### Comparing Khan Academy’s “Procedures” to Shormann Math’s “Story” for Teaching High School Math

June 14, 2017

In a 2012 Education Week article, Justin Reich, an internet education specialist, wrote that Khan Academy’s math courses overemphasize procedure. In other words, Khan’s math video lectures explain the steps to solve a problem, but they don’t take time to explain the concept behind the steps. In the words of the author, “writing about mathematics, developing a disposition for mathematical thinking, demonstrating a conceptual understanding of mathematical topics are all more important than procedures.”

But, procedures ARE important, and sometimes, that is what you need. For example, if you are stuck on the side of the road with a flat tire, someone needs to know the steps required to fix the problem in as few steps as possible. You are not interested in the physics behind hydraulic jacks or who invented vulcanized rubber (Charles Goodyear). You have a crisis, and it requires a pragmatic solution. So, maybe you are studying for a big test like the SAT, and it’s in 2 weeks, and suddenly you realize there’s a concept you need to practice some more. This would be a time when Khan Academy might be helpful to you.

But, a good education isn’t really about pragmatism, about skimming through a subject, learning the bare minimum, so you can check it off your transcript or pass a standardized test. And then forget about it.

Shormann Math is different. Certainly, there are times when procedure is emphasized, like our step-by-step video solutions for every homework problem, for example. But there are more things, deeper things, that Shormann Math emphasizes that others, like Khan or Reich or the National Council of Mathematics Teachers either don’t, or won’t.

At the heart of mathematics is a story, an amazing story of the history of humans seeking to discover more about the world around them. And it’s a story that is best understood from a Christian foundation.

Here’s why. To his credit, in Khan Academy’s introductory Algebra 1 lesson, Sal Khan dives into the origins of algebra.  In describing the date of the first algebra book (820 A.D.), Khan makes a well-meaning, respectful attempt to distinguish the “religious” B.C. and A.D. from the “non-religious” common era descriptions of historical dates. Of course, the problem here is that Christianity is the only “religion” considered here. But Christianity is most definitely not a religion, a mere set of rules to keep or procedures to follow.

At its core, Christianity is about a relationship. And that’s a surprisingly hard truth for some to acknowledge. Christianity is about a relationship between God the Father, Son and Holy Spirit, between humans and God, and between humans and humans. Simply put, Christianity is about how this relates to that. But so is mathematics, which is not surprising since its normal for created things to reflect the attributes of their designers. Relationships always tell a story, over time. Which is why history matters in Christianity, and therefore in mathematics, too.

So, with Khan Academy, a student might feel connected to mathematics when they are finished, which is not a bad thing. With Shormann Math though, while our students are connecting to mathematics in measurable ways (see next post on results), we are also connecting them to the story behind mathematics.  And the story is that, throughout history, mathematics is a tool for studying the world around us. So, we give students the mathematical tools to use in their thinking about the world, and give them a chance to practice using them in a variety of situations they might encounter in their everyday lives. But we also tell them who discovered the tools, plus some interesting things about their life stories.

Everyone loves a good story! That the story of mathematics is largely missing from popular, secular math teaching methods like Khan Academy could partly explain why mathematics is often the least-liked, most dreaded subject of all. Overemphasizing procedure may get you an algebra credit, but it won’t necessarily develop the STEM and STEAM skills so often desired.

But what if story is included, so that students get to know the major players influencing modern mathematics? With Shormann Math, we are finding that telling the story of mathematics makes learning math more real, and in the end, easier. If students are inspired by the experiences of historical figures, or by what God’s word says about math, they are more likely to know what to do with the math tools they are becoming fluent with. And if Shormann Math students are more fluent than students using more secular and disconnected methods, then when the opportunity to use math comes along, Shormann Math students will likely be more prepared.

### 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’s 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.

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!