TWO TEXTBOOKS – FOUR YEARS
Most students who encounter difficulties in a Saxon Algebra 1 or Saxon Algebra 2 textbook do so because of one or both of two reasons. Either they are not properly prepared for the subject material from their previous math courses of instruction, or they are still weak in many aspects of these basics and unable to simultaneously handle both the algebra and the geometry contained in these textbooks â€“ or both!
Using the Saxon algebra one and algebra two textbooks as four separate math courses, or the concept of "lesser inclusive credit" is an idea recommended by the author in 1992, subsequently approved by the Oklahoma State Board of Education in 1992, and still used by some school districts in the states of Oklahoma, Arkansas, Missouri, New Mexico, and Colorado.
It is often difficult to determine which students will encounter difficulty in algebra one or algebra two regardless of their previous level of instruction or academic grade in that subject material. Negative circumstances beyond the control of educators often come into play in the middle of a school year or grading period that affect a students' performance in the course after they have apparently done well.
In my previous school district, we had two types of math students, one group "I will refer to the "fast trackers" took Saxon Pre-algebra in the seventh grade, Saxon Algebra 1 in the eighth grade, and Saxon Algebra 2 in their freshman year at the high school. The other group contained students who were enrolled in Saxon Algebra 1 their freshman year at the high school.
The concept of awarding "lesser inclusive credit" would hold true for either student if they encountered difficulty in either algebra one or algebra two their first time in that course at the high school level. Basically, all students are either enrolled in algebra one or algebra two their freshman year at the high school. When the high school algebra one student encounters difficulty in that course by having their test grades fall below an overall "C" average by the end of the first or even the second nine week period, their transcript should be changed to reflect pre-algebra, or introduction to algebra 1. They remain in the algebra one course and still attempt the material presented in the remainder of the algebra one text, but they are graded on a "lesser included grading scheme." (e.g. instead of 90, 80, 70, use 70. 60, 50, etc.). They repeat the same textbook course the next year. This time over ninety percent will be successful and their transcript then reflects a second HS level math course of algebra 1, advanced algebra 1, or algebra 1 (w/intro to geometry).
These students will now take any state mandated algebra test and will do well. An algebra 2 student who encounters the same difficulty, has introduction to algebra 2 entered on their transcript. They remain in the algebra two courses, and still attempt the material presented in the remainder of the algebra two texts, but they are also graded on a "lesser included grading scheme." (e.g. instead of 90, 80, 70, use 70, 60, 50, etc.). The following year they repeat the same course using the same textbook the second year and then algebra 2, or algebra 2 (w/geometry) is then entered on their transcript for the second course. Again, ninety percent or more do exceptionally well given the second opportunity.
Using this technique, my former high school not only raised math ACT scores from 13.4 to 22.2 (above the National Average) in a three-year period, but also doubled the number of HS students taking the ACT test. We increased the number of seniors in math classes above algebra two to more than ninety percent!
What makes the concept feasible is that the Saxon Algebra 1 and Saxon Algebra 2 textbooks are really tough, no-nonsense, cumulative textbooks. Adding to the positive side â€“ the Saxon Algebra 2 textbook easily meets the requirements to be designated as an Honors Course. And using this system, we have shown that any student, who truly masters the content of these two textbooks, in four years of high school, can successfully pass any college level algebra course at any university from MIT to Stanford! If they attend their classes on a regular basis!
The student is not given anything. The student who sits and does nothing in any of the classes receives his just reward as in any academic situation. In the nine years we had this program, I have never met a student or parent who, when the program was properly explained to them, did not look favorably upon the program as a second (or even a third) chance to honorably master both John Saxon's Algebra 1 and Algebra 2 textbooks.
Additionally, John Saxon's Algebra 2, 2nd or 3rd edition textbooks both qualify an Honors Courses because of the Geometry and Trigonometry included in the entirety of the textbook. While John Saxon's Algebra 1, 3rd Ed. textbook also contains some geometry, the geometry content is more at an introductory level and does not therefore warrant including the Algebra 1, 3rd Ed. textbook in the Honors Program.
Not all students respond to a specific situation alike. If you still have any questions about using this program, email me at firstname.lastname@example.org. Please also include your telephone number so that I can ask some questions â€“ if necessary â€“ that will enable me to make a more accurate recommendation for your child's success.
Have a Merry Christmas and a Blessed New Year!
THIS MONTH'S NEWS ARTICLE IS NOT ABOUT MATHEMATICS.
IT IS ABOUT A VETERAN OF WORLD WAR I - A DOUGHBOY - MY FATHER!
Each year on the 11th of November our country celebrates Veteran's Day. This is the day our nation has set aside to recognize military veterans of all branches of service for the sacrifices they have made throughout our country's history; Sacrifices that have ensured our continued freedom. This day of recognition in November of each year originated from the date of the signing of the armistice at the end of World War I. The armistice was signed in a railroad car in the forest near the French village of Compiegne. The document was signed exactly at the eleventh hour of the eleventh day in the eleventh month in the year 1918. There are no more living veterans of WWI, but if you know or meet a veteran of any armed conflict from World War II to the Korean or Vietnam Conflicts, or the Gulf, Iraq or Afghanistan conflicts, and you get the chance this coming Veteran's Day, shake their hand and thank them for their service - and tell them "Welcome Home!"
Private John William Reed, Infantryman
Company F, 358th Infantry
90th Infantry Division
(Wounded at St. Mihiel, France on September 12, 1918)
My father was twenty-two years old when he received his induction notice from the local draft board in Minneapolis, Minnesota on April 22, 1918 (Order # 651, Serial # 356, Division #4). He was ordered to report to the draft board one week later on April 29, 1918 for immediate induction into the United States Army. Immediately after his induction, he was shipped to Camp Davis, Texas for training and deployment with the 358th Infantry of the 90th Infantry Division. In less than two months, he would be on a troop ship headed overseas for the War in France. In less than five months from the day he was inducted, he would find himself in battle near the small French village of St. Mihiel.
The 90th Infantry Division was activated on August 25, 1917 at Camp Travis, Texas. It was nicknamed the "Alamo Division" and sometimes referred to by the enlisted men as the "Tough Ombres" (for Texas and Oklahoma). Initial members of the 90th Division came from Texas and Oklahoma; however, just before the division deployed to France in the summer of 1918, it received a large number of new recruits from other states like Minnesota. The division began its embarkation from Hoboken, New Jersey in early June of 1918, and by June 30th all of the units of the 90th Infantry Division had sailed from Hoboken. The division initially landed in England where, on July 4th, 1918, the 358th Infantry (including my father) paraded before the Lord Mayor of Liverpool. That evening, the entire 358th Infantry was hosted at a banquet given by the city of Liverpool, England.
The 358th Infantry arrived in France shortly thereafter and was stationed at Minot, France. In early September, the unit was moved about 192 km NE to a small village east of Paris in the northeast part of France. The name of the village was "Villers - en - Haye." It had a population then of only 96 people. In 2007, the population of "Villers - en - Haye" was still only 167).
Their first engagement with the German army came on September 12, 1918, at a town called St. Mihiel. The town was much larger than "Villers - en - Haye" having a population in 1918 of slightly more than 2000 residents. It was located 42 km from "Villers - en - Haye" on the edge of the Meuse River. The town had grown around a Benedictine abbey founded in 709 A.D. At the time of the battle, there were still several Abbey buildings in the town constructed in the 17th and 18th century. The town church had a door that dated back to Roman times. Both the church and the Abby buildings are still there today, undamaged by the fierce fighting that occurred there more than ninety-five years earlier. In 2008, the population of St. Mihiel had increased to 4,816.
The World War I battle that took place at St. Mihiel on September 12 - 14, 1918, was the first major American military offensive of the war. The campaign against the German fortifications at St. Mihiel involved 550,000 men of the U.S. First Army commanded by Gen. John J. "Black Jack" Pershing. The 90th Infantry Division (including the 358th Infantry Regiment) was part of that force.
The three-day campaign led by the U.S. First Army was successful. They forced the Germans to relinquish a military fortification held by the Germans since 1914. In those first three days of battle in mid-September of 1918, the 90th Infantry Division suffered a total of 37 officers and 1,042 enlisted men killed in action and another 266 officers and 8,022 enlisted men wounded and mustard gassed during the battle with the German units.
In just three days, the division had lost more than half of its men! Private John William Reed, Company F, 358th Infantry, was among those wounded and mustard gassed by the Germans that first day of battle, on September 12, 1918. Today, more than 4,150 American soldiers, killed in that September offensive, are buried in the American Military Cemetery at St. Mihiel.
Now for the "Rest of the Story . . . . . !"
More than half a century later, while I was stationed with the U.S. Army in Heidelberg, Germany, my wife and I were visiting the nearby town of Schwetzingen, Germany located several kilometers from Heidelberg. My wife wanted to visit the world famous historical doll maker Ilse Ludecke. While she visited with the doll maker, I practiced my German by conversing with Ilse's older sister. After I mentioned that my father had fought in France during World War I, she smiled and commented that I was too young to have a father who was in the First World War. "Mein Vater diente im Ersten Weltkrieg" - "My father served in the First World War," she said. "Sie sind gerade ein Baby. Sie sind zu jung, um einen Vater zu haben, der in diesem Krieg war." - "You are just a baby. You are too young to have a father who was in that war."
I then told her that my father had fought near Verdun at St. Mihiel, France in September of 1918 and that he was wounded and mustard gassed by the opposing German forces in that battle. She stared at me and momentarily looked somewhat confused, and then she excused herself and went upstairs, returning shortly clutching a scroll. She handed me the scroll and asked me to read it. As I unrolled the scroll and began reading it (mentally translating the German words into English), I could not believe what I was reading. It was a certificate addressed to Oberst (Colonel) Ludecke, Kommandant (Commander) of the 81st Chemical Brigade for a special mission against the American 90th Infantry Division in September of 1918. It was signed by Kaiser Wilhelm II, and dated in 1918.
Without thinking, I turned to her and said "Your father killed my father!" She turned pale and appeared weak-kneed. I quickly put my arm around her shoulders and, realizing the ramifications of what I had just blurted out, I said to her "But he knew enough to marry my mother who was German." I then told her that my mother's parents were born in the small town of Mohringen just on the outskirts of Stuttgart. She looked at me and laughed. "Sie sind nicht deutsch, Sie sind Swaibish" - "You are not German, you are Swaibish," she said. It should be noted that the "Swaibish" are well known throughout Europe as a hard headed (or bull headed) clan of Germans living in the Stuttgart area of Germany.
She said something to her sister Ilse and they laughed about the "Swaibish" revelation. Then the two of them invited my wife and me to accompany them upstairs to their home above the store. I learned later that day when speaking with one of the neighbors that Ilse Ludecke and her sister had never before invited Americans upstairs to their home. As we came up the stairway and entered the large living room, I noticed there were paintings of military officers lining the walls. Judging by the uniforms worn by each of the men in the paintings, most of them dated back before World War I. The older sister pointed to the painting of her father and grandfather as well as one of her great-grandfather telling me that all were once officers in the Prussian Army. She explained that when the American soldiers came through their town during WWII, she and her sister would take the military paintings down and hide them in the closet. When the American soldiers left, they would return the paintings to the wall.
Frau Ludecke walked over to a closet behind a beautiful ornate wood burning stove and returned with a small brown cardboard box. She opened the box and showed me a large piece of shrapnel from a WWI mustard gas shell. The shell fragment was about nine inches in length. She explained that her father did not want to be in the military, that he always wanted to be an artist.
He had brought home this painting he had made depicting a battle scene near Verdun. Painted on the side of this large piece of shrapnel was a scene from one of the small French villages that her father's unit had shelled. She explained that while the mustard gas had eventually killed my father from his wounds on the battlefield that day in France, her father also died of cancer just a few short years after returning from the war.
She believed her father's cancer had developed from him mixing the chemicals and handling the mustard gas mortar rounds just as sure as she believed those mustard gas shells that her father had fired upon the American soldiers during the St. Mihiel campaign had caused them to later die of cancer as well. We talked for awhile longer and as we left, Ilse's sister gave me a hug and whispered in my ear, "Ihr Vater machte eine kluge Wahl, welcher feiner Sohn, den er hat." - "Your father made a wise choice, what a fine son he has."
Two weeks later, my family and I left Germany for stateside, and several months later the handmade dolls my wife had ordered arrived at our home. I thought one of the doll boxes was a bit heavy for just the doll and after opening the box and removing the doll, I noticed a second small brown cardboard box at the bottom. Upon opening the box, I noticed the note on top. It read "Besser haben Sie das als wir" - "Better you have this than us." Inside was the piece of shrapnel she had showed me that day. It was the one her father had picked up on the battlefield and upon which he had painted a portrait of the French village he had shelled and where my father was wounded that September day in 1918. Here is a photo of that mustard gas shell fragment painted by Frau Ludecke's father:
I←------------------------------------ 8.5 inches ---------------------→I
Below is a photo of my father taken just after he was released from a military hospital in December of 1918. He was medically discharged from the U.S. Army in January of 1919. He spent the next several decades going from one VA hospital to another, courageously fighting against the debilitating effects of the cancer caused by the mustard gas. Dad died in my presence in 1945 - when I was 9 years old - at the Hines VA Hospital, located just outside Chicago in Hines, Illinois.
Private John William Reed, January 1919
I cannot believe it, but more than fifty years ago - while still on active duty and visiting a Junior High School somewhere in North Carolina and speaking to one of the classes about my experiences in Special Forces - I recall being asked by one young man "what was the most important thing about being successful as a Special Forces soldier?"
Without hesitating, I replied ATTITUDE! I went on to explain to the young men and women in that classroom why attitude was so important, recalling that I had mentioned several times that ATTITUDE had to always be one hundred percent of one's efforts in Special Forces. As I surveyed the room - while continuing to speak - I observed the young man who had asked that question had stopped paying attention.
The silence in the room - brought about by my having stopped talking - caused the young man to suddenly look up and in an excited gesture he wildly waved his arm. Just as I was just about to ask him why he had asked me the question then failed to pay attention, he shouted "Sir, you're right ATTITUDE does equal 100!"
The young man excitedly jumped up from his desk and, running up to where I was standing, showed me the piece of paper with his arithmetic clearly displayed. Having 26 letters in our alphabet, the young man had assigned a numerical value to each letter from A=1 to Z=26, then he had circled the letters in ATTITUDE as follows: A = 1,D = 4, E = 5, I = 9, T = 20, and U = 21. Then he had neatly added them up to reflect that he was correct ATTITUDE = 100!
I told this story every year to my new freshmen High School Math classes. Invariably there was always one freshman boy - who would ask why there were only 48 stars on the "FLAG" displayed in my room. (See NOTE: at the end of this paragraph) - I never was asked that question by any of the freshman girls. I always assumed they knew that we would eventually get to why the story and what it had to do with their algebra class.
NOTE: The term "Color" appropriately describes the flag of the United States trimmed on three sides with gold fringe. The material for the flag itself is usually silk since it is meant to be used indoors and in special ceremonies, which is why the command "Post the Colors" is used. So the question "Mr. Reed how come there are only 48 stars on your flag?" received the following response: "Young man, it is not referred to as a Flag but as a Color, and your mission is to find out why there are only 48 stars on it and report back to this class tomorrow."
Now, what has this all have to do with mathematics? Well, I would then go on to discuss that very question with the new incoming freshmen. I told them that I could not understand why parents would spend several hours outdoors to brave the cold, rain, and sometimes even snow - or - spend several hours each day in a hot sweaty gym to watch their sons and daughters practice sports - and then call me to tell me that these same outstanding young athletes kept complaining about spending an hour on their mathematics every evening.
You don't jump out of a perfectly good aircraft at 20,000 ft and wonder - as you're exiting that aircraft and plummeting earthward at over 200mph - if your parachute will open. Nor do you wonder just before you strike the ground that you will break an ankle or foot or knee in a poor landing. Nor do you upon entering a combat zone - and find yourself being shot at - wonder if you will come out of it alive.
These ATTITUDES are not acceptable any more than moaning and groaning about spending an hour doing math homework is. As parents and homeschool educators it is our responsibility to be cheerleaders for these future leaders within our society. If your student receives a minimum score of 80 on a Saxon math test they have mastered enough concepts to move on in the book. That score of 80 - on a weekly cumulative Saxon Math test - equates to an "A" in other non-Saxon math textbooks that utilize a review section before taking their periodic tests. Saxon's weekly cumulative tests determine what the student has mastered - as opposed to what he would have memorized from the review just before taking a test in the other math curriculums.
If you have not already read them, please take a few minutes and read the following news articles: March, April, May, July, August, and September of 2023. If you still have concerns or need a specific question or situation resolved, feel free to email me at the following email address: email@example.com. Please include your telephone number in case I need to call you to ask an important question or two to ensure a more accurate reply.
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 Â½, 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," replies the coach. "I've scheduled the next game with an elementary school."
I do not believe the answer is to find an easier math curriculum. I believe the answer is to find out why the students are encountering difficulty in the math curriculum they are currently using, and then find a viable solution to that situation. As John Saxon often said, algebra is not difficult; it is different!
Because every child is also different, I cannot offer a single solution that will apply to every child's situation, but before I present a general solution to Saxon users, please be aware that if you call my office and leave your telephone number or if you email me, I will discuss the specifics of your children's situation and hopefully be able to assist you. My office number is 580-234-0064 (CST) and my email address is firstname.lastname@example.org.
When Saxon students encounter difficulty in their current level math book before they reach lesson 30-40 or so, it is generally because one or more of the following conditions contributed to their current dilemma:
- 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.
- 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 Mastery of Math textbooks.
- 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.
- 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.
REASONS FOR STUDENT FRUSTRATION OR FAILURE WHEN USING JOHN SAXON'S MATH BOOKS - (PART 2)
In last month's news article we discussed the Essential Do's when using John Saxon's math books. This month we will go over the Essential Don'ts that will help Home School Educatorsensure a student's success when using John Saxon's math books.
Don't Skip the First 30 – 35 Lessons in the Book. Many home school parents still believe that because the first thirty or so lessons in every Saxon math book appear to be a review of material in the last part of the previous textbook, they can skip them. Let's review the two elements of automaticity. The two critical elements are: repetition – over time!
Yes, some of the early problems in the textbook appear similar to the problems found in the last part of the previous textbook. They have, however, been changed from the previous textbook to ensure that the student has mastered the concept. Remember, part of the concept of mastery involves leaving the material for a period of time and then returning to it. Students are supposed to have sixty to ninety days off in the summer to rest their thought processes. They need this review to reinstate that thought process! Additionally, while the first lessons in the books do contain some review, they also contain new material as well.
I would add you the same question I have asked thousands of classroom teachers and Home School Educators these past nine years. "Must students always have to do something they do not know how to do? Why can't they do something they already know how to do? What is wrong with building or reinforcing their confidence in mathematics through review?"
Don't Skip Textbooks. Skipping a book in Saxon is like tearing out the middle pages of your piano sheet music and then attempting to play the entire piece while still providing a meaningful musical presentation. In my book, under the specific textbook descriptions, I discuss any legitimate textbook elimination based upon specific abilities of the individual students. However, these recommendations vary from student to student depending upon their background and ability.
Don't Skip Lessons. Incremental Development literally means introducing complicated math concepts to the students in small increments, rather than having them tackle the entire concept all at once. It is essential that students do a lesson a day and take a test every four to five lessons, depending on what book they are using. So what happens when you skip an easy lesson or two? Very simply, the student cannot process the new material satisfactorily without having had a chance to read about it, and to understand its characteristics. Some students attempt to fix this shortcoming by then working on several lessons in a single day, to catch up to where they should be in the book. This technique is also not recommended.
As I have told my classroom students on numerous occasions, "The only way to eat an elephant is one bite at a time."
Don't Skip Problems in the Daily Assignments. When students complain that the daily workload of thirty problems is too much, it is generally the result of one of the following conditions:
Don't Let Students use the Solutions Manual to do their Daily Assignments.
- Students are so involved in a multitude of activities that they cannot spend the thirty minutes to an hour each day required for Saxon mathematics.
- Students are at a level above their capabilities and unable to adequately process the required concepts in the allotted time because of this difficulty.
- The student is either a dawdler or just lazy!
- Doing just the odd or just the even numbered problems in a Saxon math book is not the solution to those difficulties. As I mention in one of the early chapters in my book, there are two of each type of problem for several reasons – and doing just the odd or even is not one of those reasons!
Why not? When I attended Homeschool Conferences, I often spoke at seminars and one of the analogies I would use is that of the honey bee. If you cut the bee out of the beeswax cell – to save it the struggle it must take to remove itself and speed its departure from the hive – the bee will not be able to fly because while struggling to get through the beeswax, it strengthens itself – and – in making it "easier" by removing the beeswax, you took away that advantage. The same goes with a math student who follows along every day with what someone else has laid out as the solution to every problem in their daily assignment. That encourages memorizing – it does not foster mastery.
Don't Grade the Student's Daily Work.
In all the years I taught John Saxon's math at the high school, I never graded a single homework paper. I did monitor the student's daily work to ensure it was done and I would speak with students whose test grades were falling below the acceptable minimum of eighty percent. I can assure you that having the student do every problem over – that he failed to do on his daily assignments – does not have anywhere near the benefit of going over the problems missed on the weekly tests because the weekly tests reveal mastery – or lack thereof – while the daily homework only reveals their daily memory! If you have not already read the September 2021 news article, please do so as it goes into more detail about why there is no need to grade the daily work.
While my book goes into more detail, I believe these few simple rules about what TO DO
and what NOT TO DO
to ensure success when using John's math books will benefit classroom math teachers as well as home school educators who use, or are contemplating using, Saxon Math books – from Math 54 through John's Calculus and Physics textbooks.
So long as you use the books and editions I referenced in my book, and later re-iterated in my September 2021 news article
, you will find that Saxon math books remain the best math books on the market today – if used correctly! Those referenced books and editions will be good for your child's math education – from fourth grade through their senior year in high school – for several more decades – or longer! And the proper use of them will more than adequately prepare that same math student for any of the current state or federal "Common Core"
Email: email@example.com Telephone:
"Do not worry about your difficulties in mathematics; I can assure you that mine are far greater."
REASONS FOR STUDENT FRUSTRATION OR FAILURE WHEN USING JOHN SAXON'S MATH BOOKS - (PART 1)
The unique incremental development process used in John Saxon's math textbooks - coupled with the cumulative nature of the daily work - make them excellent textbooks for use in either a classroom or home school environment. If the textbooks are not used correctly, however, they will eventually present problems for the students.
Some years ago, I was asked to help a school district in the Midwest recover from falling test scores and an increased failure rate in their middle and high school math programs. The teachers in the district had been using - actually misusing - their Saxon math books for several years. After I had a chance to tell the group of school administrators and teachers some of the reasons for their difficulties, the district superintendent commented. "What I hear you saying Art, is that we bought a new car, and since we already knew how to drive, we saw no reason to read the owner's manual – wouldn't you agree?" To which I replied, "It's worse than that, sir! You all thought you had purchased a car with an automatic transmission, but Saxon is a stick shift! It is critical that certain procedures be followed - just as well as some should be dropped - or you will strip the gears!"
The uniqueness of John Saxon's method of incremental development, coupled with the cumulative nature of the daily work in every Saxon math textbook, requires a few specific rules be followed to reduce failure and frustration and to ensure success – and ultimately mastery! If properly used at the correct levels, students will not have any trouble with what has been recently introduced into the educational system as "Common Core" requirements.
In the next several news articles, we will discuss the ESSENTIAL DO'S and DON'T'S when using John Saxon's math books.
This month I will discuss the ESSENTIAL DO'S that should be followed when using John Saxon's math books.
Do Place the Student in the Correct Level Math Book. Probably the vast majority of families who dislike John Saxon's math books do so because the student is using a math book above his or her capability. Since all of John's math books were written at the appropriate reading level of the student (or a grade level below), the problem is not one of students not being able to read the material presented to them, but their not being able to comprehend the math concepts being presented to them. This frustration is then interpreted as being created by the book and not by incorrect placement of the student.
Do Always Use the Correct Edition. Using the wrong edition of a Saxon math book can quickly lead to insurmountable problems. For example, moving from the first or second edition of Math 76 to the second or third edition of Math 87, or the third edition of Algebra Â½ would be like moving from Math 65 to Algebra Â½ in the current editions. For more information on which editions of John's books are still valid, read the earlier published April 2022 Newsletter, or read pages 15 – 18 in my book.
Do Finish The Entire Book. Finishing the entire textbook is critical to success in the next level book. I know, parents and teachers often ask me, "Why finish the last twenty or so lessons when much of that same material is presented in the first thirty or so lessons of the next level textbook?" While the first twenty or so lessons of the next level Saxon book may appear to cover the same concepts as the last thirty or so lessons in the previous book, the new textbook presents the review concepts in different and more challenging ways. Additionally, there are new concepts mixed in with them. The review is used to enable a review of necessary concepts while building the student's confidence back up after a few months off during the summer. Then comes the argument from some home school educators, "But we do not take any break between books – we go year round, so the review is not necessary."
My only reply to that is "Why must students always do something they do not know how to do? Can't they sometimes just review to build their confidence and mastery by doing something they already know how to do? If they are continuing year round, and already know how to do some of the early concepts in the next textbook, then it won't take them long to do their daily assignment. I once had a public school superintendant ask me "Which is more important, mastery or completing the book?" To which I replied, "They are synonymous."
Do All of the Problems - Every Day. There is a reason the problems come in pairs, and it is not so the student can do just the odd or even problems. The two problems are different from each other to keep the student from memorizing the procedure, as opposed to mastering the concept. Students who cannot complete the thirty problems each day in about an hour are either dawdling, or are at a level of mathematics above their capabilities, based upon their previous math experiences.
Do Follow the Order of the Lessons. I am often asked by parents at workshops and in email "Why study both lessons seventeen and eighteen? After all, they both cover the same concept?" Why not just skip lesson eighteen and go straight to lesson nineteen?" Why do both lessons? Well, because the author took an extremely difficult math concept and separated it into two different lessons. This allowed the student to more readily comprehend the entire concept, a concept which will be presented again in a more challenging way later in lesson twenty-seven of that book!
Do Give All of the Scheduled Tests – On Time. In every test booklet, in front of the printed Test 1 is a schedule for the required tests. Not testing is not an option! I have often heard home school parents say, "He does so well on his daily work; why test him?" To which I reply, "The results of the daily work reflect memory – the results of the weekly tests reflect mastery!" The results of the last five tests in every book give an indication of whether or not the student is prepared for the next level math book. Scores of eighty or better on any test reflect minimal mastery achieved. Scores of eighty or better on the last five tests in the series tell you the student is prepared to advance to the next level.
In next month's news article, I will discuss the ESSENTIAL DON'T'S to follow when using John Saxon's math books.
Email: firstname.lastname@example.org Telephone: 580-234-0064 (CST)
"Do not worry about your difficulties in mathematics; I can assure you that mine are far greater."
WHICH SAXON HIGH SCHOOL MATH COURSES CAN BE TRANSCRIPTED AS HONORS COURSES?
Several years ago – I believe in March of 2021 – I wrote an article about how to transcribe your student's courses in Algebra 2 and the Advanced Math book as well. I did not include the Algebra one textbook because I thought it did not quite meet the standards for describing an Honors Course – although it still is an excellent algebra textbook.
I am going to retransmit that article because I did not include it in my book and I felt that the readers needed to be reminded as they prepared their student's transcripts for them attending college this fall.
Almost two decades ago – when I wrote the book on how to use John Saxon's Math books – I did not include a chapter on honors courses because I mistakenly thought that by then everyone knew about them. My apologies, but the subject should have been included in the book. Since it was not, I thought I would publish the subject in the monthly news articles and make it available for homeschool educators to print a copy as an addendum to the book. (Click Here for a printable copy)
I would like to say that all of John Saxon's Math Books are honors courses. The contents of John's math books are no-nonsense, straightforward, rigorous, challenging, and conceptually sound. These outstanding math books enable mastery of the concepts, not just memorization; however – I would be stretching the accepted definition of honors courses. Generally, the title of honors course when applied to math classes is reserved for the higher-level math courses that cover more material and are therefore more rigorous and challenging than regular courses.
Yes, the term "honors course" can be applied to non-math courses as well; however, in this article, I will restrict use of the term to just mathematics courses – and more specifically – to John Saxon's math courses.
Unless your State Board of Education has created its own standards regarding who can certify an honors curricula, the classroom mathematics teacher can authorize an honors course. There are no official rules or standards that list what defines an honors course. However; the term is generally applied to high school courses considered to be more rigorous and therefore more academically challenging. With some exceptions, a student must acquire the classroom teacher's approval to enroll in an honors course along with an overall grade average of a B or higher in prerequisite math courses.
I am a qualified State certified secondary mathematics teacher with more than twelve years' experience teaching high school mathematics while using John Saxon's math books from algebra through calculus.
There is no doubt in my mind that the courses in John Saxon's high school math curriculum that qualify for honors courses are the Saxon Algebra 2 (only the 2nd or 3rd Ed), Saxon Advanced Mathematics (2nd Ed. – whether taught in a single year or in three or four semesters) and the Saxon Calculus textbook (1st or 2nd Ed). Let me briefly state why each of these qualify for the title of "Honors Course."
Algebra 2, 2nd or 3rd. Why not the new 4th Edition? In my opinion, the new fourth edition of this book will not allow the student to satisfactorily enter the Advanced Math textbook – nor would it qualify for the title of "Honors Course." This new edition was not created by John Saxon. It was created by a publishing company that stripped all references to geometry from the fourth edition textbook. You can read more detail about the potential problems with using this non-Saxon edition in my Nov 2019 News Article. The challenges and rigorous nature of John Saxon's Algebra 2, 2nd or 3rd Ed. textbook have been reduced to a standard high school algebra 2 textbook in this new non-Saxon 4th Ed. version.
Now, what is it that makes the 2nd or 3rd editions of John's Algebra 2 textbook qualify as an honors course? When using the 2nd or 3rd Ed. of John's Algebra 2 textbook, students have 30 problems to tackle every day through all 129 lessons as well as a weekly test to determine their mastery of the material. Unlike a regular algebra 2 course, students must not only master the daily menu of some very rigorous algebra 2 concepts, but they must also master the rigorous geometry concepts found in the first semester of a high school geometry course – plus the introduction of trigonometric functions midway in the book as well.
It is acceptable to use Algebra 2 w/Geom (1 credit) on the student's HS transcript and in an appropriate place indicate honors credit for that course. Don't forget when a student takes an honors course, the GPA is scored differently: An A is worth 5 pts, a B is worth 4 pts, a C is worth 3 pts, and a D is 2 points, The grade of F is still 0.
I recall at a homeschool convention several years ago, a homeschool parent told me that she was told by a homeschool friend you could not award a semester of HS geometry because there were no two-column proofs in the Saxon Algebra 2 (2nd or 3rd Ed) textbooks. My reply was "Your friend did not finish the book, he probably stopped at lesson 122 ("Venn Diagrams"), because there are more than 15 rigorous two-column proofs in the six lessons between lesson 123 and 129 (the end of the book).
As I promised my students and their parents – and I will promise you – if students get no further than successful mastery of the Saxon Algebra 2 textbook (2nd or 3rd Ed) when they graduate from high school, they will be able to pass any freshman college algebra course from MIT to Stanford – provided they attend class every day, pay attention, complete assignments, and do not sleep in class. Oh, and – one more minor requirement – show up on test days!
Advanced Mathematics, 2nd Ed: John designed this course to be taken in three, or four semesters. I taught the textbook as a four semester (2 year) course. If you would go to this link on my website, you can watch a short seven minute video on why and how you transcript the course:https://usingsaxon.com/flvplayer.html
Unless textbooks have drastically changed in the field of collegiate freshman mathematics, this textbook is tougher than any collegiate freshman algebra textbook I have seen or previewed. Students who complete the entirety of the textbook and successfully master the material presented will score in the 90th – or higher – percentile on either the ACT or SAT math score. As described in the referenced video, both of the course titles described in the four semester use of the book definitely qualify as honors courses.
Calculus (1st or 2nd Ed.): Either calculus textbook would qualify as an honors course in a high school environment. And, while successful completion of all 117 lessons of the older 1st edition textbook prepares students for the AB portion of the College Board's Advanced Placement (AP) program for calculus, I recommend you use the newer 2nd edition. That edition prepares students for both the AB (through lesson 102) – and the BC (all 148 lessons) portions of the College Board's Advanced Placement (AP) program for calculus. The 2nd Ed. Of John's Calculus textbook contains 31 more lessons than the older 1st Ed.
Lastly, the new 2nd Ed. Of John's Calculus textbook has the added feature of the lesson reference numbers which appear in parenthesis under each problem number as used earlier in the third editions of Saxon's Algebra 1 and Algebra 2 textbooks. They direct students to the lesson that introduced the concept of that problem they may need to revisit. It saves the student wasted hours of valuable time trying to find the lesson that introduced the concept without knowing the correct terminology of what it is they are looking for.
HOW TO SUCCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 THROUGH CALCULUS
Here is the final article in the three part series describing situations I have encountered these past three decades while teaching Saxon in a rural high school as well as providing curriculum advice to homeschool educators for John Saxon. As with the previous two parts of the series, I have added my thoughts about why you want to avoid them:
- ATTEMPTING THE ADVANCED MATHEMATICS TEXTBOOK IN A SINGLE YEAR: Since there are only 125 lessons in the textbook, it seems reasonable to assume this is possible.
RATIONALE: "My son had absolutely no trouble in the Algebra 2 book and I believe he will have no trouble in this book either. The book has fewer lessons than the Agebra 2 book has. Besides, he is a junior this year and we want him to be in calculus before he graduates from high school."
FACTS:The second edition of John Saxon's advanced mathematics textbook is tougher than any college algebra textbook I have ever encountered. The daily assignments in this book are not impossible, but they are time consuming and can take most math students more than several hours each evening to complete the thirty problems. This generally results in students doing just doing the odd or even numbered problems to get through the lessons. I must have said this a thousand times "Calculus is easy; students fail calculus because they do not understand the algebra." Speeding through the advanced mathematics textbook by taking shortcuts does not allow the student the ability to master the advanced concepts of algebra and trigonometry to be successful in calculus. And if the only argument is that the student will not take calculus in high school, then what is the rush?
The DVD tutorial series for the second edition of John's Advanced Mathematics book that I have prepared allows students three different choices based upon their needs and capabilities.
- They can follow my advice and take the course in two years (doing a lesson every two days). Thereby gaining credit for the first academic year of "Geometry w/Advanced Algebra," with a first semester credit for Trigonometry and a second semester credit for Pre-calculus in their second academic year.
- Or -
- They can take the course in three semesters. Their first semester credit would be titled Geometry, followed by a second semester credit for Trigonometry w/Advanced Algebra; ending with a third semester credit for Pre-calculus.
- Or -
- While not recommended — they can take the entire 125 lessons in the Advanced Mathematics book in a single school year gaining credit for a full year of Geometry along with a semester credit for Trigonometry w/Advanced Algebra. In all the years that I taught the subject, I only had one student complete the entire Advanced Math course of 125 lessons in a single school year – with a test average above ninety percent - and she was a National Merit Scholar whose father taught mathematics with me at the local university.
The specific details of how the transcript is recorded are covered in my book, but if you have any questions regarding your son or daughter's high school transcript, please feel free to send me an email (Include your phone number as I may need to ask you some questions to ensure an accurate recommendation).
- IS IT CRITICAL FOR STUDENTS TO TAKE CALCULUS IN HIGH SCHOOL? Students lacking a solid base in algebra and a basic knowledge of trigonometry will find taking calculus at any level difficult, if not impossible.
RATIONALE: "I want our son to take calculus his senior year in high school. The only way we can accomplish that is to have him speed through the Saxon Algebra 2 and Advanced Mathematics book to finish them by the end of his junior year. He may even have to use the summer months for math as well."
FACTS: Even if students successfully complete a calculus course their senior year in high school, whether at home or at a local community college, I would strongly recommend that they enroll in "Calc I" as a freshman at the university or college they choose to attend for several reasons.
First: If they truly understand enough of their calculus I course (usually encompassing derivatives) they can enjoy a solid five hours of "A" on their transcript for their first five hours of math as a freshman. They can also make some nice extra money tutoring their less fortunate classmates.
Second: While they think they understand everything there is about calculus, they will see much more as they sit back and "understand" what the professor is talking about. They might even learn something they never fathomed in the high school textbook they went through.
Third: Their solid "A" the first semester in a calculus I class lets the professors know what kind of student they are. That perception by the professor makes a big difference should they encounter difficulties later in their second semester of calculus II (usually through integrals). Finishing John Saxon's second edition of Advanced Mathematics at a pace that allows the student to grasp all of the material in that textbook, without being frustrated or discouraged, is paramount to their success in calculus at the university or college level.
- DO HIGH SCHOOL STUDENTS NEED A SEPARATE GEOMETRY TEXTBOOK? To reflect that a student has received a well-rounded math background, states that require three or more math courses require that geometry be recorded on a student's high school transcript, along with algebra 1, algebra 2, trigonometry, etc.
RATIONALE: "It is too difficult for high school students to learn both algebra and geometry at the same time." My son did just fine in the Saxon Algebra 1 textbook. However, he is only on lesson 35 in the Saxon Algebra 2 book, and he is already struggling." - or - their rationale is – "I have been told by other home school parents that there are no two-column proofs in John Saxon's Algebra 2 textbook."
FACTS: Many of my top students' worst test in the Saxon Algebra 2 course was their very first test. This happened because they did not realize the book covered so much geometry review from the algebra 1 text, as well as several key new concepts taught early in the Algebra 2 text. They quickly recovered and went on to master both the algebra and the geometry concepts. From my experiences, most students who encountered difficulty early in John Saxon's Algebra 2 textbook did so - not because they did not understand the geometry being introduced - but because their previous experiences with the Saxon Algebra 1 course did not result in mastery of the math concepts necessary to handle the more complicated algebra concepts introduced early in the Algebra 2 textbook. I would not recommend students attempt John Saxon's Algebra 2 math book if they have done any one or more of the following:
- Never finished all of the lessons in the Saxon Algebra 1 textbook.
- Hurried through the Saxon Algebra 1 textbook doing two lessons a day and then only did the odd or even numbered problems from each lesson.
- Received multiple test scores of less than seventy-five on their last four or five tests in the Algebra 1 textbook (Not counting partial credit).
What about the students who never took the tests, because parents used the students' daily homework grades to determine their grade average? What does that reveal about the students' ability? Establishing a students' grade average based upon their daily work reflects what they have "memorized." The weekly tests determine what they have "mastered."
The successful completion of John Saxon's Algebra 2 textbook (2nd or 3rd Editions) gives students an additional equivalent of the first semester of a high school geometry course (including two-column proofs). Successful completion of the first sixty lessons of the Saxon Advanced Mathematics textbook (2nd Ed) ensures they receive the equivalent of the second semester of high school geometry, in addition to the advanced algebra and trigonometry concepts they also receive in the latter half of the book.
But what about the lack of two-column proofs in the Saxon Algebra 2 book (2nd or 3rd Ed)? Whenever I hear Homeschool Educators make the comment that "John Saxon's Algebra 2 book does not have any two-column proofs," I immediately know they stopped before reaching lesson 124 of the book which is where two-column proofs are introduced. The last six lessons of the Saxon Algebra 2 textbook (2nd or 3rd editions) contain thirty-one different problems dealing with two-column proofs. The following year, in the first half of the Advanced Mathematics textbook, they not only encounter some heavy duty algebra concepts, but they will also complete the equivalent of the second semester of a regular high school geometry course. The first thirty of these sixty lessons contain more than forty different problems dealing with two-column proofs.
So why then did John Saxon not want to publish a separate geometry textbook? As I mentioned in my April newsletter earlier this year, a group of professors who taught mathematics and science at the University of Chicago bemoaned the fact that educators continued to place a geometry course between basic algebra (Algebra 1) and the advanced algebra course (Algebra 2) to the detriment of the student. AND THEY WROTE THIS 108 YEARS AGO!
In the preface to their book titled "Geometric Exercises for Algebraic Solution," published in 1907, the professors explained that it is this lengthy "void" between the two algebra courses that prevents students from retaining the necessary basic algebra concepts learned in basic algebra (algebra 1) to be successful when encountering the rigors of advanced algebra (algebra 2).
Then apparently aware of this situation, and knowing John Saxon's position on the subject, why did HMHCO (the current owners of John's books) go ahead and create and publish the new fourth editions of Saxon Algebra 1, Algebra 2, and a separate first edition Saxon Geometry textbook? I do not know why they did, but I do know that three textbooks will make more money for a publisher than two textbooks will. I also know that the new books – while initially sold only to the schools on the company's school website, are now offered to Homeschool Educators as well. Having to decide between the two different editions of algebra makes the selection process more confusing; however, I would not recommend any student go from the fourth edition of Saxon Algebra 2 to John Saxon's Advanced Mathematics textbook.
If you stick with the editions of John Saxon's math books that I listed in my April 2022 Newsletter, you will have the best math books on the market today – good for several more decades to come.
As I mentioned last month, there will always be exceptions that justify the rule. However, just because one parent tells you their child did any one or all of the above, and had no trouble with the Advanced Math course does not mean you should also attempt it with your child. Those parents might not have told you that one or more of the following occurred.
- Their children encountered extreme difficulty when they reached Saxon Algebra 2, and even more difficulty and frustration or even failure with the Saxon Advanced Mathematics or Calculus courses.
- They had switched curriculum after experiencing difficulty in Saxon Algebra 1.
- Their son or daughter had to take remedial (no credit) college algebra because that received low scores on the universities mathematics entrance exam.
For those readers who do not have a copy of my book, please don't forget to take a minute and read that April 2022 news article for information that will help you select the correct level and edition of John Saxon's math books. As I said earlier, these editions will remain excellent math textbooks for many more decades.
If your child is already experiencing difficulty in one of the Saxon series math books, and you need to find a workable solution, please email me at: email@example.com (Don't forget to include your telephone number as I may some questions generated by your comments). Or feel free to call me at my office using (580) 234-0064 (CST).
HAVE A GREAT SUMMER – HOWEVER, IF YOU DO SCHOOL WORK THROUGH THE SUMMER – MAKE SURE YOU GIVE STUDENTS AT LEAST A MONTH OFF BEFORE STARTING INTO THE FALL SEMESTER TO RELAX AND GIVE THEIR BRAIN A REST!
HOW TO SUCCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 THROUGH CALCULUS
As I promised last month here are several more of the common misuses I have encountered during the past three decades of teaching and providing curriculum advice to homeschool educators. I have added my thoughts about why you want to avoid them:
1) THE EFFECTS OF DOING JUST THE ODD OR EVEN PROBLEMS: Allowing the student to do just the odd or even problems in each daily lesson may appear to save time, but it creates a false sense of mastery of the concepts.
RATIONALE: "Each lesson shows two of each of the different problems, and it saves us valuable time by doing just one of the pair. Besides, since they both cover the same concept, why take the extra time doing both of them?"
FACT: The reason there are pairs of each of the fifteen or so concepts found in the daily assignments is because each of the problems in each pair is different from the other. While both problems in each pair address the same concept, they are different in their approach to presenting that concept. One goes about presenting the concept one way while the second one approaches the concept from a totally different perspective. Doing both of them gives the student a broader basis for understanding the concept and prevents the student from memorizing a particular procedure rather than mastering the concept based upon solving the two different formats or procedures.
Whenever I receive an email from a homeschool educator or student, and they need help with solving a particular
problem on one of the tests remarking that they never saw this test question in any of their daily work, I can tell that
they have been doing either the "odds" or the "evens" in their daily work because this test question resembled an
approach to the concept that was contained in the set they never did. Additionally, doing only half of the daily
assignment restricts the student's ability to more quickly and easily master the concepts. Doing two a day for
fourteen days increases the student's ability to more quickly master those concepts than doing just one a day for
that same period of time.
The "A" or "B" student who has mastered the material should take no more than fifty minutes to complete
the daily assignment of thirty problems if their grade is based upon their weekly test scores and not upon
their daily homework. The "C" student should complete the daily assignment of thirty problems in about
ninety minutes. The additional time above the normal fifty minutes is usually the result of the "C" student
having to look up formulas or concepts that might not have yet been mastered. This is why I recommend
using "formula cards."
Use of the formula cards saves students many hours of time flipping through the book looking for a formula
to make sure they have it correctly recorded. The details on how to implement using these cards is explained
in detail on page 94 of my book. If you have not yet acquired that book, you can find information on how to
make and use them in my February 2022 Newsletter.
2) THE EFFECTS OF DOING MORE THAN ONE LESSON A DAY: Permitting the students to do two or three lessons a day believing this will allow them to complete the course faster.
RATIONALE: "My son wants to finish the Saxon Calculus course by the end of his junior year. The only way he can do that is to finish the Algebra 2 book in six rather than nine months. Besides, he told me that he already knows how to do most of the material from the previous Algebra 1 book."
FACT: To those who feel it necessary to "speed" through a Saxon math book, I would use the analogy of eating one's daily meals. Why not just eat once or twice a week to save time preparing and eating three meals each day? Not to mention the time saved doing all those dishes. The best way I know to answer both of these questions is to remind the reader that our bodies will not allow us to implement such a time saving methodology any more than our brains will allow us to absorb the new math concepts by doing multiple lessons at one sitting.
I have heard just about every reason to support doing multiple lessons, skipping tests to allow another lesson to be taken, or taking a lesson on a test day. All of these processes were attempted solely to speed up completing the textbook. Students who failed calculus did so, not because they did not understand the language and concepts of calculus, but because they did not sufficiently master the algebra.
Why must students always be doing something they do not know? What is wrong with students doing something they are familiar with to allow mastery as well as confidence to take over? Why should they become frustrated with their current material because they "rushed" through the previous prerequisite math course?
The two components of "automaticity" are time and repetition and violating either one of them in an attempt to speed through the textbook (any math book) results in frustration or failure as the student progresses through the higher levels of mathematics. I recall my college calculus professor filling the blackboard with a calculus problem and at the end, he struck the board with the chalk, turned and said "And the rest is just algebra." To the dismay of the vast majority of students in the classroom - that was the part they did not understand and could not perform. When I took calculus in college, more than half of my class dropped out of their first semester of calculus within weeks of starting the course, because their algebra backgrounds were weak.
3) ENTERING THE SAXON MATH CURRICULUM AFTER MATH 76: Switching to Saxon Algebra 1 or Algebra 2 because you have found the curriculum you were previously using was not preparing your child for the ACT or SAT and you wanted them to be more challenged.
RATIONALE: "We were having trouble with math because the curriculum we were using, while excellent in the
lower grades, did not adequately prepare our son and daughter for the more advanced math concepts. We
needed a stronger more challenging math curriculum, so we switched to Saxon algebra 1."
FACT: Switching math curriculums is always a dangerous process because each math curriculum attempts to
bring different math concepts into their curriculum at different levels. Constantly moving from one math
curriculum to another - looking for the perfect math book - creates "mathematical holes" in the students' math
background. It also creates a higher level of frustration for these students because, rather than concentrating on
learning the mathematics, they must concentrate on what the new textbook's system of presentation is and
spend valuable time trying to analyze the new format, method of presentation, test schedule, etc.
If you intend to use Saxon in the middle and upper level math courses because of its excellence at
these levels of mathematics, I would strongly recommend that you start with the Math 76, 3rd or 4th Ed textbook.
The cumulative nature of the Saxon Math textbooks requires a solid background in the basics of fractions,
decimals and percentages. All of these basics, together with the necessary prerequisites for success in pre-
algebra or algebra 1 are covered in Saxon's Math 76, 3rd or 4th Edition textbook. This math textbook is what I
refer to as the "HINGE TEXTBOOK" in the Saxon math curriculum.
Successful completion of this book will take
care of any "Math Holes" that might have developed from the math curriculum you were using in grades K – 5.
Successful completion of this book can allow the student to move successfully to the Saxon algebra ½ textbook
(a pre-algebra course). Should students encounter difficulty in the latter part of the Math 76 text, they can move
to the Saxon Math 87, 2nd or 3rd Ed and, upon successful completion of that book, move either to the Algebra ½
or the Algebra 1 course depending on how strong their last 4 or 5 test scores were. Yes, some students have
been successful entering the Saxon curriculum at either the Algebra 1 or the Algebra 2 levels, but the number of
failures because of weak math backgrounds from using other curriculums, roughly exceeds the number of
successes by hundreds!
As I mentioned last month, there will always be exceptions that justify the rule. However, just because one
parent tells you their child did any one or all of the above, and had no trouble with their advanced math course,
does not mean you should also attempt it with your child. That parent might not have told you that:
- Their child encountered extreme difficulty when they reached Saxon Algebra 2, and even more difficulty and frustration or failure with the Saxon Advanced Mathematics course, or –
- They had switched curriculum after experiencing difficulty in Saxon Algebra 1, or –
- Their child had to take remedial college algebra when they enrolled at a university, because they had received a low score on the university's math entrance exam.
For those readers who do not have a copy of my book, please read my April 2022 news article for information that will help you select the correct level and edition of John Saxon's math books. These editions will remain excellent math textbooks for many more decades.
If your child is already experiencing difficulty in one of the Saxon series math books from Math 76 to Advanced Mathematics, and you need to find a workable solution, please email me at: firstname.lastname@example.org. Include your telephone number as it helps provide a quicker solution to your dilemma.
In next month's issue, I will cover:
- ATTEMPTING THE ADVANCED MATH TEXTBOOK IN A SINGLE YEAR:
- IS IT CRITICAL FOR STUDENTS TO TAKE CALCULUS IN HIGH SCHOOL?
- DO HIGH SCHOOL STUDENTS NEED A SEPARATE GEOMETRY TEXTBOOK?
HOW TO SUCCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 THROUGH CALCULUS AND PHYSICS (Part 1)
Both homeschool educators as well as public and private school administrators often ask me "Why do John Saxon's math books require special handling? Another question I am also frequently asked is "If John Saxon's math books require special instructions to use them successfully, why would we want to use them"? Before the end of this newsletter, I hope to be able to answer both of these questions to your satisfaction.
There is nothing "magic" about John Saxon's math books. They were published as a series of math textbooks to be taken sequentially. Math 54 followed by Math 65, and then Math 76, followed by either Math 87 or Algebra ½, and then algebra 1, etc. While other publishers were "dumbing-down" the content of their new math books, John Saxon was publishing his new editions with stronger, more challenging content. Homeschool families, attempting to save money by buying older used Saxon Math books and inter-mingling them with the newer editions were unaware that the older out-of-print editions were often incompatible with these newer, more challenging editions. The same problem developed in the public and private school sector adding to the confusion about the difficulty of John's math books.
For example, a student using the old first or second edition of Math 76 would experience difficulty entering the newer second or third editions of Math 87 because the content in the outdated first or second editions of Math 76 was about the same as that of the material covered in the newer editions of Math 65 (the book following Math 54 and preceding Math 76). Jumping from the outdated older edition of Math 76 to the newer editions of either Math 87 or Algebra ½ would ultimately result in frustration or even failure for most, if not all, of the students who attempted this.
Many homeschool educators and administrators were also unaware that – when finishing a Saxon math book, they were not to use the Saxon placement test to determine the student's next book in the Saxon series. The Saxon placement test was designed to assist in initially placing non-Saxon math students into the correct entry level Saxon math book. The test was not designed to show parents what the student already knew, it was designed to find out what the student did not know. Students taking the placement test, who are already using a Saxon math book, receive unusually high "false" placement test scores. These test results may erroneously recommend a book one or even two levels higher than the level book being used by the student (e.g. from their current Math 65 textbook to the Math 87 textbook – skipping the Math 76 textbook).
By far, the problems homeschool educators as well as classroom teachers encounter using – or shall I say misusing – John's math books are not all that difficult to correct. However, when these "short-cuts" are taken, the resulting repercussions are not at first easily noticed. Later in the course, when the student begins to encounter difficulty with their daily assignments – in any level of Saxon math books, the parent or teacher assumes the student is unable to handle the work and determines that the student is not learning because the book is too difficult for the student.
Here are some of the most common misuses I have encountered literally hundreds of times during these past several decades of teaching and providing curriculum advice to home school educators:
- NOT FINISHING THE ENTIRETY OF THE TEXTBOOK: Not requiring the student to finish the entirety of one book before moving on to the next book in the sequence.
RATIONALE: "But the beginning twenty or so lessons of the new book covers the same material as in the last lessons of the book we just finished, so why repeat it"?
FACT: The student does encounter review of this material in the next book. However, because the student has not done sufficient work on these concepts in the previous book to "master" them in the short time left in the school year, their review in the new book is essential to later success in the new book. Skipping the last twenty or so lessons in the previous level textbook means the students are encountering these concepts for the first time. This does not initially appear to create a problem until the student gets to about lesson thirty or so in the book, and by then both the parent and the student have gotten so far into the new book that they do not attribute the student's problem to be the result of not finishing the previous textbook. They start to think the material is too difficult to process correctly and do not see the error of their having skipped the last twenty to thirty or so lessons in the previous book. They now fault the excessive difficulty of the current textbook as the reason the student is failing.
Always finish the entirety of every Saxon math textbook! Because all students are not alike, if as you're reading this article you have already encountered this particular phenomenon with your child, there are several steps you can take to satisfactorily solve the problem without harming the child's progress or self-esteem. So that we can find the correct solution, please email me – and include your telephone number – and I will call you with a solution for your child's particular situation that same day.
- MISUSE OF THE SAXON PLACEMENT TEST: Skipping one of the books in the sequence (e.g. going from Math 54 to Math 76) because the "Saxon Placement Test" results clearly showed the student could easily handle the Math 76 material.
RATIONALE: "He even got some of the Math 87 level questions correct. Besides, we had him look at the material in the Math 65 book and he said that he already knew that material, so why bother doing the same concepts again."
FACT: First, as I wrote earlier, the Saxon Placement Test was designed to place non-Saxon math students into the correct level math book. It was designed to see what the child had not encountered or mastered, not what he already knew. Saxon math students who take the Saxon placement test receive unusually high "false" test scores. The only way to determine if the student is ready for the next math book is to evaluate their last four or five tests in their current Saxon math book to determine whether or not they have mastered the required concepts to be successful in the next level book. The brain of young students cannot decipher the difference between recognizing something and being able to provide solutions to the problems dealing with those concepts. So when they thumb through a book and say "I know how to do this" what they really mean is "I recognize this." Recognition of a concept or process does not reflect mastery.
- USING DAILY HOMEWORK TO DETERMINE A STUDENT'S GRADE: Skipping the weekly tests and using the student's daily assignments to determine their grade for the course reflects memory rather than mastery of the material.
RATIONALE: I cannot count the number of times I have been told by a parent "He does not test well, so I use the daily assignment grades to determine his course grade. He knows what he is doing because he gets ninety's or hundreds on his daily work."
FACT: Just like practicing the piano, violin, or soccer, the student is not under the same pressure as when they have to perform in a restricted time frame for a musical solo or a big game. The weekly tests determine what a student has mastered through daily practice. The daily homework only reflects what they have temporarily memorized as they have access to information in the book not available on tests. Answers are provided for the odd numbered problems and some students quickly learn to "back-peddle." This phenomenon occurs when the student looks at a problem and does not have the foggiest idea of how to work the problem. So they go to the answers and after seeing the answer to that particular problem, suddenly recall how to solve the problem. However, later, when they take the test, there are no answers to look up preventing them from "back-peddling" through to the correct solution.
As with anything, there are always exceptions that justify the rule. However, just because one parent says their child did any one or all of the above, and had no trouble with their math, does not mean you should also attempt it with your child. That parent might not have told you that (1) their child encountered extreme difficulty when they reached Saxon Algebra 2, and even more difficulty with the Saxon Advanced Mathematics textbook, or (2) they had switched curriculum after experiencing difficulty in Saxon Algebra 1, or (3) their child had to take remedial college algebra when they enrolled at the university because they had received a low score on the university's math entrance exam.
If your child is already experiencing trouble in one of the Saxon series math books, and you need to find a workable solution, please email me at: email@example.com. Include our telephone number as it helps provide a quicker solution to your dilemma..
In next month's issue, I will cover:
- THE EFFECTS OF DOING JUST THE ODD OR EVEN PROBLEMS:
- THE EFFECTS OF DOING MORE THAN ONE LESSON A DAY:
- ENTERING THE SAXON MATH CURRICULUM AFTER MATH 76:
THAT OLD "GEOMETRY BEAR" KEEPS RAISING ITS UGLY HEAD
Home School Educators frequently ask me about students taking a non-Saxon geometry course between algebra 1 and algebra 2, as most public schools do. They also ask if they should buy the new geometry textbook recently released to homeschool educators by HMHCO (the new owners of Saxon). As I mentioned in a previous newsletter late last year, a group of professors who taught mathematics and science at the University of Chicago bemoaned the fact that educators continued to place a geometry course between basic algebra (Algebra 1) and the advanced algebra course (Algebra 2) to the detriment of the student. AND THIS WAS MORE THAN 110 YEARS AGO!
The danger of using a separate geometry textbook as described by these professors more than one hundred and ten years ago - still exists today! Placing a nine month geometry course between the Algebra 1 and Algebra 2 courses creates a void of some fifteen months between the two algebra courses. How did I arrive at fifteen months? In addition to the nine month geometry course, you must also add the additional six months of summer between the two courses when no math is taken. The professors went on to explain in their book that it was this "lengthy void" that prevented most students from retaining the necessary basic algebra concepts from the basic algebra (Algebra 1) to be successful when encountering the rigors of the Algebra 2 concepts.
Home school educators also asked about using the new fourth editions of Saxon Algebra 1 and Algebra 2 recently released by HMHCO (the new Saxon owners) together with their new separate geometry textbook now offered for homeschool use. To create the new fourth editions of both the Algebra 1 and Algebra 2 textbooks, all the geometry was gutted from the previous third editions of both Algebra 1 and Algebra 2. Using the new fourth editions of their revised Saxon Algebra 1 and Algebra 2 now requires also purchasing their new Saxon Geometry book to receive any credit for geometry. That makes sense, if you consider that publishers make more money from selling three books than they do from selling just two. Regardless of which editions you finally choose to use, I would add a word of caution. If you intend to use John's Advanced Mathematics, 2nd Ed textbook, do not use the new fourth editions of Algebra 1 or Algebra 2.
So what Saxon math books should you use? The editions of John Saxon's math books from fourth through twelfth grades that should be used today appears on page 15 of my book. These editions remain the best math books on the market today, and they will remain so for decades to come.
If you desire more information about the pros and cons of using a separate Geometry textbook, please read my January 2022 Newsletter. Should you still have questions or reservations, feel free to email me at firstname.lastname@example.org or call my office any week-day at 580-234-0064 (CST).
The Infallible Professor
As we start a new year, I thought I would share a quick story about an experience I had while a student in college decades ago, an experience I am certain many of your sons and daughters encounter in their classrooms as well.
More than 50 years ago while attending a university in the South – as an active duty member of the armed forces – I encountered a rather single minded professor in a sociology class who – in his own words – "Did not want to hear any student's thoughts or opinions." Needless to say – having grown up in Chicago – I violated his edict and was ejected from his class when I questioned some rather obvious misinformation he was putting out about large cities – obvious at least to anyone who had the opportunity to live in these cities. There were about twenty young men and women in the class all from rural areas of the state and it was clear that none of them had yet – except for perhaps a vacation – traveled outside the state or came from a large city he was referring to.
Later in the afternoon, I went to his office to discuss why he had ejected me from his class. He was still quite openly angry with me and quite adamant about me accepting a "C" with the added stipulation that I was not to return to his class. I reminded him that I had earned an "A" in his class at that point. He would not budge from his position, so I left his office. That evening I wrote the following poem and had it published in the school newspaper several days later.
The Infallible Professor
"With my professor I must agree.
Not he with me, but me with he!
How then am I to learn what's true
And pass on to you the knowledge
Of mankind – when my thoughts are
thoughts of a professor's mind?"
The day after it was published, the professor contacted me and after a sometimes heated discussion, we both agreed upon some ground rules. He would allow me to return to class with the grade I had earned to that point. And I would not be penalized again for questioning anything he brought up in class. While we tangled in class a bit over other items he brought up – he never again lost his temper. And I passed his class with my earned grade of an "A"!
What had angered me most at that time was that my question was brought up in a respectful way. I gave several actual existing locations in the city of Chicago that made his statement of fact untrue – that all large cities were not identical in their physical layouts. Rather than asking me to explain in detail what I had just stated was fact – contradicting his premise – he immediately took on the aura of a dictator and attempted to shut me down by loudly and angrily shouting at me to "shut up" and loudly and angrily shouting that this was his classroom and if he wanted my opinion he would have asked for it.
I wanted to tell him that it was my money paying him to teach us — not to dictate to us. I wanted to tell him that we lived in a free democracy and that all ideas are open for meaningful and polite discussion. I wanted to remind him that is what my uncles and cousins — and my father — had fought and died for during two World Wars. But somehow I also realized that this was not the time or place for that discussion and I quietly picked up my notes and book and left his room.
I realize that his persona lives on in some college professor that your son or daughter may encounter. And I thought the poem I wrote more than half a century ago (change "he" to "she" if necessary) may be used again by any student if it brings the same peace of mind to that young student that it brought to me that night.
I promise to get back to mathematics next month.
Have a Blessed, Safe, and Happy New Year!