Posted tagged ‘Shormann Mathematics’

It Only Takes an Instant

December 1, 2014
Two images of a wave in Waimea Bay, Hawaii, taken 0.1 s apart, reveal how quickly things can change from beauty to chaos (or vice versa).

Two images of a wave in Waimea Bay, Hawaii, taken 0.1 s apart, reveal how quickly things can change from beauty to chaos (or vice versa). © 2014 David E. Shormann

I never cease to be amazed by the technology of today’s digital cameras. By pushing a few buttons, anyone crazy enough to bob around in a 6-8′ high shore break can capture some amazing beauty in God’s creation! But as the photos above reveal, the beauty only lasts for an instant.

It seems impossible that things can change from beauty to chaos, or vice-versa, in so short a time. But big changes can and do occur in even less time than the tenth of a second that elapsed between these two photos.

Strangely enough, instantaneous change, something us humans really can’t fully comprehend, is behind almost every major technological achievement of the past 300+ years!  How can that be? How can something we will never fully understand help us make all sorts of useful devices? Well, some things we just have to take on faith. Faith is at the heart of the branch of mathematics known as calculus. And calculus is all about the study of instantaneous change.

Subjects like calculus are easier to grasp when we consider the Author of every instant of time, and Creator of the biggest  and best instantaneous changes of all. Paul writes in 1 Corinthians 15:52 how we will be changed “in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised imperishable, and we shall be changed.”

Leonhard Euler (1707-1783), a devout Christian man considered the best mathematician ever, wrote that “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; so that men are always indebted to God, for the means which promote their salvation.”

Euler understood God’s relationship with man and creation very well. He also understood mathematics really well, too! Much of the way we teach mathematics today comes from Euler’s textbooks on the subject.

In our new Shormann Mathematics curriculum, we believe that all 10 major topics covered, including and especially calculus, are best understood by connecting the study of mathematics to Jesus Christ, the founder of all knowledge, and the founder and perfecter of our faith (Hebrews 12:2).

Using Math to Unlock Mysteries, Reveal God’s Beauty, and Interact With Others

September 8, 2014

The following is the sixth 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.

Mathematics has so many uses, including modeling the beautiful arcing leap of a bottlenosed dolphin! Image ©2009 by David E. Shormann.

Mathematics has so many uses, including modeling the beautiful arcing leap of a bottlenosed dolphin! Image ©2009 by David E. Shormann.

Shormann Math teaches students that mathematics is the language of science, and therefore an important tool for unlocking mysteries and revealing the amazing beauty found in God’s creation. It is also an important tool for interacting with others, such as when buying and selling things. Shormann Math will train students to become skillful at using mathematics in a way that will help them become productive members of God’s world, using their talents to serve Him and serve others.

Shormann Math teaches students what mathematics is, and how to solve problems using mathematical concepts. Problem solving is simply the application of mathematical concepts in new situations. It is about building on foundations that have already been laid, using mathematical tools developed over the centuries and applying those in new situations to solve problems. This is the essence of deductive reasoning, which is simply about applying rules. Mathematics is primarily deductive in nature, while scientific investigations are inductive (about finding rules).

What follows is a partial list of areas that mathematics is used, and that you may see covered in a Shormann Math Practice Set. At least one problem in each Practice Set will be about one of these areas. If you don’t see an area you think we should cover, let us know. One thing is for certain, Shormann Math students will not be asking the “what am I ever gonna use this for” question regarding math!

Science: astronomy, chemistry, biology, physics, biochemistry, computer science, oceanography, meteorology, medicine

Farming: animals, plants, aquaculture

Natural history: geology, volcanism, genealogy

Business: marketing, accounting, finance, business startup, productivity, employment

Engineering: mechanical, electrical, petroleum, aerospace, civil, industrial, robotics

Architecture

Art

Sports: baseball, football, basketball, soccer, fishing, tennis, NASCAR, track & field, volleyball

Music

Mathematics History Matters

August 18, 2014

The following is the fourth 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.

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What does Leonardo DaVinci’s famous painting, “The Last Supper”, have to do with geometry? Use Shormann Mathematics and find out!

History helps connect students to their world and their Creator.

Most modern mathematics curricula ignore math history. But core ideas have consequences, and studying history often reveals which ideas are worth repeating and which ones aren’t. Did you know that Isaac Newton, author of the most famous science book ever written (The Principia), based the format of his book off of Euclid’s Elements, the most famous math book ever written? Did you know Shormann Math bases its format off Euclid’s and Newton’s famous works, stating rules and definitions up front, and using these as the building blocks to learn new concepts? Did you know that modern mathematics has a rich Christian heritage? Well, if you use Shormann Math, you will learn all about these things and more! Whether or not you are using a classical, trivium/quadrivium approach to your child’s education, understanding mathematics within a biblical, historical framework will help students make more sense out of what they are learning and why they are learning it.

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Screenshot of a part of Lesson 9 from Shormann Mathematics, Algebra 1. Did you know there is a connection between the U.S. Declaration of Independence and Euclid’s famous geometry text, “The Elements?” Did you know Scripture predates Euclid’s main idea of “self-evident truths?” Shormann Mathematics uses history to connect students to their world and their Creator.

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!