Posted tagged ‘John Saxon’

C.S. Lewis Destroys Common Core in One Sentence

December 3, 2015

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Common Core Cancer

A brave Texas 7th-grader alleges that during an assignment about Common Core’s fake version of critical thinking, the teacher directed students to label God as a myth. This type of “anchor chart” assignment forces students to wrongfully classify all statements as either fact, opinion, or commonplace assertion. Here’s how these categories are defined in a typical Common Core-diseased classroom:

  • fact: Something that is true about a subject and can be tested or proven.
  • opinion: What someone thinks, feels or believes
  • commonplace assertion: Stating something is true without supporting it with facts or proof.

Notice how only facts are considered “true”, while opinions and commonplaces assertions are categorized as things that are either false or just “true for me but not necessarily true for you.”

This type of assignment is at the heart of Common Core educational standards (standards that supposedly aren’t taught in Texas. Surprise!). In his excellent March 2015 New York Times article about this fundamental problem with Common Core , philosopher Justin McBrayer described how students are required to fit things into one, and only one of these categories. In other words, you can’t believe in a fact, and only facts can be true. So, God can’t be believed in AND also be a fact! But neither can you believe that 2+2 = 4, the sky is blue, or grass is green. Those are just facts, not things you also believe, you silly non-Common Core indoctrinated person!

I hope you agree with me that it is absolutely absurd to force students to categorize all statements into only one of three “anchor chart” categories, and then call it a “critical thinking” assignment. It is sad that so many millions of students are being taught “how to think” using such irrational methods. And it doesn’t just start in 7th grade; McBrayer spotted the same type of anchor chart assignment in his child’s 2nd grade classroom!

 

The Katy ISD 7th-grade teacher directed the class to categorize the statement “There is a God” as opinion by labeling God as a myth. This is a fine tactic for someone who hates God to employ, because when most people, not just Common Core indoctrinated schoolchildren, hear the word myth, they think “legend,” or “fake story about the past.”

C.S. Lewis to the Rescue

 

But, could a great story about the past also be true? Why does myth have to always make us think “fake Greek sky gods?” Here’s where C.S. Lewis rescues us from oversimplifying our world in a way that gives us a false view of reality:

Now the story of Christ is simply a true myth: a myth working on us the same way as the others, but with this tremendous difference that it really happened: and one must be content to accept it in the same way, remembering that it is God’s myth where the others are men’s myths: i.e., the Pagan stories are God expressing Himself through the minds of poets, using such images as He found there, while Christianity is God expressing Himself through what we call ‘real things’.

In one long, beautiful, eloquent, God-glorifying sentence, C.S. Lewis destroys the Common Core’s ridiculous “anchor chart.” Lewis words reassure us that legends can also be true! Or in Common Core language, opinions can also be facts, facts can be assertions, etc.

Tools to Use in Your Thinking

You see, school-aged children don’t need to be trained “what to think,” nor do they need to be trained “how to think.” As math-teaching legend John Saxon once said,

God gives students the ability to think. Society does not give children that ability.

God designed us with the ability to think critically. The 7th grade Katy ISD student is a perfect example of that, as she was able to spot the flaw in her teachers’ fake “critical thinking” assignment, an assignment that will no longer be taught in Katy ISD thanks to her efforts.

What students need are tools to use in their thinking. And one of the best tools is mathematics. Some math curriculum to consider include any John Saxon-authored courses, as well as my company’s new curriculum, Shormann Math, a curriculum built on a solid foundation of mathematics’ legends, with Jesus Christ as the common core. Logic is another course worth considering. At a minimum, study this logical fallacy poster. Another resource is Introductory Logic by Roman Roads Media.  Books by Nancy Pearcey are also excellent resources for understanding the negative impact of oversimplifying the ‘real things’ C.S. Lewis was describing. Total Truth, Saving Leonard0, and Finding Truth are all excellent. And of course, any books or essays by C.S. Lewis! And last but not least, the Bible, without which we would not know that we are supposed to reason together (Isaiah 1:18).

 

Shormann Algebra 1: Results Matter

July 31, 2015

Why do results matter?

Shormann Math builds on a solid foundation of time-tested teaching methods, including the incremental development + continual review format pioneered by John Saxon(1923-1996). And not just Saxon’s teaching methods, but his teaching thoughts as well, including his thought that

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

One of the primary reasons John Saxon developed his math curriculum in the 1980s was because new ways of teaching math were not working. Math “educrats” at the time were promoting their untested “visions” of math teaching. But with 3 engineering degrees, John was a math user before he became a math teacher. Not only that, he was a test pilot. If anyone knew the extreme value and importance of testing a new product, it was John!

Results matter because they reveal whether or not a new product really works. And while statistics certainly don’t reveal everything about a new product, they can certainly reveal many things. Most math curricula don’t provide this level of detail on student performance. But with Shormann Math, each new course is beta-tested in a live, online setting first before releasing it to the general public. The following are statistics from the beta-test of Shormann Algebra 1. The results show that the majority of students made an A! The following statistics, plus other detailed information about the course, can also be found in our Shormann Algebra 1 teacher’s guide. To purchase Shormann Math, click here.

Overall Performance

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Discussion: The average student in our beta test made an A in the class! Because each new Shormann Math course is beta-tested in a live online class setting, Dr. Shormann gets to know the students on more than just a “numbers only” basis. And we all know that God doesn’t make clones, so the fact that not every student performed the same should not be a surprise. Natural talent definitely matters, but so do things like attitude and maturity.  Dr. Shormann spends time during the video lectures encouraging students to develop fruits like patience and self-control (Galatians 5:22-23), as well as persevering with joy (James 1:2-3), and gratefulness (I Thessalonians 5:18).

Practice Sets

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Discussion: You’ve probably never seen statistics on student performance in a math class before, which is why it is important to discuss the data! The decreasing trend over time is exactly what we expected. Two big factors are responsible for the trend: 1) There’s more review of previously-learned concepts at the beginning, so it’s easier and 2) student effort tends to decrease the closer you get to the end of the year!

What we had hoped for was a Practice Set average above 85%, and that was achieved in all 4 quarters! 85% is a good cutoff for determining whether students are understanding, and retaining most of the concepts learned.

Note also the high first quarter average. Because Shormann Math is built on John Saxon’s method of integrating geometry and algebra, students using Saxon Math 8/7 or Saxon Algebra ½ will be most comfortable starting Shormann Math. However, not all beta-test students used Saxon previously, so the high first quarter average is a good indication that students who successfully completed any pre-algebra course should do just fine in Shormann Math.

Weekly Quizzes

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Discussion: Weekly Quizzes show a similar trend to the Practice Sets, challenging the students more as the year progressed. A score of 8 out of 10 or higher is a good indication of whether students understood the lessons covered that week. We are pleased that scores were well above this in all four quarters!

Quarterly Exams

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Discussion: Notice the Quarterly Exams do not follow the same trend as Practice Sets or Weekly Quizzes, with Quarter 1 having the lowest average. And this is where beta-testing a new product is so valuable. We realized that we were asking a lot for 9th-grade level students, most of which had never taken a cumulative exam like this. The solution? Practice exams! Just like when learning a sport, a musical instrument, etc., good practice results in good performance. The beta-test students clearly performed best on first quarter Practice Sets and Quizzes. Most likely, if they were given practice exams prior to their quarterly exam 1, this would have been their highest exam average. Now, all quarterly exams have two practice exams that students use to study for their actual exam.

85%+ is an indicator of good retention and understanding of concepts covered in a quarter. For all 4 quarters, student averages were at, or well above 85%. Because of Shormann Math’s format of continual review, we are basically asking students to be responsible for “all their math, all the time.” These results show that on average, students are responding very well!

Producer Math

June 27, 2012

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When you eat the labor of your hands, you shall be happy, and it shall be well with you. Psalm 128:2

Failing at producing

You may have heard the phrase that America has turned into a “nation of consumers”. If you think that is an incorrect assessment, take a look at this graph:

United States Imports Minus Exports, 1960-2011

This year, 2012, will likely be the 37th consecutive year that the United States of America has imported more than it has exported. In other words, we are consuming hundreds of billions of dollars more than we produce. As a whole, Americans are less productive, which means we are also less creative, than we were back in the 1960s.

For Christians, a trend like this should be unsettling, because it goes against the most basic of Christian principles. One of God’s very first commands to humans was to “be fruitful and multiply” (Genesis 1:28). Created in His image, we are designed to create, too. To be productive. To bear fruit and “eat the labor of your hands”, as Psalm 128:2 teaches. “Bearing fruit” is not just about having children, or raising corn and cattle, building houses, bearing spiritual fruits, etc. Bearing fruit is ultimately about fulfilling the Great Commission by spreading the Gospel to the ends of the Earth (Matthew 28:18-20). And God didn’t make us all clones, and give us all the same exact plan for fulfilling the Great Commission. He designed us to be creative in this task.

Unfortunately in America, we answered the trend towards excessive consumption by developing “consumer math” classes for high school and college students. Such classes usually contain basic arithmetic and very little algebra, and are designed to help students understand common-sense ideas such as not spending more money than you earn. Less obvious topics like interest rate are also covered. However, most topics are a review of what students already learned in elementary and middle-grade math courses. Also called “business math”, Wikipedia describes these courses as “subjects taught to students who are not planning a university education.” In other words, the classes are for people who are not planning to be producers, just consumers.

Training up backward-thinking consumers

Now, don’t get me wrong. I certainly believe non-university bound students can also be productive members of society! However, by taking “consumer math” instead of an advanced math or calculus class in high school, you are essentially falling in line with secular and non-Christian education standards. For example, the National Council of Teachers of Mathematics claims “For those whose formal education will end with high school, the needs of citizens and consumers for increasing mathematical sophistication dictate a collection of courses based on consumer and career needs”. See, there it is again! Non-university-bound students are just consumers. And citizens. But I didn’t say that, “they” did! The average government school is training students to be consumers and citizens who are told of their supposed not-so-special origin from a monkey-man. Shouldn’t they, shouldn’t we, instead be training students to be forward-thinking producers? Of course! If you are in a government school, you should fight against this kind of demoralizing miseducation. If you homeschool or private school, don’t use the government schools as your guide! Instead make sure your child gets a good dose of Christ-centered science, and it’s language, mathematics.

You are more than a consumer

University bound or not, current Christian or not, I hope you can see the problem with consumer math. Of course, some consumer math is a good idea, but “producer math” should be the priority, especially in high school and college. Because human beings are designed by God to be creative, creativity comes naturally for us. But creativity always requires tools, and in the 21st Century, good mathematics skills are definitely one tool that will help spark creativity, and in turn, productivity. All humans are consumers, but life is about so much more than that. Being a producer as well means that you and/or the company you work for need to 1) Create something to sell and 2) have the ability to sell it AND make a profit. And it is the profit (fruit) that you can use to grow your family, grow your church, and be a wise ruler of God’s creation as you fulfill the Great Commission.

Three of the many math skills that are important for 21st Century producers, two of which you won’t see much of until Algebra 2 or later, include 1) Unit multipliers (conversion factors), 2) Analytical Geometry, and 3) Calculus. And in all three of these, an understanding of fractions is key.

Good skills with unit multipliers are helpful when you are designing a new cancer-fighting nanotechnology, and you need to convert micrograms per liter per hour to ppm per day. Or, maybe you are setting up a spreadsheet to help you determine cost per unit of an invention that you patented, and now want to sell. Analytical geometry is helpful in computer graphics and other applications, where knowledge of not only shape, but exact spatial positioning is important. And calculus is where rates of change are studied, which has applications in more areas than you will ever imagine in a lifetime.

Math for producers

John Saxon (1923-1996) wrote some of the best “producer math” books available. While newer editions are moving away from his tried and true methods, the pre-2009 Saxon textbook editions are the best I’ve seen at helping students learn producer math. Avoid the newer, blue-covered hardback Saxon texts, published by Houghton Mifflin Harcourt, and NOT written by John Saxon. In texts written and approved by John, unit multipliers are taught beginning in the elementary grades, and continue through Calculus. Consumer math topics are also included. For example, sales tax, a topic that would be taught in a high school “consumer math” course, is introduced in the elementary-level Saxon Math 5/4. Students continue building their consumer math skills from this point on through Saxon Calculus.

As I get closer to creating my own mathematics curriculum, I hope to take the best of John Saxon’s principles, and build on those. As I develop this curriculum, I am taking note of the fact that John Saxon  never wrote a “consumer math” textbook. Indeed he frowned upon the very idea of placing students in these classes.  Regarding consumer, or “basic” math, John Saxon said “We cannot take kids and relegate them to the trash heap in this technological society. We label them as failures when we put them in basic math”(from John Saxon’s Story, by Niki Hayes, p. 276). And Saxon wasn’t the only successful teacher opposed to these courses. The book Standing and Delivering by Henry Gradillas highlights the story of how he and teacher Jaime Escalante eliminated “dumb dumb” math classes from Garfield High School in Los Angeles, and by doing so, turned around math education, with many students passing the AP Calculus exams.

So is “producer math” harder than “consumer math”? Well, is buying a blueberry bush, planting it, watering it, nurturing it, harvesting the fruit and then taking it to market to sell, harder than consuming a bowl of blueberries? Yes! But what does Scripture say about doing hard things? Does it say to run from them? Certainly not! It says to count our trials as joy (James 1:2-3). Parents and teachers who seek to help students be producers will get more heartache, more complaints, and more trials to deal with. But 10 years later, those parents will probably get more “thank you’s” from their children than from the ones who failed to challenge.

Christians have been called to handle the hard stuff with grace and thanksgiving. Parents, you know your child best. Are they capable of doing more producer math? The majority of them are, so push them with much love, patience, and perseverance. And if they fail the first time, give them a second chance the next year. And the next. But if you are certain your child is not capable of things like calculus, then do what it takes to teach them as much producer math as you can. Being a producer is not just the American way, it’s the Christian way, and us parents need to make sure we are training our children up to be more than consumers. Much more!

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.