Posted tagged ‘Common Core’

Comparing Khan Academy’s Mastery Approach to Shormann Math’s Fluency Approach for Teaching High School Math

May 25, 2017

This is the first in a series of posts comparing Khan Academy’shormann khan comparison memes online math courses to our new Shormann Math curriculum. Shormann Math is part of DIVE Math and Science.

When Sal Khan started tutoring his cousins in 2003 using digital whiteboard video lectures, my family’s small business was already in its third year of producing similar products. Since then, both Khan Academy and DIVE have continued to offer digital video lectures for learning mathematics and other subjects, leveraging the ever-improving array of digital content delivery methods. Today in 2017, both Khan Academy and DIVE offer self-paced eLearning math courses. So, while there are obvious similarities between the two, there are also some pretty big differences.

Khan’s Store-Bought Layer Cake vs. Shormann Math’s Homemade Pizza

To begin, it is important to understand that Khan Academy teaches a Common Core-based “layer cake” approach to high school math. Shormann Math, on the other hand, teaches an integrated approach pioneered in Europe and Asia (you know, the countries that always beat us on international math tests), and introduced to the United States by the late John Saxon. John Saxon believed in the common-sense idea that results, not methodology are what mattered most(we’ll explore Khan Academy vs. Shormann Math results in a later post).

With the layer-cake approach, high school math is taught in layers, beginning with Algebra 1. Geometry is next, then Algebra 2. Each course is typically covered in one school year.

With the integrated approach, students learn algebra and geometry together. For example, Shormann Math does not have a separate geometry course, because geometry is integrated into Algebra 1 and 2. A geometry credit is included in Shormann Algebra 1 and 2, so students can take 3 years to complete the two courses and be “on track.”

Using a food analogy, both a store-bought layer cake and a homemade pizza can be delicious. With a store-bought layer cake, everybody gets the same thing, which is not always a bad thing, but can be. With a layer cake, if you just like vanilla, you can focus on eating the vanilla and not the chocolate. Or vice-versa.

With a homemade pizza, at least the one my family has made for years, each bite is an integrated medley of cheeses, meats, and vegetables. It is unique, diverse, and anchored in an amazing story that originated on float trip adventures deep in the Alaskan wilderness. Our homemade pizzas are about more than pizza, just like our Shormann Math courses are about more than math.

homemade pizza

Shormann Math, like our family’s legendary pizza, is a savory recipe developed over time with proven ingredients.

From my experience, a layer-cake approach is good for reviewing a particular subject, or specific concepts within a subject. Our CLEP and AP test prep courses employ this method. In other words, the layer-cake approach is good for review, which means Khan Academy math is good for testing your math skills in a particular subject. Khan Academy can help you determine if you have mastered a particular concept for the short-term.

Shormann Math, on the other hand, can help you build fluency in mathematics, which means you develop mastery and you retain it for the long term because you keep using it. In the beginning of every Shormann Math course, we define mathematics as the language of science and a God-given tool for measuring and classifying pattern and shape. I am not sure how Khan Academy defines mathematics, as I couldn’t find a definition anywhere. When you learn a new language, you don’t just learn nouns for a year, then verbs for a year, etc. You learn a little of the basics of everything, then you start putting them into sentences, which you practice. And practice some more. And then you review some more. And practice some more.

Building on fundamentals is how you learn a language, or a sport, or an instrument, or just about anything that you, eventually, hope to excel at. Building fluency takes time. Up next, we’ll explore Khan Academy’s “math procedures” to Shormann Math’s “math story,” followed by real data from real Shormann Math students on how the fluency approach can turn a bad math student into a good one. Stay tuned and thanks for reading!




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).


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!

Jesus Christ, the Common Core of all DIVE courses

May 7, 2014

A Brief History of University

Late in the 12th Century, a phenomenon unique to Europe appeared, the university. University is actually a combination of two words, unity and diversity. Originally, universities were schools that owned no real estate, but were instead an association of teachers or students. Although not always theologically or scholarly accurate, what under girded the university was the unification of all subjects by an all-encompassing worldview. Christianity provided the unity that connected the diversity of courses offered.*

In other words, Jesus Christ was at the core of the worldview of original universities! Unfortunately, in the 21st Century, Christianity is no longer at the core of most educational systems. In the United States, the government’s new Common Core program has a godless, purposeless, evolutionary worldview at its core.

Who Interprets the Facts Matters

Cornelius Van Til (1895-1987), author of Essays on Christian Education, made the wise statement that, in this world, there exists a whole collection of facts. Would you rather have those facts interpreted to your child through a Christian or a non-Christian worldview?

For Christians, the answer should be simple. Jesus Christ is, or should be, the common core of all the subjects we teach our children. To the extent that we are able to, we should try to use curriculum taught from a Christian worldview. But that also doesn’t mean we need to fear books and courses that are taught from a non-Christian, or even anti-Christian worldview. We just need to train our children how to think critically about these things. If we teach them the Truth, they will be more capable of detecting false “philosophy and empty deceit.” (Colossians 2:8)

Pray that more Christian families will realize the problems of sending their children day after day to be taught in schools where Jesus Christ is not the common core. Pray that we can find new and creative ways to help those who, for various reasons, it would be extremely difficult or impossible to home school or attend a private Christian school. Pray for Christian families in countries where homeschooling and Christian schooling is illegal, that they will be able to help their children test everything they are learning, holding onto the good (I Thessalonians 5:21).

If you are interested in learning more about DIVE Math and Science courses, where Jesus Christ is the common core, click here.

*Paraphrased from Mathematics, is God Silent?, by James Nickel.