Posted tagged ‘Algebra 1’

Shormann Math Builds Effective Study Habits

October 19, 2015

With Shormann Math, using 21st Century technology to create a math course allows us to obtain valuable information revealing that, regardless of skill level, students who want to learn math, can, and Shormann Math has the tools for them to do so.

For example, during quarterly exam week, students are provided with two full-length practice exams. Practice exams allow students to prove to themselves that they really do (or don’t) know the material covered that quarter. Besides the practice exams, they are given other guidelines on how to prepare for the exams. The guidelines are based on years of teaching experience, as well as observing university professors. Between my bachelor’s in aerospace engineering, and a PhD in aquatic science, I had a lot of professors and exams! And the best professors, the ones who really wanted you to learn the material, did two things: 1) they kept a file of previous exams in the library that students could check out and study, and 2) they had office hours so students could ask questions. Shormann Math provides both, with 1) practice exams that reward students for a good study effort and 2) free email Q&A any time.

But are the practice exams helpful? Well, see for yourself. The following graph displays the recent results of Quarterly Exam 1 scores for Shormann Algebra 1 and 2(beta) students.* The bottom line is that students with “Good” study habits made A’s on the exam. The graph is a display of the obvious fact that good study habits build fluency, resulting in good scores on the actual exam. Being fluent in math means you know how to use the rules to solve new problems. And the purpose of the Practice Exams in Shormann Math is to provide new problems so the student can prove to themselves whether they are fluent, and if not, what they need to review.

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At some point in your life, you will be tested on a large amount of information. Whether it’s for a job you really want, a driver’s license, an SAT, ACT, MCAT, etc., sooner or later, test day is coming. And if you really want that license, or that job, etc., you are going to put the personal effort into it to study. Shormann Math is designed to help students build effective study habits in a less important setting where the stakes aren’t as high. But, as the results above reveal, the best curriculum in the world won’t make a bit of difference if the student doesn’t put that personal effort into following directions and studying effectively.

*Graph details: Scores are from Quarterly Exam 1 taken by students in Dr. Shormann’s live online Algebra 1 and 2 classes, October 2015. The three categories are based on student performance on the 2 practice exams take prior to the actual exam. The students are allowed to take the practice exam, review mistakes using the solutions manual provided, and then take it again. Students who put the effort into retaking each practice exam were rewarded for their effort with a higher grade. Students are also encouraged to show work on their paper, solving each problem by hand. For the actual exam, they are required to submit handwritten work on each problem. The practice exams were counted as one of their homework grades, providing further encouragement to complete them. The three categories were broken down as follows: “Good” students averaged 95% or better on the practice exams, all of which took at least one of the exams more than once in order to get a higher score, which means they took the time to correct their mistakes and study the problems they missed. “Mediocre” students took each exam once, but averaged below 95%, and showed little to no effort to try the exam again, missing a valuable opportunity to review and build fluency. “Poor” students did not attempt either practice exam. Of special note is the fact that the trend was consistent, regardless of which course students were doing (Algebra 1 or 2).  Also, because the students had the opportunity to retake each practice exam until they received a 100, study effort, and not skill level, was the main factor influencing performance on the actual exam. Not all students are equally gifted in math (or any subject), but students who are less-skilled at math can do better by studying harder. These results provide good evidence that, with Shormann Math, students who want to learn math, can, regardless of skill level!

The New Shormann Math vs. Saxon Math and Common Core

April 21, 2015

Summary: If mathematics is the language of science, then fluency should be the goal, which means the traditional “layer cake” approach to 3 years of high school math (Algebra 1, Geometry, Algebra 2) is probably not the best approach. The shapers of Common Core’s math standards realized this, and now states that adopt their standards can choose between two high school “pathways”, either the layer cake or integrated approach, where students learn algebra and geometry together. John Saxon* actually pioneered the integrated approach in the United States back in the 1980’s, but his integrated approach was only one small part of his textbooks’ successes. His method of “incremental development with continual review,” combined with a constant encouragement for students to learn by doing, were the keys. Shormann Math builds on John Saxon’s efforts to really teach math like the language of science that it is, by not just connecting students to their world, but, more importantly, to their Creator. In doing so, students learn to wisely mingle concepts like science and Scripture, faith and reason. Doing so makes it easier to learn subjects like calculus, which really does require a faith commitment in order to make sense of it. Because of its obvious connections to God’s attributes, secular calculus courses steer clear of this, and in so doing make it much more difficult to learn. Shormann Math will change that.

*John Saxon passed away in 1996, and the company he founded, Saxon Publishers, is now owned by Houghton-Mifflin/Harcourt. They have since created some Saxon-in-name-only Algebra 1, 2, and Geometry textbooks. Click here to read our review of the new books and to learn why we don’t recommend them.

The 10 Major Topics of Shormann Math

The 10 major topics of Shormann Math, compared to John Saxon's books and Common Core standards.

The 10 major topics of Shormann Math, compared to John Saxon’s books and Common Core standards.

Measurement is a topic that is a natural part of any math course seeking to teach math as the language of science. That it’s missing from three years of Common Core high school math is a huge problem. As a science class and lab teaching assistant during graduate school, one of the biggest math-related struggles I remember was students’ inability to convert from one unit to another. And it’s not just Common Core, most government school standards are weak in teaching measurement-related topics.

All Shormann Math high school courses will keep students fresh with working with measurements. Computers are also a very real part of every students’ world, so knowing about some of the mathematics behind them should be a priority. And, as mentioned in the Summary above, calculus becomes a normal part of high school math when one of the priorities is to connect students to their Creator.

Foundations and Pedagogy

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As Euclid famously said centuries ago, there is no royal road to learning. However, some methods are definitely better than others, and the Common Core’s integrated pathway (click here to read an Education Week review) is definitely a step in the right direction. However, the integrated approach has it’s own challenges. To really teach math like the active, hands-on language of science that it is, you have to teach it like languages are taught, or sports, or instruments, etc. You teach students a little bit about something, give them time to practice it, and then build on it. John Saxon called this “incremental development with continual review,” which is missing from Common Core.

Also missing from Common Core is the importance of math history. Understanding why they are learning the different math topics makes math more relevant to students. Learning some things about the people behind the math concepts they are learning, as well as some of the great, and not-so-great things they did, makes math more meaningful. And the connection to history also shines a bright light on the rich Christian heritage of mathematics, especially regarding algebra and calculus. Showing students how God’s attributes are clearly revealed in mathematics can make a huge difference in their comprehension and success in the course.

Shormann Math’s emphasis on math history means that, in developing the course, I dove deep into the classic works of Euclid, Newton, Euler, etc. Rather than reinventing the wheel, this study of the classics allowed me to develop a curriculum that stands on the shoulders of giants (a phrase often attributed to Isaac Newton). It should be a huge confidence-booster to parent and student alike to know your course is built on time-tested and proven methods for learning math.

What 3 Years of Math Covers

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By focusing on what matters most, Shormann Math does more in 3 years than either Common Core or Saxon. In the first two years, Shormann Math covers all the concepts presented on the SAT (the new 2016 version), the ACT, and both the CLEP College Algebra and CLEP College Math exam. A full credit of geometry is integrated into the first two years as well. This is different from John Saxon-authored texts, which include the geometry credit in years 2 and 3 (Algebra 2 and the first 1/3 of Advanced Math). And before you think Shormann Math couldn’t possibly have enough geometry, consider that we will cover all the standards, like perimeter/area/volume, similarity and congruence, circle and triangle theorems, and proofs. In addition, we will show students how the proof technique is not some isolated subject you only learn in geometry class, which is what most students, and parents, think it is. We’ll introduce students to proofs by studying the master, Euclid, covering several of his propositions. We’ll do the standard triangle proofs and circle proofs, but will also apply proof technique in other topics like algebra. And students will learn how proof is used in the real world. They’ll even learn how geometry is used in art and architecture. And on top of all that, we’ll introduce non-Euclidean geometry in Algebra 2, diving deeper in Precalculus. We’ll also use CAD programs like Geometer’s Sketchpad to complete proofs and more.

Finally, Shormann Math will introduce calculus fundamentals. By year 3 (precalculus), Shormann Math students will be very comfortable finding limits, and will have a solid grasp of derivatives and integrals. We hope all students will continue on to Shormann Calculus, but if not, they will be more than ready for college-level calculus. Of all the courses in college, calculus is the subject that opens the door to virtually every college major, or if the student cannot pass the class, closes the door on about 80% of majors. The first three years of Shormann Math will give students the confidence they need to take college calculus, and be at a level to help their peers learn it, which can also open up opportunities to build relationships and share the gospel. And completing 4 years of Shormann Math will allow students to possibly prepare for and pass either the CLEP or AP Calculus exam, receiving college credit for their efforts.

But Saxon + DIVE Lectures do a lot of this already. Why make a new curriculum?

There are many reasons, here are a few:

  • We can build the curriculum on a Christian and historical foundation, rather than bringing these fundamentals in from the side, like we do with the DIVE Lectures that teach Saxon Math.
  • The one topic John Saxon didn’t integrate was calculus. We think it just might be the most important topic to integrate, and our current Shormann Math students are proving Algebra 1-level students can learn some calculus fundamentals!
  • We don’t know how long Houghton Mifflin/Harcourt will continue to sell John Saxon-authored textbooks.
  • We can take advantage of 21st Century technology and e-learning to provide more efficient and effective learning. Our self-paced e-learning format includes many powerful learning tools, including video lectures and video solutions to homework, all for about the same price as the Saxon home study kits. The following table lists some detailed differences between Shormann Math and Saxon Math.

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What is the prerequisite for Shormann Math Algebra 1?

Students who have successfully completed a standard pre-algebra course, including either Saxon 8/7 or Saxon Algebra Half, are ready for Shormann Math Algebra 1.

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Do you have any questions? Feel free to leave a comment!

Click here for a detailed description of Shormann Math, including sample video lectures and pricing information.

Shormann Math Core Ideas: Jesus Christ is the “Common Core.”

August 5, 2014

The following is the third in a series of posts covering Shormann Mathematics, Algebra 1, the newest product from DIVE Math and Science! Click here to read the complete document that covers Shormann Math core ideas, course description, and Algebra 1 table of contents.

Jesus Christ is the “Common Core” of Shormann Math

Perhaps you have heard of the United States government’s “Common Core” curriculum. Perhaps you have also heard that a lot of people are concerned about it. Leading experts believe the Common Core’s mathematics standards will not prepare students to study science, technology, engineering, and math (STEM) in a selective four-year college. And a white paper by the Pioneer Institute concludes by saying

“At this time we can conclude only that a gigantic fraud has been perpetrated on this country, in particular on parents in this country, by those developing, promoting, or endorsing Common Core’s standards.”

Unfortunately, man and his ever-changing ideas are at the core of this curriculum. At DIVE, we strive to place Jesus Christ at the core of all our products, and we pray that this will result in students learning math and science for His glory and the service of others. So, even though our primary goal is NOT to prepare students for STEM, we believe by putting Christ at the foundation, just like the world’s original universities did, students will naturally learn to use mathematical tools that will connect them to their world and their Creator.

Shormann Math Core Ideas: Defining Mathematics

July 30, 2014

The following is the second in a series of posts covering Shormann Mathematics, Algebra 1, the newest product from DIVE Math and Science! Click here to read the complete document that covers Shormann Math core ideas, course description, and Algebra 1 table of contents.

Thinking of mathematics as the "ship," and the definition as the "captain," the way we define mathematics can greatly influence how we use it.

Thinking of mathematics as the “ship,” and the definition as the “captain,” the way we define mathematics can greatly influence how we use it.

Definitions Matter

Thinking of mathematics as the “ship” and the definition as the “captain”, a good captain can use the ship for what it’s designed for. A good captain knows who built the ship. A good captain can help others better understand what the ship is capable of. Here is how mathematics is defined in Shormann Math:

mathematics: The language of science and a God-given tool for measuring and classifying pattern and shape.

This definition tells us that mathematics, with all of its unique symbols, is best thought of as a language. It is a language we can use to study creation. Next, this definition tells us mathematics is about measuring things. It also tells us mathematics helps us find truth, goodness, beauty, and unity and diversity as we classify pattern and shape.

But most importantly, this definition of mathematics tells us “who built the ship.” Mathematics is not man-made, it is God-given. Created in His image (Genesis 1:26), we are designed by God to use this tool to be creative, too! God designed us to be creative and to engage in fruitful, productive activities (Genesis 1:28). Click here to learn more about the Shormann Math definition of mathematics.

Shormann Math, Algebra 1 Overview

July 22, 2014

The following is an overview of Shormann Mathematics, Algebra 1, the newest product from DIVE Math and Science! Click here to read the complete document that covers Shormann Math core ideas, course description, and Algebra 1 table of contents.

Algebra 1 course description

A complete math curriculum

Unlike our DIVE Math Lectures that teach the content in textbooks authored by the late John Saxon, Shormann Math is a standalone curriculum.  Shormann Math is designed to connect students to their world and their Creator by using an incremental approach with continual review to teach 10 major math concepts from a Christian foundation. The 10 major concepts are: number, ratio, algebra, geometry, analytical geometry, measurement, trigonometry, calculus, statistics, and computer math. The first course produced will be Algebra 1, followed by Algebra 2, Precalculus and Calculus.

Math, the language of science

If you are wondering “Where’s the geometry?” in the 4 courses listed, it’s there! Because scholars consider mathematics to be “the language of science,” Shormann Math teaches math like a language, where you don’t just learn nouns for a year, verbs for another year, etc. You learn a little of each concept, combined with lots of review, and then you combine the different concepts together. So, Shormann Math Algebra 1 and 2 in particular will also contain a rigorous survey of geometry, including lots of proofs, even some straight out of Euclid’s famous book, The Elements. We’ll even cover non-Euclidean geometry, and show students how the concept of proof applies to all of mathematics, not just geometry. All the geometry, and trigonometry, that a student needs to be ready for the SAT or ACT will be covered in Algebra 1 and 2. Scroll down to the Algebra 1 Table of Contents where you can see more detail about geometry coverage.

Connecting your child to their world and their Creator

While Shormann Math will guide your child through high school algebra and geometry, that is not our primary goal. And it is definitely not our goal to align Shormann Math with the Common Core standards. Our goal is to connect your child to their world and their Creator by teaching them math, the language of science, from a Christian foundation. And because the last 300+ years of technological innovations can be connected to calculus in one way or another, we will present calculus early and often, and not in an intimidating way, but in a way that is based off things students already know.

Standing on the shoulders of giants

Unlike many new math programs, Shormann Math is not about an entirely different approach. Instead, Shormann Math builds on a foundation of time tested and proven methods. Famous mathematicians and math educators like Euclid, Euler, Saxon, Whitehead, Kline, Sawyer, Nickel, etc. were studied for years before work on Shormann Math began.

For 2014-15, Shormann Math will be offered as a live, online class only. For more details on Shormann Math, including the Algebra 1 Table of Contents, click here. Then, if you are ready to dive into this new adventure in learning math, click here to register!

Defining Mathematics

July 11, 2014
Thinking of mathematics as the "ship," and the definition as the "captain," the way we define mathematics can greatly influence how we use it.

Thinking of mathematics as the “ship,” and the definition as the “captain,” the way we define mathematics can greatly influence how we use it. (Wikipedia photo of the tall ship “Elissa.”)

The Challenge of Defining Mathematics

Throughout history, humans have never settled on one particular definition for mathematics. Part of the reason is the abstract nature of mathematics, and the way general mathematical truths can apply to an infinite number of situations. For example, think of numbers. Numbers are abstract ideas. The number 3 is an idea of “threeness,” and can be used to describe 3 bears, 3 cars, 3 words, etc.

Here are a few of the ways famous mathematicians and mathematics teachers have defined mathematics:

  • The science which investigates the means of measuring quantity(L. Euler, Elements of Algebra, 1765).
  • The foundation of exact thought as applied to natural phenomena(A.N. Whitehead, An Introduction to Mathematics, 1911).
  •  Mathematics is the classification and study of all possible patterns(W. W. Sawyer, Prelude to Mathematics, 1955).
  • A study of space and quantity (Kline, Mathematics and the Physical World, 1959).

If Math is the Ship, Then its Definition is the Captain

Do you think it matters how mathematics is defined in the math courses you or your children do? I’ve been thinking about this question for many years now, and I think the answer is most definitely “yes!” A good definition can set the foundation for the entire course. And for a mathematics curriculum writer like myself, it can set the foundation for not just one course, but the entire curriculum. Thinking of mathematics as the “ship” and the definition as its “captain,” a good captain can use the ship for what it’s designed for. A good captain knows who built the ship. A good captain can help others better understand what the ship is capable of.

How Shormann Mathematics Defines Math

At DIVE, we are getting close to launching our own standalone mathematics curriculum, Shormann Mathematics. Algebra 1 is the first course. For the first year, it will be available as a live, online class (click here to register). In Shormann Mathematics, we will use the following definition for mathematics:

mathematics: the language of science and a God-given tool for measuring and classifying pattern and shape.

This definition tells us that mathematics, with all of its unique symbols, is best thought of as a language. It is a language we can use to study creation. Next, this definition tells us mathematics is about measuring things. It also tells us mathematics helps us find truth, goodness and beauty as we classify pattern and shape.

But most importantly, this definition of mathematics tells us “who built the ship.” Mathematics is not man-made, it is God-given. Created in His image (Genesis 1:26), we are designed by God to use this tool to be creative, too! God designed us to be creative and to engage in fruitful, productive activities (Genesis 1:28).

What’s the “Common Core” of Your Math And Science Curriculum?

A lot is being discussed right now about “Common Core” curriculum promoted by the United States government. Unfortunately, man and his ever-changing ideas are at the core of this curriculum. At DIVE, we strive to place Jesus Christ at the core of all our products, and we pray that this will result in students learning math and science for His glory and the service of others. We would appreciate your prayers as we seek to put a new captain at the helm of the ship of mathematics, helping students use the ship for what God intended it for!

Weighing the Differences in 3rd and 4th Edition Saxon Algebra 1

February 8, 2012

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Over the past few months, many parents have contacted us, asking if we plan to make a DIVE CD to teach the new Saxon Algebra 1, 4th edition textbook.  The short answer is “no”, and the short reason is that we believe the newer Saxon textbooks have strayed too far from John Saxon’s (1923-1996) original, tried and tested vision for teaching mathematics.  This new textbook was not published by John Saxon, but by Houghton Mifflin Harcourt (HMH). If you would like to know more about our reasons, please read on.

Physical Differences

Saxon Algebra 1 4th ed. (left), Saxon Algebra 1 3rd ed. (center), and Leonhard Euler’s Elements of Algebra (right), a text that most modern algebra books are based upon.

The 4th edition cover is noticeably different from earlier Saxon editions. For comparison, I have included a copy of Leonhard Euler’s Elements of Algebra, a textbook whose subject matter is the foundation of most modern algebra courses. Euler lived from 1707-1783, and is considered by most scholars to be one of the best, if not the best, mathematician ever. While I am in awe of his ability to write original research at the rate of 800 pages per year for most of his adult life, I am more impressed by his understanding of God. One of my favorite quotes is from his book, Letters to a German Princess:

“It is God, therefore, who places men, every instant, in circumstances the most favourable, and from which, they may derive motives the most powerful, to produce their conversion.”

Euler was a genius, but he was also a humble, Christian family man, and I think his biblical understanding of the world helped him excel at mathematics. Helping students understand the importance of a biblical foundation to their education is one way our DIVE Math lectures differ from instruction found in either new or traditional Saxon textbooks.

When I titled this post “Weighing the Differences”, I meant it, literally! I put the books on a scale, and the 4th edition is quite a monster at 4.75 lbs, a 58.3% increase over the 3rd edition.

The 4th edition weighs 58.3% more than the 3rd edition.

Content differences

You might be scratching your head right now, wondering “what does book weight have to do with anything?” Well, it matters to students! A bigger book means more weight to lug around in the backpack, but even more dreadful, it means more content! Sure enough, the 4th edition sports a whopping 66.3% increase in the number of pages.

The 4th edition has 374 more pages than the 3rd edition.

Some of that increase is because the 4th edition often has more practice problems for each lesson, which may be helpful to some students, but most of the increase is from new content. Both textbooks have 120 “Lessons”, but in the 4th edition, there are an additional 59 lessons the student must learn.

The 4th edition has an almost 50% increase in the number of individual lessons a student must learn.

To understand why there is such an increase in content, understand that in order to sell textbooks to all government schools, publishers must include content that satisfies the educational standards of every state in the nation. The increase in the 4th edition’s content is partly because states don’t all agree on what should and shouldn’t be taught in algebra class. Like any business, textbook publishers must be profitable. If their main goal is to sell to government schools, they will make more money if they can satisfy every state’s requirements. Selling to government schools is clearly the priority for HMH, which results in really large books! Something else to keep in mind is that the goal of publishers is to satisfy state standards; whether or not their books produce good results is often overlooked. Surprised? John Saxon wasn’t.

Differences in methodology

One cool math teacher. John Saxon was a test pilot for the U.S. Air Force in the 1950s. Photo courtesy of Niki Hayes, author of John Saxon’s Story, A Genius of Common Sense in Math Education.

John Saxon was known for his “Saxonisms”, one of which was

“Results, not methodology, should be the basis of curriculum decisions. Results matter.”

A methodology, or way of doing something, does make a difference, but what John Saxon meant is that when it comes to educating a child, the methodology should never trump the results. An Air Force test pilot with three engineering degrees, after retirement Saxon started teaching algebra at the local junior college. Appalled at the results he was seeing, Saxon wrote and published his first algebra book in 1981. His methodology produced good results, so he stuck with it, and when he died in 1996, Saxon Publishers annual sales were at $27 million. You can read more about John Saxon in Niki Hayes’ book, John Saxon’s Story, A Genius of Common Sense in Math Education.

You will hear many people say mathematics is the “language of science”, but to my knowledge, math books published by John Saxon and the original Saxon Publishers are about the only books that actually teach math this way. Just like learning a language, the original Saxon methodology begins with the fundamentals and provides students ample time to practice these before gently introducing more advanced material.

Original Saxon textbooks are also the best I’ve seen at teaching mathematics as one subject. Traditional American government math courses teach algebra and geometry separately. Many home educators follow the lead of government schools, without realizing that most European and Asian countries teach algebra and geometry together. You know, the same countries that consistently outperform the United States on international math exams (click here, see p. 7).  It makes sense that a student who is learning algebra and geometry together will probably understand all math better and be more ready to apply it in science and engineering fields. High school students will probably be able to outperform other students on college admissions tests, because these tests present algebra and geometry together.

Another distinguishing feature of John Saxon’s methodology was his desire for high school students to learn calculus. Again, Saxon shows its uniqueness in that, to my knowledge, it is one of the only curricula with a high school calculus course.

And finally, John Saxon was proud of his work. He had created something that produced good results, and he wanted to share it with others. Putting his name on the front of every book and naming the company after his family were ways of claiming ownership and responsibility for what he had done.

How true to the Saxon methodology is the new Algebra 1, 4th edition text?

While the 4th edition retains some of the pattern of incremental development with review, there is an obvious lack of understanding of what John Saxon was trying to accomplish. One thing John Saxon was fairly insistent on was teacher training for using his books. To an outside observer, the Saxon format looks fairly random, and if the teacher or student didn’t understand this was part of the incremental process, the format could be confusing. This is one reason our DIVE CDs have been helpful to so many learners, because we help students make the proper connections between lessons. However, many students are able to make the connections on their own, because when a new lesson builds on previous ones, John would normally mention this. For example, Lesson 25 in the 3rd edition begins with “In Lesson 23 and 24, we were introduced to the …” This gives the student a great reminder that what they are learning now is not all new, but is building on previous material, and they know where to find it if they need to review. By contrast, Lesson 23 in the 4th edition builds on Lesson 19 and 21, but no mention of this is made in Lesson 23, making it less likely the student will know where to go to review that concept. The lack of connection to previously learned material should be of particular concern to homeschoolers, as it makes self-directed learning more difficult.

The 4th edition also seems less adept at providing continual review. A good example is unit multipliers (a.k.a unit conversions, conversion factors, etc.). Saxon is the only curriculum I have seen that makes a real effort to teach students how to convert from one unit to another, a necessary skill when analyzing data collected in a science experiment, when building almost anything, in financial transactions, etc. Unfortunately, the 4th edition only has one lesson on unit multipliers (Lesson 8). One thing I liked was that they included an example of converting from one foreign currency to another, a useful skill in our increasingly global economy. What I didn’t like though was that after Lesson 30, I could not find any more homework problems on unit multipliers. Contrast that with the 3rd edition, where unit multipliers are taught in Lesson 4, 10, and 53, and students continue to have homework problems through Lesson 90. For assuring that a student learn a fundamental concept with such important implications, the choice is clear.

Besides the 66.3% increase in pages, the most glaring difference between the editions is that in the 4th edition, geometry was shoved to the “Skills Bank” section in the back of the book. Students are never taught these concepts beforehand, and I couldn’t really find where they ever practice many of the skills banks concepts. There is 1 geometry problem in every homework set, compared to 2 or more geometry problems in the 3rd edition. The geometry/algebra integration is essentially gone, and with their new, 887-page Geometry course, the newer Saxon editions look more like all the other government school textbooks that teach algebra and geometry separately.

A final, perplexing difference between the 3rd and 4th edition texts is that the authors’ names are not listed on the 4th edition (or on the new Geometry for that matter). I have quite a few math textbooks in my office, and all of them display the author’s name on the front or the spine. So who authored the new Saxon books? Is HMH being a little deceptive by not putting the real authors’ names on the book so that people will think John Saxon (dead since 1996) wrote them? Is HMH embarrassed by the new editions? I don’t know what the answer is.

So how different are the 3rd and 4th editions of Saxon Algebra 1? The differences remind me of a scene from a favorite childhood movie, Chitty Chitty Bang Bang. Caractacus Potts has built a “fantasmagorical motor car”, named Chitty Chitty Bang Bang, that can drive, fly, and swim, and the evil King of Vulgaria wants one, too! The king tries to kidnap Caractactus, but mistakenly kidnaps his father instead, who has no knowledge of how to build a Chitty Bang Bang. The king then uses the father to direct a crackpot team of engineers to build his own Chitty Bang Bang, which fails miserably. Like the Vulgarian king’s engineers, Houghton Mifflin Harcourt seems to have built Saxon Algebra 1, 4th edition with a limited understanding of the original designer’s plan and purpose. When it comes to understanding “incremental development with continual review”, a hallmark of the Saxon methodology, HMH doesn’t seem to get it.

When you try to build something without fully understanding what you’re doing, disaster usually results.

To conclude, I believe Saxon Algebra “peaked” with its 3rd editions of Algebra 1 and 2, so I won’t be making a DIVE CD for the 4th editions.  Fortunately, HMH is still selling the 3rd editions, and they show no signs of discontinuing them.

Time to DIVE

Since Saxon Publishers was first sold in 2004, I’ve feared that any new editions might lose their original Saxon methodology that strives to teach mathematics like the language of science that it is. The new 4th edition confirms this. And finally, since the sale, I have thought that, Lord willing, if the Saxon curriculum took a turn for the worst, then I would be ready to stand on the shoulders of giants like John Saxon, Leonhard Euler, Isaac Newton, Euclid and others, learn from them, and build a better curriculum. My goal has never been to just be a “Saxon Math Teacher”, but to teach students math and science so they can know their Savior and better serve Him and their fellow man. As providence would have it, John Saxon created a curriculum that I thought was the best, and so that’s what I’ve been teaching with since 1997. But since Saxon Publisher’s sale, I’ve had 8 years to think and pray about what to do, and I believe the time to act has come. Coming soon from DIVE,  look for a new, and I trust better, way to learn math.

June 2015 update:

Our new curriculum, Shormann Math, is here! Click here to learn more.