REASONS FOR STUDENT FRUSTRATION OR FAILURE WHEN USING JOHN SAXONâS MATH BOOKS - (PART 1)
The unique incremental development process used in John Saxonâs math textbooks - coupled with the cumulative nature of the daily work - make them excellent textbooks for use in either a classroom or home school environment. If the textbooks are not used correctly, however, they will eventually present problems for the students.
Some years ago, I was asked to help a school district in the Midwest recover from falling test scores and an increased failure rate in their middle and high school math programs. The teachers in the district had been using - actually misusing - their Saxon math books for several years. After I had a chance to tell the group of school administrators and teachers some of the reasons for their difficulties, the district superintendent commented. âWhat 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 ownerâs manual â wouldnât you agree?â To which I replied, âItâs worse than that, sir! You all thought you had purchased a car with an automatic transmission, but Saxon is a stick shift! It is critical that certain procedures be followed - just as well as some should be dropped - or you will strip the gears!â
The uniqueness of John Saxonâs method of incremental development, coupled with the cumulative nature of the daily work in every Saxon math textbook, requires a few specific rules be followed to reduce failure and frustration and to ensure success â and ultimately mastery! If properly used at the correct levels, students will not have any trouble with what has been recently introduced into the educational system as âCommon Coreâ requirements.
In the next several news articles, we will discuss the ESSENTIAL DOâS and DONâTâS when using John Saxonâs math books.
This month I will discuss the ESSENTIAL DOâS that should be followed when using John Saxonâs math books.
Do Place the Student in the Correct Level Math Book. Probably the vast majority of families who dislike John Saxonâs math books do so because the student is using a math book above his or her capability. Since all of Johnâs 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 Â˝ would be like moving from Math 65 to Algebra Â˝ in the current editions. For more information on which editions of Johnâs books are still valid, read the earlier published April 2013 Newsletter, or read pages 15 â 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, âWhy 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?â 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 studentâs confidence back up after a few months off during the summer. Then comes the argument from some home school educators, âBut we do not take any break between books â we go year round, so the review is not necessary.â
My only reply to that is âWhy must students always do something they do not know how to do? Canât 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 wonât take them long to do their daily assignment. I once had a public school superintendant ask me âWhich is more important, mastery or completing the book?â To which I replied, âThey are synonymous.â
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 âWhy study both lessons seventeen and eighteen? After all, they both cover the same concept?â Why not just skip lesson eighteen and go straight to lesson nineteen?â 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 â 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, âHe does so well on his daily work; why test him?â To which I reply, âThe results of the daily work reflect memory â the results of the weekly tests reflect mastery!â The results of the last five tests in every book give an indication of whether or not the student is prepared for the next level math book. Scores of eighty or better on any test reflect minimal mastery achieved. Scores of eighty or better on the last five tests in the series tell you the student is prepared to advance to the next level.
In next monthâs news article, I will discuss the ESSENTIAL DONâTâS to follow when using John Saxonâs math books.
TRANSCRIPTION OF MATH CREDITS â TWO BOOKS, FOUR YEARS
The first year I started teaching high school mathematics, I encountered freshman students who, while having passed an eighth grade pre-algebra course, could not manage John Saxonâs Algebra 1 textbook. The frustration and failure rate was incredible and many upper level students were shying away from any math course above Algebra 1.
I soon became aware of the distinct difference between receiving good grades and mastery of the concepts. That summer I developed an alternate curriculum using Johnâs Algebra 1 and Algebra 2 books. The plan would allow students the ability to accept the challenge of algebra without having to accept failure. I went to Oklahoma City and briefed the Director of Curriculum for the Oklahoma State Department of Education on my plan.
After my briefing, he sat quietly for a few seconds then said to me, âMr. Reed, I wish that my daughter would have had the opportunity to use your plan when she was struggling with algebra in high school.â He then went on to explain that anything can be entered on a studentâs transcript so long as it is an honest evaluation of what was being taught in the classroom. He approved the plan and we implemented it that following fall at the high school.
In the following three years, our ACT average math scores went from 13.4 to over 21.9 (above both the state and national averages). In that same time period, we had over ninety percent of our high school students enrolled in math courses above Algebra 1 and the number of students taking the ACT test tripled.
The plan is simple. The student has to complete the entire algebra one textbook. However, the student who struggles through John Saxonâs Algebra 1, 3rd Ed textbook - and receives an overall second semester test average of 50 â 60 (a D or F) - can receive credit for a âlesser inclusive course.â The title of âBasic Algebra,â âPre-Algebra,â or âIntroduction to Algebra 1â can be used on the transcript and the grade recorded as a âC. The student then retakes the same course the next year and should receive an average test grade of 80 or better. The course is recorded on the transcript the second year as âAlgebra 1.â Since the students have now mastered the material they previously missed the first time through the book.
Ninety percent of these students only needed the âlesser inclusive courseâ assist in Algebra 1. However, a small percent needed the same assist in Algebra 2, so we came up with âIntroduction to Algebra 2â for the first attempt and âAlgebra 2â for the second attempt. Thus the title of the program, âFour Years â Two Books.â
The difficulty many students encounter in John Saxonâs Algebra 1 or Algebra 2 books generally stems from their having had a weak math background in previous math courses. Some students need a second chance to master this material because of this weaker math background. Or, they might have moved through several different math curriculums in the past few years and developed holes in their math background. They hit a brick wall because they now encounter advance math concepts they never saw before at the introductory level.
What makes this concept work so well is that John Saxonâs Algebra 1 and Algebra 2 textbooks are really tough, no-nonsense, cumulative math textbooks. Using this system, we have shown that any student who truly masters the content of these two textbooks in four years of high school will successfully pass any college level algebra course at any university.
There is considerably more detail in my book, but if you have a question or situation that requires immediate assistance, please feel free to email me at [email protected] - and include your telephone number so I can call you. Or â if you prefer - you can reach me at my office any week-day between 9:00 am and 4:00 pm at 580-234-0064 (CST).
My experience in assisting homeschool educators is that a telephone conversation allows an immediate exchange of ideas not readily afforded in lengthy email sent back and forth over several days. A few minutes spent on the telephone will be less frustrating to the homeschool educator and will more often result in a successful solution for both the student and the homeschool educator.
I realize that every student is different, and what works for one may not work for another. However, my experience these past twenty years is that there is a solution for your son or daughter â we just need to find the right one!
THE COLLEGE LEVEL EXAMINATION PROGRAM (CLEP)
Over the years, I have had parents ask about the advantages of having their child take a test under the College Level Examination Program (CLEP) - or as some of my students would say "CLEP out of a Course." For those not familiar with the program, the 90-minute CLEP tests are administered by The College Board at any of their more than 1800 test centers or at one of the 2900 colleges or universities that accept them.
The College Board states it is a not-for-profit membership association whose mission is to connect students to college success and opportunity. It was founded in 1900, and the association has a membership of more than 5,600 schools, colleges, universities and other educational organizations. Each year, the College Board serves more than seven million students through major programs and services in college readiness, college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning.
While most homeschool educators are more familiar with the College Board's SAT and AP programs, their CLEP Program can also save students considerable course fees if they can pass the appropriate tests. For a fee of $80.00 per course, students can take CLEP tests in any of the more than 33 subjects in the areas of Literature, Foreign Languages, History and Social Studies, Science and Mathematics, and Business.
One word of caution - the College Board advises students that:
"Before you take a CLEP exam, learn about your college's CLEP policy. Most colleges and
universities grant credit for CLEP exams, but not all. There are 2,900 institutions that grant
credit for CLEP and each of them sets its own CLEP policy; in other words, each institution
determines for which exams credit is awarded, the scores required and how much credit will
be granted. Therefore, before you take a CLEP exam, check directly with the college or
university you plan to attend to make sure that it grants credit for CLEP and review the
specifics of its policy."
Not every university or college may accept every College Board CLEP test score, and not all have the same scoring levels for credit. For example, while one university may award three credit hours for a score of 55 on the college algebra CLEP test, another may require a higher score, while still a third university may not accept the College Board CLEP results for that particular test at all. It may require that students take their individual university CLEP test for a particular subject.
In the area of mathematics, parents also need to know what levels of high school math courses correspond to what level CLEP test. For example, the student who takes the college algebra CLEP test before mastering John Saxonâs Algebra 2 course will, in all likelihood receive a failing grade. Each of the CLEP math tests indicate the subject matter included in the tests. Following the math book's index will give you a pretty good idea of whether or not the student can handle that particular test.
I will say this about John Saxon's second edition of Advanced Mathematics. All students who have mastered the first ninety lessons in that book should easily pass the College Board's CLEP test for College Algebra and College Mathematics. If they have mastered the entire Advanced Mathematics book and also finished the first 25 lessons of calculus, they can easily pass not only those same two course tests, but the College Board pre-calculus CLEP test as well.
I recall that when I was teaching in the high school, one of my calculus students went down to the OU campus and took the calculus CLEP test and passed it. While in my senior calculus class, he was happy with just a "C" because he was going to study "Communications" at OU and openly admitted that he did not really need the math. He never took another math course in his life. When I asked him why he did not just take the college algebra CLEP test, he smiled and said, "I just wanted to be able to tell people that I had passed college calculus at OU." The College Board tests are a great way to get a few basic courses out of the way and save mounting college tuition costs, but if the students are going into engineering or research science, I would recommend they not use the CLEP tests to replace core courses in their field. They need to revisit these courses at the collegiate level.
WHY DO HOMESCHOOL EDUCATORS EITHER STRONGLY LIKE OR DISLIKE JOHN SAXON'S MATH BOOKS?
I was online at a popular website for home school educators a while back and I noticed some back and forth traffic about the benefits and drawbacks of John Saxonâs math books. One of the homeschool parents had just commented about the benefits of Johnâs books. As she saw them - through their use of continuous repetition throughout the books - she thought the process contributed to mastery as opposed to just memorizing the math concepts in each lesson for the upcoming test.
One reader replied to her comment with the following:
âOr, one can use a math program that makes the mathematical reasoning clear from the outset as a matter of course rather than believing that a child will grasp the mathematical concepts by repeating procedures ad nauseam. I think the Saxon method is flawed.â
This reminds me of one of Johnâs favorite sayings when challenged with similar logic. Johnâs reply would be to the effect that âIf you are setting about to teach a young man how to drive an automobile, you do not try to first have him understand the workings of the combustion engine; you put him behind the wheel and have him drive around the block several times.â
I recall when teaching incoming freshman the Saxon Algebra 1 course that I would first present students with several conditions such as having them all stand up and then asking if they were standing on a flat surface or a curve. Then I explained to them that an ant moving around on the side of the concrete curve of the quarter mile track at the high school would think he was moving in a straight line and he would never realize that, because of his minute size when compared to the enormity of the curve, he thought the curve to be a straight line.
I would then go on to explain that â like the antâs experience in his world - they were standing on an infinitesimal piece of another curve which appears to be a flat surface to them. I would continue by telling the students that in âSpatial Geometryâ there are more than 180 degrees in a triangle. It never failed, but about this time someone would put up their hand and â as one young lady did - say âMr. Reed, I am getting a headache, could we get on with Algebra 1?â
It was a different story when presenting the same conditions to seniors in the calculus class. They would excitedly begin discussing how to evaluate or calculate them. And telling them there were no parallel lines in space did not seem to upset them either. Could it be because the seniors in calculus were all well grounded in the basic math concepts, and they understood the difference between the effects of these conditions in âFlat Landâ as opposed to their âSpatial Application?â
Perhaps John and I are old fashioned, but both of us thought it was the purpose of the high school to create a solid educational foundation - a foundation upon which the young collegiate mind would then advance into the reasoning and theory aspects of collegiate academics. Both John and I had encountered what I referred to as âAt Risk Adultsâ while teaching mathematics at the collegiate level. These students could not fathom a common denominator, or exponential growth. They were incapable of doing college level mathematics because they had never mastered the basics in high school.
Students fail algebra because they have not mastered fractions, decimals and percents. They fail calculus - not because of the calculus, for that is not difficult - they fail calculus because they have not mastered the basics of algebra and trigonometry. I recall my calculus professor after he had completed a lengthy calculus problem on the blackboard - filling the entire blackboard with the problem. Striking the board with the chalk he turned and said âThe rest is just algebra.â I saw many of my freshman contemporaries with quizzical looks upon their faces. Being the âold manâ in the class, I quickly said âBut sir that appears to be what they do not understand. Could you go over those steps?â Without batting an eye, he replied âThis is a calculus class Mr. Reed, not an algebra class.â
I firmly believe that what causes individuals to so strongly dislike John Saxonâs math books is, not from their having âusedâ the books, and suffering frustration or failure, but from their having âmisusedâ the books. Orâmore importantlyâfrom having entered the Saxon curriculum at the wrong math level assuming the previous math curriculum adequately prepared the student for this level Saxon math bookâwhen in reality it had not!
So when home school parents place the student into the wrong level Saxon math bookâand the student quickly falters in that bookâit stands to reason they would blame the curriculum, when in reality, their student was not prepared for the requirements at that level.
Why? Because Saxon math books do not teach the test, they require mastery of concepts introduced in previous levels of math to enable the student to proceed successfully at every level of the curriculum.
Taking the Saxon Placement Test before entering a Saxon math book from Math 54 through Algebra 2, will ensure the student and parent can adequately evaluate the studentâs ability to proceed at a certain level with success based upon what they have previously mastered.
The Placement Tests can be found on this website at the link shown below:
WHY USE SAXON MATH BOOKS?
The title of todayâs news article was the title of my seminar at Homeschool Conventions when I travelled the Homeschool Convention circuit several years ago. What I wanted to convey to homeschool educators at these seminars was factual information on why John Saxonâs math books â when properly used â remain the best math curriculum for mastery of mathematics on the market today.
Why did I emphasize âwhen properly usedâ? The reason is because improper use of Saxon math books is one of their major weaknesses. The vast majority of students who encounter difficulties in a Saxon math textbook do so, not because the book is âtoughâ or âdifficultâ, but because they either entered the Saxon curriculum at the wrong math level or because they skipped books and have not properly advanced through the series. Or - for one reason or another - they had been switching back and forth between different math curriculums. Because of switching curriculums, the students had all developed âholesâ in their basic math concepts, concepts critical for future success in the math book they were now using. In John Saxonâs math books these âmath holesâ created frustration and failure for the students who were returning to the Saxon curriculum in the upper level math books.
At every convention, there were always a half dozen or more homeschool parents who came to the booth - all facing the same dilemma! Their sons or daughters had recently completed or were currently completing another curriculum of instruction in algebra, and while they said they were happy with the curriculum they were using, they expressed concern that their son or daughter was not mastering sufficient math concepts to score well on the upcoming ACT or SAT tests. I asked each of them to have their student take the on-line Saxon algebra one placement test which consisted of fifty math questions. The test was actually the final exam in the Saxon pre-algebra book (Algebra Â˝, 3rd Ed).
In almost every case, regardless of which math curriculum the students were using, the answer was always the same. Not one of the students passed the test. It was not a matter of receiving a low passing grade on the test. The vast majority of them failed to attain fifty percent or better. The curriculums the students were using were not bad curriculums. They correctly taught students the necessary math concepts in a variety of ways. But unlike John Saxonâs method of introducing incremental development coupled with his application of âautomaticityâ to create mastery of the necessary math skills, none of these curriculums enabled students to master these concepts. They taught the test!
In those cases where the parents asked for my advice after learning about the failed pre-algebra test, we worked out a successful plan of action to ensure that the failed concepts were mastered and the âmath holesâ were filled. The plan enabled each of the students to successfully move to an advanced algebra course later in their academic schedule.
Now to address another topic that arose during the seminars. Several attendees asked whether or not they should use the new fourth editions of algebra one and algebra two textbooks as well as the new separate geometry textbook. I told the audience that the new fourth editions were initially created for the public school system together with the companyâs creation of a new geometry textbook. After all, donât you make more money from selling three math books than you do from selling just two?
I explained that the daily geometry review content as well as the individual geometry lessons had been gutted from the third editions of Johnâs original Algebra one and Algebra two to create the new fourth editions of those books In my professional opinion, I replied to the homeschool educators that they should stay with the current third editions of Johnâs original Algebra one and Algebra 2 two books and not fall into the century old trap of using a separate geometry text in-between the algebra one and algebra two courses.
One homeschool parent commented that I was mistaken because she had called the company customer service desk and they told her there was geometry in the new fourth edition of their Saxon Algebra 1 book. I have a copy of that edition. It was designed to be sold to the public schools along with the companyâs new geometry textbook, and it does not integrate geometry into the content of the bookâs one hundred twenty lessons as Johnâs third edition of Algebra one does.
Here are the facts regarding the geometry content in the two books. I will let you draw your own conclusions:
1. In the index of the third edition of John Saxonâs Algebra 1 textbook, there are seventeen references dealing with the calculation of total area, lateral surface area, and volume of spheres, cones, cylinders, etc. In the new fourth edition index, there are only four references to area and volume and they are not geometric references. They deal with determining correct unit conversions of measure and the application of ratios and proportions in their solution, all of which are algebraic not geometric functions.
2. In the index of the third edition of Johnâs Algebra 1 book there are nine references to the word âangles.â In the index of the fourth edition, there are none. The reference term âanglesâ does not appear.
3. In the third edition index of Johnâs Algebra 1 book, there are three references to âGeometric Solids.â In the fourth edition index, the word âGeometric Solidsâ does not appear.
4. The only reference to the word âgeometryâ in the fourth edition index is the phrase âGeometric Sequencesâ and that term is not a geometry term. It refers to an algebraic pattern determined through the use of a specific algebraic formula.
5. Geometry references, terms, concepts and daily problems dealing with them are found throughout Johnâs third edition of Algebra one. This does not occur in the fourth edition of algebra one created by HMHCO - the new owners of Saxon Publishers.
So why was the homeschool educator told there was geometry in the new fourth edition of algebra one?
Well, let me see if I can explain what I believe the marketing people came up with. I say marketing people because several of us have tried for several years to find out who authored the new fourth edition and no one at the company could â or would â tell us who the author is. Someone commented that it was given to a textbook committee to create the new fourth editions of algebra one and two as well as the new geometry textbook.
At the back of the new fourth edition of algebra one, just before the index, is a short section of thirty-two pages referred to as the âSkills Bank.â Within these thirty-two pages are thirty-one separate topics of which only twelve deal with geometric functions and concepts. Each of the concepts is about a half page in length and covers just a few practice problems dealing with the concepts themselves. Since they are not presented or practiced throughout the book, I believe it makes it difficult if not impossible for the student to master any of these concepts encountering them this late in the book â if they are encountered at all.
Here are several examples of how these geometry concepts are presented in the âSkills Bankâ of the new fourth edition of algebra one:.
1. Skills Bank Lesson 14: Contains two short sentences explaining how to classify a quadrilateral. The student is then given only three practice problems on the concept.
2. Skills Bank Lesson 16: Contains two short explanatory sentences describing congruency followed by only two practice problems.
3. Skills Bank Lesson 19: Contains five brief statements describing the various terms used to describe a circle and its component parts, immediately followed by two problems asking the students to identify all of these parts.
The âSkills Bankâ concept is fine as far as using a brief addendum to define what those geometric terms mean. But when does the student get to work these concepts so that the review creates âmasteryâ as Johnâs original books were designed? âThe âfrequent, cumulative assessmentâ of John Saxonâs math program is referenced by the company on page 5 of their new textbook as one of the key elements of the new book. However, those attributes are never developed for the geometry concepts. Additionally, the companyâs use of colored âDistributive Strandsâ reflecting the distribution of functions and relations throughout the textbook does not list any geometry functions or relation strands showing up anywhere in the book â at least not in the book they sent me.
The new algebra one fourth edition textbook created by HMHCO - under the Saxon name â may be a good algebra textbook. However, it does not contain geometry concepts on a daily basis as Johnâs third edition of algebra one does. Before you make a decision to use a separate geometry textbook along with the new fourth edition of algebra one and two, please read my September 2015 news article. If you need to discuss the issue further, please do not hesitate to call or email me.
SHOULD YOU GRADE THE DAILY SAXON MATH ASSIGNMENTS?
I continue to see comments on familiar blogs about correcting â or grading â 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, Johnâs math books were designed to test the studentâs 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 âpracticeâ 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, â as I like to describe it â they put on their âTest Hatâ 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 Saxonâs methodology are weekly tests (every four lessons from Algebra Â˝ 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 weekâs 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 âYes, they must get 100 percent on every paper or they do not move on.â 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 weekâs 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 âgolden oldieâ 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 Saxonâs 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 â or lack thereof - while the daily homework only reveals their daily memory!
NOTE: The upper level Saxon math textbooks from algebra Â˝ through calculus have a test every four lessons, making it easy to standardize the tests always on a Friday - with a weekend free of math homework. However, from Math 54 through Math 87, the tests are taken after every five lessons which either require a Saturday test or place the test day on a rotating schedule. You can easily remedy this by having the student do the fifth lesson in the test series on Friday morning, then later that day, have them take the weekly test leaving them to concentrate on resolving the oneâs they missed on the test - with no week-end homework. This places them on the same Friday test schedule as the upper level Saxon math students.
SHOULD HOMESCHOOL STUDENTS TAKE CALCULUS?
Calculus is not difficult! Students fail calculus not because the calculus is difficult - it is not - but because they never mastered the required algebraic concepts necessary for success in a calculus course. However, not everyone who is good at algebra needs to take a calculus course.
A number of the students I taught in high school never got to calculus their senior year because they could not complete the advanced mathematics textbook by the end of their junior year. They ended up finishing their senior year with the second course from the advanced math book titled "Trigonometry and Pre-calculus" and then taking calculus at the university level. This worked out just fine for them as they were more than adequately prepared and had an opportunity to share the challenge with likeminded contemporaries on campus.
Some of my students advanced no further than completing Saxon Algebra 2 by the end of their senior year in high school. They were able to take a less challenging math course their first year of college by taking the basic college freshman algebra course required for most non-engineering or non-mathematics students. These students would never have to take another math course again - unless of course they switched majors requiring a higher level of mathematics. And, if they did, they would be adequately prepared for the challenge.
I believe the answer for homeschool students in these same situations is what we in Oklahoma call "concurrent enrollment." In other words, don't take a calculus course at home by yourself. Under the guidelines of "concurrent" or "dual" enrollment - or whatever your state calls it - take the course at a local college or university and share the experience with likeminded contemporaries. If your state has such a program a high school student can also receive both high school and college credit for the course. I would not recommend taking calculus under "concurrent" or "dual" enrollment at a local community college unless you first verified that the college or university your child was going to attend will accept that level credit for the course. Many of them will accept those credits but only as electives and not as required courses in the student's major field of studies. Check with the head of the mathematics department or the registrar's office before you enroll in the local community college.
The concept of "concurrent" or "dual" enrollment was just beginning to take hold in the field of education when I was teaching and there were not many high school students taking these college courses enabling them to receive both a high school and college math credit for their efforts. As we gained experience with the new program, we learned that our high school juniors and seniors who had truly mastered John Saxon's Algebra 2 course could easily enroll at the local university in the freshman college algebra course and could - provided they went to class - easily pass the course. And, if they were English or Art majors, they would never have to take another math course if they so desired.
Students who were eligible and wanted to take a calculus course their senior year looked forward to taking it at the local university and receiving "concurrent" or "dual" credit for the course. Many of these same students went on to become research technicians in the field of bio-chemistry and physics. However, several of them never took another math course in their college careers because they were English or Art History majors. They took the college freshman calculus course because they wanted to prove they could pass the course. They wanted to be able to say "I took college calculus my senior year of high school."
So, what does all this mean? Home school students whose major will require calculus at the college level should adjust their math sequence to complete John Saxon's advanced mathematics textbook (2nd Ed) by the end of their junior year of high school, and then take calculus the first semester of their senior year at a local college or university. Not only will this enable them to receive "concurrent" or "dual" - unless their state prohibits it - but they will enjoy the camaraderie of other likeminded college students taking the course with them.
There is a final serendipity to all of this. When enrolling at most universities, honors freshman and freshman with college credits enroll before the "masses" of other freshman students. This would virtually guarantee the student with college credits the courses and schedule they desire - not to mention the potential for scholarship offers with high ACT or SAT scores and earned college credits in a course titled "Calculus I" recorded on their high school transcript.