Solar Eclipse, Math, & Praising the Creator

This upcoming Monday, August 21, 2017, be prepared for a period of darkness in the middle of the day as we experience a solar eclipse.

While solar eclipses occur periodically, it’s rare that the entire United States can view it. According to Time and Date, the last time “a total solar eclipse was visible from coast to coast was almost 100 years ago, on June 8, 1918.”

This short article by Kahn Academy offers a brief overview of a solar eclipse. NASA’s website on the eclipse is complete with information, along with a page of math challenges.

Math challenges? Yes. Math is the tool that we use to explore God’s creation—including the movement of the heavenly bodies overhead. While we can easily read online dates and times that the eclipse will occur in different parts of the world, it’s worth noting that math was used to predict those dates and times. You see, God governs creation so predictably and reliably that we can use math to know ahead of time when something like an eclipse will take place.

It is fascinating to go back and read the works of Johannes Kepler, known for discovering the Laws of Planetary Motion (i.e., mathematical ways of describing the consistent way God causes planets to orbit the sun). His work (which contains a lot of math, by the way) is interspersed with praises to the Creator, such as this one:

Crying out with the royal Psalmist: Great is our Lord and great His virtue and of His wisdom there is no number…To Him be praise, honour, and glory, wourld without end. Amen.[1]

As we experience the eclipse Monday, may we pause and praise the great Creator, exclaiming with the Psalmist:

The heavens declare the glory of God; and the firmament sheweth his handywork. Day unto day uttereth speech, and night unto night sheweth knowledge. There is no speech nor language, where their voice is not heard. Their line is gone out through all the earth, and their words to the end of the world. In them hath he set a tabernacle for the sun, Which is as a bridegroom coming out of his chamber, and rejoiceth as a strong man to run a race. His going forth is from the end of the heaven, and his circuit unto the ends of it: and there is nothing hid from the heat thereof. Psalm 19:1-6 (KJV)

I hope you’ll have fun learning a little about the eclipse (see the links above to get started) and how we use math to help us describe the movement of the sun, earth, and moon (look for words like angles, elliptical, etc., as you read). And then as you’re wowed by the ellipse Monday, remember how much greater the Creator is…and that, though our sin earns us His wrath, He took that punishment upon Himself (1 Peter 2:24) and offers us eternal life with Him forever (John 3:16; John 17:3). Is there someone you know with whom you could share that incredible news?

Reminder: If you’re looking for a curriculum that teaches math in such a way that students leave math praising the Creator and using math as a real-life tool to describe His creation, be sure to check out Principles of Mathematics. We also have resources available to help you bring that perspective for other grades.


[1] Stephen Hawking, ed. On the Shoulders of Giants: The Great Works of Physics and Astronomy. Philadelphia: Running Press Book Publishers, 2002, pg. 1157.

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Math at a Concert

math-at-a-concertMusic—it’s probably not the first thing you think of when you think of math. Yet God has hidden order in every sound wave, and math helps us express, utilize, and enjoy that order.

A recent trip to a chamber ensemble left me in awe—not only at the heart-stirring music, but also at how much math applied in an orchestra hall. Here are a few ways math applies:

  • The Music Itself – Harmonics, the arrangement of notes, the arrangement of sections within a piece, the rhythm—math helps us describe and work with the order God placed within sounds.
  • The Instruments – Instruments come in all sorts of shapes and sizes…and math helps us understand the relationship between the shape, size, and sounds produced.
  • The Room – The acoustics in the room make a big difference in how the audience hears the sound. And how can the builders figure out how to build a room with good acoustics? By using math!
  • Recording – Modern technology allows us to record music and enjoy it over and over again. How? By mathematically describing and reproducing sounds, of course.
  • The Business Side – Ticket prices, facility maintenance costs, artists’ schedules—math helps out in multiple ways behind the scenes of a concert.

The list could go on, but hopefully you get the idea. Math helps us both describe the order God placed within sounds and proves useful in making music and sharing it with others! Next time you find yourself staring at a math problem, remember that those apparently meaningless numbers in the textbook really represent real-life quantities and consistencies—such as aspects of music.

P.S. (Added 05/13/15) – I spent the morning researching more details about the harmonics and math in music itself and now really can’t wait to guide students through exploring some aspects of it in Book 2 of Principles of Mathematics: Biblical Worldview Curriculum. (Book 2 is scheduled to come out later this year/early next; Book 1 should ship by the end of the month.) The order God has placed in the very sounds around us is simply amazing!

When Math Feels Daunting – Plus Summer Reading Coupon

Math—especially upper-level math—can feel daunting. Teaching it can seem insurmountable.

How do we do it? Step by step. Whether a course, concept, or problem, it becomes doable when we break it down into steps.

In our next post, we’ll take a look at some ways to help to teach your child problem-solving skills. For now, I just want to point out that the same principle of breaking problems down to steps applies to teaching. While it may be tempting to look at your child’s whole future math courses and wonder how you’ll get through it, just take each day step-by-step. Trust that God will provide solutions at each stage. He gives us our daily bread, not grace for the rest of our lives. Run to the One who knows math inside out and seek His grace and wisdom. As you do, you just might find math class teaching you (and your students) more than just math.

Side note: Summertime is a great time of year to explore supplemental math resourcesBiblical Math Resources you might not have time for during the school year. To help, we’re offering 10% off the math resources in our store through June 30, 2014. Just use code SUMMER10.

Whether you have your older students work through something like Revealing Arithmetic (just have them read the first section of each chapter to gain a biblical view of arithmetic) or Mathematics: Is God Silent?, or have fun Exploring the World of Mathematics together or doing some of the hands-on suggestions in Revealing Arithmetic, we hope you enjoy!

Remember, too, that your library may have some hands-on math books with great summertime ideas, and feel free to explore our blog for some other resources we’ve mentioned over the years.

Math: A Gift

Have you ever thought about how our very ability to use math is an amazing gift? To start with, you’re able to read the numbers! Your eyes take in an image. Your brain turns that image right-side up, connecting it with what you’ve learned about the language of mathematics, and gives an interpretation. And all that happens automatically…and much faster than it takes us to describe it.

We don’t often think of the gift of being able to assimilate math, but it’s been on my mind a lot lately due to lingering post-concussion syndrome that’s made my brain not function as usual. I’m realizing in a fresh way how utterly reliant we are on God for even the brainpower to be able to learn and use math. We truly cannot do anything without His enabling.

Whether it’s grasping multiplication facts or algebra, your ability to learn (or teach) math is nothing short of an incredible gift. We are indeed fearfully and wonderfully made.

“I will praise thee; for I am fearfully and wonderfully made: marvellous are thy works; and that my soul knoweth right well.” Psalm 139:14 (KJV)

When You Feel Like Giving Up

I buried my head in my hand, frustrated beyond words and feeling completely incapable. I’d been trying to get through this chapter for days now, and it just wasn’t jelling. To top it, the computer was misbehaving, and I wasn’t feeling well. Why was I writing this again?

As you teach your children math, do you ever find yourself feeling discouraged or frustrated? If so, you’re not alone. We live in a world where things do get difficult. But we also serve a God who works all things together for good for those who love Him (Romans 8:28).

For me, the discouragement forced me to reexamine why I was doing what I was doing. I realized anew it was because I’d been called—and with that came the knowledge that, much as I felt otherwise, if God had called me to a task, then I could do it in Him. I couldn’t carry on—but He could. And if He’d called me to do this, He would make a way.

If an aspect of math—or the thought of teaching high school math—has you scared, run to your King. If He has called you to do it, then He will make a way…and you’ll be so blessed as you watch Him work.

P.S. I’d love for you to write me and let me know what areas of math are causing frustrations. It would be an honor to pray for you and to share any thoughts I might have.

Keeping the Heart

heartWriting a math curriculum has given me a new appreciation for how easy it is to lose the heart in math. We want students to understand how to convert units, how to find a volume, how to multiply, etc. Before we realize it, we get so focused on drilling the mechanics that we lose sight of the things that matter most–seeing the Lord, worshiping Him, etc.

I keep having to remind myself to step back from the details and remember the big picture–to remember that within math, we have an opportunity to ponder God’s faithfulness (without which none of math would work), His greatness, His care, etc. But just as we have to be intentional in life to keep our minds upon God, we have to intentionally focus on God in math too…or the most important things get buried in the details.

Watch next week for a few thoughts on how measurement reminds us of God’s greatness…in the meantime, please leave a comment with how your math school year is going and any thoughts or suggestions you’d like to share.

Math and the Gospel

Below is a short extract from Revealing Arithmetic–please feel free to share with others! There’s a PDF Version available if you’d like to print it.

For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse: Romans 1:20 (KJV)

Within math, we see a glimpse of God’s eternal power and Godhead. His power keeps one plus one consistently equalling two. His infinity makes infinite numbers possible.

Although we might try our hardest, we cannot change math. We can change the symbols or names, but no matter how we refer to or write it, one of something plus one of something else will consistently equal two. Math is not relative. Why? Because God is God and we are not. He, not us, decides how things will be. He set and keeps certain principles in place, and if we want a math that will actually work, we have to conform to those principles.

We tend to change God and His truths to fit our understanding or thinking. We think, “Surely there must be some good in me. God must want me to fix myself up and be a good person. And He would not send me to hell when I tried so hard.” But we need to heed what God says in His Word. Just as we cannot change math principles, we cannot change truth. God decides truth, not us.

So what does God say? The Bible teaches that God created a perfect universe, one that was “very good” (Genesis 1:31). There was originally no suffering, sickness, or death. But man rebelled (Genesis 3). This rebellion is sin, and the penalty for sin is death.

The moment the first man, Adam, sinned, death came into the world. Man’s relationship to God was no longer perfect. His body began to die. Creation, too, suffered the effects of sin—sickness, suffering, and death had entered the world. One day, Adam would die completely. Unless someone saved him from sin, he would spend eternity separated from his Creator in Hell, a place of perpetual torment.

God, in His loving kindness, already had a plan in place even before He laid the foundation of the world (1 Peter 1:20). Right there in the Garden of Eden, God clothed the first man and woman with garments of skin (Genesis 3:21), foreshadowing the sacrifice of His own Son, Jesus Christ, whom He would send into the world to take the penalty for our sin upon Himself.

We see God’s plan of redemption woven throughout the Bible. Over and over again, God showed mankind his need for a savior—and promised to send one. He gave the Law to show mankind how incapable we are of being holy. Just look at the 10 Commandments (Exodus 20)—by their standard, each one of us falls short. As descendents of Adam, we are born in sin, incapable of doing anything good at all. Psalm 51:5 says, “Behold, I was shapen in iniquity; and in sin did my mother conceive me.” Jeremiah 13:23 adds, “Can the Ethiopian change his skin, or the leopard his spots? then may ye also do good, that are accustomed to do evil.” Even the good things we do are as “filthy rags” in God’s sight (Isaiah 64:6). God wants us to realize how much we need Him to save us. We simply cannot save ourselves!

Yet God can save us. The Bible tells us Jesus, God the Son, took on the form of a man (John 1:1-5). Since He was born of a virgin (Matthew 1:23), He was not born with Adam’s sinful nature. He was the second perfect man—the second Adam. “For as in Adam all die, even so in Christ shall all be made alive” (1 Corinthians 15:22).

Jesus lived on earth as fully God and fully man, living a perfect life. He then allowed His own creation to beat, mock, and nail him to a tree. Jesus—the very One who upholds all things so consistently that one plus one consistently equals two—humbled himself to die and bear the wrath for all the evil mankind has ever and will ever do (John 19). It is as if He said, “I did that” to every sin ever committed. Can you imagine a king willingly giving his life for one who tried to take his throne? Yet what Jesus did is far greater than even that. The Giver of life and Creator of all died for the very ones who nailed Him to the tree!

Just before He gave up His spirit, Jesus cried out, “It is finished” (John 19:30). He had completed all that was necessary for our salvation. He had paid our penalty.

But the glorious gospel message does not end there. Three days later, Jesus rose again from the dead. In so doing, He conquered death forever (1 Corinthians 15). He now sits at the right hand of the throne of God (Hebrews 12:2). And one day soon, He is coming back again (Revelation 22:20).

God’s way of salvation is clear: “Believe on the Lord Jesus Christ, and thou shalt be saved” (Acts 16:31). God offers us Jesus’ righteousness and eternal life in exchange for our sin. What an exchange!

If you have not yet handed your life to God and asked Him to credit Jesus’ righteousness to you in exchange for your sin, do not delay! Go to Him in prayer right now. What God says, He means and is able to perform, as math’s very consistency so clearly reminds us. God’s Word tells us both of His wonderful salvation and eternal life for those who trust Him, and of a coming judgment for those who do not.
If you have already trusted in Jesus as your savior, ask yourself, “Am I living in the truth of the gospel?” The Bible tells us we are to live the same way we are saved—admitting our own inability and trusting and clinging to Jesus and His righteousness.

As ye have therefore received Christ Jesus the Lord, so walk ye in him: Colossians 2:6 (KJV)

Note: If your heart has been touched by this explanation of the gospel or if you have any questions regarding it, please contact me. I, or one my family members, would be delighted to share more with you on this topic.

 

Math Behind Fireworks, GPS Units, and More

This week, I thought it might be helpful to take just a moment to reflect on teaching math OUTSIDE of the textbook. Since math describes the consistencies God placed and sustains all around us, we find it useful in all sorts of situations–including ones that don’t instantly make us think of math.

For example, this past July 4, our family went to see the fireworks. As I was watching the fireworks, I wondered how they timed the fireworks so perfectly. It hit me: they must use math! Sure enough, a quick Internet search later confirmed my suspicions. (If you’d like to learn more, see www.ohiorc.org/pm/math/richproblemmath.aspx?pmrid=16 for a somewhat technical description.)

On the way home from the firework display, we plugged in the GPS unit. How did the unit know where we were? Once again, it was using math! Here are two easy-to-understand resources I found that offer an overview of the math behind GPS units.

http://electronics.howstuffworks.com/gadgets/travel/gps1.htm

http://www.youtube.com/watch?v=3zRlbboMvb0

My point is simply that if we take the time to explore how something works (the mechanics behind a device), we’ll likely find yet another example of math in action. Being inquisitive about everyday life will turn up lots of wonderful opportunities to show your children that math is a tool to describe consistencies in God’s creation.

Musings on Algebra

For our first specific concept post (see the schedule), I thought I’d offer some general thoughts on a part of math that confused me for years: algebra. Hopefully, this will help you see God’s handiwork amid the xs and ys.

What is algebra?
Algebra is the process of using letters and symbols to describe general quantities and relationships.

For example, say I head into a store with $20 and come out with $5. I would have spent $15.

$20 – $5 = $15.

My starting dollars minus my ending dollars showed me how much I spent in the store.

starting dollars – ending dollars = dollars spent

Let’s use letters to represent this relationship. We’ll use z to represent the starting dollars, y for our ending dollars, and x for the dollars spent.

z – y = x

We now have represented a general relationship that holds true for more than one situation! (We could use it to see how much we’d spent in any store.)

The above is one example of using letters to describe a relationship. By recording a relationship rather than a specific situation, we’re able to solve for unknowns and discover other relationships. This process proves useful in MANY areas (electricity, interest rates, gravity, laws of motion, etc.)

Algebra is based on the idea that certain relationships consistently hold true–that objects operate in a predictable fashion. Dollars do not mysteriously multiply in our wallets. Objects fall in a predictable way. The relationship between the power and voltage and current in an outlet remains the same. Why do things operate so predictably?

Because an unchanging God holds every aspect of this universe together! If God were not keeping everything together in an amazingly predictable manner, algebra would be completely useless. But because of God’s unchanging hand over creation, we can use letters and symbols to name and describe the predictable world around us.

What about all the rules?
A large portion of algebra textbooks focus on rules and conventions. Each “rule” is one standardized convention to represent a real-life consistency.

For years men did not use our current conventions at all! The graphic shows some different ways an algebraic equation has been expressed.

Why does algebra often seem so meaningless?
So often, algebra students completely miss seeing the amazing consistency algebra records because they get lost in the mechanics. As Morris Kline points out, “The usefulness of the techniques of algebra has caused many people to mistake the means for the end and to emphasize these menial techniques to the exclusion of the larger ideas and goals of mathematics. The students who are bored by the processes of algebra are more perceptive than those who have mistakenly identified algebraic processes with mathematics.” [Morris Kline, Mathematics and the Physical World (1959; repr. and slightly corrected, Mineola, NY: Dover Publications, 1981), p. 68.]

Conclusion
As you teach algebra, beware of emphasizing the means (i.e., the rules and conventions) to the point that your student loses site of algebra’s purpose–to record consistent relationships. Remember to let your mind pause and consider the greatness, power, and consistency of the God who, day in and day out, governs all things consistently enough for us to record general relationships and expect them to hold true in various situations. His power, might, and faithfulness truly know no bounds!

“I am the LORD: that is my name: and my glory will I not give to another, neither my praise to graven images.” Isaiah 42:8 (KJV)

Note: Watch for more on algebra soon!