESSENTIAL DEFINITIONS

Type of Block Scheduling:  Over the past decade, several variations of the original block scheduling have been developed.  This particular document addresses the block-scheduling plan where students meet for ninety minutes on alternating school days to accomplish two lessons of a Saxon Math Book. This type of schedule dictates that they meet three days a week, on Monday, Wednesday and Friday of each week. 

Time Management in a non-Block Classroom:  In a regular fifty-minute daily class period, a Saxon math teacher or a home educated student successfully covers a lesson each day and one test on Friday of each week. Depending on the time lost due to mandatory state testing, school drug/alcohol assemblies, etc., this routine permits the Saxon math teacher and Home Educator to cover a minimum of 125 lessons in a school year that has 175 teaching days.  The remaining days are used for the weekly tests.  In this daily routine, students get used to having a minimum of thirty to thirty-five minutes in each day's class period to work on their daily assignment - often completed in the timeframe of that classroom.

Time Management in a Block Scheduled Class:  As John Saxon once wrote, "Do not be a Sage on the Stage."  Students do not learn math by listening to someone lecturing.  They learn by doing the math, so the concept of not lecturing half of the class period becomes even more important when teaching under the block concept.  While limiting lecture time was essential in the daily Saxon class period, it is critical in the block schedule classroom. If you use my online classes of instruction, (teachingsaxon.com) you will notice that almost all of the lessons I teach take no longer than 15 minutes - most less than 10 minutes. If you want to use my online lessons in this speeded-up environment, please send an email to me immediately after purchasing one of the three online series. I will add the previous textbooks' online lessons free of charge for the students' use during this six month period, knowing that the student may not quite yet have mastered all of the concepts in that previous textbook.

Failing Students: If students begin failing in the Saxon math textbook, this occurs over a period of time.  In order for them to get back to where they were before they began their decent, they (and their parents) should understandthat it would normally take as long a period of time to recover as it took to decline.  The cumulative nature of the Saxon math textbook however, allows the teacher and the parent the opportunity to use those latter tests, after recovery, to determine the students' true grade point average.  We want not to grade the fall, but the recovery. especially since the cumulative nature of the textbook (and tests as well) reflect that the recovered students have in fact mastered the material they previously were failing to grasp.  In the block system of instruction, the decline occurs more rapidly and the parent or classroom teacher must monitor the test grades more frequently, and respond more quickly.

Daily Assignments: Since two lessons (concepts) will be covered every other day, there will be an attempt by the students to develop an alternative homework assignment schedule such as odd in one lesson and even in the other, or all the odd, or all the even in both.  The only successful way is to do all the problems in all the lessons every day. While this amounts to sixty problems every day, remember they will have at least one immediate hour in class, and another extra day before they must turn in the assignments.

Student Assignments:  As they enter the classroom, students are required to place their completed work in a box located near the door inside the room.  They are required to place the number of problems they understood and completed in the center top of the top sheet of each assignment done by them.  Have them circle this number.  They are also to indicate just below their name, class, etc. (in the upper right or left corner of the same page) which problems they did not understand (e.g. 2, 3, 8,13) (See Appendix A).  These are the problems the instructor will record on the class tally sheet to determine which problems will be reviewed during the class period (See Appendix B). When student interest reflects duplicates, pick the tougher of the two - time constraints will preclude doing more than one of each type problem.

Grades/Weights:  As Saxon math textbooks are cumulative, the weekly tests are the only indicator of whether or not the student understands the material covered in class.  Regardless of whether or not the instructor requires notebooks, research papers, or other extraneous material, or how much weight is given these documents, the only student who takes tests "poorly" is the ill prepared student who does not understand the daily assignments.  The weekly tests should comprise at least eighty percent (hopefully ninety percent) of the student's grade.  As with the sports teams' daily practices, we rely on the weekly "game test" to determine how well the students are doing, not on how well their daily practices went.  Students (or parents) will eventually question how it is possible for their son or daughter to get "nineties" or better on daily assignments, but only "sixties" (or lower) on weekly tests.  This can be resolved by giving each student a copy of the document "Three Easy Ways to Fail This Course" at the start of the school year.  (See the April 2024 News Article)

Grading the Homework: You must become a believer in "Managing by Exception."  If you weight homework more than ten to twenty percent, and you grade each day's homework, you will be a nervous wreck at the end of the first nine weeks of school and you will have no clue as to which students really know what they should.  A recommended grading scale for the daily assignments can be found at the end of this article. You record the number of homework problems the student said they understood and completed. That's what the circled number in the center of the page means.  If they "fudge" that number they are only cheating themselves.   When their test grade indicates otherwise, you get involved.  If students tell you they understand and do twenty-three to twenty-five problems every day and they keep getting eighties or better on their tests, what is there to grade?  You want to spend your time with the student who says he did and understood twenty to twenty-five problems every day - and just got a low sixty on the his test!

The Lesson:  To enable weaker students to absorb and practice each concept, and to keep from losing these students, it is better to break the ninety-minute period into two separate forty-five minute classes, each one completely independent of the other. Students need to learn "time management."  The student who learns to stay on task and do fifteen to eighteen problems in thirty minutes will also be able to complete a twenty-question test in forty-five to fifty-minutes.

Daily Review:  In the Saxon methodology, daily review is essential, in the block system, it is critical.  For each lesson taught in one ninety-minute block of instruction, four to six problems are reviewed based upon the problems recommended by the students. It is better to review the four to six problems from each lesson at two different times in the ninety-minute block period rather that attempt to put them together at the beginning of the class.  You will lose the students if you do!!  Students need a five to ten minute break from working, and besides, they may have run aground on one of the review type problems from the first session and need another quick review.

Giving the Test:  If you give the test the first half of the ninety-minute period, the students will never stop whining about not having enough time and want to use more of the second half as well. It is far better to stop the class about five minutes before the mid-way point, clear the desks and hand out the tests giving them fifty minutes to complete the test.  When students learn they have fifty minutes for the test, they will move swiftly when on their time.  When the bell rings, they are done.  I recommend you use your cell phone alarm and keep it with you as someone will know how to shut it off. The switch side is that a few of the more ingenious and lazy students will attempt to use the first forty minutes that day as a review period.  The smart teacher or enlightened parent, can easily stop this chicanery.

GRADING DAILY HOMEWORK ASSIGNMENTS
(A Suggestion)

NUMBER COMPLETED OR UNDERSTOOD 28 - 30 25 - 27 22 - 24 19 - 21 17 - 18 15 - 16 Less Than 15

POINTS 100 90 85 80 70 60 0

LETTER GRADE A A - B B - C C - D or F

Note: If a student cannot (or will not) complete at least twenty-five problems each day, he will fail the course (at a minimum escape with a low D). Also, by giving the greatest value (eighty or ninety percent) to the test grades, students soon learn that "Magic Homework" won't get them a passing grade. Whatever the student's final average for the homework is, take no more than 10 or 20 percent.

Remember your math teacher's 50/50 grading method that allowed 50% of 100 = 50 for homework and 50% of 50 = 25 for the test grade giving the lazy guy or gal in the class a final grade of "75."  Earning for them a nice "C" because they had utilized the "Copy Someone's Homework" concept to get a final grade of 75 instead of the actual failing grade of a "45" they had rightfully earned.  

MANAGING THE NINETY-MINUTE BLOCK CLASSROOM

(A recommended way to get done what is needed)

Note:  Before you proceed, make sure you have completely read the Essential Definitions or you will not understand
what we are talking about and will not know what to do.

ELAPSED TIME	POINTS
0 Min (1st Bell)	Students enter the classroom and place both assignments due from the previous class day's assignment in the box reserved for their daily work. They proceed to their desks, open their books, and immediately begin working on the next assignment. Even though the new increment has not yet been taught, there are at least twenty-five review problems the student can immediately start working. No questions of the instructor are permitted at this time.
0 Min (2nd Bell)	After taking attendance, the instructor picks up the student work from the box and takes them to his desk to record the problems that will be reviewed.
4-5 Min	Record individual requests for problem review on separate reviewsheets (e.g. all lesson 18 on one and all lesson 19 on the other).
10-15 Min	When you ask students to participate by asking them questions, make sure they respond quickly and do not drag out the process. If the student hesitates answering, move quickly to another student. The review process is just that "Review." It is designed to fill some gap in the students' concept of how that particular type of problem is to be worked. THIS IS NOT A LECTURE.

Note:  The first few weeks I did this, I let those who knew what I was reviewing keep working on their work assignments.  They only needed to stop and look up when I came to something they needed to review.  I was not very smart, in another week, I looked around and no one was paying attention to what I was saying.  I was talking to myself! Apparently no one wanted to appear they did not know what to do.  After that episode, everyone closed their book and put their pencil down.  If you even looked like you were not paying attention, guess who I kept asking the questions of?

• APPENDIX A: DAILY ASSIGNMENT COVER SHEET
• APPENDIX B: ASSIGNMENT REVIEW SHEET

 

 

May 2024

WE HAVE SWITCHED INTERNET CARRIERS

I will get out the May Newsletter in a couple of days as soon as I resolve the following dilemma. Hopefully you have not been involved in sending us an email only to not receive either a reply or a telephone call. We have switched internet carriers and no longer can send or receive email from suddenlinkmail.com or suddenlink.com. Without warning they just stopped our email several days after the transfer. Any of the following email addresses will get to me or to AJ Publishers.

For email directed for Art Reed, use one of the following:

• art.reed@teachingsaxon.com
• art.reed@homeschoolwithsaxon.com
• art.reed@usingsaxon.com

For email directed to the company AJ Publishers LLC, use one of the following:

• ajpubco@teachingsaxon.com
• ajpubco@homeschoolwithsaxon.com

I do apologize for any inconvenience this may have caused any of you.

Please give me a call if you need a reply to an errant email you have sent in the last several days and have not yet received an answer

Art Reed (1-580-234-0064)

ENTERING A SAXON MATH TEXTBOOK FROM A NON-SAXON BOOK

Because of the cumulative nature of the Saxon mathematics textbook, a student entering a Saxon classroom from a non-Saxon environment will encounter difficulty regardless of his academic ability. It is this very cumulativeness, coupled with the incremental development of the Saxon textbook that will assist the student in regaining their academic level of performance. While it is an initial shock to the student and their parent(s), regardless of their academic ability, it is possible to overcome this initial shock if incoming students and their parents will sit down and agree to several policies and procedures based upon the following conditions as they apply to each student.

1. It will take three to four weeks or more for any student to reach his academic expectations regardless of his academic abilities. Students who arrive new to the Saxon methodology generally fall into one of three categories:

• Exceptional Students: A valid "A" or "B" math student who has mastered the prerequisites for the course will take about three to four weeks to assimilate to the weekly tests and the cumulative nature of the Saxon textbook. Inform the student that initial test scores may be a bit lower than expected. However later test scores that will undoubtedly be higher, will replace these lower test scores. This will resolve the problem before the end of the nine-week grading period. This will not solve the problem if the student is not really an "A" or "B" math student (e.g. his grades were based on applying a fifty percent notebook or fifty percent homework grades, etc.)
• Average Students: Students who arrive with a low "A" or a low "B" average will experience a great deal more difficulty and will take almost an entire nine week period to assimilate to the Saxon methodology. Again, an initial conference with the student is essential.
• Below Average Students: Students who arrive with a "C" grade should be placed in the last part of the previous textbook (e.g. if the students came from the algebra 2 course, they should be placed in the last part of the Saxon algebra 1 class). To enable them to receive credit for this semester, enter algebra 1 (w/geometry) or Intro to algebra 2 on their transcripts to differentiate from the algebra 1 course they completed in the previous non-Saxon textbook. The Saxon algebra 1 textbook, unlike other algebra 1 textbooks, contains geometry and the later part of the textbook prepares the students for algebra 2, so either entry would be an accurate description. Without exception, students who received a low "C" or "D" grade in their previous math textbook should repeat whatever the course was, only now using the Saxon textbook.
  
  Upon successful completion, their transcript could either reflect the same "introductory algebra 1" or "introductory algebra 2" course or use "algebra 1 (w/geometry)" or algebra 2 (w/geometry), etc.

(1 Con't) In almost all cases, students who encounter difficulty in changing to a Saxon algebra 1 or algebra 2 textbook do so, not only because of the cumulative nature of the text, but because of the geometry as well. If the students were not properly prepared in their previous non-Saxon environment, they cannot always absorb the algebra and geometry concepts at cumulative level in the Saxon math textbooks.

Setting them back with this review process gives them the opportunity to absorb the algebra and geometry at an easier level. Use the entries "introduction" and "w/geometry" on the transcripts so they can honestly receive credit for something they have not previously encountered.

2.The later test grades should override earlier test grades. Unlike other textbooks, Saxon math books are cumulative in nature, so the student who fails the first three tests, then begins to receive passing test scores on the next three tests (e.g. scores of 40, 50, 55, 70, 80, and 85) has indicated they have finally grasped the material they were initially struggling with. There are a number of ways to encourage and enable these students to be rewarded for their hard work. One way would be to either drop a failed test for each subsequent test passed (e.g. the 40 is dropped when the student got the 70, the 50 was dropped when the student then got the 80). Another way would be to replace the failed test score with the average of the failed test and one of the recently passed tests. That would mean we would replace the 40 with the average of (70+40)/2, the 50 with the average of (80+50)/2 and the 55 with the average of the (85+55)/2, so the students'' new test grades would reflect 55, 65, 70, 70, 80, 85). In either case, if the student maintained a test average of 80 or 85 for the rest of the grading period these earlier low test scores should not affect his grade for the course. If the student continues with test grades of 80 or 85, he has indicated that he is a "B" student in this Saxon math class. If the test grades begin to fall below an 80, this procedure should not be applied.

3. Students should not attempt to make up everything all at once just to become "eligible" for extra-curricular activities. It is critical that both the parents and the students understand that this process of assimilating into the Saxon textbook will not occur within a single week or two. It may take an entire nine-week grading period. During the process, the student should show a slow but determined increase in test grades. For this reason, so long as the test grades are improving, the student should be classified as "eligible" and allowed to compete in extra-curricular activities.

4. Second nine-week grades and second semester grades can override previous term grades. Unlike other math textbooks, a student who falls behind in a Saxon textbook takes about the same amount of time to return to this previous level of understanding as it took to fall to where he is now. In other words if a "C" student starts failing, it will take the three or four weeks it took to go from the "C" to the "F" or get back to the "C" again. For that reason, students who fail the first nine-week period, but see the error of their ways and recover to a passing "C" or even a "B" the second nine week period, should receive that "C" or "B" for the first semester grade. Again, is it the cumulative nature of the Saxon textbook that logically and legally supports this. Depending on their actual test scores, attitude, and individual circumstances, students who fail their first semester should either be reassigned to the second semester algebra 1 class to review the concepts they do not comprehend, or be given the opportunity to continue and have their second semester grade also replace their first semester grade.

5. Re-evaluate the student's progress after two or three weeks. Remember, not every "A" or B" student coming from a non-Saxon environment may really be prepared for the no nonsense Saxon Methodology. If the student's test grades are not slowly getting better, it is critical that that you brief the student to alert him to the possibility of his reassignment to the "introductory" or "w/geometry" Saxon level courses.

6. Give credit for a "lesser inclusive" subject. Using a single case as an example, the reader can extrapolate to other levels and courses. Let us assume we have a student who switches from a non-Saxon textbook to a Saxon Math book at the start of the second nine-week period with a grade of "B" in the non-Saxon Algebra 2 course.

And you and he both feel it would be beneficial to switch to the Saxon Algebra 2, 3rd Ed textbook. After three tests of 45 and 50, and 45, it is apparent that the student is not able to handle the material. You recommend the student be assigned to the Saxon algebra 1, 3rd Ed textbook and complete the Algebra 1 course. Depending on the student's latter test scores, his transcript would either reflect the Algebra 1 w/Geometry or the Introduction to Algebra 2. Assume the student's final five or so test scores are low "C"s" (70-75) the students transcript could reflect a "C" for an Intro to Algebra 2 course and they would repeat the algebra course the next year and their transcript would be annotated to reflect Algebra 2 (w/geometry). Recall that 3rd Ed textbook qualifies as an Honors Course.

Don't forget to read the December 2023 News Article titled

TWO TEXTBOOKS - FOUR YEARS.

If you already have questions about this particular problem please email me your telephone number with just a quick question and include your telephone number and I will call you rather than each of us sending a small book to each other - and I painfully type with two fingers!

 

 

April 2024

THREE EASY WAYS TO FAIL ANY SAXON MATH COURSE
(Hereafter referred to as Magic Homework)

It has been more than thirty years since I retired from teaching high school math at a rural high school in North Enid, Oklahoma. I can still remember the talk I gave my students their first day of class. I explained to them that the course was relatively easy if they did all of their daily practice work "known as homework" every day.

It was easy to bring sports into the equation as I then told them that if they did not want to practice their putting on a daily basis - don't expect to compete in any golf tournaments. If you don't want to take daily batting practice don't gripe about your low batting average. And if you do not do all of the problems in the daily assignment don't gripe when you start failing the weekly tests.

I went on to explain to them that I had probably heard every excuse used by a student to explain why they were starting to fail - or were already failing - a Saxon Math course. In this case my math class. Then I told them to not take any notes as I would provide each of them with a copy of these excuses known as Magic Homework. I went on to explain that I would also give them an extra copy to give their parents so when their grade began falling to a "C" or lower they could simply tell their parents it was because of reason 1, 2 or 3.

1. NOT DO ALL THE DAILY ASSIGNMENTS: Why should I have to do all this boring "Make Work" stuff when I already know it? I listen in class every day and I understand what Mr. Reed is saying. Why should I have to waste my time doing all these stupid problems just to keep me busy? I know this stuff, and besides I have a job after school and I don't have the time for this "Make Work" stuff.

2. COPY SOMEONE ELSES HOMEWORK: My friend writes neater than I do and besides, I know how to do this "dumb stuff." I just don't have the time and besides you won't accept Xerox copies, so my friend copies it for me. Sometimes I copy it myself and it is just like doing it myself because I learn as I am writing it down.

3. WRITE DOWN JUST THE ANSWERS: Most of the time I use "scratch paper" to show my work. You told me it is too messy to read and I cannot turn it in. So now I neatly write down the answer so you know I did the problem correctly. Besides, I can do this stuff in my head! All you need is just the answer, so you know I can do the work.

 

 

March 2024

WHAT DETERMINES THE DIFFERENCE BETWEEN MASTERY AND MEMORY?

Think back to your days in high school and your algebra classes. Do you recall having your math teacher hand out a review sheet a few days before the big test? So what did you do with this review sheet? Right! You memorized it knowing that most of the questions would appear on the test in some form or other. We are the only industrialized nation in the world that I know of where parents proudly announce "Oh, I was never very good at math." Not hard to explain considering you probably memorized the material for a passing test grade, and then after the test was over, quickly forgot the material. On the front of this website I have inscribed in red:

"When you are dissatisfied, and
Yearn to return to your youth
Think of Algebra!"

I still see students in the local public school receiving a passing math grade using the "review sheet" technique, even though their test grades never get above a sixty. How can this happen? Easy! The student's grades are based upon a grading system that ensures success even though the student cannot pass a single test (unless you consider a sixty a passing grade). Many students' overall average grades are computed based upon fifty percent of their grade coming from the homework (easily copied by them) and another fifty percent determined from their test scores (following the review sheet). So the student who receives hundreds on the daily homework grades and fifties or sixties on the tests is cruising along with an overall grade average of a high "C" or a low "B." Yet, that student cannot explain half of the material in the book.

I have often explained to parents of students who were struggling in my math classes that their struggle was akin to the honey bee struggling its way through the wax seal of the comb. It is that struggle that strengthens the bee's wings and enables it to immediately fly upon its exit from the hive. Cut the wax away for the young bee and it will die because its wings are too weak to allow it to fly. Yes, there is a difference between struggling and frustration! The home educator as well as the classroom teacher must be ever vigilant to recognize the difference.

While we all would like the student to master the new concept on the day it is introduced, that does not always happen. Not every math student completely understands every math concept on the day it is introduced. It is because of this that John Saxon developed his incremental approach to mathematics. When John's incremental development is coupled with a constant review of these concepts, "mastery" occurs.

Mastery occurs through a process referred to by Dr. Benjamin Bloom as "automaticity." The term was coined by Dr. Bloom, of "Bloom's Taxonomy," while at the University of Chicago in the mid 1950's. He described this phenomenon as the ability of the human mind to accomplish two things simultaneously so long as one of them was over-learned (or mastered). The two critical components for mastery are repetition over time.

Automaticity is another way to describe the placing of information or data into long term memory. The process requires that its two components—repetition over time—be used simultaneously. It is this process in John Saxon's math books that creates the proper atmosphere for mastery of the math concepts. Violating either one of the two components negates the process. In other words, you cannot speed up the process by taking two lessons a day or doing just the odd or even numbered problems in each lesson.

Trying to take shortcuts with mathematics would be like trying to save meal preparation time every day. Why not just eat all the meals on weekends and save the valuable time spent preparing meals Monday through Friday. Just as your body will not permit this "short-cut," your mind will not allow mastery of material squeezed into a short time frame for the sake of speeding up the process by reducing the amount of time spent on the individual math concepts.

In a single school year of nine months, the student using John Saxon's math books will have taken more than twenty-five weekly tests. Since all the tests are cumulative in content, passing these tests with a minimum grade of "80" reflects "mastery" of the required concepts - not just memory!

While a student may periodically struggle with an individual test or two throughout the entire range of the tests, it is not their test "average" that tells how prepared they are for the next level math course, nor is it the individual test scores (good or bad) they received on the early tests that matter. What is important are the individual test scores the student receives on the last five tests in the course. It is these last five test scores that reflect whether or not the student is ready for the next level math course.

Students who receive individual test scores of 80 or higher—first time tested—on their last five tests in any of John Saxon's math books are well prepared for success in the next level math course. I strongly recommend that you not tell the students of this until they reach the fifth test of the last five tests. Believe me, even the best of students will never really apply themselves to the first 25 or so tests thinking that they do not really count. By the time they reach the last five tests - if they even do - it will be too late as mastery has not taken hold. They will be lucky to even reach test 25 having not really applied themselves on the first 10 or so tests.

 

 

February 2024

JOHN WAS RIGHT! — SOME THINGS HAVEN'T CHANGED — EVEN AFTER MORE THAN A HUNDRED YEARS!

Homeschool educators are constantly faced with the dilemma of deciding whether or not their son or daughter needs to take a separate high school geometry course because some academic institution wants to see geometry on the high school transcript. Or, because the publishers offer it as a separate math textbook in their curriculum — implying it is to be taken as a separate course. Remembering, of course, that selling three different math textbooks books brings in more revenue than selling just two different math textbooks will.

John Saxon's unique methodology of combining algebra in the geometric plane and geometry in the algebraic plane all in the same math textbook had solved that dilemma facing home school educators for these past twenty-five years. However, unknown to John, this same problem had been addressed over a hundred years earlier at the University of Chicago.

Knowledge of this information came to me by way of a gift from my wife and her two sisters. Since 2003, after their mom and dad had passed away, my wife and her sisters had been going through some fifty years of papers and books accumulated by their parents and stored in the attic and basement of the house they all grew up in. When asked by friends why it was taking them so long, one of the daughters replied "Mom and Dad took more than a half century to fill the house with their memories. It won't hurt to take a couple more years to go through them."

Among some of the treasures they found in the basement were letters to their great-grandfather written by a fellow soldier while both were on active duty in the Union Army. One of these letters was written to their great-grandfather while his friend was assigned to "Picket Duty" on the "Picket Line." His fellow Union Soldier and friend was describing to his friend (their great-grandfather) the dreary rainy day he was experiencing. He wrote that he thought it was much more dangerous being on "Picket Duty" than being on the front lines, as the "Rebels" were always sneaking up and shooting at them from out of nowhere.

The treasure they found for me was an old math book that their father had used while a sophomore in high school in 1917. The book is titled "Geometric Exercises for Algebraic Solutions — Second Year Mathematics for Secondary Schools." It was published by the University of Chicago Press in October of 1907.

The authors of the book were professors of mathematics and astronomy at the University of Chicago, and they addressed the problem facing high school students in their era. Students who had just barely grasped the concepts of the algebra 1 text, only to be thrown into a non-algebraic geometry textbook and then, a year or more later being asked to grasp the more complicated concepts of an algebra 2 textbook. The book they had written contained algebraic concepts combined with geometry. It was designed as a supplement to a geometry textbook so the students would continue to use algebraic concepts and not forget them.

John never mentioned these authors — or the book — so I can only assume he never knew it existed. For if he had, I feel certain that it would have been one more shining light for him to shine in the faces of the high-minded academicians that he — as did these authors — thought were wreaking havoc with mathematics in the secondary schools.

In the preface of their textbook, the professors had written:

"The reasons against the plan in common vogue in secondary schools of breaking the continuity of algebra by dropping it for a whole year after barely starting it, are numerous and strong . . . With no other subject of the curriculum does a loss of continuity and connectiveness work so great a havoc as with mathematics . . . To attain high educational results from any body of mathematical truths, once grasped, it is profoundly important that subsequent work be so planned and executed as to lead the learner to see their value and to feel their power through manifold uses."

So, should you blame the 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 for the original Homeschool third editions of John Saxon's Algebra one half, Algebra one and Algebra two textbooks still contain geometry as well as algebra — as does the advanced mathematics textbook. In fact, John introduces some basic algebraic and geometric concepts as early as the sixth grade in the second and third editions of his sixth grade Math 76 book.

Any home school student — using John Saxon's Homeschool math textbooks — who successfully completes Algebra one, (2^nd or 3^rd editions), Algebra 2, (2^nd or 3^rd editions), and at least the first sixty lessons of the Advanced Mathematics (2^nd edition) textbook, has covered the same material found in any high school algebra one, algebra two and geometry math textbook — including two-column formal proofs. Their high school transcripts — as I point out in my book — can accurately reflect completion of an algebra one, algebra two, and a separate geometry course.

When home school educators tell me they are confused because the school website offers different materials than what is offered to them on the Homeschool website, I remind them that - unless they want to purchase a hardback version of their soft back textbook - they do not need anything being offered on the Saxon school website. In fact, they are getting a better curriculum by staying on the Homeschool website. You can still purchase the original versions of John Saxon's math textbooks that he intended be used to develop "mastery" as recommended by the University of Chicago mathematics professors over a hundred years ago.

Because many of you do not have a copy of my book, I have reproduced that list from page 15 of the book so you can see what editions of John Saxon's original math books are still good whether acquired used or new. These editions will easily remain excellent math textbooks for several more decades.

Math 54 — The hard cover second edition — or — the new soft cover third edition.

Math 65 — The hard cover second edition edition — or — the the new soft cover third edition.

Math 76 — The hard cover third edition edition — or — the the new soft cover fourth edition.

Math 87 — The hard cover second edition edition — or — the the new soft cover third edition.

Algebra ½ - The hard cover third edition.

Algebra 1 — The hard cover third edition.

Algebra 2 — The hard cover second edition — or — the third editions.

Advanced Mathematics — The hard cover second edition.

Calculus — The hard cover first - or second edition.

Physics - Hard cover first edition (there is no second edition of this book).

 

 

January 2024

WHY IS THERE THIS "LOVE - HATE" RELATIONSHIP WITH SAXON MATH BOOKS

Over the past forty-some years, I have noticed that parents, students, and educators I have spoken to, either strongly like or - just as strongly - dislike John Saxon's math books. During my workshops at home school conventions, I was often asked the question about why this paradigm exists. Or, as one home school educator put it, "Why is there this Love - Hate relationship with Saxon math books?" It is easy to understand why educators like John's math books. They offer continuous review while presenting challenging concepts in increments rather than overwhelming the student with the entire process in a single lesson. They allow for mastery of the fundamentals of mathematics.

More than forty years ago, in an interview with William F. Buckley on the FIRING LINE in 1983, John Saxon responded to educators who were labeling his books as "blind, mindless drill." He accused them of misusing the word "drill." John reminded the listeners that:

"Van Cliburn does not go to the piano to do piano drill. He practices - and - Reggie Jackson does not take batting drill, he takes batting practice."

John went on to explain that

"Algebra is a skill like playing the piano, and practice is required for learning to play the piano. You do not teach a child to play the piano by teaching him music theory. You do not teach a child algebra by teaching him advanced algebraic concepts that had best be reserved till his collegiate years after he has mastered the fundamentals - and can then better understand the advanced concepts."

As John would often say, "Doing precedes Understanding - Understanding does not precede Doing."

It is my belief that, John Saxon's math books remain the best math books on the market today for mastery of math concepts! Successful Saxon math students cannot stop telling people how they almost aced their ACT or SAT math test, or CLEP'd out of their freshman college algebra course. And those who misuse John Saxon's math books, and ultimately leave Saxon math for some other "catchy - friendly" math curriculum, rarely tell you that their son or daughter had to take a no-credit algebra course when they entered the university because they failed the entry level math test. Yes, they had learned about the math, but they did not master or retain it.

Just what is it that creates this strong dislike of John Saxon's math books? During these past forty-some years I have observed there are several general reasons that explain most of this strong dislike. Any one of these - or a combination of several - will create a situation that discourages or frustrates the student and eventually turns both the parent and the student against the Saxon math books.

Here are several of those reasons:

ENTERING SAXON MATH AT THE WRONG LEVEL: Not a day goes by that I do not receive an email or telephone call from frustrated parents who cannot understand why their child is failing Saxon Algebra 1 when they just left another publisher's pre-algebra book receiving A's and B's on their tests in that curriculum. I explain that the math curriculum they just left is a good curriculum, but it is teaching the test, and while the student is learning, retention of the concepts is only temporary because no system of constant review was in place to enable mastery of the learned concepts.

Every time I have encountered this situation, I have students take the on-line Saxon Algebra 1 placement test - and without exception, these students have failed that test. That failure tends to confuse the parents when I tell them the test the student just failed was the last test in the Saxon Pre-Algebra textbook. Does this tell you something? This same entry level problem can occur when switching to Saxon at any level in the Saxon math series from Math 54 through the upper level algebra courses; however, the curriculum shock is less dynamic and discouraging when the switch is made after moving from a fifth grade math curriculum into the Saxon sixth grade Math 76 book.

MIXING OUTDATED EDITIONS WITH NEWER ONES: There is nothing wrong with using the older out-of-print editions of John Saxon's original math books so long as you use all of them - from Math 54 to Math 87. However, for the student to be successful in the new third edition of Algebra 1, the student has to go from the older first edition of Math 87 to the second or third edition of Algebra ½ before attempting the third edition of the Saxon Algebra 1 course.

But when you start with a first edition of the Math 54 book in the fourth grade and then move to a second or third edition of Math 65 for the fifth grade; or you move from a first or second edition of the sixth grade Math 76 book to a second or third edition of the seventh grade Math 87 book, you are subjecting the students to a frustrating challenge which in some cases does not allow them to make up the gap they encounter when they move from an academically weaker text to an academically stronger one.

The new second or third editions of the fifth grade Saxon Math 65 are stronger in academic content then the older first edition of the sixth grade Math 76 book. Moving from the former to the latter is like skipping a book and going from a fifth grade to a seventh grade textbook. Again, using the entire selection of John's original first edition math books is okay so long as you do not attempt to go from one of the old editions to a newer edition. If you must do this, please email or call me for assistance before you make the change.

SKIPPING LESSONS OR PROBLEMS: How many times have I heard someone say, "But the lesson was easy and I wanted to finish the book early, so I skipped the easy lesson. That shouldn't make any difference." Or, "There are two of each type of problem, so why do all thirty problems? Just doing the odd numbered ones is okay because the answers for them are in the back of the book." Well, let's apply that logic to your music lessons.

We will just play every other musical note when there are two of the same notes in a row. After all, when we practice, we already know the notes we're skipping. Besides, it makes the piano practice go faster. Or an even better idea. When you have to play a piece of music, why not skip the middle two sheets of music because you already know how they sound and the audience has heard them before anyway.

My standard reply to these questions is "Must students always do something they do not know how to do? Can they not do something they already know how to do so that they can get better at it?" The word used to describe that particular phenomenon is "Mastery!"

USING A DAILY ASSIGNMENT GRADE INSTEAD OF USING THE WEEKLY TEST GRADES: Why would John Saxon add thirty tests to each level math book if he thought they were not important and did not want you to use them? Grading the daily assignments is misleading because it only reflects students' short term memory, not their mastery. Besides, unless you stand over students every day and watch how they get their answers, you have no idea what created the daily answers you just graded.

Doing daily work is like taking an open book test with unlimited time. The daily assignment grades reflect short term memory. However, answering twenty test questions - which came from among the 120 - 150 daily problems the students worked on in the past four or five days - reflects what students have mastered and placed in long term memory. John Saxon's math books are the only curriculum on the market today that I am aware of that require a test every four or five lessons. Grading the homework and skipping the tests negates the system of mastery, for the student is then no longer held accountable for mastering the concepts.

MISUSE OF THE SAXON PLACEMENT TESTS: When students finish one Saxon level math book, you should never administer the Saxon placement test to see what their next book should be. The placement tests were designed to see at what level your child would enter the Saxon series based upon what they had mastered from their previous math experiences. They were not designed to evaluate Saxon math students on their progress. The only valid way to determine which the next book to use would be is by evaluating the student's last four or five test scores in their current book. If those test scores are eighty or better, in a fifty minute test - using no partial credit - then they are prepared for the next level Saxon math book.

In March of 1993, in the preface to his first edition Physics textbook, John wrote about "The Coming Disaster in Science Education in America." He explained that this was a result of actions by the National Council of Teachers of Mathematics (NCTM). He went on to explain that the NCTM had decided, with no advance testing whatsoever, to replace testing for calculus, physics, chemistry and engineering with a watered-down mathematics curriculum that would emphasize the teaching of probability and statistics and would replace the development of paper-and-pencil skills with drills on calculators and computers. John Saxon believed that this shift in emphasis "... would leave the American student bereft of the detailed knowledge of the parts - that permit comprehension of the whole."

If you use the books as John Saxon intended them to be used, you will join the multitude of other successful Saxon users who value his math books. I realize that every child is different. And while the above situations apply to about 99% of all students, there are always exceptions that justify the rule. If your particular situation does not fit neatly into the above descriptions, please feel free to email me at art.reed@thesaxonteacher.com or call me at (580) 234-0064 (CST). If you email me, please include your telephone number and I will gladly call you at my expense.

HAVE A BLESSED - and - HAPPY NEW YEAR!