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Newsletters
WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS?
MYTH 3: Saxon Algebra 2 Does Not Contain Formal Two-Column Proofs.
When you hear someone say that if you use John Saxon's Algebra 2 textbook, you will need a separate geometry book because "There are no two-column proofs in John Saxon's Algebra 2 textbook," they are telling you that either (1) they have never used that textbook or (2) if they did use it, they never finished the book - they stopped before reaching lesson 124, or (3) they used the new fourth edition which has no geometry content.
Whether they are using the second or third edition of John's Algebra 2 book, students will encounter more than forty informal and formal two-column proof problems in the last six lessons of the textbook. The first ten or so geometry proof problems students encounter in lesson 124 of the textbook are the more informal method of outlining a proof. John felt this introduction to the informal outline would get the students better prepared for the more formal two-column proofs that they will encounter later. Then, from lesson 125 through lesson 129, students will be asked to solve more than thirty formal two-column proofs that are as challenging as any the students will encounter using any separate geometry textbook.
If they proceed onto the Saxon Advanced Mathematics course the following school year, they will encounter two dozen informal proofs in the first ten or so lessons followed by more than forty-six formal two-column proofs in the next thirty or so lessons. They will encounter at least one formal two column proof problem in every lesson through lesson forty and then encounter them less frequently through the next twenty or so lessons of the book.
When I was teaching high school math in a rural public high school, I taught both Saxon Algebra 2 as well as John's Advanced Mathematics course. The students who took my Advanced Mathematics class came from my Algebra 2 class as well as another teacher's Algebra 2 class. I recall the students in my Advanced Mathematics class who had taken Saxon Algebra 2 from me would comment that the two-column proofs in the Advanced Mathematics book were easier than those they had encountered last year in our Algebra 2 book. "Perhaps you have learned how to do two-column proofs" was my reply
However, the students who came from the other teacher's Algebra 2 class moaned and groaned about how tough these two-column proofs were in the Advanced Mathematics book. After discussing the situation with the other teacher, I found that she knew I would cover two-column proofs in the early part of the Advanced Mathematics textbook so she stopped at lesson 122 in the Algebra 2 course - never covering the introduction to the two-column proofs.
The geometry concepts encountered in John Saxon's Algebra 2 textbook - whether the second or third edition - are the equivalent of the first semester material of a regular high school geometry course and that includes a rigorous amount of formal two-column proofs!
If you are using the new fourth edition of Algebra 2, you must also purchase a separate geometry textbook to acquire geometry credit as the new fourth editions of the revised HMHCO Algebra 1 and Algebra 2 textbooks have had the geometry content removed from them.
Myths that will be discussed in future News Articles:
You Must Use the New Saxon Geometry Textbook to Receive Geometry Credit.
Advanced Mathematics Can Easily be Taken in a Single School Year!
You Do Not Have to Finish the Last Twenty or So Lessons of a Book.
WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS?
MYTH 2: Saxon Math is Just "Mindless Repetition."
More than a decade ago, at a National Council of Teachers of Mathematics (NCTM) Convention, John and I encountered a couple of teachers manning their registration booth. When John introduced himself, they made a point to tell him that they did not use his math books because they felt the books were just "mindless repetition."
John laughed and then in a serious note told the two teachers that in his opinion it was the NCTM that had denigrated the idea of thoughtful, considered repetition. He quickly corrected them by reminding them that the correct use of daily practice results in what Dr. Benjamin Bloom of the University of Chicago had termed "Automaticity." Dr. Bloom was an American educational psychologist who had made significant contributions to the classification of educational objectives and to the theory of mastery-learning.
Years earlier, John Saxon had taken his Algebra 1 manuscript to Dr. Bloom to evaluate his manuscript's methodology. John wanted to find out if there was a term that described the way his math book was constructed. Dr. Bloom informed John that he had not created a new teaching method. He himself had named this same methodology in the early 1930's
Dr. Bloom referred to this method of mastery - the same one contained in John's manuscript - as "Automaticity." He described it as the ability of the human mind to accomplish two things simultaneously so long as one of them had been overlearned (or mastered). He went on to explain to John that the two critical elements of this phenomenon were repetition and time. John had never heard this term used before, but while in military service, he had encountered military training techniques that used this concept of repetition over extended periods of time, and he had found them extremely successful.
If you think about it, professional sports players practice the basics of their sport until they can perform them flawlessly in a game without thinking about them. By "Automating" the basics, they allow their minds to concentrate on what is occurring as the game progresses. Basketball players do not concentrate on dribbling the basketball, they concentrate on how their opponents and fellow players are moving as each play develops and they move down the floor to the basket while automatically dribbling the basketball.
Baseball players perfect their batting stance and grip of the bat by practicing hitting a baseball for hours every day so that they do not waste time concentrating on their stance or their grip at the plate each time they come up to bat. Their full concentration is on the pitcher and the split second timing of each pitch coming at them at eighty or ninety miles an hour.
How then does applying the concept of "Automaticity" in a math book differentiate that math book from being just "mindless repetition?" John Saxon's math books apply daily practice over an extended period of time. They enable a student to master the basic skills of mathematics necessary for success in more advanced math and science courses. As I mentioned earlier, the two necessary and critical elements of "Automaticity" are repetition over time. If one attempts to take a short cut and eliminate either one of these components, mastery will not occur. You cannot review for a test the day before the test and call that process "Automaticity." Nor can you say that textbook provides mastery through review.
Just as you cannot eat all of your weekly meals on Saturday or Sunday - to save time preparing meals and washing dishes daily - you cannot do twenty factoring problems one day and not do any of them again until the test without having to create a review of these concepts just before the test. When a math textbook uses this methodology, it does not promote mastery; it promotes memory of the concepts specifically for the test. That procedure would best be described as "Teaching the Test."
John Saxon's method of doing two problems of a newly introduced concept each day for fifteen to twenty days, then dropping that concept from the homework for a week or so, then returning to see it again, strengthens the process of mastery of the concept in the long term memory of the student. Saxon math books are using this process of thoughtful, considered repetition over time to create mastery!
Myths that will be discussed in future News Articles:
Saxon Algebra 2 does not Contain Two-Column Proofs.
You Must Use the New Saxon Geometry Textbook to Receive Geometry Credit.
Advanced Mathematics Can Easily be Taken in a Single School Year!
You Do Not Have to Finish the Last Twenty or So Lessons of a Book.
WHAT ARE SOME OF THE MYTHS SURROUNDING JOHN SAXON'S MATH BOOKS?
MYTH 1: Saxon Math is Too Difficult.
This common myth is generated by public and private schools as well as homeschool educators who place a transfer student into the wrong level of Saxon math - usually a level above the students ability. I recall a homeschool parent at one of the Homeschool Conventions this past summer telling me she was going to switch to Saxon Math. She wanted to buy one of my Algebra 2 DVD tutorial series. I asked her what level book her son had just completed and she said it was an Algebra 1 textbook from (you fill in the name) company.
Since she lived in the area and was coming back to the convention the next day, I asked her if she would have her son take the Saxon Algebra 1 Placement test that night and come back the next day with the results so we could make sure he was being placed into the correct level Saxon math textbook. The next day, she came by the booth and informed me that her son had failed the Saxon Algebra 1 Placement Test. When I told her that test was the final exam in the Saxon pre-algebra course, she became quite concerned. I told her that the problem was not a reflection upon her son's intelligence.
The problem her son had encountered was that the previous textbook he had used taught the test. However, the cumulative nature of Saxon math books requires mastery of the concepts, which is why there is a weekly test. Had her son used the Saxon Algebra 2, 3rd Ed book - by the time he reached lesson twenty - he would have become painfully aware of what he and his mother would believe to be the "Difficulty" of the book. They would have blamed the Saxon book as being "Too Difficult." They would never have realized that his difficulty in the Saxon Algebra 2 book was that the previous math book allowed him to receive good test grades through review for each test the night before, rather than requiring mastery of the concepts as Saxon books do through the weekly tests.
This parent is not alone. Every week I receive emails or telephone calls from homeschool educators who are trying to accomplish the same thing. And until they have their student take the Saxon Math Placement Test, homeschool educators do not realize that they could very well be placing the student in a Saxon math book at a level above the students' capabilities.
The Saxon Math Placement Tests were not designed to test the students' knowledge of mathematics; they were designed to seek out what necessary math concepts had been mastered by the student to ensure success in the next level Saxon math book. Low test results on a specific Placement Test tell us that the student has not mastered a sufficient number of necessary math concepts to be successful in that level math book.
Saxon Placement Tests should not be used at the end of a Saxon math book to evaluate the students progress. Classroom teachers as well as homeschool educators should use the student's last five test scores of the course to determine their ability to be successful in the next level course. If the last five test scores are clearly eighty or better, the student will be successful in the next level Saxon math course - or anyone else's math textbook should you elect to change curriculum.
NOTE: Students should be given no more than 60 minutes to complete each test of a particular
Saxon math course. Each test question is awarded five points if correct. Test questions
should be graded as either right or wrong with no partial credit awarded for partially
correct answers.
Myths that will be discussed in future News Articles:
Saxon Math is Just Mindless Repetition.
Saxon Algebra 2 does not Contain Two-Column Proofs.
You Must Use the New Saxon Geometry Textbook to Receive Geometry Credit.
Advanced Mathematics Can Easily be Taken in a Single School Year!
You Do Not Have to Finish the Last Twenty or So Lessons of a Book.
DO YOU REALLY HAVE TO DO THE DAILY "WARM-UP" BOX AND "PRACTICE PROBLEMS"?
I receive several emails each week about the excessive amount of time some home school students spend on their math assignments each day. In almost every case, the students have spent between thirty minutes and an hour on the "Warm-Up" box and the six to eight "Practice Problems" before they even get started on the thirty problems of the Daily Assignment.
It has been a little more than a decade since I have been in a public classroom, and I am not sure if public school middle school math teachers still lean on what they used to call a math "Warm-Up" at the start of each class. The purpose of the "Warm-Up" was to settle their students down and get them ready for the math regimen of the day.
Using the "Warm-Up" box at the beginning of each lesson in the Saxon Math 54 through Math 87 textbooks can become quite frustrating to students who do not have the advantage of a seasoned classroom math teacher gently guiding them in the direction of the correct solution for the problem of the day - knowing that problem came from a concept not yet introduced to the students.
But what about the "Daily Math Facts Practice" and the "Mental Math"; how will students receive training in those areas? While these two areas are essential to the student becoming well-grounded in the old pen and pencil format of adding, subtracting, multiplying and dividing, graded by the teacher, that format has been improved with a computer model. Using the computer format allows the students to instantly know whether their answers are right or wrong. Additionally, while the home educators can easily spot the results tallied on the computer as the student moves along, it saves them the time spent manually grading the documents. I have placed a link to a wonderful Math Facts site on my website. Readers can find it by going to my home page, and from the list on the left side of the home page, click on "Useful Links." When the new window appears, select the second link from the top labeled "On-Line Math Facts Practice."
That link takes you to a math facts practice site that allows the student to select from seven different levels of difficulty in adding, subtracting, multiplying and dividing. If the answer is correct, a smiling gold star appears and if the answer is wrong, the correct solution appears along with an unhappy red stop sign. Five to ten minutes on this site every day at the appropriate level for the student to be challenged without being frustrated is just as good as the mental math or facts practice found in the "Warm-Up" box. While the Math 87 book still reflects the same "Warm-Up" box that the previous three math textbooks do, a student should have mastered the facts practice by this time. If this is the case, skipping the entire box is acceptable - unless - the student particularly enjoys the challenge of the "Problem Solving" exercise.
Now let's see if I can explain why I am recommending you stop having the student take time to do the six to eight practice problems at the front of each of the mixed practices (the daily assignments). The original purpose of these practice problems was for the classroom teacher to use all or some of them in explaining the concept on the board so that the teacher did not have to make up their own or use the homework problems. Sometimes teachers would use some of them to have students come to the board to show their understanding of the new concept.
My experience in teaching John's method of mastering math has shown me that there are only two possibilities that can exist after the student has read and/or had the concept of the daily lesson explained to them.
Possibility 1: The student understands the concept and after doing the two homework problems dealing with that new concept, completely understands what to do and has no trouble doing them. Mastery of this concept will occur over the next five to six days as the student does two more each of these days. If this is a critical concept linked to other steps in the math sequence, they will keep seeing this concept periodically throughout the rest of the book.
Possibility 2: When students encounter the two homework problems that deal with the new concept, they have difficulty doing them. So, on their own, should they go back to these practice problems and get another six to eight more problems wrong? If they did the practice problems before they started their daily work, would anything have changed? If they cannot do the two homework problems because they do not understand the new concept, why give them another six to eight problems dealing with the new concept to also get wrong? This approach ultimately leads to more frustration on the part of the student. Students will have spent thirty minutes or more on these additional six to eight practice problems and still not understand the new concept. Not every student completely grasps a new concept on the day it is introduced which is why John's books do not test a new concept until the student has had five to ten days to practice that concept.
Those practice problems were not placed there to give the student more problems to do in addition to the thirty they are already assigned for the day. As i mentioned earlier, they were placed there for the classroom teacher to use on the blackboard to teach the new concept so they did not have to develop their own or use the student's homework problems. There is nothing wrong with a home school educator asking a student to do one or two of them to show them the student understands the new concept; however, doing more than that could be a waste of time and effort in either possibility.
Not every child is the same and I realize that because of a particular child's temperament, there may be some instances where the parent has to go over more than one or two of the practice problems with the child - and this is okay - but for most students this is not necessary. If the student really enjoys the challenge of the daily "Problem Solving:" that is okay - except parents should make sure that the student does not spend an excessive amount of time on that individual challenge and allow the real goal of completing the thirty problems of the Daily Assignment to become a secondary goal - and later a bother to the student.
THAT OLD "GEOMETRY BEAR" KEEPS RAISING HIS UGLY HEAD .
Home School Educators frequently ask me about students taking a non-Saxon geometry course between algebra 1 and algebra 2, as most public schools do. They also ask if they should buy the new geometry textbook recently released to homeschool educators by HMHCO (the new owners of Saxon). As I mentioned in a previous newsletter late last year, a group of professors who taught mathematics and science at the University of Chicago bemoaned the fact that educators continued to place a geometry course between basic algebra (Algebra 1) and the advanced algebra course (Algebra 2) to the detriment of the student. AND THIS WAS 105 YEARS AGO!
I recently attended the homeschool convention in Wichita, Kansas and the question about the pros and cons of using a separate geometry textbook came up again. The danger of using a separate geometry textbook as described by these professors more than a hundred years ago - still exists today! Placing a nine month geometry course between the Algebra 1 and Algebra 2 courses creates a void of some fifteen months between the two algebra courses because - in addition to the nine month geometry course - for some students, you must also add the additional six months of summer between the two courses when no math is taken. The professors went on to explain in their book that it was this "void" that prevented most students from retaining the necessary basic algebra concepts from the basic algebra (Algebra 1) to be successful when encountering the rigors of the Algebra 2 concepts. Even if you are one of the home school families that schools the year round without taking a summer break, the student will still encounter a nine month "void" from the concepts of algebra during the separate nine month geometry course.
Home school educators also asked about using the new fourth editions of Saxon Algebra 1 and Algebra 2 recently released by HMHCO together with their new separate geometry textbook now offered for homeschool use. To create the new fourth editions of both the Algebra 1 and Algebra 2 textbooks, all the geometry was gutted from the previous third editions of both Algebra 1 and Algebra 2. Using the new fourth editions of their revised Saxon Algebra 1 and Algebra 2 now requires also purchasing their new Saxon Geometry book to receive any credit for geometry. That makes sense, if you consider that publishers make more money from selling three books than they do from selling just two. Regardless of which editions you finally choose to use, I would add a word of caution. If you intend to use John's Advanced Mathematics, 2nd Ed textbook, do not use the new fourth editions of Algebra 1 or Algebra 2.
So what Saxon math books should you use? The editions of John Saxon's math books from fourth through twelfth grades that should be used today are listed at the end of my December 2011 Newsletter. This same list appears on page 15 of my book. These editions remain the best math books on the market today, and they will remain so for two or three decades to come.
If you desire more information about the pros and cons of using a separate Geometry textbook, please read my August 2011 Newsletter. Should you still have questions or reservations, please feel free to either email me at art.reed@usingsaxon.com or call my office any week-day at 580-234-0064 (CST).
WHAT TO DO WHEN A SAXON STUDENT ENCOUNTERS DIFFICULTY EARLY IN THE COURSE.
By the time the first several months of the new school year have passed, most Saxon math students are about a fourth of the way through their respective math books and are quickly finding out that the easy review of the previous textbook's material has come to a sudden halt. They are now entering the part of the textbook that determines whether or not they have mastered sufficient material from the previous textbook to be prepared for their current course of instruction.
For students who start school in August - using the Saxon middle or high school math series from Math 76 through Algebra 2 - this generally occurs sometime in mid-October around lesson 35 or so. Or it can occur sometime in late November, if they started the course in September. This past school year I received a number of email and telephone calls from home school parents who had students who were experiencing difficulty after completing about thirty or so lessons of the course. They were mostly upper middle school or high school students using John Saxon's Algebra 1/2, Algebra 1, or Algebra 2 textbooks.
The symptoms described by the home school parents were similar. The daily assignments seem to take much longer than before and the test grades appear to be erratic or on a general downward trend. The student becomes easily frustrated and starts making comments like, "Why do I have to do every problem?" - or - "There are too many of them and it takes too long." - or - "Why can't I just do the odd problems since there are two of each anyway?" They might even say things like "This book is too hard." - or - "It covers too many topics every day." Or even worse - "I hate math."
About that time, many homeschool educators do the same thing that parents of public or private school students do. They question the curriculum. They immediately look for another - easier - math curriculum so that their children can be successful. Since the students apparently did fine in the previous level book, the parents believe there must be something wrong with this textbook since their sons or daughters are no longer doing well.
Looking for an "easier" math course is like a high school football coach who has just lost his first ten high school football games. However, he assures the principal that they will definitely be successful in their next football game. "How can you be so sure that you will be successful in your next football game?" asks the principal. "Oh that's easy," says the coach. "I've scheduled the next game with an elementary school."
I do not believe the answer is to find an easier math curriculum. I believe the answer is to find out why the students are encountering difficulty in the math curriculum they are currently using, and then find a viable solution to that situation. As John Saxon often said, algebra is not difficult; it is different!
Because every child is also different, I cannot offer a single solution that will apply to every child's situation, but before I present a general solution to Saxon users, please be aware that if you call my office and leave your telephone number or if you email me, I will discuss the specifics of your children's situation and hopefully be able to assist you. My office number is 580-234-0064 (CST) and my email address is art.reed@usingsaxon.com.
When Saxon students encounter difficulty in their current level math book before they reach lesson 30 or so, it is generally because one or more of the following conditions contributed to their current dilemma:
1) They did not finish the previous level book because someone told them they did not have to since the first 30
or so lessons in the next book contained the same material anyway.
2) In the previous level math book, when students complained the daily work took too long the parents allowed
them to do only the odd problems. Doing this negates the built-in automaticity of John Saxon's math program.
3) In the previous level math book, to hasten course completion, the parents allowed the students to combine
easy lessons, sometimes doing two lessons a day, but only one lesson's assignment.
4) The students did not take the weekly tests in the previous courses. Their grades were predicated upon their
daily homework. NOTE: The daily homework grade reflects memory. The weekly test grade reflects mastery.
There are other conditions that contribute to the students encountering difficulty early in their Saxon math book. Basically, they all point to the fact that, by taking shortcuts, the students did not master the necessary math concepts to be successful in their current level textbook. This weakness shows up around lesson 30 - 40 in every one of John's math books. The good news is that this condition - if caught early - can be isolated and the weaknesses corrected without re-taking the entirety of the previous level math book.
There is a procedure to "Find and Fill in the Existing Math Holes" that allows students to progress successfully. This procedure involves using the tests from the previous level math book to look for the "holes in the student's math" or for those concepts that they did not master. This technique can easily tell the parent whether the student needs to repeat the last third of the previous book or if they can escape that situation by just filling in the missing concepts - or holes.
If you have my book, then you already know the specifics of the solution. If you do not have my book, then you can call me or email your situation to me and I will assist you and your child. Regardless of what math book is being used, students who do not enjoy their level of mathematics are generally at a level above their capabilities.
WHAT DETERMINES THE DIFFERENCE BETWEEN MASTERY AND MEMORY?
Think back to your days in high school and your math 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.
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" - and 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 and time - be used simultaneously. It is this process in John Saxons 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 on their last five tests in any of John Saxon's math books are well prepared for success in the next level math course.
WHAT ARE THE DIFFERENCES AMONG THE VARIOUS SAXON MATH TUTORIALS ON
THE MARKET TODAY?
While at Home School Conventions, I am repeatedly asked by Homeschool Educators to explain to them the difference between the "DIVE" CDs, the "Saxon Teacher" CDs, the "Teaching Tapes Technology" DVD series, and the DVD series "MASTERING ALGEBRA, John Saxon's Way," taught by Art Reed. That is an excellent question because some companies confuse Homeschool Educators when they advertise their CDs as "video" products when in fact they are not videos, but only CDs containing a graphic presentation with audio (called a whiteboard presentation). The abbreviation DVD stands for "Digital Video Disc." The DVDs are "video" products that will work on a computer (either a PC or MAC) or on a television DVD player. The CD products however, are not "videos." They will only work on a computer. They cannot be viewed on a television using a DVD player.
Basically, here are the differences among them:
DIVE CD: The product covers John Saxon's math books from Math 54 through Calculus. Each level textbook has a single CD containing instruction corresponding to each individual lesson in that textbook. The presentation is a whiteboard presentation which means there is no teacher to watch at the board. The student hears the voice in the background and watches writing appear on the screen. The CD will not work in a television DVD player because it is not a true "Digital Video Disc," but rather a graphic presentation with audio (a white board presentation). The product will not work on a television DVD player. As a CD, it is restricted to being played only on a computer. Each individual CD costs $50.00 plus shipping. They are available from Math 54 through calculus.
SAXON TEACHER CDs: The product supports John Saxon's math books from Math 54 through Advanced Mathematics. Similar to the DIVE CD, the Saxon Teacher CD is a graphic whiteboard presentation which means there is no one to watch presenting the material. The student hears the voice in the background as the writing appears on the board. The individual in each of the individual series of CDs goes over every problem in the textbook and the individual problems on the tests as well, which is why there are four or more CDs to this product as opposed to the single CD sold by DIVE. These CD graphic "audio" solutions cost about $97.35 (plus shipping and handling). There is also a printed paper booklet version of the solutions for each of the daily problems sold by the company as well. The printed version is titled "Solutions Manual" (which contains the same printed information as the more expensive CD). The printed Solutions Manual sells for between $27.00 for the new Math 54 course to $45.00 for the Advanced Mathematics course. If you have purchased the new soft cover editions of Math 54, 65, 76 or 87, the solutions manuals are included in the price of the Homeschool Kit for these four courses. These CDs are not "videos" and they can only be used on a computer. They cannot be viewed on a television set using a DVD player.
TEACHING TAPE TECHNOLOGY DVDs: The product is a DVD "video" set of lessons which means they can be used on either a television or computer DVD player. The entire series covers Math 54 through Calculus. As advertised by the company, the individual lessons are taught by a state certified math teacher. The individual series for a particular math book in the upper level math series sell for anywhere from $175 for the Math 54 series to $200 for the Algebra 1/2 series to $245 for the Calculus series. The calculus series requires the first edition of calculus. Each DVD series for a specific textbook contains from fourteen to twenty individual DVD discs. The teacher on these videos goes over one or more of the sample and practice problems from each lesson. Unlike the DIVE CD and Saxon Teacher CD, these are DVD "digital video disc" presentations and they will work on either a television or computer DVD player.
MASTERING ALGEBRA "John Saxon's Way" taught by Art Reed DVDs: This product is also a DVD "video" presentation which means the DVDs will work on both a computer as well as a television DVD player. This capability would enable several students or a group of home school students to watch together, on a single television set, as they would in a regular math or CO-OP classroom. Each series is a video tutorial of every lesson in the book. The concepts of every lesson are taught by an experienced Saxon math teacher with over twelve years teaching experience using Saxon Math books in a rural public classroom. The examples used on the board are not those already explained in the textbook, but created by the teacher to enable the student to master the concept as opposed to memorizing the steps used in solving the sample problem shown in the textbook. Students see an experienced Saxon math teacher at the board teaching the concepts contained in that lesson. There are ten to twelve individual DVDs in each of the DVD series which run from Math 76 through the first twenty-five lessons of the calculus textbook (covering limits of functions and derivatives). The Advanced Mathematics course is taught in a two year presentation awarding credit for a full year of geometry as well as providing semester credits for both trigonometry and pre-calculus. Each of the seven individual DVD tutorial series sells for $49.95 (This price includes free shipping anywhere within the USA and its territories, including APO and FPO addresses).
Before you buy any of these products, sit down with your student and look at each of the samples provided by the companies on their websites. Make sure the student will be able to work with the instructor and the material as they are presented. Here are the four websites:
diveintomath.com; saxonhomeschool.com; teachingtape.com or usingsaxon.com
For more information on using these products, please read my April and July 2010 Newsletters.
HOW CAN STUDENTS OVERCOME THEIR DIFFICULTY WITH ALGEBRA?
When John Saxon published his original series of math textbooks, they were designed to be taken in order from Math 54 to Math 65, followed by Math 76, then Math 87, then Algebra 1/2, then on to Algebra 1, then Algebra 2, followed by Advanced Mathematics (which, coupled with Algebra 2, gave the high school geometry and trigonometry credits) culminating with the calculus textbook for some students.
The books were not originally intended to be "grade" oriented textbooks, but were intended to be taken in sequential order based upon a student's knowledge and capabilities without regard to the student's grade level. But schools and homeschool educators quickly assigned Math 54 to the fourth grade level, Math 65 to the fifth grade level, Math 76 to the sixth grade, and Math 87 to the seventh grade level to be followed by the pre-algebra course titled Algebra 1/2. When the new third edition of Math 76 came out in the summer of 1997, it was much stronger academically than its predecessor, the older second edition textbook. It did not take long for confusion to develop around which textbooks were now the correct editions to be used and what the correct sequencing would be.
In the thousands of telephone calls I received over the years I served as Saxon Publishers' Homeschool Curriculum Director for Math 76 through calculus, the question that arose most often among classroom teachers as well as Homeschool educators was whether the student should go from the new stronger Math 76 book to Math 87 or to Algebra as both the Math 87 and the Algebra 1/2 textbooks appeared to contain basically the same material. Adding to the confusion, after John Saxon's death, was the fact that the new soft cover third edition of Math 87 had the title changed to read Math 8/7 'with pre-algebra.'
So what Saxon math book does a student who has completed Math 76 use? Well, that depends upon how well the student did in the Math 76 book. The key word is "successfully completed," not just "completed" Math 76. If a student completed the entirety of the Math 76 textbook and his last five tests in that book were eighty or better, he would have "successfully completed" Math 76 and he could move on to the Algebra 1/2 book. However, if the student's last five test grades were all less than seventy-five, that student has indicated that he will in all likelihood experience difficulty in the Algebra 1/2 materials and should therefore proceed first through the Math 87 textbook.
While both the Math 87 and the Algebra textbooks will get the student ready for the Algebra 1 course, the Math 87 book starts off a bit slower with more review, allowing the student to "catch up." The student who then moves successfully through the Math 87 textbook, receiving eighties or better on the last five tests, can then skip the Algebra 1/2 book and move directly to the Algebra 1 textbook.
However, if the student finishes the Math 87 book and the last five test grades reflect difficulty with the material, that student should then be moved into the Algebra 1/2 book to receive another - but different - look at "pre-algebra" before attempting the Algebra 1 course. Students fail algebra because they do not understand fractions, decimals and percents; they fail calculus because they do not understand the basics of algebra. Attempting to "fast track" a student who had weak Math 76 test scores - into Algebra 1/2 - then on to Algebra 1, will most certainly result in frustration if not failure in either Algebra 1/2, or Algebra 1.
So what have we been talking about? If the students have to take all three courses (Math 76, Math 87 and Algebra 1/2), how will they ever get through algebra 1? When I taught Saxon math in a public high school, we established three math tracks for the students. Fast, Average, and Slower math tracks to accommodate the difference in learning styles and backgrounds of the students.
Listed below are the recommended three math tracks. Please note there are no grade levels associated with these courses, but Math 76 was generally taught in the 6th grade at the middle school. The course titled "Introduction to Algebra 2" was the student's first attempt at the Algebra 2 course which resulted in low test scores, so the course was titled as an "Introduction to Algebra 2" on the student's transcript and the student repeated the entirety of the same book the following year.
Over ninety-five percent of all these students received an "A" or "B" their second year through the Algebra 2 course. In the ten years we used the system, I only had one student who received a "D" in the course and he did so because he did little or no studying the second year and still passed the course with a 65 percent test average.
I will make you the same promise I made to the parents of my former students. If students can accomplish no more than "mastering" John Saxon's Algebra 2 course by the time they are seniors in high school, they will pass any collegiate freshman algebra course from MIT to Stanford (provided they go to class). Remember, they can still take calculus at the university if they have changed their mind and need the course in their new major field of study. And because they now have a strong algebra background, they will be successful!
FAST MATH TRACK: Math 76 - Algebra 1/2 - Algebra 1 - Algebra 2 - Geometry with Advanced Algebra - Trigonometry and Pre-Calculus - Calculus. NOTE: The Saxon Advanced Mathematics textbook was used over a two year period allowing the above underlined two full math credits after completing Saxon Algebra 2. (TOTAL High School Math Credits: 5)
AVERAGE MATH TRACK: Math 76 - Math 87 - Algebra 1/2 - Algebra 1 - Algebra 2 - Geometry with Advanced Algebra - Trigonometry and Pre-Calculus. (TOTAL High School Math Credits: 4)
SLOWER MATH TRACK: Math 76 - Math 87 - Algebra 1/2 - Algebra 1 - Introduction to Algebra 2 - Algebra 2 - Geometry with Advanced Algebra. (TOTAL High School Math Credits: 4)
NOTE 1: YOU SHOULD USE THE FOLLOWING EDITIONS AS THEY ARE ACADEMICALLY
STRONGER THAN THE EARLIER EDITIONS ARE, AND MIXING THE OLDER EDITIONS
WITH THE NEWER EDITIONS WILL RESULT IN FRUSTRATION OR FAILURE FOR THE
STUDENT.
Math 76: Either the hardback 3rd Ed or the new soft cover 4th Ed. (The Math content of both
editions is the same)
Math 87: Either the hardback 2nd Ed or the new soft cover 3rd Ed. (The Math content of both
editions is the same)
Algebra 1/2: Use only the 3rd Edition. (Book has the lesson reference numbers added)
Algebra 1: Use only the 3rd Edition. (Book has the lesson reference numbers added)
Algebra 2: Use either the 2nd or 3rd Editions. (Content is identical. Lesson reference numbers
added to the 3rd Ed)
Advanced Mathematics: Use only the 2nd Edition: (Lesson reference numbers are found in
the solutions manual, not in the textbook)
Calculus: Either the 1st or 2nd Edition will work. However, if the student uses my DVD tutorials,
they will need the 2nd Edition textbook.
NOTE 2: WHEN RECORDING COURSE TITLES ON TRANSCRIPTS, USE THE FOLLOWING TITLES:
Math 76: Record "Sixth Grade Math."
Math 87: Record "Pre-Algebra."(If student must also take Algebra 1/2, then use "Seventh Grade Math")
Algebra 1/2: Record "Pre-Algebra."
Algebra 1 & Algebra 2: Self explanatory.
Advanced Mathematics: Record "Geometry with Advanced Algebra" (1 credit) if they
only complete the first 60 - 70 lessons of that textbook.
Record "Trigonometry and Pre-calculus" (1 credit) if they have
completed the entirety of the Advanced mathematics textbook.
Under no circumstances should you record the title "Advanced Mathematics" on the student's transcript as the colleges and
universities will not know what math this course contains, and
they will ask you for a syllabus for the course.
Calculus: Self explanatory.
Each child is unique and what works for one will not always work for another. Whatever track you use, you must decide early to allow students sufficient time to overcome any hurdles they might encounter in their math journey before they take the ACT or SAT. If you have any questions, please feel free to email me at art.reed@usingsaxon.com or call me at (580) 234-0064 (CST) and leave your telephone number and a brief message and I will return your call.
HOW TO SUCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 THROUGH
CALCULUS AND PHYSICS
(PART III)
Here is the final series describing situations I have encountered these past three decades while teaching Saxon in a rural high school as well as providing curriculum advice to homeschool educators. As with the previous two parts of the series, I have added my thoughts about why you want to avoid them:
1) ATTEMPTING THE ADVANCED MATHEMATICS TEXTBOOK IN A SINGLE YEAR:
Since there are only 125 lessons in the textbook, it seems reasonable to assume
this is possible.
RATIONALE: "My son had absolutely no trouble in the Algebra 2 book and I believe
he will have no trouble in this book either. The book has fewer lessons than the
Algebra 2 book has. Besides, he is a junior this year and we want him to be in
calculus before he graduates from high school."
FACTS: The second edition of John Saxon's advanced mathematics textbook is
tougher than any college algebra textbook I have ever encountered. The daily
assignments in this book are not impossible, but they are time consuming and
can take most math students more than several hours each evening to complete
the thirty problems. This generally results in students doing just doing the odd
or even numbered problems to get through the lessons. I must have said this a
thousand times "Calculus is easy!" Students fail calculus not because of the
calculus, but because they do not understand the algebra. Speeding through the
Saxon Advanced Mathematics textbook by taking shortcuts does not allow the
student the ability to master the advanced concepts of algebra and trigonometry
to be successful in calculus. And if the only argument is that the student will not take
calculus in high school, then what is the rush?
The DVD tutorial series for the second edition of John's Advanced Mathematics book that I have prepared allows students three different choices based upon their needs and capabilities.
a) They can follow my advice and take the course in two years (doing a lesson every
two days). They can then gain credit for the first academic year for the course of
"Geometry w/Advanced Algebra," with a first semester credit for Trigonometry
and a second semester credit for Pre-calculus in their second academic year.
- or -
b) They can take the course in three semesters. Their first semester credit would
be titled Geometry, followed by a second semester credit for Trigonometry with
Advanced Algebra; ending with a third semester credit for Pre-calculus.
- or -
c) Lastly, while not recommended, they can take the entire 125 lessons in the
Advanced Mathematics book in a single school year gaining credit for a full year
of Geometry along with a semester credit for Trigonometry w/Advanced Algebra
In all the years that I taught the subject, I only had one student who was able to
complete the entire Advanced Math course of 125 lessons in a single school
year - with a test average above ninety percent - and she was a National Merit
Scholar whose father taught mathematics with me at the local university.
The specific details of how the transcript is recorded are covered in my book, but if you have any questions regarding your son or daughters high school transcript, please feel free to send me an email.
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2) IS IT CRITICAL FOR STUDENTS TO TAKE CALCULUS IN HIGH SCHOOL? Students
lacking a solid base in algebra and a basic knowledge of trigonometry will find that
taking calculus at any level will be very difficult, if not impossible.
RATIONALE: "I want our son to take calculus his senior year in high school. The only
way we can accomplish that is to have him speed through the Saxon Algebra 2 and
Advanced Mathematics book to finish them by the end of his juni or year. He may
even have to use the summer months for math as well."
FACTS: Even if students successfully complete a calculus course their senior year
in high school, whether at home or at a local community college, I would strongly
recommend that they enroll in calculus I as a freshman at the university or college
they choose to attend for several reasons.
First: If they truly understand enough of their calculus I course (usually
encompassing derivatives) they can enjoy a solid five hours of "A" on their
transcript for their first five hours of math as a freshman. They can also make
some nice extra money tutoring their less fortunate classmates.
Second: While they think they understand everything there is about calculus, they
will see much more as they sit back and "understand" what the professor is talking
about. They might even learn something they never fathomed in the high school
textbook they went through.
Third: Their solid "A" the first semester in a calculus I class lets the professors know
what kind of student they are. That perception by the professor makes a big difference
should they encounter difficulties later in their second semester of calculus II (usually
through integrals). Finishing John Saxon's second edition of Advanced Mathematics
at a pace that allows the student to grasp all of the material in that textbook without
being frustrated or discouraged, is paramount to their success in calculus at the
college or university level.
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3) DO HIGH SCHOOL STUDENTS NEED A SEPARATE GEOMETRY TEXTBOOK? To reflect
that a student has received a well rounded math background, states that require
three or more math courses require that geometry be recorded on a students high
school transcript, along with algebra 1, algebra 2, trigonometry, etc.
RATIONALE: "It is too difficult for high school students to learn both algebra and
geometry at the same time. My son did just fine in the Saxon Algebra 1 textbook.
However, he is only on lesson 35 in the Saxon Algebra 2 book, and he is already
struggling." - or their rationale may be - "I have been told by other home school
parents that there are no two-column proofs in John Saxons Algebra 2 textbook."
FACTS: Many of my top students' worst tests in the Saxon Algebra 2 course were their
very first test. This happened because they did not realize the book covered so much
geometry review from the algebra 1 text, as well as several key new concepts taught early
in the Algebra 2 text. They quickly recovered and went on to master both the algebra and
the geometry concepts. From my experiences, most students who encountered difficulty
early in John Saxon's Algebra 2 textbook did so - not because they did not understand the
geometry being introduced - but because their previous experiences with the Saxon
Algebra 1 course did not result in mastery of the math concepts necessary to handle the
more complicated algebra concepts introduced early in the Algebra 2 textbook. I would
not recommend students attempt John Saxon's Algebra 2 math book if they have done
any one or more of the following:
a) Never finished all of the lessons in the Saxon Algebra 1 textbook.
b) Hurried through the Saxon Algebra 1 textbook doing two lessons a day and
then only did the odd or even numbered problems from each lesson.
c) Received multiple test scores of less than seventy-five on their last four or five
tests in the Algebra 1 textbook (not counting partial credit).
What about the students who never took the tests because parents used the students' daily homework grades to determine their grade average? What does that reveal about the students' ability? Establishing a students grade average based upon their daily work reflects what they have "memorized." The weekly tests determine what they have "mastered."
The successful completion of John Saxon's Algebra 2 textbook (2nd or 3rd Editions) gives students an additional equivalent of the first semester of a high school geometry course (including two-column proofs). Successful completion of the first sixty lessons of the Saxon Advanced Mathematics textbook (2nd Ed) ensures they receive the equivalent of the second semester of high school geometry, in addition to the advanced algebra and trigonometry concepts they also receive in the latter half of the book.
But what about the lack of two-column proofs in the Saxon Algebra 2 book (2nd or 3rd Ed)? Whenever I hear Homeschool Educators make the comment that "John Saxon's Algebra 2 book does not have any two-column proofs," I immediately know they stopped before reaching lesson 124 of the book which is where two-column proofs are introduced. The last six lessons of the Saxon Algebra 2 textbook (2nd or 3rd editions) contain thirty-one different problems dealing with two-column proofs. The following year, in the first half of the Advanced Mathematics textbook, they not only encounter some heavy duty algebra concepts, but they will also complete the equivalent of the second semester of a regular high school geometry course. The first thirty of these sixty lessons contain more than forty different problems dealing with two-column proofs.
So why then did John Saxon not want to publish a separate geometry textbook? As I mentioned in my newsletter last December, a group of professors who taught mathematics and science at the University of Chicago bemoaned the fact that educators continued to place a geometry course between basic algebra (Algebra 1) and the advanced algebra course (Algebra 2) to the detriment of the student. - AND THEY WROTE THIS 105 YEARS AGO!
In the preface to their book titled "Geometric Exercises for Algebraic Solution," published in 1907, the professors explained that it is this lengthy "void" between the two algebra courses that prevents students from retaining the necessary basic algebra concepts learned in basic algebra (algebra 1) to be successful when encountering the rigors of advanced algebra (algebra 2).
Then apparently aware of this situation, and knowing John Saxon's position on the subject, why did HMHCO (the current owners of John's books) go ahead and create and publish their new fourth editions of Saxon Algebra 1, Algebra 2, and a separate first edition Saxon Geometry textbook? I do not know why they did, but I do know that three textbooks will make more money for a publisher than two textbooks will. I also know that the new books while initially sold only to the schools on the school website, are now offered to Homeschool Educators as well. Now having to decide between the two different editions of algebra makes the selection process more confusing. However, I would not recommend any student go from the new fourth edition of Saxon Algebra 2 to John Saxon's Advanced Mathematics textbook.
For those readers who do not have a copy of my book, please take a look at the end of my December 2011 news article for information that will help you select the correct level and edition of John Saxon's math books. These editions will remain excellent math textbooks for many more decades.
If your child is already experiencing difficulty in one of the Saxon series math books, and you need to find a workable solution, please email me at: art.reed@usingsaxon.com or feel free to call me any weekday during normal business hours at (580) 234-0064 (CST).
HOW TO SUCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 THROUGH CALCULUS AND PHYSICS (PART II)
As I promised last month here are several more of the common misuses I have encountered during the past three decades of teaching and providing curriculum advice to homeschool educators. I have added my thoughts about why you want to avoid them:
1) THE EFFECTS OF DOING JUST THE ODD OR EVEN PROBLEMS: Allowing the
student to do just the odd or even problems in each daily lesson may appear
to save time, but it creates a false sense of mastery of the concepts.
RATIONALE: "Each lesson shows two of each of the different problems, and it
saves us valuable time by doing just one of the pair. Besides, since they both
cover the same concept, why take the extra time doing both of them?"
FACT: The reason there are pairs of each of the fifteen or so concepts found
in the daily assignments is because each of the problems in each pair is
different from the other. While both problems in each pair address the same
concept, they are different in their approach to presenting that concept. one goes
about presenting the concept one way while the second one approaches the
concept from a totally different perspective. Doing both of them gives the student
a broader basis for understanding the concept and prevents the student from
memorizing a particular procedure rather than mastering the concept based
upon solving the two different formats or procedures.
Whenever I receive an email from a homeschool educator or student, and they need
help with solving a particular problem on one of the tests remarking that they never
saw this test question in any of their daily work, I can tell that they have been doing
either just the "odds" or the "evens" in their daily work because this test question
resembled an approach to the concept that was contained in the set they never did.
Additionally, doing only half of the daily assignment restricts the student's ability to
more quickly and easily master the concepts. Doing two a day for fourteen days
increases the students ability to more quickly master those concepts than doing
just one a day for that same period of time.
The "A" or "B" student who has mastered the material should take no more than fifty
minutes to complete the daily assignment of thirty problems if their grade is based
upon their weekly test scores and not upon their daily homework. The "C" student
should complete the daily assignment of thirty problems in about ninety minutes.
The additional time above the normal fifty minutes is usually the result of the "C"
student having to look up formulas or concepts that might not have yet been
mastered. This is why I recommend students use "formula cards."
Using formula cards saves students many hours of time flipping through the book
looking for a formula to make sure they have it correctly recorded. The details on
how to implement using these cards is explained in detail on page 94 of my book.
If you have not yet acquired that book, you can find information on how to make and
use them in my September 2011 Newsletter.
***************************************************
2) THE EFFECTS OF DOING MORE THAN ONE LESSON A DAY: Permitting the students
to do two or three lessons a day believing this will allow them to complete the
course faster.
RATIONALE: "My son wants to finish the Saxon Calculus course by the end of his
junior year. The only way he can do that is to finish the Algebra 2 book in six rather
than nine months. Besides, he told me that he already knows how to do most of the
material from the previous Algebra 1 book."
FACT: To those who feel it necessary to "speed" through a Saxon math book, I
would use the analogy of eating one's daily meals. Why not just eat once or twice
a week to save time preparing and eating three meals each day? Not to mention
the time saved doing all those dishes. The best way I know to answer both of these
questions is to remind the reader that our bodies will not allow us to implement
such a time saving methodology any more than our brains will allow us to absorb
the new math concepts by doing multiple lessons at one sitting.
I have heard just about every reason to support doing multiple lessons, skipping
tests to allow another lesson to be taken, or taking a lesson on a test day. All of
these processes were attempted solely to speed up completing the textbook.
Students who failed calculus did so, not because they did not understand the
language and concepts of calculus, but because they did not sufficiently master the
algebra.
Why must students always be doing something they do not know? What is wrong
with students doing something they are familiar with to allow mastery as well as
confidence to take over? Why should they become frustrated with their current
material because they "rushed" through the previous prerequisite math course?
The two components of "automaticity" are time and repetition and violating either
one of them in an attempt to speed through the textbook (any math book) results in
frustration or failure as the student progresses through the higher levels of
mathematics. I recall my college calculus professor filling the blackboard with a
calculus problem and at the end, he struck the board with the chalk, turned and said
"And the rest is just algebra." To the dismay of the vast majority of students in the
classroom - that was the part they did not understand and could not perform. When I
took calculus in college, more than half of my class dropped out of their first
semester of calculus within weeks of starting the course, because their algebra
backgrounds were weak.
***************************************************
3) ENTERING THE SAXON MATH CURRICULUM AFTER MATH 76: Switching to Saxon
Algebra 1 or Algebra 2 because you have found the curriculum you were previously
using was not preparing your child for the ACT or SAT and you wanted them to be
more challenged.
RATIONALE: "We were having trouble with math because the curriculum we were
using, while excellent in the lower grades, did not adequately prepare our son and
daughter for the more advanced math concepts. We needed a stronger more
challenging math curriculum, so we switched to Saxon algebra 1."
FACT: Switching math curriculums is always a dangerous process because each
math curriculum attempts to bring different math concepts into their curriculum at
different levels. Constantly moving from one math curriculum to another - looking for
the perfect math book - creates "mathematical holes" in the students' math
background. It also creates a higher level of frustration for these students because,
rather than concentrating on learning the mathematics, they must concentrate on
what the new textbook's system of presentation is and spend valuable time trying to
analyze the new format, method of presentation, test schedule, etc.
If you intend to use Saxon in the middle and upper level math courses because of
its excellence at these levels of mathematics, I would strongly recommend that you
start with the Math 76, 3rd or 4th Ed textbook. The cumulative nature of the Saxon
Math textbooks requires a solid background in the basics of fractions, decimals and
percentages. All of these basics, together with the necessary prerequisites for
success in pre- algebra or algebra 1 are covered in Saxon's Math 76, 3rd or 4th
Edition textbook. This math textbook is what I refer to as the "HINGE TEXTBOOK" in
the Saxon math curriculum. Successful completion of this book will take care of any
"Math Holes" that might have developed from the math curriculum you were using in
grades K - 5.
Successful completion of this book can allow the student to move successfully to the
Saxon algebra textbook (a pre-algebra course). Should students encounter difficulty
in the latter part of the Math 76 text, they can move to the Saxon Math 87, 2nd or 3rd
Ed and, upon successful completion of that book, move either to the Algebra 1/2 or
to the Algebra 1 course depending on how strong their last 4 or 5 test scores were.
Yes, some students have been successful entering the Saxon curriculum at either
the Algebra 1 or the Algebra 2 levels, but the number of failures because of weak
math backgrounds from using other curriculums, roughly exceeds the number of
successes by hundreds!
***************************************************
As I mentioned last month, there will always be exceptions that justify the rule. However, just because one parent tells you their child did any one or all of the above, and had no trouble with their advanced math course, does not mean you should also attempt it with your child.
That parent might also not have told you that:
(1) Their child encountered extreme difficulty when they reached Saxon Algebra 2, and even
more difficulty and frustration or failure with the Saxon Advanced Mathematics course.
- or -
(2) They had switched curriculum after experiencing difficulty in the Saxon Algebra 1 course.
- or -
(3) Their child had to take the "no credit" remedial college algebra when they enrolled at a
university because they had received a low score on the university's math entrance exam.
For those readers who do not have a copy of my book, please read my February 2010 news article for information that will help you select the correct level and edition of John Saxon's math books. These editions will remain excellent math textbooks for many more decades.
If your child is already experiencing difficulty in one of the Saxon series math books, and you need to find a workable solution, please email me at: art.reed@usingsaxon.com. Or feel free to call me any weekday during normal business hours at (580) 234-0064 (CST).
In next month's issue, I will cover:
1) ATTEMPTING THE ADVANCED MATH TEXTBOOK IN A SINGLE YEAR:
2) IS IT CRITICAL FOR STUDENTS TO TAKE CALCULUS IN HIGH SCHOOL?
3) DO HIGH SCHOOL STUDENTS NEED A SEPARATE GEOMETRY TEXTBOOK?
HOW TO SUCESSFULLY USE JOHN SAXON'S MATH BOOKS FROM MATH 54 THROUGH CALCULUS AND PHYSICS (Part I)
Both homeschool educators as well as public and private school administrators have asked me "Why do John Saxon's math books require special handling?" Another question I am also frequently asked by them is "If John Saxon's math books require special instructions to use them successfully, why would we want to use them?" Before the end of this newsletter, I hope to be able to answer both of these questions to your satisfaction.
There is nothing "magic" about John Saxon's math books. They were published as a series of math textbooks to be taken sequentially. Math 54 followed by Math 65, and then Math 76, followed by either Math 87 or Algebra 1/2 (John's pre-algebra book), then algebra 1, etc. While other publishers were "dumbing-down" the content of their new math books, John Saxon was publishing his new editions with stronger, more challenging content.
Homeschool families, attempting to save money by buying older used Saxon Math books and inter-mingling them with the newer editions were unaware that the older out-of-print editions were often incompatible with these newer, more challenging editions. The same problem developed in the public and private school sector adding to the confusion about the difficulty of John's math books.
For example, a student using the old first or second edition of Math 76 would experience a great deal of difficulty entering the newer second or third editions of Math 87. This difficulty arose because the content in the outdated first or second editions of Math 76 was about the same as that of the material covered in the newer editions of Math 65 (the book following Math 54 and preceding Math 76). Jumping from the outdated older edition of Math 76 to the newer editions of either Math 87 or algebra 1/2 would ultimately result in frustration or even failure for most, if not all, of the students who attempted this.
Many homeschool educators and administrators were also unaware that when finishing a Saxon math book, they were not to use the Saxon placement test to determine the student's next book in the Saxon series. The Saxon placement test was designed to assist in initially placing non-Saxon math students into the correct entry level Saxon math book. The test was not designed to show parents what the student already knew, it was designed to find out what the student did not know. Students taking the placement test, who are already using a Saxon math book, receive unusually high "false" placement test scores. These test results may recommend a book one or even two levels higher than the level book being used by the student (e.g. from their current Math 65 textbook to the Math 87 textbook).
By far, the problems homeschool educators as well as classroom teachers encounter using - or shall I say misusing - John's math books are not all that difficult to correct. However, when these "short-cuts" are taken, the resulting repercussions are not at first easily noticed. Later in the course, when the student begins to encounter difficulty with their daily assignments - in any level of Saxon math books - the parent or teacher assumes that the student is unable to handle the work and determines that the student is not learning because the book is too difficult for the student.
Here are three of the most common misuses that I have encountered literally hundreds of times during these past twenty years of teaching and providing curriculum advice to home school educators:
1) NOT FINISHING THE ENTIRETY OF THE TEXTBOOK: Not requiring the student to
finish the entirety of one book before moving on to the next book in the sequence.
RATIONALE: "But the beginning of the new book covers the same material as that in
the last lessons of the book we just finished, so why repeat it"?
FACT: The student encounters some review of this material in the next book, but this
review assumes the student has already encountered the simpler version in the
previous text. The review concepts in the new book are more challenging than the
introductory ones they skipped in the previous book. This does not initially appear to
create a problem until the student gets to about lesson thirty or so in the book, and by
then both the parent and the student have gotten so far into the new book that they do
not attribute the student's problem to be the result of not finishing the previous
textbook.
They start to think the material is too difficult to process correctly and do not
see the error of their having skipped the last twenty to thirty or so lessons in the
previous book. They now fault the excessive difficulty of the current textbook as the
reason the student is failing. Students should always finish the entirety of every Saxon
math textbook! I realize that all students are not alike, so if as you're reading this article
and you are already encountered this particular phenomenon with your child, there are
several steps you can take to satisfactorily solve the problem without harming the
child's progress or self-esteem. So that we can find the correct solution, please email
me and include your telephone number and I will call you that same day - on my dime!
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2) MISUSE OF THE SAXON PLACEMENT TEST: Skipping one of the books in the
sequence (e.g. going from Math 54 to Math 76) because the "Saxon Placement Test"
results clearly showed the student could easily handle the Math 76 material.
RATIONALE: "He even got some of the Math 87 level questions correct. Besides, we
had him look at the material in the Math 65 book and he said that he already knew
that material, so why bother doing the same concepts again."
FACT: As I wrote earlier, the Saxon Placement Test was designed to place non-Saxon
math students into the correct level math book. It was designed to see what the
student had not yet encountered or mastered. It was not designed to find out what
the student already knew. Saxon students who take the Saxon placement test receive
unusually high "false" test scores. The only way to determine if the student is ready for
the next level math book is to evaluate their last four or five tests in their current Saxon
math book to determine whether or not they have mastered the required concepts to
be successful in the next level book.
The brain of young students cannot decipher the difference between recognizing
something and being able to provide solutions to the problems dealing with those
concepts. So when they thumb through a book and say "I know how to do this" what
they really mean is "I recognize this." Recognition of a concept or process does not
reflect mastery.
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3) USING DAILY HOMEWORK TO DETERMINE A STUDENT'S GRADE: Skipping the
weekly tests and using the student's daily assignments to determine their grade for
the course reflects memory rather than mastery of the material.
RATIONALE: I cannot count the number of times I have been told by a parent "He does
not test well, so I use the daily assignment grades to determine his course grade. He
knows what he is doing because he gets ninety's or hundreds on his daily work."
FACT: Just like practicing the piano, violin, or soccer, the student is not under the
same pressure as when they have to perform in a restricted time frame for a musical
solo or a big game. The weekly tests determine what a student has mastered
through daily practice. The daily homework only reflects what they have temporarily
memorized as they have access to information in the book not available on tests.
Answers are provided for the odd numbered problems and some students quickly
learn to "back-peddle." This phenomenon occurs when the student looks at a problem
and does not have the foggiest idea of how to work the problem. So they go to the
answers and after seeing the answer to that particular problem, suddenly recall how
to solve the problem. Later in the week, when they take the test, there are no answers
to look up preventing them from "back-peddling" through to the correct solution.
As with anything, there are always exceptions that justify the rule. However, just
because one parent says their child did any one or all of the above, and had no trouble
with their math, does not mean you should let your child attempt it. That parent might
not have told you that (1) their child encountered extreme difficulty when they reached
Saxon Algebra 2, and even more difficulty with the Saxon Advanced Mathematics
textbook, or (2) they had switched curriculum after experiencing difficulty in Saxon
Algebra 1, or (3) their child had to take a non-credit remedial college algebra course
when they enrolled at the university or college because they had received a low score
on their required math entrance examination.
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For those readers who do not have a copy of my book, please read my February 2010 news article for information that will help you select the correct level and edition of John Saxon's math books. These editions will remain excellent math textbooks for several more decades.
If your child is already experiencing difficulty in one of the Saxon series math books, and you need to find a workable solution, please email me at: art.reed@usingsaxon.com. Or feel free to call me any weekday during normal business hours at (580) 234-0064 (CST). In next month's issue, I will cover:
1) THE EFFECTS OF DOING JUST THE ODD OR EVEN PROBLEMS.
2) THE EFFECTS OF DOING MORE THAN ONE LESSON A DAY.
3) ENTERING THE SAXON MATH CURRICULUM AFTER MATH 76.
HAHAVE A VERY HAPPY, HEALTHY, AND BLESSED NEW YEAR!
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