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 books brings in thirty-three percent more revenue than selling just two.
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 sisters. After their mother's death in 2003, my wife and her sisters spent the next six years going through some sixty 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 serving 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 friend was describing to 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 Solution - 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 that 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 wrote:
"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 home school educators using John Saxon's math books for the original home school third editions of John Saxon's algebra one and algebra two textbooks still contain geometry as well as algebra - as does the advanced mathematics textbook.
Any home school student using John Saxon's math textbooks who successfully completes algebra one, (2nd or 3rd editions), algebra 2, (2nd or 3rd editions), and at least the first half of the advanced mathematics (2nd 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 Saxon 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 remain excellent math textbooks for several more decades.
Math 54, 2nd Ed (Hardcover) - or - new 3rd Ed (Softcover).
Math 65, 2nd Ed (Hardcover) - or - new 3rd Ed (Softcover).
Math 76, 3rd Ed (Hardcover) - or - new 4th Ed (Softcover).
Math 87, 2nd Ed (Hardcover) - or - new 3rd Ed (Softcover).
Algebra 1/2, 3rd Ed (Hardcover).
Algebra 1, 3rd Ed (Hardcover).
Algebra 2, 2nd or 3rd Ed (Hardcover) - content is identical.
Advanced Mathematics, 2nd Ed (Hardcover)..
Calculus, 1st or 2nd Ed (Hardcover).
Physics, 1st Ed (Hardcover) - there is no second edition of this book.
"May you have a very Blessed and Merry Christmas."
SHOULD YOU GRADE THE DAILY SAXON MATH ASSIGNMENTS?
I continue to see comments on familiar blogs about correcting - or grading - the daily work of Saxon math students. That is a process contrary to what John Saxon intended when he developed his math books. Unlike any other math book on the market today, John's math books were designed to test the student's knowledge every week. Why would you want to have students suffer the pains of getting 100 on their daily work when the weekly test will easily tell you if they are doing well?
I always tell homeschool educators that grading the daily work, when there is a test every Friday, amounts to a form of academic harassment to the student. Like everything else in life, we tend to apply our best when it is absolutely necessary. Students will accept minor mistakes and errors when performing their daily "practice" of math problems. They know when they make a mistake and rather than redo the entire problem, they recognize the correction necessary to fix the error and move on without correcting it. They have a sense when they know or do not know how to do a certain math problem; however, when they encounter that all important test every Friday, - as I like to describe it - they put on their "Test Hat" to do their very best to make sure they do not repeat the same error!
In sports, daily practice ensures the individual will perform well at the weekly game, for without the practice, the game would end in disaster. The same concept applies to daily piano practice. While the young concert pianist does not set out to make mistakes during the daily practice for the upcoming piano recital, he quickly learns from his mistakes. Built into John Saxon's methodology are weekly tests (every four lessons from Algebra 1/2 through Calculus) to ensure that classroom as well as homeschool educators can quickly identify and correct these mistakes before too much time has elapsed.
In other words, the homeschool educator as well as the classroom teacher is only four days away from finding out what the student has or has not mastered during the past week's daily work. I know of no other math textbook that allows the homeschool educator or the classroom teacher this repetitive check and balance to enable swift and certain correction of the mistakes to ensure they do not continue. Yes, you can check daily work to see if your students are still having trouble with a particular concept, particularly one they missed on their last weekly test, which can be correlated to their latest daily assignment. However, as one home school educator stated recently on one of the blogs "Yes, they must get 100 percent on every paper or they do not move on." While this may be necessary in other math curriculums that do not have 30 or more weekly tests, it is a bit restrictive and punitive in a Saxon environment.
John Saxon realized that not all students would master every new math concept on the day it is introduced, which accounts for the delay allowing more than a full week's practice of the new concepts before being tested on them. He also realized that some students might need still another week of practice for some concepts which accounts for his using a test score of eighty percent as reflecting mastery. Generally, when a student receives a score of eighty on a weekly test, it results from the student not yet having mastered one or two of the new concepts as well as perhaps having skipped a review of an old concept that appeared in the assignment several days before the test. When the students see the old concept in the daily work, they think they can skip that "golden oldie" because they already know how to do it! The reason they get it wrong on the test is that the test problem had the same unusual twist to it that the problem had that the student skipped while doing the daily assignment.
In all the years I taught John Saxon's math at the high school, I never graded a single homework paper. I did monitor the daily work to ensure it was done and I would speak with students whose test grades were falling below the acceptable minimum of eighty percent. I can assure you that having the student do every problem over that he failed to do on his daily assignments does not have anywhere near the benefit of going over the problems missed on the weekly tests because the weekly tests reveal mastery - or lack thereof - while the daily homework only reveals their daily memory!
SAXON MATH - WHEN USED CORRECTLY - IS STILL THE BEST MATH CURRICULUM!
Over the last twenty-some years, I have heard just about every story told by public and private school classroom teachers, school administrators, and home school educators about how difficult John Saxon's math books are. I believe that home school educators who speak poorly about John Saxon's math books are like the classroom teachers and administrators I encountered who always blamed the math book for students' poor showing. They never became aware that misusing John Saxon's math books was a major contributing factor to the student's difficulty. They never received or asked for any special training on how to correctly use John Saxon's math books. Why should they? After all, isnt one math textbook just like another?
More than a decade ago, while briefing the superintendent of a large school district in Colorado I related to him - from my observations - that the vast majority of the districts math teachers were not properly using John Saxon's math books. His district had been using (rather misusing) John's books for more than five years and the students math scores were getting worse, not better! I told him that it was not the books, but rather this misuse of the books that accounted for the district's failing math scores.
In the middle of my briefing, he stopped me and said, "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 be dropped, or you will strip the gears!" I went on to tell him that while I was not the owner of the company, if John Saxon were alive today, standing up here addressing them under these circumstances, he would tell them to either use his books correctly or get rid of them, and blame someone else's textbooks for the failing grades.
On another occasion while briefing administrators at a school district in the state of Missouri whose math teachers were guilty of the same misuse, I promised their superintendent the same results I had promised the superintendent in Colorado that if they would make some adjustments and use the books correctly, they would develop a successful math program and their students math scores would go up. The district decided to implement the changes I had recommended. About eighteen months later, I received a letter from the superintendent. She wrote that their middle school students had scored the highest of any middle school in the state on their end-of-year math exams.
During these past several decades of advising and assisting homeschool parents about curriculum choices for their children, I noticed many of their calls and email to me were the result of having received inaccurate or inadequate - sometimes downright erroneous - advice. This erroneous advice came from other home school parents, discussion groups, well-meaning but uninformed or inexperienced publishing company employees, or from well meaning, but inexperienced employees of homeschool textbook distributors.
With all the new math books and supplemental math products on the market today - and textbook publishers promising every home school parent that if you use their books, your sons and daughters would score well on the ACT or SAT tests - I thought it appropriate to take this opportunity to defend John's math books for the benefit of the home school educators and their students.
I do not sell John Saxon's math books - I never have! But I firmly believe that John's math books remain the best math textbooks on the market today. I also believe that some of these new book fads, advertising how their product makes math fun, will ultimately leave your child short of mastering the requisite fundamentals of mathematics necessary to succeed in the collegiate realm of engineering, architecture, science, medicine, et al.
Students fail calculus - not because they do not understand the calculus - but because they never mastered the fundamentals of algebra, and they will fail a basic algebra course if they have not mastered the concepts of decimals, fractions and percents. John Saxon's math books were designed to create mastery of mathematics at all levels, and the infusion of repetition over time (referred to by Dr. Benjamin Bloom as "automaticity") creates this mastery at every level for every student who uses John Saxon's math books properly.
While home school students have a great deal more academic flexibility than the public or private classroom students do, they can just as easily fall prey to the same difficulties in mathematics as the public classroom students if they are using one of John Saxon's math books incorrectly. Parents of home school students who have displayed poor progress while using John Saxon's math books, generally have unknowingly contributed to the student's poor performance by taking shortcuts and preventing the student from receiving the full benefit of John Saxon's methods.
Earlier this year, in the January and February news articles, I went over the essential Do's and Don't's together with my comments and recommendations on how to correct them and have your child enjoy mathematics and realize mastery of the material using the best mathematics curriculum on the market today - John Saxon's math books!
If you need to discuss a special situation concerning your son or daughter's math progression or difficulty, please do not hesitate to either email or call me at:
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”
WHAT ARE FORMULA CARDS? WHAT ARE THEY USED FOR?
WHERE CAN I GET THEM?
Having been repeatedly threatened by my high school math teachers that I would be doomed to fail their tests if I did not memorize all those math formulas, I was somewhat surprised later in a college calculus course when the professor handed out "formula cards" containing over ninety geometry, trigonometry identities, and calculus formulas. He explained that they could be used on his tests. He did not bat an eye as he handed them out and reminded us that selecting the correct formulas and knowing how and when to use them was far more important than trying to memorize them or write them on the desk top.
So, when I started teaching at the high school, I announced to the students that they could make "formula cards" by using 5 x 8 inch cards, lined on one side and plain on the other. It never failed. Immediately, one of the students would ask why I did not have them printed off and handed out, saving them a considerable amount of time and money creating their own.
I told my students that whenever they encountered a formula in their textbooks, writing it down would strengthen the connection more than if they just read it and tried to recall it later while working a problem. Reading the formula in the textbook was their first encounter and there would not yet be a strong connection between what they were reading and what they tried to remember. However, when they took the time to create a formula card for that particular formula, they would be strengthening that connection. As they used the card when doing their daily assignments, they would continue the process and eventually place the formula in their long term memory.
So, how can you get formula cards? Simple! Each student makes his own. I allowed my students to use them starting with Math 87 or Algebra 1/2. One young lady in my Algebra 2 class used blue cards for geometry formulas and white cards for the algebra formulas to save her time looking through the cards. The cards should be destroyed after completion of the course, requiring the next student to make his own. Then how do you make formula cards?
Have the students use 5 x 8 cards - and write or print clearly and big. On the plain side of the card they print the title of the formula such as the formula for the area of a sector found on page 16 of the third edition of the Algebra 2 textbook.
So, on the front of the card (the plain side) in the center of the card the student would print::
AREA OF A SECTOR
When you turn the card over, in the upper right hand corner is the page number of the formula to enable the student to immediately go to that page should he need more information (in this case p 16). Recording the page number saves flipping through the book looking for the information and wasting time, especially when the student encounters a difficult problem some twenty lessons later.
After writing down the appropriate page number, they neatly record the formula: (double checking to make sure they have recorded it correctly.)
Area of Sector = Pc/360 times [(pi)(r)]^2 (where the piece (Pc) equals the part of the sector given.)
NOTE: If diameter is given remember to divide by two before squaring the value.
Remember, students may also use the formula cards on tests - and if you watch them - the dog eared cards seldom get looked at after awhile.
For those of you concerned about students taking the ACT or SAT, unless they have changed their policy, students are given a sheet of formulas for the math portion of the test. Again, this requires the student to know which formula to select and what to do with it - rather than remembering all those formulas!
IS THERE ANY VALUE TO USING A SEPARATE GEOMETRY TEXTBOOK?
Have you ever seen an automobile mechanic's tool chest? Unless things have changed, auto mechanics do not have three or four separate tool chests. They have one tool chest that contains numerous file drawers separating the tools necessary to accomplish their daily repair work. But the key is that all of these tools are in a single tool chest.
What if the auto mechanic purchased several tool chests thinking to simplify things by neatly separating the specific types of tools from each other into separate tool chests rather than in separate drawers in the one tool chest? Each separate tool chest would then contain a series of complete but distinctly different tools. If mechanics did this, there would now exist the possibility that they would find themselves trying to remember which tool chest contained which tools - and - the extra tool chests would cost them more!
It is somewhat like that in mathematics. Each division of mathematics has its strengths and weaknesses and like the auto mechanic who selects the best tool for a specific job, so the physicist, engineer, or mathematician selects the best math procedure to meet the needs of what they are doing.
But how do we address the argument that geometry provides a distinct and essential thought process unlike that used in algebra? The advent of computers has provided educators with an alternative course titled Computer Programming. A computer programming course teaches students the same methodology or thought process that the two-column proofs of geometry do. Basically, it teaches the student that he cannot go through a door until he has opened it - meaning - the student must use valid statements that are logically and correctly placed to reach a valid conclusion and to prove that conclusion valid by having the computer program work correctly.
Before computers, educators in the United States felt that providing the separate geometry course would benefit those students interested in literature and the arts, who enjoyed the challenge of geometry without the burden of algebra, while still allowing students entering the fields of science and engineering, who had to take more math, to take the course also. When I was in high school, most geometry teachers taught only geometry, they never taught an algebra course - as I soon learned!
I recall encountering that little known fact when I took high school geometry from one such teacher. I was sharply rebuked early in the school year when I kept using the term "equal" to describe two triangles that had identical measures of sides and angles. The first time I said the two triangles that contained identical angles and sides were "equal," she told me I was wrong. She then proceeded to tell me and the class that the only correct term to describe two identical triangles was the term "congruent." She did not say my answer was technically correct, but that in the geometry class, we used the term "congruent" rather than "equal" - she specifically pointed out that I was "wrong."
The next day in geometry class, I really got in trouble when I stood and read Webster's definition of the word congruent.
Con-gru-ent - adj. 1) In agreement or harmony: ... 2) Geometry (of figures):
identical in form:
Coinciding exactly when superimposed ...
Just before I was told to go to the office and tell the principal that I was being rude, I asked her why the two triangles could not also be said to be equal since they had identical angles and sides and were equal in size. Then I drove the final nail in my coffin when I proceeded to read Webster's definition of "equal."
Equal - adj. 1) Being the same in quantity or size...
Half a century later, when I taught both the algebra and geometry concepts simultaneously while using John Saxon's math books at a rural high school, I made it clear to the students that while they should become familiar with the terminology of the subject, they were free to interchange terms as long as they were correctly applied. I also made it clear to them that the object of learning geometry and algebra was to challenge and expand their thought processes and for them to understand the strengths and weaknesses of each and apply whichever math tool best served the problem being considered.
While many tout the separate geometry textbook as necessary to enable a child to concentrate on a single subject rather than attempting to process both geometry and algebra simultaneously, I would ask them how a young geometry student can solve for an unknown side in a particular triangle without some basic knowledge of algebraic equations. In other words, if you are going to use a separate geometry textbook, it cannot be used by a student who has not yet learned how to manipulate algebraic equations. This means that a separate geometry book is best introduced after the student has successfully completed an algebra 1 course.
For most students this means placing the separate geometry course between the Algebra 1 and Algebra 2 courses creating a gap of some fifteen months between them. (Two summers off, plus the nine month geometry course). As was true in my high school days, this situation creates a problem for the vast majority of high school students who enter the Algebra 2 course having forgotten much of what they had learned in the Algebra 1 course fifteen months earlier.
So what am I getting at? Must we have a separate geometry textbook for students who cannot handle the geometry and algebra concurrently? Well, let me ask you, if students can successfully study a foreign language while also taking an English course or successfully study a computer programming course while also taking an algebra course, why can't they study algebra and geometry at the same time, as John Saxon designed it?
Successful completion of John Saxon's Algebra 2, (2nd or 3rd editions) not only gives the student a full years' credit for the Algebra 2 course, but it also incorporates the equivalent of the first semester of a regular high school geometry course. I said "Successful Completion" for several reasons. FIRST: The student has to pass the course and SECOND: The student has to complete all 129 lessons.
Whenever I hear home school educators make the comment that "John Saxon's Algebra 2 book does not have any two-column proofs," I immediately know that they stopped before reaching lesson 124 of the book which is where two-column proofs are introduced. The last six lessons of the Algebra 2 textbook (2nd or 3rd editions) contain thirty-one 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 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 problems dealing with two-column proofs.
So why then did John Saxon not want to publish a separate geometry textbook? As I mentioned in one of my newsletters several years ago, 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) one and the advanced algebra course (Algebra 2) to the detriment of the student. AND THEY WROTE THIS 104 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" that prevents students from retaining the necessary basic algebra concepts learned in basic algebra to be successful when encountering the rigors of advanced algebra.
We remain one of the only - if not the only - industrialized nations that have separate math textbooks for each individual math subject. When foreign exchange students arrive at our high schools, they come with a single mathematics book that contains geometry, algebra, trigonometry, and when appropriate, calculus as well. Is it any wonder why we are falling towards the bottom of the list in math and science?
When students take a separate geometry course without having gradually been introduced to its unique terminology and concepts, they encounter more difficulty than do students using John Saxon's math books The beauty of using John's math books, from Math 76 through Algebra 1 is that students receive a gradual introduction to the geometry terminology and concepts.
If you are going to use John Saxon's math books through Advanced Mathematics or Calculus you do not need a separate geometry book. This means you must use the third editions of John Saxon's Algebra 1 and Algebra 2 books because the current owners of Saxon Publishers (HMHCO) have stripped all of the geometry from the new fourth editions of their versions of Algebra 1 and Algebra 2. And you do not want a student to go from the fourth edition of Algebra 2 to the Saxon Advanced Mathematics textbook.
NOTE: Please Click Here to watch a short video on how to receive credits for Geometry, Trigonometry and Pre-calculus using John Saxon's Advanced Mathematics textbook - and how to record the course titles on the student's transcript.
HOW MUCH TIME SHOULD STUDENTS SPEND ON MATH EACH DAY?
One of several arguments advanced by home school educators regarding the efficiency of the Saxon math curriculum is that from Math 54 through Advanced Mathematics the courses require too much time to complete the daily assignment of thirty problems. Their solution to this often takes one of two approaches. Either they allow the student to take shortcuts to reduce the time spent on daily assignments, or they find another math curriculum that takes less time – you know – you’ve heard them say, “We found another math curriculum that is more fun, easier, and it does not require so much time.”
In this year’s, January and February newsletters, I addressed some of the ramifications of taking these shortcuts when using John Saxon’s math books. In these two articles, I described in detail the effects upon students who used some or all of them, so I will not go over them again here. I would ask you to read those two newsletters if you have not already done so. What I want to discuss here is what may be causing the excessive amount of time taken by the students and also, what constitutes excessive time to an educator who taught in a public classroom using Saxon math books for over a decade.
While I was teaching high school mathematics in a rural Oklahoma high school, I would often go and watch my students who were on the the high school track, basketball, or football teams during their practice sessions after school. I was able to chat with the mothers and fathers who were also watching these practices. This one-on-one conversation often gave me an insight into their priorities regarding their children’s education.
While they sometimes complained about the rigors of my math classes, they never once complained about the length of time their sons and daughters were out on the field in the heat or cold - or on the basketball court – practicing – after just spending six academic hours in the classroom. In fact, when coaches were forced to cancel a practice for one reason or another, some of the parents would vocally complain that the practices should continue. They expressed concern that skipping practice would take the “edge” off their son or daughter’s playing ability and inhibit their athletic “sharpness” for the next game.
Strange then that some parents would complain the 45 – 60 minutes spent each day on mathematics “practice” would be excessive - and more unusual - that they would seek an easier course of action. They never discussed the ramifications that doing so might take the “edge” off their child’s math “sharpness” for the next math course or the state mandated math test. I never heard the high school parents complain about watching the tough daily drills and practices run by the coaches. I never heard a parent complain about the hour spent each day by the students diligently practicing their piano lessons, or having to come in before school early each day to spend 45 minutes in the weight room.
At least several times each week I receive email from home school parents who express concern that their son or daughter was taking an inordinate amount of time on their daily math assignment in one of the books from Math 54 through Advanced Mathematics. The solution to the excessive time spent by students using the Advanced Mathematics textbook is easy to resolve. The solution to that unique situation is explained in a short video clip (Click Here to view that video).
I have interacted with several thousand parents and students in the twelve years that I taught mathematics at that rural high school. I have also advised thousands more home school educators and home school students in the succeeding decade after my retirement while serving as one of the Homeschool Curriculum Advisors (for Math 76 through Calculus and Physics) for Saxon Publishers and later for Harcourt-Achieve who bought the company from John’s children. And while every child and home school situation is different, my experiences have shown me that there exist several situations that contribute to excessive time spent on daily work by students, whether home schooled or attending a public or private classroom.
These situations are:
The Student is in The Wrong Level Math Course: If after lesson thirty in any Saxon math book, students continue to receive 80% on the weekly tests of twenty questions, within a maximum of fifty minutes with no partial credit (all right or all wrong) and no calculator (until Algebra 1), then they are in the correct level Saxon math book. If the test scores are constantly below that or if they fall below an 80 on their first five or so tests, then that is a good indication they are in the wrong level Saxon math book. This situation can result from any one or more of the following conditions:
- They did not finish the previous Saxon math book.
- They took shortcuts in the preceding math book.
- Their previous math book was not a Saxon math book.
- They did not take the weekly tests in the previous math book, using the daily grade as an indication of their level of proficiency.
- Their last five tests in the preceding course were well below 80% (minimal mastery).
The Student is Required to Re-do Math Problems from Yesterday’s Lesson: Why do we want students to get 100% on their daily practice for the weekly test? When we grade their daily work and have them go over the ones they missed on the previous day’s assignment, nothing is accomplished except to “academically harass” the students. The daily work reflects nothing but the status of the students’ temporary learning curve. It is the weekly tests and not the daily work that reveal what the student has mastered from the previous weeks and months of work. Not every student masters every concept the day it is introduced, which is why there is a four to five day delay from when the concept is introduced to when it is tested. In the twelve years that I taught John Saxon’s math books in high school, I did not grade one homework paper – but I did grade the weekly tests which reflected what the students had mastered as opposed to their daily work which did not. Remember, John Saxon’s math books are the only books I am aware of that use weekly tests to evaluate a student’s progress. There are a minimum of thirty weekly tests in every one of John’s math books from Math 54 on.
Too Much Time is Spent on The Warm Up Box: From Math 54 through Math 87, there is what used to be called a “Warm Up” box at the top of the first page of every lesson. I recall watching a sixth grade teacher waste almost thirty minutes of class time while three boys took turns giving different opinions as to how the “Problem of The Day” was to be solved – and arguing as to which had the better approach. After class, I reminded the teacher that the original purpose of the box was to get the students settled down and “focused” on math right after the second bell rang. I said to her, “Why not immediately review a couple of the problems from yesterday’s lesson at the start of class for the few who perhaps did not grasp the concept yesterday? Then move immediately to the new lesson.” This process would take about 10 to 20 minutes and would leave students with about 40 minutes of remaining class time to work on their new homework assignment.
NOTE: In any of John Saxon’s math books from Math 54 through Algebra 2, the “A” and “B” students will get their 30 problems done in less than 40-50 minutes. The “C” students will require more than an hour.
The Student is Required to Do All of The Daily Practice Problems: The daily practice problems were created for teachers to use on the blackboard when teaching the lesson’s concept so they did not have to create their own or use the homework problems for demonstrating that concept. Many of the lessons from Math 54 through Math 87 have as many as six or more such problems and if the student understands the concept, they are not necessary. If the student has not yet grasped the concept, having the student do six or more additional practice problems of the same concept will only further frustrate him. Remember, not every student grasps every concept on the day it is introduced. The five minutes spent on review each day is essential to many students.
The Student is a Dawdler or a Dreamer: There is nothing wrong with being a “Dreamer,” but some students just look for something to keep them from doing what they should be doing. I call these students “Dawdlers.” I recall the first year I taught. I had to constantly tell some students in every class to stop gazing out the window at the cattle grazing in the field outside our classroom – and get on their homework. That summer, I replaced the clear glass window and frame with a frosted glass block window - and in the following eleven years I had absolutely no problem with my “Dawdlers.”
The Student is Slowed by Distractions: Is the student working on the daily assignment in a room filled with activity and younger siblings who are creating all sorts of distractions? Even the strongest math student will be distracted by excessive noise or by constantly being interrupted by younger siblings seeking attention. Did you leave the student alone in his room only to find he was on his cell phone talking or texting with friends or listening to the radio? Or worse, does he have a television or computer in his room and does he use the computer to search the internet for a solution to his math problems or engage in something equally less distracting by watching the television?
Please do not misinterpret what I have discussed here. If you desire to do all of the above and the student takes two hours to complete a daily assignment, and both you and the student are satisfied, then that is acceptable. But if you are using this excessive time as an excuse for your child’s frustration and as an argument against John Saxon’s textbooks, I would remind you of what John once told a school district that did everything John had asked them not to do and they were now blaming John’s books for their district’s low math test scores. John told them, “If you want to continue your current practices, get rid of my books and buy someone else’s book to blame.”
JUST WHAT IS THE DIFFERENCE BETWEEN MATH 87 AND ALGEBRA 1/2 ?
There appear to be varying explanations regarding whether a student should use Math 87 or Algebra 1/2 after completing the third or fourth edition of John Saxon’s Math 76 textbook. Let me see if I can shed some light on the best way to determine which one, or when both, should be used.
First, whenever I discuss the Math 76 textbook in this article, I am talking about the third or fourth editions of that book. I am not talking about the old first or second editions of John’s Math 76 books. These two older editions have been out of print for almost fifteen years now and their content, while acceptable at the time, would not now enable a math student to proceed successfully through either the second or third editions of Math 87 or the third edition of Algebra 1/2.
Second, whenever I discuss using the Math 87 textbook, I am talking about either the second or third editions of that book and not the older first edition which has also been out of print for more than a decade.
Let me assure you that, except for the new soft cover, the addition of a solutions manual, and the varied numbering of the pages, there is absolutely no difference between the 120 lessons and the 12 Investigations of the hard cover second edition of Math 87 and the new soft cover third edition of Math 87. Oh yes, the new third edition has added a TOPIC A at the end of the book (after Investigation 12) dealing with Roman Numerals and Base 2. And even though the marketing folks at the publishers have added the word “Prealgebra” under the cover title of the soft cover third edition textbook, these two additional topics, while interesting and nice to know, are not pre-algebra material and will not create any shortfall for the student in Algebra 1 or even later in Algebra 2.
Both the Math 87 and Algebra 1/2 textbooks prepare the student for any Algebra 1 course. The main difference between using the Math 87 and the Algebra 1/2 books depends upon the student’s success in the Math 76 textbook. The Math 87 book starts out a little slower than the Algebra 1/2 book does because it assumes the student needs the additional review resulting from the student encountering difficulty in the latter half of the Math 76, textbook. Also, If you were to open to any lesson in the Algebra 1/2 textbook, you would immediately notice that the “Warm-Up’ box common in all Saxon math books from Math 54 through Math 87, is noticeably absent.
If there exists a math savvy student of John Saxon’s Math 76 textbook, who received test grades of 85 or better on the last five tests in Math 76 (50 - 55 minute test period, no calculator, and no partial credit), then that student would be more challenged and, from my teaching experience, much better off in the Algebra 1/2 book. However, if his last five test scores are below 85, then from my experiences, that indicates that student should proceed to Math 87, and upon completion of that book, if his or her last five tests are now 80 or better (minimal mastery), then that student can easily skip Algebra 1/2 and go on to success in Algebra 1.
If however, a student encounters difficulty going through both Math 76 and Math 87, then proceeding through the Algebra 1/2 textbook before attempting Algebra 1 will allow the student to regain his confidence. Doing so will further ensure the student has mastered a solid conceptual base necessary for success in any Algebra 1 course.
Students will fail an Algebra 1 course if they have not mastered fractions, decimals and percents which are emphasized before the student reaches that course. I realize that not every child fits neatly into a specific mold, but John Saxon’s Math 76, Math 87, and Algebra 1/2 textbooks allow the Saxon home school educator sufficient flexibility to satisfy every student’s needs and to ensure the students’ success in any Algebra 1 course.
ARE JOHN SAXON'S ORIGINAL MATH BOOKS GOING THE WAY OF THE DINOSAUR?
In the past several weeks I have been asked by some home school educators whether or not I will create my teaching DVD “videos” for the new fourth editions of Algebra 1 and Algebra 2, and the resulting new first edition of Geometry now being sold on the Saxon Homeschool website by the new owners of Saxon Publishers.
The answer is no, I will not do so. My creation of the current DVD video series for John’s math books, based upon rock solid editions created by John Saxon, was not to make money. Using my Saxon classroom teaching experiences, I wanted to create a classroom environment for home school students who wanted to master high school mathematics using John’s unique math books. However, publishing math textbooks redesigned to be like all the other math textbooks on the market is not what John intended when he created his unique style of math books.
John Saxon would not have sanctioned gutting his Algebra 1 and Algebra 2 textbooks of their geometry to create a separate geometry textbook. He believed that using a separate geometry textbook was not conducive to mastering high school mathematics. More importantly, each of John’s math books had an author - an experienced classroom mathematician - behind them. These three new editions, created under his Saxon title, do not.
When Harcourt-Achieve bought John Saxon’s dream - Saxon Publishers - from his children, I made the comment that the new owners were certainly smart enough to recognize the uniqueness of John’s books. I predicted that they would not change the content of John’s books. Certainly, I commented. “They would never take their prize winning bull and grind it up into hamburger” – or so I thought!
Well the new owners of Saxon Publishers appear to have done just that, and the time has come for me to apologize because they are now selling the hamburger on the Homeschool website. I have previously cautioned home school Saxon users not to use the new fourth editions of Algebra 1 and Algebra 2 then offered only on the school website because the company had gutted all geometry from them to enable them to publish a separate geometry textbook desired by the public school system. But they are now selling them on the Homeschool site as well.
Having been affiliated with one of the larger publishing companies - after Saxon Publishers was sold - I observed that the driving force in the company was not so much the education of the children, but the quarterly profit statement. And that is okay, but being around their VP’s and upper level executives showed me that to them “a book is a book is a book.” I still believe they have not the foggiest idea of just how unique and powerful John’s math books are when used correctly. However, I may be wrong, because they may have already observed that it is this “uniqueness” that requires special handling and that requires special training, and that costs money – reducing quarterly profits.
If you are serious about using John Saxon’s original math series through high school, I recommend you not buy these new fourth editions of Algebra 1 and Algebra 2. I strongly recommend you immediately acquire the home school editions of John’s math books that I discussed in my February 2010 news article - which include the third editions of Algebra 1 and Algebra 2. The news article not only explains the correct editions that will still be good for several more decades, but it explains the correct sequencing of the books as well.
I do not believe the publishing company will long suffer the expense of publishing both the third and fourth editions of Algebra 1 and Algebra 2. It is my opinion they may well stop printing and selling the third editions of Algebra 1 and Algebra 2 when current stocks run out. This will then require that home school educators using Saxon math books buy the separate geometry book also. After all, “Don’t you make more money from selling three books than you do from just selling two?”
Maybe I am wrong, and the publishers of John Saxon's math books will not stop printing the third editions of Algebra 1 and Algebra 2 as I am predicting - but then again I could be wrong - again!
WHY IS THERE A “LOVE – HATE” RELATIONSHIP WITH SAXON MATH BOOKS?
Over the past twenty-five 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 am 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.
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 junior year in college when he has mastered the fundamentals.”
As John would 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 twenty-five 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 is 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 email@example.com or call me at (580) 234-0064 (CST). If you email me, please include your telephone number and I will call you at my expense.
ARE THE NEW SAXON MATH BOOKS BETTER THAN THE OLD EDITIONS?
Some of you may remember that in the summer of 2004, the Saxon family sold Saxon Publishers to Harcourt Achieve. Just to put everything in perspective, Harcourt Achieve, Inc. was then owned by the Harcourt Corporation which in turn was later acquired by the multi-billion dollar conglomerate Reed-Elsevier who then sold Harcourt, Inc. to Houghton Mifflin creating the current company (that owns Saxon Publishers) which is now the Houghton-Mifflin Harcourt Company also known as HMHCO. It all reminds me of when the Savings and Loan Companies got the nickname “Velcro banks” because they changed names so often before they disappeared the way of the dinosaurs.
When I published my June 2007 news article, I told readers “Not to worry!” As I had said earlier when Harcourt acquired John Saxon’s publishing company in 2004, the new sale should not affect the quality of John’s books. I asked the obvious question, “Why would anyone buy someone’s prize-winning ‘Blue Ribbon Bull’ to make hamburger with?” I did not believe that this new sale would change John’s books much either, and I told the readers that if these changes became more than just cosmetics, I would certainly keep them informed.
Well, it is time to mention that some of the changes are no longer cosmetic. Some of the new editions are not what John Saxon had intended for his books. These new editions are vastly different, and both home school educators as well as classroom teachers must be aware of these changes and be selective about what editions and titles they should and should not use if they desire to continue with John Saxon’s methods and standards.
Initially, these revised new editions were offered only to the public and private schools and not to the home school community. However, introduction of their new geometry textbook to the home school web site tells me that it may not be long before the new fourth editions of Algebra 1 and Algebra 2 replace the current third editions now offered on the website.
I could be wrong. Perhaps they added the geometry textbook to the home school website because some home school parents were unaware that a full year of high school geometry was already offered within the Algebra 2 textbook (first semester of geometry) and the first sixty lessons of the Advanced Mathematics textbook (second semester of geometry). Additionally, placing the geometry course in between the Saxon Algebra 1 and Saxon Algebra 2 textbooks is a sure formula for student frustration in Saxon Algebra 2 since the new geometry book does not contain algebra content. The only reference to “Geometry” in the new fourth edition of Saxon Algebra 1 is a reference in the index to “Geometric Sequences” found in lesson 105. That term is not related to geometry. It is the title given to an algebraic formula dealing with a sequence of numbers that have a common ratio between the consecutive terms.
It would be my hope that the senior executives at HMHCO would recognize the uniqueness and value of the current editions of John Saxon’s math books that continue his methods and standards. However, to ensure you have the correct editions of John Saxon’s math books, as he published them, you can go to my February 2010 news article where I list the correct editions to use from Math 54 through Calculus. The editions I referenced in that article will be good for many more decades.
What are some of the main causes for student frustration or failure when using John Saxon’s math books? (Part 2)
Last month we discussed the ESSENTIAL DO'S when using John Saxon’s math books.
This month we will go over the ESSENTIAL DONT'S:
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 what I have asked thousands of home school parents 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 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:
- 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!
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.”
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 home school educators who use, or are contemplating using, Saxon math books.
So long as you use the books and editions I referenced in my book, and later re-iterated in my February 2010 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!
What are some of the main causes 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.
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 specific rules be followed to ensure success – and ultimately mastery!
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 we will discuss the ESSENTIAL DO’S.
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 ½ would be like moving from Math 65 to Algebra ½ in the current editions. For more information on which editions of John’s books are still valid, read the earlier published February 2010 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 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 the February newsletter, we will discuss the ESSENTIAL DON’T’S when using John’s books.