Shormann Math Core Ideas: Defining Mathematics

Posted July 30, 2014 by gensci
Categories: Teaching Mathematics

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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.

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The following following was 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.

Shormann Math, Algebra 1 Overview

Posted July 22, 2014 by gensci
Categories: Teaching Mathematics

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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

Posted July 11, 2014 by gensci
Categories: Teaching Mathematics

Tags: , , , , ,
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!

An Unimaginable Boom

Posted June 6, 2014 by gensci
Categories: Novarupta, Volcanoes

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It’s hard to imagine that the 380 m wide by 68 m tall Novarupta dome is the site of the largest volcanic eruption in over 100 years! However, the undulating pattern of the surface in the foreground is the first clue that something more powerful than any of us have witnessed occurred here not so long ago.

 

What is the loudest explosion you have ever heard? How far away could you hear it? 1 mile? 2 miles? 10 miles? What about 100 miles? If something exploded, and you could hear it from over 100 miles away, that would be impressive, wouldn’t it! I can’t imagine an explosion that big. Now, think about an explosion that could be heard 800 miles away, and you are on the scale of the explosion that started the Novarupta-Katmai eruption of 1912!

Today, June 6, 2014, is the anniversary of the largest volcanic eruption in over 100 years, the June 6-8, 1912 eruption of Novarupta-Katmai. Located in Katmai National Park in remote Southwest Alaska, the eruption was more like an explosion. The 60-hour blast filled the surrounding valley with sand-like flows up to 700 feet thick in places. And most of that occurred in the first 16 hours!

As magma blasted out of Novarupta’s vent, the magma chamber supporting nearby Mt. Katmai also started to empty out Novarupta. With its internal support gone, the top of Mt. Katmai collapsed, creating a massive hole (caldera) that all the buildings in New York City and then some could fit inside.

Although I’ve spent a considerable amount of time in Katmai National Park studying this gigantic eruption, it is still hard to imagine what it must have looked like as ash clouds bellowed and the surrounding valley rapidly filled with one ignimbrite package (sandflow) after another. But it did happen, it happened very quickly, and the evidence is there for all to see.

Surrounding Novarupta-Katmai, evidence also exists for an Ice Age, preceded by Noah’s flood. You see, Novarupta-Katmai materials rest atop glacial till (Ice Age deposits). And the Ice Age deposits rest atop the 15,000 foot thick Naknek formation, a water-deposited sedimentary rock layer (Flood deposit).

Would you like to learn more about this amazing eruption? One way is by purchasing our new Journey to Novarupta audio adventure. Produced by the creators of the popular Jonathan Park creation adventure series, Journey to Novarupta follows our 2009 and 2011 trips to the volcano. It also flashes back to the 1900’s and the expeditions of Dr. Robert Griggs, the first human to see the eruption site. Journey with us as we search for and find evidence of Noah’s Flood, reveal huge problems in the radiometric dating methods use as evidence for millions of years, and more. This family adventure will build your faith as you discover powerful scientific evidence for a young and active planet!

Journey to Novarupta is on sale now through June 12, 2014! Click here to listen to the opening scene, and/or to order. To receive the sale price, copy/paste coupon code JourneySale682014. Digital downloads are on sale for $7.99 and CDs for $11.99.

 

 

 

 

 

Jesus Christ, the Common Core of all DIVE courses

Posted May 7, 2014 by gensci
Categories: Teaching Mathematics, Teaching Science

Tags: , , , , , , , , , ,

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.

Thinking of Resurrection Bay

Posted April 21, 2014 by gensci
Categories: Spreading His Word

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Resurrection Bay in Seward, Alaska. It was named by Alexandr Baranov, who was forced to retreat into the bay during a bad storm in the Gulf of Alaska. When the storm settled it was Easter Sunday. Today, Resurrection Bay, and all of Alaska, are part of the United States, purchased from Russia in 1867 for 2 cents an acre. Russia at the time was strained economically, after being humbled in the Crimean War of 1853-1856.

Resurrection Bay, Seward, Alaska

Yesterday (April 20, 2014) we celebrated Resurrection Day. The day got me thinking of one of my favorite places, Resurrection Bay in Seward, Alaska. The bay was named in the late 1700’s by Alexandr Baranov, a Russian fur trader who retreated into the bay during a bad storm in the Gulf of Alaska. When the storm settled it was Easter Sunday.

Today, Resurrection Bay, and all of Alaska, are part of the United States, purchased from Russia in 1867 for 2 cents an acre. Russia at the time was strained economically, after being humbled in the Crimean War of 1853-1856. Vladimir Putin has been compared with the czarist emperor, Nicholas I, who lacked the foresight to see how his prideful 19th Century actions in Crimea would adversely affect Russia.

Pray that Vladimir Putin will change his arrogant ways, before he leads his country through yet another death and resurrection. Like all countries, Russia doesn’t need another prideful leader, they need a servant leader whose king is Jesus Christ. Pray also that you and I can have some death and resurrection of our own prideful ways as well, and do more than just point out the folly of national leaders.

“Pride goes before destruction, and a haughty spirit before a fall.” Proverbs 16:18.

A sea otter feeds on mussels in Resurrection Bay.

A sea otter feeds on mussels in Resurrection Bay.

Resurrection Bay's beautiful, yet rugged coast.

Resurrection Bay’s beautiful, yet rugged coast.

A humpback whale surfaces in Resurrection Bay.

A humpback whale surfaces in Resurrection Bay.

Rockfish from Resurrection Bay.

Rockfish from Resurrection Bay.

Build a Better Engine

Posted April 17, 2014 by gensci
Categories: Creation/Evolution, Spreading His Word, Teaching Mathematics

Tags: , , , , , , , , , , ,

Over the last few years, I have talked to a lot of people who spew propaganda claiming Bible-believing Christians are “anti-science.” Because people like me are skeptical of the history claims of evolutionists and futurology claims of global warming alarmists, we are labeled “anti-science.” Fortunately, discerning between what is and is not a scientific claim is as easy as understanding a chocolate chip cookie recipe. Unfortunately, some refuse to acknowledge the differences, using the “Christians are anti-science” fallacy to create political division. For others,  it’s just another excuse to hate their neighbor.

One pattern I’ve noticed among the “Christians are anti-science” crowd is that the most outspoken individuals tend to have little or no background in science or engineering. When God gives me an opportunity to talk to unbelievers that promote this agenda, I have learned to 1) let them know Christians like me are most assuredly pro-science, 2) present the Gospel, and 3) encourage them to stop doing what they are doing and get into a science and engineering field.

Something I have encouraged more than one unbeliever to do is “build me a better engine.” Promoting the idea that fossil fuels are causing catastrophic global warming is foolish. In spite of increased atmospheric CO2 levels, there has been no warming for 17 years and 8 months now. If, instead of promoting unscientific future climate ideas and labeling those who disagree as “anti-science,” why not do something meaningful?  Why not be actively involved in designing less expensive, more fuel efficient engines, ones that could reduce air pollution and provide better lives for the poor? Wouldn’t a pro-science, love-your-neighbor mindset be better than an unscientific, hate-your-neighbor one? Well, of course it would, but the former is a difficult concept for those who don’t believe the foolishness of God is wiser than men (I Corinthians 1:25).

Unless God changes their hearts and they repent and turn to Christ, foolish actions are to be expected from unbelievers (Psalm 14:1). Fortunately, there are young Christian men and women out there who love God and His creation, and want to “build a better engine” for His glory. Listen to this testimony from David K., a homeschooling senior that is currently using our DIVE Calculus course (bold emphasis mine):

“Thank you also for all the work you have put into the DIVE CDs. Your teaching is clear, easy to understand, and you explain everything really well. Your lectures have helped me immensely, and I don’t know where I would be in math with out them. I definitely agree with you, in that God has allowed us to understand math so that we can get to know Him better. I love looking in Creation and seeing God Himself! I am a senior in high-school, and I plan to go to college to study Engineering Physics, with mechanical emphasis. I want to eventually perform engine research to produce a more financially feasible engine. I would do this by creating a new energy conversion process that does more work per unit of fuel than engines today. I have always had a love for science and math, and I really look up to people like you who know so much and use it for the glory of God. Thank you for being a great example for me to follow.” 

While David K’s words are incredibly kind and humbling to me, I hope they are an encouragement to you! A lot of people are surrounded by hopelessness and despair, but there’s also a lot of hope out there, too!

Are you a young person like David K who loves the Lord and wants to take what God has made and use it to design things that will serve others? Are you currently an unbeliever? Whoever you are, it is important to be intellectually honest and spread the word that Christians are pro-science. History proclaims this truth, as do present actions of humans all over the world.  So, enough of this blog post, get out there and build a better engine!


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