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February 2026

WHY USE SAXON MATH BOOKS?

The title of today’s news article was the title of my seminar at Homeschool Conventions – when   I travelled the Homeschool Convention circuit more than a decade ago. What I wanted to convey to homeschool educators at these seminars was factual information on why John Saxon’s math books – when properly used – remain the best math curriculum for mastery of mathematics on the market today. 

Why did I emphasize “when properly used”? 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 “tough” or “difficult”, 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 “holes” in their basic math concepts, concepts critical for future success in the math book they were now using.  In John Saxon’s math books these “math holes” created frustration and failure for the students who were returning to the Saxon curriculum in the upper level math books.

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 ½, 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 Saxon’s method of introducing incremental development coupled with his application of “automaticity” 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 “math holes” 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 new owner’s company’s creation of a new geometry textbook. After all, don’t 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 John’s original Algebra one and Algebra two to create the new fourth editions of those books by the new owners of Saxon.  In my professional opinion, I replied to the homeschool educators that they should stay with the current third editions of John’s original Algebra 1 and Algebra 2 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 company’s new geometry textbook, and it does not integrate geometry into the content of the book’s one hundred twenty lessons as John’s third edition of Algebra one does.

Here are the facts regarding the geometry content in the two books. I will let you draw your own conclusions:

1. In the index of the third edition of John Saxon’s 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 John’s Algebra 1 book there are nine references to the word “angles.” In the index of the new fourth edition, there are none.  The reference term “angles” does not appear.
3. In the third edition index of John’s Algebra 1 book, there are three references to “Geometric Solids.”  In the new fourth edition index, the word “Geometric Solids” does not appear. 
4. The only reference to the word “geometry” in the new fourth edition index is the phrase “Geometric Sequences” and that term is not a geometry term.  It refers to an algebraic pattern determined through the use of a specific algebraic formula.
5. Geometry references, terms, concepts and daily problems dealing with them are found throughout John’s third edition of Algebra one.  This does not occur in the new 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 – or would – 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 “Skills Bank.” Within these thirty-two pages are thirty-one separate topics of which only twelve deal with geometric functions and concepts. Each of the concepts is about a half page in length and covers just a few practice problems dealing with the concepts themselves. 

Since they are not presented or practiced throughout the book, I believe it makes it difficult if not impossible for the student to master any of these concepts encountering them this late in the book – if they are encountered at all. 

Here are several examples of how these geometry concepts are presented in the “Skills Bank” of the new fourth edition of algebra one:

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 “Skills Bank” concept is fine as far as using a brief addendum to define what those geometric terms mean.  But when does the student get to work these concepts so that the review creates “mastery” – as John‘s original books were designed?  “The “frequent, cumulative assessment” of John Saxon’s math program 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 company’s use of colored “Distributive Strands” reflecting the distribution of functions and relations throughout the textbook does not list any geometry functions or relation strands showing up anywhere in the book – at least not in the book they sent me.

The new algebra one fourth edition textbook created by HMHCO – under the Saxon name – may be a good algebra textbook.  However, it does not contain basic introductory geometry concepts on a daily basis as John’s third edition of algebra one does.  Before you make a decision to use a separate geometry textbook along with the new fourth edition of algebra one and two, please also take a look at the April 2025 and April 2022 news articles. 

 

January 2026

WHY DO HOME SCHOOL 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 Saxon's math books. One of the homeschool parents had just commented about the benefits of John's 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:

"Or, one can use a math program that makes the mathematical reasoning clear from the outset as a matter of course rather than believing that a child will grasp the mathematical concepts by repeating procedures ad nauseam. I think the Saxon method is flawed."

This reminds me of one of John's favorite sayings when challenged with similar logic. John's reply would be to the effect that "If you are setting about to teach a young man how to drive an automobile, you do not try to first have him understand the workings of the combustion engine; you put him behind the wheel and have him drive around the block several times."

I recall when teaching incoming freshman the Saxon Algebra 1 course that I would first present students with several conditions such as having them all stand up and then asking if they were standing on a flat surface or a curve. Then I explained to them that an ant moving around on the side of the concrete curve of the quarter mile track at the high school would think he was moving in a straight line and he would never realize that, because of his minute size when compared to the enormity of the curve, he thought the curve to be a straight line.

I would then go on to explain that – like the ant's experience in his world – they were standing on an infinitesimal piece of another curve which appears to be a flat surface to them. I would continue by telling the students that in "Spatial Geometry" there are more than 180 degrees in a triangle. It never failed, but about this time someone would put up their hand and – as one young lady did – say "Mr. Reed, I am getting a headache, could we get on with Algebra 1?"

It was a different story when presenting the same conditions to seniors in the calculus class. They would excitedly begin discussing how to evaluate or calculate them. And telling them there were no parallel lines in space did not seem to upset them either. Could it be because the seniors in calculus were all well grounded in the basic math concepts, and they understood the difference between the effects of these conditions in "Flat Land" as opposed to their "Spatial Application?"

Perhaps John and I are old fashioned, but both of us thought it was the purpose of the high school to create a solid educational foundation – a foundation upon which the young collegiate mind would then advance into the reasoning and theory aspects of collegiate academics. Both John and I had encountered what I referred to as "At Risk Adults" while teaching mathematics at the collegiate level. These students could not fathom a common denominator, or exponential growth. They were incapable of doing college level mathematics because they had never mastered the basics in high school.

Students fail algebra because they have not mastered fractions, decimals and percents. They fail calculus – not because of the calculus, for that is not difficult – they fail calculus because they have not mastered the basics of algebra and trigonometry. I recall my calculus professor after he had completed a lengthy calculus problem on the blackboard – filling the entire blackboard with the problem. Striking the board with the chalk he turned and said "The rest is just algebra." I saw many of my freshman contemporaries with quizzical looks upon their faces. Being the "old man" in the class, I quickly said "But sir that appears to be what they do not understand. Could you go over those steps?" Without batting an eye, he replied "This is a calculus class Mr. Reed, not an algebra class."

I firmly believe that what causes individuals to so strongly dislike John Saxon's math books is, not from their having "used" the books, and suffering frustration or failure, but from their having "misused" the books. Or – more importantly – from having entered the Saxon curriculum at the wrong math level. They assumed the previous math curriculum had adequately prepared the student for this level Saxon math book – in reality it had not!

So when home school parents place the student into the wrong level Saxon math book – and the student quickly falters in that book – it 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 student's 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:

https://homeschoolwithsaxon.com/saxon_placement_tests.php