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April 2024

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

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

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

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

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

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

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

 

 

March 2024

WHAT DETERMINES THE DIFFERENCE BETWEEN MASTERY AND MEMORY?

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

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

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

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

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

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

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

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

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

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

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

 

 

February 2024

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

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

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

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

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

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

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

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

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

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

So, should you blame the publishers for publishing a separate geometry textbook? Or is it the fault of misguided high-minded academicians who — after more than a hundred years — still demand a separate geometry text from the publishers? I am not sure, but thankfully, this decision need not yet face the homeschool educators using John Saxon's math books for the original Homeschool third editions of John Saxon's Algebra one half, Algebra one and Algebra two textbooks still contain geometry as well as algebra — as does the advanced mathematics textbook. In fact, John introduces some basic algebraic and geometric concepts as early as the sixth grade in the second and third editions of his sixth grade Math 76 book.

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

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

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

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

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

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

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

Algebra ½ - The hard cover third edition.

Algebra 1 — The hard cover third edition.

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

Advanced Mathematics — The hard cover second edition.

Calculus — The hard cover first - or second edition.

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

 

 

January 2024

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

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

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

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

John went on to explain that

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

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

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

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

Here are several of those reasons:

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

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

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

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

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

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

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

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

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

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

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

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

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

HAVE A BLESSED - and - HAPPY NEW YEAR!