This article is in response to a question about DIVE, an online mathematics and science program for homeschool and/or private school students. Its focus has been on using *Saxon Math* but the program creator and director, Dr. David Shormann, has now written his own online mathematics program called *Shormann Math*. It is based in part on the Saxon methodology of incremental learning and continual review but now has integrated material that he feels is necessary for today’s students to be successful in math and science programs. This includes technology applications, computer math, real-world problems, and non-standard solutions. See more at https://diveintomath.com/shormann-math.

Dr. Shormannearned a bachelor’s degree in aerospace engineering and a master’s degree in marine chemistry from the University of Texas. His doctorate in limnology (a study of inland waters) is from Texas A&M University. He has an extensive background working with mathematics and science from aerospace engineering to oceanography. Presently living in Hawaii, Dr. Shormann said he is currently working on a patent-pending design. “It is a biomimetic airfoil based off a humpback whale’s pectoral fins. LOTS of math application going on with that. It’s got everything from Fibonacci ratios to computational fluid dynamics!”

I contacted him because I had heard he was changing some of the methods used in *Saxon Math*. This seemed unacceptable to me since *Saxon Math* is successful when users follow Saxon methods with little to no exception.

We talked by telephone on Thursday, March 14. This is a summary of that 70-minute conversation:

*Saxon Math*** ****unchanged:*** *

*Saxon Math*

*Saxon Math* is still being offered with no changes to its requirement of 30 homework problems and its methodology. Video lectures to accompany *Saxon Math* are still available in grades 4-12.

**On homework:**

However, his own *Shormann Math* materials presently cover Algebra 1, Algebra 2, and Advanced Math. These have 100 video lectures and lessons in each subject with 20 homework problems, as compared to *Saxon Math* with its 125 lessons/30 homework problems per lesson in Algebra 1; 129 lessons/30 homework in Algebra 2; and 125 lessons/30 homework in Advanced Mathematics.

With 20 homework problems which MUST be worked in each of the 100 lessons, that equals 2,000 homework problems for each course. Dr. Shormann believes this is adequate homework practice. (All homework problems in *Saxon Math* MUST also be worked.)

Considering how many schools are limiting or eliminating homework today, and one of the reasons public schools *Saxon Math* with its demand that all 30 homework problems be solved, I find Dr. Shormann is remaining true to the Saxon philosophy that completion of all homework problems supports a student’s retention and learning of information in daily lessons

**Struggling by students:**

I was concerned that students are not being allowed to see the solutions manual until after they had made several efforts to work out a problem. I interpreted that to reflect the progressive philosophy that students learn best by “struggling” through a lesson. Dr. Shormann explained that with online coursework, the easy answer for students is often simply to look at the solutions manual. He wants to be sure they have made good-faith efforts to work the problems; he doesn’t want students to “struggle,” but he does want them to put in the time to try and reach the correct solution. That made sense to me.

**Non-standard solutions:**

We discussed the issue of “non-standard solutions,” which is a particularly egregious topic with me for elementary and middle school students. Dr. Shormann said these solution processes are now required on the SAT and ACT. That is, a traditional procedure for finding an answer may need to be supported with alternative procedures to prove the student understands the concept within the SAT question.

I accepted, therefore, that non-standard solutions may need to be taught now at the high school level, but I explained those are being required, as interpreted with Common Core standards by publishers and teachers, in grades 1-8. I believe it is unacceptable to require these unfamiliar, non-standard methods in such early grade levels. For one thing, too many parents cannot help their children with lesson assignments that use such unfamiliar methods. (There are many other reasons against supplanting traditional procedures with these non-standard methods at the K-8 level.)

**Real world problems:**

I asked about the use of “real world” problems that Dr. Shormann promotes on his website. John Saxon hated that progressives used the term “real world” problems simply to promote politically correct ideas within their curriculum. Dr. Shormann’s problems are from

#### Integrated math:

I said the description of “integrated” mathematics is a loaded term used by progressives and resisted by many traditionalists. Based on European and Asian math programs that are not separated into distinct subjects such as algebra and geometry, and thus are “integrated” materials, Dr. Shormann believed that Saxon pioneered integrated math in America by integrating geometry throughout the Saxon algebra books and advanced math.

I explained Saxon did that for only one reason: He said geometry is used here as a “wedge” course to weed out students from advanced math classes. That is, when students take a sequence of Algebra 1, Geometry, and then Algebra 2, the year between the algebra courses causes weaker students to struggle in Algebra 2. He believed that was eliminating many students who could have worked Algebra 2 successfully if they had had continuity with their learning in the subject. By spacing geometry over three courses, Saxon’s goal was simply to provide an uninterrupted access for more students entering higher mathematics and science.

I’m still concerned that use of the word “integrated” in math education conjures up the weak progressive materials that are not written on the level of European or Asian courses. They are, instead, at fault for much of the failure of math education programs in America. John Saxon’s precise use of “incremental learning” and “continual review” offers more clarity in describing his sometimes-called “blended” or “scaffolding” methods.

#### Summary:

Dr. Shormann and I discussed many other topics. At this point I will say that I believe his online program is an excellent one and his heart truly is in the right place for students’ learning. The traditional *Saxon Math* can be taken or his new *Shormann Math* with its integrated materials is available.

While my heart will always be with the pure and proven *Saxon Math* at all levels, I appreciate Christian values that support mathematics, or vice-versa, being available in lessons to non-public school students. Because I had a semester course in the history of mathematics years ago that hooked me on the subject, I am also pleased that he’s incorporating people and topics from that rich history into his lessons. This can help explain how greatly the world of mathematics has always transcended throughout, and thus supported, other subject areas.

I hope this information is helpful regarding the DIVE mathematics education program.