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Newsletter
WHY DO HOMESCHOOL EDUCATORS EITHER STRONGLY LIKE OR DISLIKE JOHN SAXON'S MATH BOOKS?
I was online at a popular website for home school educators and I noticed some back and forth traffic about the benefits and drawbacks of John Saxon’s math books. One of the parents had just commented about the benefits of John’s books as she saw them by their creation of repetition over time which she thought contributed to mastery as opposed to memory of the basic math concepts.
One gentleman replied to her comment with the following:
“Or, one can use a math program that makes the mathematical reasoning clear from the outset as a matter of course rather than believing that a child will grasp the mathematical concepts by repeating procedures ad nauseum. I think the Saxon method is flawed.”
This reminds me of one of John’s favorite sayings when challenged with similar logic. John’s reply would be to the effect that “If you are setting about to teach a young man how to drive an automobile, you do not try to first have him understand the workings of the combustion engine; you put him behind the wheel and have him drive around the block several times.”
I recall when teaching incoming freshman the Saxon Algebra 1 course that I would first present students with several conditions such as having them all stand up and then asking if they were standing on a flat surface or a curve. Then I explained to them that an ant moving around on the side of the concrete curve of the quarter mile track at the high school would think he was moving in a straight line and he would never realize that, because of his minute size when compared to the enormity of the curve, he thought the curve to be a straight line.
I would then go on to explain that – like the ant’s experience in his world - they were standing on an infinitesimal piece of another curve which appears to be a flat surface to them. I would continue by telling the students that in “Spatial Geometry” there are more than 180 degrees in a triangle. It never failed, but about this time someone would put up their hand and – as one young lady did - say “Mr. Reed, I am getting a headache, could we get on with Algebra 1?”
It was a different story when presenting the same conditions to seniors in the calculus class. They would excitedly begin discussing how to evaluate or calculate them. And telling them there were no parallel lines in space did not seem to upset them either. Could it be because the seniors in calculus were all well grounded in the basic math concepts, and they understood the difference between the effects of these conditions in “Flat Land” as opposed to their “Spatial Application?”
Perhaps John and I are old fashioned, but both of us thought it was the purpose of the high school to create a solid educational foundation - a foundation upon which the young collegiate mind would then advance into the reasoning and theory aspects of collegiate academics. Both John and I had encountered what I referred to as “At Risk Adults” while teaching mathematics at the collegiate level. These students could not fathom a common denominator, or exponential growth. They were incapable of doing college level mathematics because they had never mastered the basics in high school.
Students fail algebra because they have not mastered fractions, decimals and percents. They fail calculus - not because of the calculus, for that is not difficult - they fail calculus because they have not mastered the basics of algebra and trigonometry. I recall my calculus professor after he had completed a lengthy calculus problem on the blackboard - filling the entire blackboard with the problem. Striking the board with the chalk he turned and said “The rest is just algebra.” I saw many of my freshman contemporaries with quizzical looks upon their faces. Being the “old man” in the class, I quickly said “But sir, that appears to be what they do not understand. Could you go over those steps?” Without batting an eye, he replied “This is a calculus class Mr. Reed, not an algebra class.”
I firmly believe that what causes educators to so strongly dislike John Saxon’s math books is, not from their having ‘used” the books - and suffering frustration or failure - but from their having “misused” the books. In next month’s newsletter, I will discuss the main causes for failure in the Saxon math books and how to prevent them, from Math 54 through calculus.
May each of you have a very Blessed and Merry Christmas.
DOES THE STUDENT'S GRADE IN THE COURSE REFLECT THE STUDENT'S
UNDERSTANDING OF THE CONCEPTS?
Recently I read a math teacher’s syllabus that stated how their seventh grade Saxon math class would be graded. The syllabus stated that the grading scale would be the standard 90-100 A; 80-89 B; 70-79 C; 60-69 D; 59 and below was failing. The syllabus then explained that 10% of the student’s grade would be awarded for class participation and timely submission of the daily work. Accuracy of the daily work comprised another 40% of the student’s grade, and test grades comprised the remaining 50% of the student’s overall grade.
What this means is that a student who does not understand the material, reflected by weekly test grades in the 50’s, but who has enough initiative to copy his friend’s homework paper via the telephone, email, or other means – and who then receives a daily homework grade of 100 – will receive an overall math grade of a 75 (a good solid ‘C) reflecting he understands the work – which he clearly does not! How did I arrive at that passing grade? Easy. Fifty percent of a homework grade of one hundred is 50. Fifty percent of a test grade of only fifty is 25. Adding them together, you can easily see how the student quickly calculates the critical value of the daily assignment grades.
The greatest mistake a classroom teacher or a home school educator can make in establishing a grading system for a mathematics course is to put too much weight upon the daily grade as this does not reflect mastery of the material. Teachers have little or no idea how students acquired the answers to the daily work unless they stand over the students as they do their work – which is not a recommended course of action.
The beauty of the Saxon math curriculum is the weekly tests which tell the parent or teacher how the student is progressing. The daily work is nothing more than practice for that weekly test as the 20 test questions come from the 150 questions the student encounters in the previous five days of daily work. However, unlike students using some textbooks which provide a “test review” section, the Saxon students have no idea which of the 150 problems will be on the upcoming test. The Saxon students cannot memorize the concepts they encounter. They must understand them.
Oh yes, I almost forgot. The syllabus went on to explain to the parents and students that “after every test, students will be given the opportunity to retake a similar test, after more practice, and be given full credit.” A sure way to ensure students will pass the course - whether they understood the concepts or not. Have you ever known any student to receive a lower grade on a re-take of the same test? I say re-take because the Saxon classroom test booklet has an A and a B version of each test. Both versions are identical in content except the numbers are changed resulting in different numerical answers. The two versions were designed – not for re-takes – but for make-up tests to ensure the student taking the make-up test on Monday, did not receive the answers from another student who took the test on Friday.
John Saxon’s math books are the only math books on the market today (that I am aware of) that require a weekly test to determine how well the student is progressing. That means that in a school year of about nine months, the student takes about 30 tests. My grandson has been in his sophomore high school math class for over eight weeks now and he just took his first test. He passed it with a 94, but what if he had received a 60? How do you review material covered in over two months of instruction? In a Saxon math curriculum, if the teacher or parent never looked at the student’s homework - and the student never asked for help - the teacher or parent would know on a weekly basis how the student is progressing, allowing sufficient time for review and remediation if necessary.
The two scenarios I have discussed above are what I would define as the difference between “Memorizing” and “Mastering.” Both reflect “knowledge”, but the mastery reflects what the student has placed in long term memory as opposed to what the student has memorized for the short term benefit of a good test grade. In a Saxon curriculum, the mastery enables the student to effortlessly move from middle school math (the foundation for upper level math) to the challenges of upper level algebra, trigonometry and geometry, pre-calculus and calculus should they so desire.
Grades in the Saxon curriculum (after K – 3) are based upon test scores. It is the test scores that determine mastery or acquisition of knowledge – not the daily assignment grades.
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. If you know a veteran of any conflict and you get the chance on 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 them 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. 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 village of “Villers – en –Haye” had a population of only 96 people. (In 2000, the population of “Villers – en – Haye” was still only 181).
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. 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 Abby buildings are still there today, undamaged by the fierce fighting that occurred there some ninety years earlier. (In 1993 the population of St. Mihiel had increased to about 5,435)
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 358 Infantry Regiment) was part of that force. The successful three day campaign by the U.S. First Army forced the Germans to relinquish a military fortification they had held 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 or mustard gassed during the battle. 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, September 12, 1918.
Now the “Rest of the Story . . . . . !”
More than half a century later, while I was stationed with the U.S. Army in Heidelberg, Germany, my wife and I were visiting the town of Schwetzingen, Germany. The town is 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 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 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 alleged to be 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. 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 a 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 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:
THE COLLEGE LEVEL EXAMINATION PROGRAM (CLEP)
Over the years, I have had parents ask about the advantages of having their child take a College Placement Test (CLEP) - or as some of my students would say “CLEP out of a Course.” For those not familiar with the program, it is administered by The College Board at CLEP test centers located at more than 1600 universities and colleges located throughout the states.
The College Board states it is a not-for-profit membership association whose mission is to connect students to college success and opportunity. It was founded in 1900, and the association has a membership of more than 5,600 schools, colleges, universities and other educational organizations. Each year, the College Board serves more than seven million students through major programs and services in college readiness, college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning.
While most homeschool educators are more familiar with the College Board’s SAT® and AP® programs, their CLEP Program can also save students considerable course fees if they can pass the appropriate tests. For a fee of $77.00 per course, students can take CLEP tests in any of the more than 33 subjects in the areas of Literature, Foreign Languages, History and Social Studies, Science and Mathematics, and Business.
One word of caution - the College Board advises students that:
“Before you take a CLEP exam, learn about your college's CLEP policy. Most colleges and universities grant credit for CLEP exams, but not all. There are 2,900 institutions that grant credit for CLEP and each of them sets its own CLEP policy; in other words, each institution determines for which exams credit is awarded, the scores required and how much credit will be granted. Therefore, before you take a CLEP exam, check directly with the college or university you plan to attend to make sure that it grants credit for CLEP and review the specifics of its policy.”
Not every university or college may accept every College Board CLEP test score, and not all have the same scoring levels for credit. For example, while one university may award three credit hours for a score of 55 on the college algebra CLEP test, another may require a higher score, while still a third university may not accept the College Board CLEP results for that particular test at all. It may require that students take their individual university CLEP test for a particular subject.
In the area of mathematics, parents also need to know what levels of high school math courses correspond to what level CLEP test. For example, the student who takes the college algebra CLEP test before mastering John Saxon’s Algebra 2 course will, in all likelihood receive a failing grade. Each of the CLEP math tests indicate the subject matter included in the tests. Following the math book’s index will give you a pretty good idea of whether or not the student can handle that particular test.
I will say this about John Saxon’s second edition of Advanced Mathematics. All students who have mastered the first ninety lessons in that book should easily pass the College Board’s CLEP test for College Algebra and College Mathematics. If they have mastered the entire Advanced Mathematics book and also finished the first 25 lessons of calculus, they can easily pass not only those same two course tests, but the College Board pre-calculus CLEP test as well.
I recall that when I was teaching in the high school, one of my calculus students went down to the OU campus and took the calculus CLEP test and passed it. While in my senior calculus class, he was happy with just a “C” because he was going to study “Communications” at OU and openly admitted that he did not really need the math. He never took another math course in his life. When I asked him why he did not just take the college algebra CLEP test, he smiled and said, “I just wanted to be able to tell people that I had passed college calculus at OU.”
The College Board tests are a great way to get a few basic courses out of the way and save mounting college tuition costs, but if the students are going into engineering or research science, I would recommend they not use the CLEP tests to replace core courses in their field. They need to revisit these courses at the collegiate level.
A NEW INTERACTIVE SCIENCE PROGRAM
As this is the buying season for homeschool educators, I wanted to take this opportunity to remind you about a new interactive science program I had mentioned in an earlier newsletter. The program is being published by a well known Saxon Math® K - 4 author, Nancy Larson.
NANCY LARSON SCIENCE for Ages 5 -11
Nancy Larson, author of the Saxon Math K - 4 series, has written an innovative interactive science program for ages 5 - 11. The curriculum is engaging and challenging for your child while being fun and easy for you to teach. The program is age-appropriate and uses a step-by-step approach that allows anyone to teach science with confidence. The materials include the Teacher’s Manual, a set of consumable student materials, and a homeschool Tool Kit. For more information about this exciting program, visit Nancy’s website at www.NancyLarsonPublishers.com. You might also want to check out her new blog site at www.BloomingScientists.com.
WHAT HOMESCHOOLERS ARE SAYING ABOUT THE DVD MATH TUTORIALS
I recently completed a random survey of homeschool educators who had purchased the DVD math tutorials. Over ninety percent of those who responded to the survey indicated they wanted our DVD math tutorials created for the Math 76 and Math 87 textbooks also. Since the DVD math tutorials from Algebra ½ through the Advanced Mathematics textbook (which include the first twenty-five lessons of the Calculus text through limits and derivatives) had already been created, I made the decision to follow the homeschool educators’ advice, delay production of the rest of the calculus series, and immediately start on production of DVD math tutorials for Math 76 and Math 87. The DVD math tutorial series for Math 76, 3rd or 4th Ed will be completed by January or February of next year and the DVD math tutorial series for Math 87, 2nd or 3rd Ed will be completed the following October.
It is difficult for homeschool educators to evaluate the varied math tutorials on the market without actually purchasing them and that can become quite expensive and sometimes disappointing. On a daily basis, I receive telephone calls and email from homeschool educators posing questions about how the varied math CD and DVD math tutorials for John Saxon’s math books are presented and how they compare with each other. To assist in making a decision regarding which product to purchase as a math tutorial for students using John Saxon’s math books, I asked The Old Schoolhouse Magazine staff to review my DVD math tutorials as they had previously reviewed my book several years ago. They agreed. The reviews were completed several months ago. Excerpts from those reviews are reflected below.
- Excerpts from the review of Art Reed’s Algebra ½, 3rd Ed DVD Math Tutorial.
“In the past few years, our family has used the DVDs from Teaching Tape Technology to give additional instruction in Saxon Math for grade levels 4th through Advanced Math . . . so when I had the opportunity to review the Mastering Algebra John Saxon's Way Algebra ½ (3rd edition) DVDs, featuring seasoned mathematics instructor Art Reed, I was intrigued . . . Could these videos measure up? Could I be objective? I can honestly answer ‘yes’ to both of those questions . . . Art Reed is a fantastic instructor. He is engaging and inspiring, but his approach is also straightforward and no nonsense . . . he also has a great sense of humor. He is a professional through and through . . . he knows his stuff. It is obvious that he enjoys teaching math and wants his students to succeed and master the material. I like his confident way of presenting each lesson . . . He does not spoon feed, but he does explain each concept thoroughly and give encouragement. He gives extra tips and information to make everything easier to understand . . . I also like the way he uses visual aids and manipulatives when needed to reinforce certain concepts . . . Overall, I think this is a wonderful set for homeschool families who use Saxon Math . . .The students have access to an experienced instructor, and they can replay the videos as many times as they need to master the material . . . I highly recommend Art Reed and the Mastering Algebra John Saxon's Way DVDs as a great investment in your child's mathematical education.”
Amy M. O'Quinn, The Old Schoolhouse® Magazine, LLC (Click Here) for the entire review.
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- Excerpts from the review of Art Reed’s Algebra 2, 2nd or 3rd Ed DVD Math Tutorial.
“Mastering Algebra is a tutorial course designed to work with Saxon Algebra 2, either the 2nd or the 3rd edition. It is 12 DVDs, containing 129 lessons and 2 review lessons to brush up before you begin. The lessons are correlated with Saxon Algebra; for those who want the tutorial benefit but are using another curriculum, a detailed scope and sequence of the lessons is available online so that you can select the lesson or skill you need to work on . . . Mr. Reed, the teacher, stands at a podium at the front of a classroom with a real white board behind him and teaches the class. He even has an oversized calculator that he uses to show exactly what you do with various calculator functions. There are no people in his classroom, however, so he interacts with the listener, not students in front of him. This adds a personal touch to the tutorial, in my opinion. . . The lectures are very understandable, and Mr. Reed has a way of breaking down and illustrating the concepts so that they are easy to comprehend--even for the ‘math-challenged.’ . . . The series is specifically geared for the home educating parent/student, and it would probably set many a homeschool mom's mind at ease to have such a competent math tutor for her high school student. At $49.95 for the entire set, this is the most inexpensive math tutoring you will ever find as well . . . I highly recommend this tutorial course—even if you aren’t using Saxon Algebra.”
Kim Kargbo, The Old Schoolhouse® Magazine, LLC, (Click Here) for the entire review.
SHOULD HOMESCHOOL STUDENTS TAKE CALCULUS?
Calculus is not difficult! Students fail calculus not because the calculus is difficult – it is not – but because they never mastered the required algebraic concepts necessary for success in a calculus course. But not everyone who is good at algebra desires or needs to take calculus. But then what does the homeschool student do who wants to take calculus, but would like to share the challenge with likeminded contemporaries?
A number of the students I taught in high school never got to calculus their senior year because they could not complete the advanced mathematics textbook by the end of their junior year. They ended up finishing their senior year with the second course from the advanced math book titled “Trigonometry and Pre-calculus” and then taking calculus at the university level. This worked out just fine for them as they were more than adequately prepared and had an opportunity to share the challenge with likeminded contemporaries on campus.
Some students advanced no further than Saxon Algebra 2 by the end of their senior year in high school. They were able to take a less challenging math course their first year of college by taking the basic freshman algebra course required for most non-engineering or non-mathematics students. These students would never have to take another math course again – unless of course they switched majors requiring a higher level of mathematics.
I believe the answer for homeschool students in these same situations is what we in Oklahoma call “concurrent enrollment.” In other words, don’t take a calculus course at home by yourself. Under the guidelines of “concurrent enrollment” – or whatever your state calls it – take the course at a local college or university and share the experience with likeminded contemporaries. And at the same time receive both high school and college credit for the course.
The concept of “concurrent” enrollment was just beginning to take hold in the field of education when I was teaching and there were not many high school students taking these college courses enabling them to receive “dual credit” for both a high school and college math credit for their efforts. As we gained experience with the new program, we learned that our high school juniors and seniors who had truly mastered John Saxon’s Algebra 2 course could easily enroll at the local university in the freshman college algebra course and could – provided they went to class – easily pass the course. And, if they were English or Art majors, they would never have to take another math course if they so desired.
Students who were eligible and wanted to take a calculus course their senior year looked forward to taking it at the local university and receiving dual credit for the course. Many of these students went on to become research technicians in the field of bio-chemistry and physics. Several of them never took another math course in their college careers because they were English or Art History majors. They took the calculus course just because they wanted to prove they could pass the course. They wanted to be able to say “I took college calculus my senior year of high school.”
So, what does all this mean? Home school students whose major will require calculus at the college level should adjust their math sequence to complete John Saxon’s advanced mathematics textbook (2nd Ed) by the end of their junior year of high school and take calculus their senior year at a local college or university. Not only will this enable them to receive dual credit – unless their state prohibits it – but they will enjoy the camaraderie of other likeminded college students taking the course with them.
There is a final serendipity to all of this. When enrolling at most universities, honors freshman and freshman with college credits enroll before the “masses” of other freshman. This would virtually guarantee the student with college credits the courses and schedule they desire – not to mention the potential for scholarship offers with high ACT or SAT scores and earned college credits in a course titled “calculus” on their high school transcript.
WHY USE SAXON MATH BOOKS?
My wife and I just returned from attending homeschool conventions in both Cincinnati, Ohio and Kansas City, Missouri. Both of us really enjoyed visiting with homeschool families from more than a dozen different states who stopped by our booth. While at each of the two conventions, I also had the opportunity to address homeschool educators in several workshop seminars.
The title of today’s news article was the title of my seminars. What I wanted to convey to homeschool educators at the seminars was factual information on why John Saxon’s math books – when properly used – remain the best math curriculum for mastery of mathematics on the market today. Why did I emphasize “when properly used”? Improper use of John’s math books is one of the weaknesses of his books. The vast majority of students who encounter difficulties in a Saxon math textbook do so, not because the book is “tough” or “difficult”, but because they have not properly advanced through the series. Or, for one reason or another they had been switching back and forth between different math curriculums. Because of switching curriculums, the students had all developed “holes” in their basic math concepts, concepts critical for future success in the math book they were now using. In John Saxon’s math books these “math holes” created frustration and failure for the students who were returning to the Saxon curriculum in the upper level math books.
There were more than a dozen homeschool parents who came to the booth all facing the same dilemma. Their sons or daughters had recently completed or were currently completing another curriculum of instruction in algebra. While they said they were happy with the curriculum they were using, they expressed concern that their son or daughter was not mastering sufficient math concepts to score well on the upcoming ACT or SAT tests. I asked each of them to have their student take the on-line Saxon algebra one placement test which consisted of fifty math questions. The test was actually the final exam in the Saxon pre-algebra book (Algebra ½, 3rd Ed).
In every case, regardless of which math curriculum the students were using, the answer was always the same. Not one of the students passed the test. It was not a matter of receiving a low passing grade on the test. Every one of them failed to attain fifty percent or better.
The curriculums the students were using were not bad curriculums. They correctly taught students the necessary math concepts in a variety of ways. But unlike John Saxon’s method of introducing incremental development coupled with his application of “automaticity,” none of these curriculums enabled students to master these concepts.
In those cases where the parents asked for my advice after learning about the failed pre-algebra test, we worked out a successful plan of action to ensure that the failed concepts were mastered and the “math holes” were filled. The plan would enable each of them to successfully move to an advanced algebra course later in their academic schedule.
Now to address a topic that arose during one of the seminars. Several attendees asked whether or not they should use the new fourth editions of algebra one and algebra two textbooks as well as the new separate geometry textbook. I told the audience that the new fourth editions were initially created for the public school system together with the company’s creation of a new geometry textbook. I explained that the daily geometry review content as well as the individual geometry lessons had been gutted from the new fourth editions of algebra one and algebra two. In my professional opinion, they should stay with the current third editions of algebra one and two and not fall into the century old trap of using a separate geometry text in-between algebra one and two.
A homeschool parent commented that I was mistaken because she had called the company customer service desk and they told her there was geometry in the new fourth edition of their Saxon algebra one book. I have a copy of that edition. It was designed to be sold to the public schools along with the company’s new geometry textbook, and it does not integrate geometry into the content of the book’s one hundred twenty lessons as John’s third edition of algebra one does..
Here are the facts regarding the geometry content in the two books. I will let you draw your own conclusions:
- In the index of the third edition of algebra one, there are seventeen references dealing with the calculation of total area, lateral surface area, and volume of spheres, cones, cylinders, etc. In the new fourth edition index, there are only four references to area and volume and they are not geometric references. They deal with determining correct unit conversions of measure and the application of ratios and proportions in their solution, all of which are algebraic not geometric functions.
- In the index of the old third edition of algebra one there are nine references to the word “angles.” In the index of the fourth edition, there are none. The reference term “angles” does not appear.
- In the third edition index, there are three references to “Geometric Solids.” In the fourth edition index, the word “Geometric Solids” does not appear.
- The only reference to the word “geometry” in the fourth edition index is the phrase “Geometric Sequences” and that term is not a geometry term. It refers to an algebraic pattern determined through the use of a specific algebraic formula.
- Geometry references, terms, concepts and daily problems dealing with them are found throughout the third edition of algebra one. This does not occur in the fourth edition of algebra one.
So why was the homeschool educator told there was geometry in the new fourth edition of algebra one? Well, let me see if I can explain what I believe the marketing people came up with. I say marketing people because several of us have tried for more than a year to find out who authored the new fourth edition and no one at the company could – or would – tell us who the author is. Someone speculated that it was given to a textbook committee to create the new fourth editions of algebra one and two as well as the new geometry textbook.
At the back of the new fourth edition of algebra one, just before the index, is a short section of thirty-two pages referred to as the “Skills Bank.” Within these thirty-two pages are thirty-one separate topics of which only twelve deal with geometric functions and concepts. Each of the concepts is about a half page in length and covers just a few practice problems dealing with the concepts themselves. Since they are not presented or practiced throughout the book, I believe it makes it difficult if not impossible for the student to master any of these concepts encountering them this late in the book – if they are encountered at all.
Here are several examples of how these geometry concepts are presented in the “Skills Bank of the new fourth edition of algebra one:.
- Skills Bank Lesson 14: Contains two short sentences explaining how to classify a quadrilateral. The student is then given only three practice problems on the concept.
- Skills Bank Lesson 16: Contains two short explanatory sentences describing congruency followed by only two practice problems.
- Skills Bank Lesson 19: Contains five brief statements describing the various terms used to describe a circle and its component parts, immediately followed by two problems asking the students to identify all of these parts.
The “Skills Bank” concept is fine as far as using a brief addendum to define what those geometric terms mean. But when does the student get to work these concepts so that the review creates “mastery” as John‘s original books were designed? “The “Frequent, Cumulative Assessment” of John Saxon’s math program - referenced by the company on page 5 of their new textbook as one of the key elements of the book - is never developed for the geometry concepts. Additionally, the company’s use of colored “Distributive Strands” reflecting the distribution of functions and relations throughout the textbook does not list any geometry functions or relation strands showing up anywhere in the book – at least not in the book they sent me.
The new algebra one fourth edition textbook created by HMHCO - under the Saxon name - is a good algebra one textbook. However, it does not contain geometry concepts on a daily basis as John’s third edition of algebra one does. Before you make a decision to use a separate geometry textbook along with the new fourth edition of algebra one and two, please do not hesitate to call or email me.
EMAIL: art.reed@usingsaxon.com TELEPHONE: 580-234-0064 (CST)
DO MATH SUPPLEMENTS REALLY HELP STRUGGLING STUDENTS?
Before addressing that question directly, let me first relate a story about a man walking across a bridge spanning a river. As he looked down at the water, he noticed a boy who had fallen into the swift current. It was apparent from the boy’s struggle that he could not swim. The man realized he had only two alternatives. He could shout instructions to the boy on how to overcome the swift current and perhaps enable him to dog paddle to safety on the shore, or he could dive into the water and rescue him. Without hesitating, the man dived into the water and immediately swam to the side of the struggling boy. Now the man had to face another dilemma. Should he pull the struggling boy to safety or should he immediately try to teach him how to swim?
Everyone would agree that when people are drowning, that is not the time to try to teach them how to swim. All one can do at that time is try to get them to a place of safety where they can overcome the swift current of the river. So it is with mathematics. In any of John Saxon’s math textbooks from Math 54 through Calculus, if student’s begin struggling before reaching lesson thirty or sooner, it is a sign that they will drown in the later lessons of the book unless they are taken to a place of safety where they can better manage and learn the concepts that they are now unfamiliar with. Concepts that are dragging them into deep water! It should become apparent that they are not prepared for the book they are in, and no amount of supplemental material will overcome those shortcomings.
Mathematics is like the swift current that challenged the drowning boy. Like the river, upper level mathematics is challenging and can easily become unforgiving. Looking for a slower moving or shallower river may create a temporary solution, but eventually that water will again become swifter and deeper and unless one is prepared, all the advice and assistance given at the time of the struggle will come too late.
While it is a noble goal for students to strive towards taking a calculus course in their senior year of high school, it is critical that they first master the algebra. The calculus is easy! It is the challenge of the algebra and to a lesser degree the trigonometry that causes students to fail calculus. Any student with a solid algebra background, entering any college or university, will pass that school’s math entrance exam and will be successful in a calculus course should they choose to do so.
When classroom teachers or home school educators take shortcuts with one of John Saxon’s math books, they are not adequately preparing the student for the deeper water ahead. More than twenty years experience with Saxon Math textbooks has shown me that classroom teachers and parents who take shortcuts with his curriculum (instead of going slowly and deliberately through as John intended) cause students to “flounder” as they encounter the “deeper” water. At this point, they find it easier to blame the book!
The classroom instructions contained within my DVD “video” tutorial series are not teaching supplements. They contain actual classroom instruction on each concept of the book. Like the book, the classroom instruction is designed for the homeschool student who is in the appropriate level math book. The instruction enhances the written word they have already read from the textbook. Many of the lessons present a different explanation by an experienced Saxon math teacher that helps the student through the difficult reading of the lesson.
However, regardless of who creates them, neither the CD white board presentations nor the DVD classroom instructions will help students who are taking a course they are ill prepared for – and they find themselves floundering in “deep” water.
TRANSCRIPTION OF MATH CREDITS – TWO BOOKS, FOUR YEARS
The first year I started teaching high school mathematics, I encountered freshman students who, while having passed an eighth grade pre-algebra course, could not manage John Saxon’s algebra one textbook. The frustration and failure rate was incredible and many upper level students were shying away from any math course above algebra one.
I soon became aware of the distinct difference between receiving good grades and mastery of the concepts. That summer I developed an alternate curriculum using John’s algebra one and algebra two books. The plan would allow students the ability to accept the challenge of algebra without having to accept failure. I went to Oklahoma City and briefed the Director of Curriculum for the Oklahoma State Department of Education on my plan.
After my briefing, he sat quietly for a few seconds then said to me, “Mr. Reed, I wish that my daughter would have had the opportunity to use your plan when she was struggling with algebra in high school.” He then went on to explain that anything can be entered on a student’s transcript so long as it is an honest evaluation of what was being taught in the classroom. He approved the plan and we implemented it that following fall at the high school.
In the following three years, our ACT average math scores went from 13.4 to over 21.9 (above both the state and national averages). In that same time period, we had over ninety percent of our high school students enrolled in math courses above Algebra 1 and the number of students taking the ACT test tripled.
The plan is simple. The student has to complete the entire algebra one textbook. However, the student who struggles through John’s Algebra 1, 3rd Ed textbook and receives an overall second semester test average of 50 – 60 (a D or F) can receive credit for a “lesser inclusive course.” The title of “Basic Algebra” or “Introduction to Algebra 1” can be used and the grade recorded as a “C. The student then retakes the same book the next year and should receive an average test grade of 80 or better. The course is recorded on the transcript the second year as “Algebra 1.” Since the students have now mastered the material they previously missed the first time through the book, you can go back and change the “C” to a “B.”
Ninety percent of my students only needed the “lesser inclusive” assist in Algebra 1. However, a small percent needed the same assist in Algebra 2, so we came up with “Introduction to Algebra 2” for the first attempt and “Algebra 2” for the second attempt.
Sometimes the difficulty students encounter in John Saxon’s Algebra 1 or Algebra 2 stems from their inability to process both the algebra and geometry concepts at the same time. Some students just need a second chance to master this material because of their weaker math background in pre-algebra. Or, they might have moved through several different math curriculums in the past few years and developed holes in their math background.
What makes this concept work so well is that John Saxon’s Algebra 1 and Algebra 2 textbooks are really tough, no-nonsense, cumulative math textbooks. Using this system, we have shown that any student who truly masters the content of these two textbooks in four years of high school will successfully pass any college level algebra course at any university.
There is considerably more detail in my book, but if you have an immediate question or situation that requires assistance, please feel free to email me at art.reed@usingsaxon.com and include your telephone number so I can call you. My experience in assisting homeschool educators is that a telephone conversation allows an immediate exchange of questions and answers not readily afforded in lengthy email sent back and forth over several days generating more questions and answers.
I will be speaking at workshop seminars at the Cincinnati, OH and the Kansas, MO Homeschool Conferences in April. We will have a booth there also. If plan to attend one of the conferences, please stop by and say hello.
MAKE SURE YOU BUY AND USE THE CORRECT EDITIONS OF JOHN SAXON’S MATH BOOKS
As we approach textbook purchasing time for homeschool educators I thought it would be advantageous to go over with you the correct editions of John Saxon’s math books to use, and also to provide you with some recommendations on how to use the textbooks correctly and reduce students’ frustration with mathematics. While there is more detail in my book, I believe the following information will help you select the correct level and edition of one of John Saxon’s math books.
All of the textbooks listed below also include an introduction to basic geometry as well as a review of the geometric terms associated with geometry at the introductory level. As the student moves from Math 54 to Algebra 1, the repetition of these terms and concepts allows for a gradual increase in their level of difficulty. However, this geometry remains at the introductory level and there is no formal credit for any geometry until successful completion of the Algebra 2 textbook where the student also earns a full credit the first semester of a regular high school geometry course.
If after reading this newsletter, you feel your particular situation has not been addressed, please feel free to email me at art.reed@usingsaxon.com or call me at 580-234-0064 (CST) before you purchase any math textbooks.
Here are those textbooks and the editions:
Math 54: 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: 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 course. 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: 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: 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, they are identical in math content. Students who successfully complete the entire textbook and score eighty-five 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 Math 87 and algebra ½ 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 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: 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 reference numbers save hours of time searching for the lesson needed to review the necessary concept. From here 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: Use the newer and academically stronger 3rd edition. 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. A scientific calculator may be used 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 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. 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: Either the 2nd or 3rd editions of the Saxon Algebra 2 textbooks are okay to use. Except for the addition of the concept reference numbers in the newer 3rd edition, the two editions are identical. If you already have the older 2nd edition textbook, and need a solutions manual, you can get 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 concept reference numbers as well as solutions to each test question – something the 2nd edition test booklet does not have. An inexpensive scientific calculator is all that is needed for this course. Upon successful completion of the entire book, students have also completed the equivalent of the first semester of a regular high school geometry course in addition to the credit for Algebra 2.
Advanced Mathematics: Use the 2nd Edition. Students who attempt this book must have successfully completed all of Saxon Algebra 2. 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. 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 read my May 2009 newsletter. An inexpensive scientific calculator is all that is needed for this course.
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.
FUZZY MATHEMATICS
If you’re not old enough to remember the old “Ma and Pa Kettle” movies, you will have to ask grandma or grandpa about them. Their movies were among the best of the funny classic black and white movies made back then. The kind of movie the entire family could watch and laugh together over. My brother and I often went to see the same movie more than once.
Today’s news item is from one of their movies. I saw it on the internet and could not resist sharing it with you and your students.
To watch this unbelievable episode of “Fuzzy Math" (Link removed)
I hope you all will have a great New Year. Next month, I will get back to the academic world of mathematics.
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