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Why High School Math? (Plus AI, Logic, & the Creator)

Does algebra even matter?

As I released my new Consumer Math course, I kept hearing how excited moms were for a high school math that was actually practical. While Consumer Math certainly is that, other high school math should be too!

In all of my math courses, I’ve striven to show students why they’re learning what they’re learning. Granted, algebra might not be something students incorporate into their daily life. However, they use technology based on it daily. For example, how fast will a metal pan heat up? We can use an algebra equation to figure that out.

formulawhere

formula

We can write formulas like the one above because of the consistent way heat transfers into pans based on their heat capacity. And why is creation so consistent? Because a faithful God governs creation in a predictable way! Algebra should be something students finish up with a deeper wow at our amazing Creator.

Now, high school math problems can get challenging and involved. Some multi-step problems can make your head spin. These problems not only prepare students for real-life math problems, but they also teach them to look at a situation where they don’t know what to do and think of different ways they could potentially approach it. That’s a skill we need with real-life non-mathematical problems too!

And then there’s logical thinking skills. If a > b and b > c, we can conclude that a must also be greater than c…but we couldn’t conclude that it’s greater than h, for instance. Why do we care? Learning how to draw logical conclusions helps us think through real-life scenarios.

I’ve put below a video Answers in Genesis recently released that shows an AI, when prompted to answer “according to strict math, logic, and mathematical probability” agreed a biblical Creator makes sense and evolution is foolish. Logic matters…and algebra and geometry help students develop it.

Looking to Help Your Students See Math’s Purpose This Year?
Check out these high school and junior high school programs, complete with optional eCourses that will walk students through the lessons. Also check out the Big Book of Math timeline, usable to add in math’s application and purpose to any curriculum. It is possible for students to see God in math while developing skills that will last a lifetime.

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Math Moment: Math & Astronomy

astronomy

Did you know that math helps us explore outer space, learning more about the vastness of God’s creation–and how perfectly designed earth is for life?

Have you ever tried to count the stars? We can’t possibly count them all, but we can use math to estimate the number of stars. While there are different ways to do this, one way is to estimate the total mass of a galaxy (which in itself takes a lot of math) and then divide that total mass by the average mass of a star (which again takes math to estimate). So how many stars are there? Well, there’s an estimated 100 to 400 billion stars in our galaxy alone, which would then need multiplied by the number of galaxies (currently estimated to be in the trillions). That’s a lot of stars! Notice we just used math to approximate the stars in our galaxy, but we can’t fully count them all!

Yet God calls each star by name–and it’s because of His power that they continue.

He determines the number of the stars; he gives to all of them their names. Psalm 147:4
Lift up your eyes on high and see: who created these? He who brings out their host by number, calling them all by name; by the greatness of his might and because he is strong in power, not one is missing. Isaiah 40:26

Think about how much greater God is than we are! We can’t even count the stars, and He calls them by name and keeps them in their places. He is greater than we can even imagine.

Have you ever wondered how we know how far it is to the moon, sun, and stars? We can’t just stretch a tape measurer across these distances! Instead, we make the measurements that we can from earth and then use geometry to figure out the distances. When we do, we see that the earth is just the right distance from the sun. If it were closer to the sun, we’d burn up…if further away, we’d freeze.

Now, the earth and the other planets don’t just sit in space; they orbit around the sun in elliptical orbits. How do we know that? Again, men used math! Johannes Kepler used data that had been recorded about Mars to figure out what orbit around the sun would result in those readings. He discovered that planets orbit in ellipses, and that no matter where they are on the ellipse, if you were to go back the same amount of time and look at the resulting area formed between those two locations and the sun, it’d always be the same. So that means God governs creation so consistently that we can mathematically describe how a planet will orbit.

When Kepler shared some of his findings, he paused to praise the Creator.

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

Well, I hope that gives you a little glimpse into how math helps us explore outer space and how as we do, we see that truly, the Heavens declare God’s praises.

math history

Discover more about how we use math to explore the heavens–along with lots of other historical and present-day applications of math in Kate’s new Math History Timeline!

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New Algebra 1 eCourse

Algebra 1 eCourse

I’m excited to have just finished an eCourse to go alongside Jacob’s Elementary Algebra!

The course, which is now available as part of the Master Book’s Academy, brings in the biblical worldview of math, presents the concepts, walks through examples, and more, offering an easy transition from Principles into high school math.

Learn more and view a sample chapter at the Master Books Academy.

P.S. I’m sorry I’ve not blogged much recently–it’s been a busy time! My husband and I just moved into our first home. We’re also still working on Algebra 2 (we expect it to be finished within a few months)…along with other math projects (stay tuned for more details in the upcoming months).

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Answering the Why Behind Math: Responding to Gracie Cunningham

algebra

My heart was recently touched to hear of the viral video posted by a teen wondering about the why behind math expressed in such statements as “Who came up with this concept?” and “How would you even start on the concept of algebra?”

The questions are ones I wondered for years too. I mean, why are there letters like x and y in math books? And what was the purpose?

While the why behind math is one that many mathematicians and philosophers have devoted their entire lives to explore in vain, I believe there are very simple answers. Below is an open letter to Gracie—and anyone else asking these questions.

Dear Gracie,

First, thank you for voicing the questions so many have asked but not spoken. They’re important questions.

I know your questions related to algebra, but bear with me for a minute, as I want to start with arithmetic and work my way up there.

Math is all based on describing the real-life consistencies we find around us. 1 + 1 consistently equals 2. If you take 1 apple and grab another, you’ll end up with 2. Throughout the years, men have used different symbols to describe that, but addition remains the same because that’s what actually happens in real life.

Now you might be asking, but why? And that’s another great question! The answer to that depends on how you look at the world. Many would try to tell you that the world operates consistently as the result of an accident (the Big Bang)—but that doesn’t really make any sense at all. If we’re just the result of an explosion, why is there such consistency?

There is no real naturalistic explanation for math. Many brilliant philosophers have tried to answer it, but failed.[1] Even Albert Einstein admitted that there was something miraculous in math.[2]

But if we look at the world from a different starting point, there is an explanation. Now, this next statement might sound a bit shocking to you, but I believe the Bible has answers to your questions. You might be thinking “The Bible, isn’t that just an old book of fairy tales!?”, or maybe you haven’t even ever thought about it, but bear with me and let’s assume what it says is true even if you don’t think it is. The Bible claims to be a revelation from our Creator; if this is true, we’d expect it to tie with what we see and explain the world in which we live. And it does.[3] It says that a faithful, consistent God created all things—including the consistencies of creation. In fact, God talks about establishing His covenant with the “fixed order of heaven and earth” (Jeremiah 33:25 ESV).

Math works because creation is consistent, created and held together by a consistent God. Thus, we can memorize multiplication facts and rely on them to always work.

The Bible also tells us that God made man in His image, which is why we, unlike the animals, can think through how to express these consistencies around us. It’s why men, like Pythagoras, have been able to attempt to explain creation.

So why algebra? Well, it’s history is long and complicated, and I’m not going to attempt to summarize it all. The Greeks developed some pieces of it, including while trying to explain the relationships within shapes (Pythagoras is known for figuring out how the sides of a triangle relate together). The Arabs developed it further (the name comes from an Arab work). And it took off during the scientific reformation, when many needed it to describe the real-life consistencies they encountered.

For example, say you did experiment after experiment measuring the net force of different sized balls when traveling at the same acceleration of 10 meters per second squared. You found these measurements.

Mass

Net Force

10 kilograms

100 Newtons

9 kilograms

90 Newtons

8 kilograms

80 Newtons

7 kilograms

70 Newtons

You might want to see if you could predict how the mass of the ball will affect its net force without having to try every possible mass. So you look for a pattern.

Such a question presupposes a consistent universe…which was a presupposition many men in the scientific reformation had. They looked at their experiments and data and figured out how it related together. In the case of the balls, you notice that in each case, the force could be found by multiplying the mass by 10—which was the exact amount of the acceleration of the balls! You could write that like this:

Force = mass x acceleration

And rather than using words, why not save time and use a symbol to stand for the words?

F = ma

Now, a lot of algebra then deals with rearranging letters on paper. All we’re doing is applying what we can observe about arithmetic to these letters we’ve used as placeholders to stand for values, such as the F, m, and a. For example, we can see that adding the same poundage to a scale that has 2 pounds on each side leaves the sides equal.

2 = 2

equal

2 + 1 = 2 + 1

equal

Because we’re relying on the created world around us to stay consistent this way, we can also add the same  quantity to both sides even if we don’t know it’s value (we’ll just use a letter to stand for that amount, whatever it is). In the case of weights on a scale, the x is standing for some unknown weight being added to both sides.

scale

2 + x = 2 + x

And we can use that knowledge to solve problems. Note again our presupposition that creation is consistent…which I would argue is shouting out at us that there’s design and order around us, put there by a Creator.

You might find it interesting to note that, apart from acknowledging a Creator who also created our minds, the most brilliant minds have been left baffled as to why what they develop on paper actually applies—and how they can really know it to be true. After all, do we know truth based on experimentation? But we can’t possibly test every value! Or do we know it independently from experimentation? Why then does it actually work?[3] Acknowledging a God answers that, giving us reason to presuppose order around us that will be consistent and that ties with our findings on paper because God has, in a limited way, given us the ability to think “God’s thoughts after him” (a quote attributed to mathematician/scientist Johannes Kepler, who was one famous man from the scientific reformation who saw math as a way of describing God’s creation).

Ultimately, I believe math’s existence and ability to work outside of a textbook is shouting out at us that there is a God to whom we must give an account one day. Just as we can’t change how math works because that’s how He governs creation, so we can’t change how He operates in other areas too.

So it’s important to know what God has said. As I said earlier, I’m starting from the standpoint that the Bible is God’s Word to us. There are many reasons why I believe it is–we could talk about how it was written over more than 1,000 years by several different authors yet has a unified message implying one inspiring author behind it, how Jesus perfectly fulfilled hundreds of prophecies written hundreds of years earlier, and more. But, as one editor for the Chicago Tribune who set out to prove Christianity false discovered, the Bible’s message centers on Jesus’ resurrection–and the historical evidence for that is overwhelming (see The Case for Christ movie or the book by the same title). There is compelling evidence that Jesus was this Creator God who really did rise from the dead, proving His power over death.

This same Jesus claimed that whoever would believe in Him, though he died, would live (John 11:15 ESV). The Bible’s core message is this: God made us, we’ve rebelled against Him and stand under His righteous judgment, but He’s made a way for us to escape the punishment we deserve, know Him, and have eternal life in Heaven through Jesus Christ when we repent of our rebellious ways and put our trust in Him alone. To quote a well-known verse: “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life” (John 3:16 ESV).

Please watch this video to learn in a nutshell what I’m trying to say:

I hope that helps answer your questions. And again, I’m really glad you asked them—they’re important questions to grapple with and understand.

Sincerely,

Kate Hannon

****

For Additional Reading…

And to learn more about the Bible’s answers to life’s tough questions, please check out BiblicalPerspective.net.

For a more technical explanation of why math works, please see this article titled “Evolutionary Math” by Dr. Jason Lisle.

You can also find some answers to common questions about the Bible and Christianity on Josh McDowell’s website–he also set out to prove Christianity a hoax and discovered the opposite. His findings are summarized in his short book, More Than a Carpenter.

Please also see the footnotes below for additional resources.

[1] See James Nickel, Mathematics: Is God Silent? (Ross House Books: Vallecito, CA: 2001). This book walks through the history of math in depth, showing how men have tried unsuccessfully to explain math apart from the biblical God.

[2] “Even if the axioms of the theory are posited by man, the success of such a procedure supposes in the objective world a high degree of order which we are in no way entitled to expect a priori. Therein lies the “miracle” which becomes more and more evident as our knowledge develops…And here is the weak point of positivists and of professional atheists, who feel happy because they think that they have not only pre-empted the world of the divine, but also of the miraculous. Curiously, we have to be resigned to recognizing the “miracle” without having any legitimate way of getting any further.” Albert Einstein (quoted in Mathematics: Is God Silent?, p. 210).

[3] See “Evolutionary Math,”  the same author’s The Ultimate Proof of Creation (and the book by the same name, both of which focuses more on logic), and AnswersinGenesis.org.


About the Author: Katherine [Loop] Hannon is the author of various resources, including Principles of Mathematics, a biblical worldview junior high math program (with Algebra 2 coming in 2020!) published by Master Books. Understanding the biblical worldview in math made a tremendous difference in her life, and she’s been researching, writing, and speaking on math, as well as other topics for over a decade now. Her heart is to point people to “seek the Lord, and His strength” (Psalm 104:4) in everything.

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Algebra, Giraffes, and God’s Handiwork

The following is adapted from the new Algebra 2 program we’re writing; check out our store for other math curriculum that will help math come alive for your students.

Ready for a glimpse of God’s handiwork as we apply algebra out of a textbook? Well, here we go! We’re going to look at how blood pressure relates to the distance from the heart.

heartFirst off, here’s a basic definition of blood pressure from Blood Pressure UK: “When your heart beats, it pumps blood round your body to give it the energy and oxygen it needs. As the blood moves, it pushes against the sides of the blood vessels. The strength of this pushing is your blood pressure.”[1]

Have you ever noticed that when a nurse takes your blood pressure, they always do it on the top part of your arm? That’s because “[m]edical personnel are trained to measure blood pressure at heart level.”[2]The top of your arm is at the same level as your heart. This is important, as, because of gravity, the pressure changes throughout the body.

If a person’s blood pressure equaled a specific amount at heart level (which we’ll call P0), then the pressure at another part of the body (which we’ll represent with a P) could be approximately found by this formula, where h is the distance from the heart:

Blood pressure at another part of the body = Blood pressure at the heart + (density of the blood)(acceleration on the blood due to gravity)(height or distance from the heart)

Giraffe 1

blood pressureTo better understand this, know that if you were to take your blood pressure on your feet while standing, it would be higher than if you were to take the pressure on your arm. That makes sense, as gravity is pulling blood downwards, creating more pressure on your feet.

This also means that if you were to elevate your feet and take your blood pressure there, there’d be less pressure. BUT your heart would have to work harder to overcome gravity to get blood to your feet.

Stop and bend over for a second. You get a head rush, don’t you? That’s because of the extra blood pressure as your head gets lower.

Now think of a giraffe. Its head is waaaay above its heart. Does its heart have to pump extra to get blood there? And when it bends down to drink, how much pressure does its head have to be able to handle?

While there’s more to blood pressure than just the distance from the heart, we can temporarily ignore those other factors and just look at the change in pressure between what it would be at the heart and what it is at a different location. In the formula above, we used P0 to stand for the blood pressure at the heart. Let’s remove that and just look at the change in the pressure from the blood pressure at the heart.

equation

We’ll also assume that the acceleration due to gravity and density stay the same: 9.807 m/s2 (which is the approximate gravity on earth), and an approximate density of blood (ρ) of 1,060 kg/m3. If we substitute these values in for ρ and g, we get this:

Giraffe-2

Depending on what value we plug in for our height (h), we’ll get a different value. The product will show us the change in pressure from the heart due to the change in height.

Let’s start by looking at a human. The top of my head is about 0.508 meters above my heart (about 20 inches). What would the approximate blood pressure be due to the distance from my heart when I bend down and touch my head to the floor? To find that, I’ll replace the h in the formula with 0.508 meters.

Giraffe-equation-3We wrote the answer in both metric units and mmHg, which is the same units you’ve probably heard your blood pressure given at the doctor’s office when you go for a checkup. Normal blood pressure runs between 80 to 120 mmHg, so it makes sense that the change in pressure would be around 39.610 mmHg which is on the same order of magnitude with normal blood pressures but still less than the average.

In comparison, what would a giraffe’s blood pressure be at the top of its head due to the distance from the heart when it bends down for a drink if it’s head was 6 ft (1.829 m) above[3] its heart? We’ll plug 1.829 m into the same formula.

Giraffe-equation-4

Notice that the change in pressure due to the distance from the heart is 142.611 mmHg versus only 39.610 mmHg  for a human. That is more than 3.5 times as much!

When they bend, giraffes have a much higher blood pressure rushing to their heads due to their larger size! If God had not specially designed the giraffe to handle this pressure, giraffes would have died out from all the blood rushing to their head went they bend down. In a 2017 article published on the Answers in Genesis website[4], Karin Viet explains what a testimony to God’s design giraffe’s are:

Evolutionists also encounter a design dilemma for the evolution of a long neck. That six-foot neck requires an intricate blood vessel system to maintain proper blood pressure between the heart and brain. A giraffe bending its neck down to drink water is a marvelous display of design. The 25-pound heart that pumps blood way up that neck against gravity suddenly pumps down with gravity, which should cause the delicate brain to explode. But the blood vessels are uniquely designed with reinforced walls, bypass valves, a cushioning web, and sensor signals to moderate the pressure when the giraffe bends its neck down.

The reverse of this intricate system happens when the giraffe raises its head so that the pressure is regained and the giraffe doesn’t pass out. In addition, the tight skin on giraffe legs has been compared to an astronaut’s G-suit, because it prevents high blood pressure from pressing blood out of the capillaries.

Math CurriculumGiraffes were given just what they need—G-suit and all—to be able to handle the higher pressure caused by their long necks. And it’s math (including algebra!) that helps us understand how giraffes are a marvel of God’s grand design![5]

Don’t let your students miss out on seeing how math helps us explore God’s handiwork. Stay tuned for our Algebra 2 curriculum…and in the meantime, check out our other math resources and curriculum.


[1] “What is blood pressure?” Blood Pressure UK, (England, 2008), http://www.bloodpressureuk.org/BloodPressureandyou/Thebasics/Bloodpressure, s.v., “Blood Pressure.”

[2] Based on physics.wm.edu/~labs/107_manual/ch11.pdf

[3] Based on a neck of 6 ft, as shared by the San Diego Zoo https://animals.sandiegozoo.org/animals/giraffe and the fact that its heart is located in the giraffe’s chest.

[4] https://answersingenesis.org/mammals/giraffes-towering-testimonies-to-gods-design/

[5]See also https://bpsfuelforthought.wordpress.com/2012/08/14/why-giraffes-dont-have-brain-damage/ for more details.

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Math, Waves, and the Creator: Light Waves

Part 2 of 3

Note: This is a continuation of a series of guest posts on Math, Waves, and the Creator by Dr. Adam F. Hannon. This particular one would be great to have middle school and high school students read in order to give them a glimpse into how math helps us shine light on God’s creation, pointing to the Creator. I hope you enjoy! – Katherine

 “And God said, Let there be light: and there was light.” Genesis 1:3 (KJV)

God spoke, and light came into being. We feel its warmth (very much so in the summer months!) and enjoy its illumination, yet math gives us a fresh glimpse into just how amazing all the light around us is.

As discussed in the previous “Wave, Math, and the Creator” blog post, light is a wave—or more specifically, two coupled waves (an electric and a magnetic wave) in one. We saw in the previous blog how we can use algebra and trigonometry to describe waves, including light waves.

Let’s continue exploring light with math—only this time, we’ll use basic math, along with just a touch of algebra (the part a pre-algebra student could still follow).

As we do so, we’ll discover amazing order God placed in the very light all around us.

Measuring the Properties of Light Waves

There are a lot of different aspects of light waves we could look at. For example, we could look at how fast a wave is traveling in a certain direction—or its velocity.

We can use a number to describe this velocity.

Velocity of Light Wave

Figure 1.1 The velocity of a wave is how fast the wave is traveling in a certain direction. For example, if the  wave above took 1 second to travel 1 centimeter toward the right, we would say its velocity was 1 centimeter per second, or 1 cm/sec.

Or we could look at how frequently one part of the wave repeats in a given amount of time, called the frequency.

Again, we can use a number to describe the frequency.

Figure 1.2: In the video, the two waves have the same wavelength but different frequencies. During the time it takes the top green wave to pass one full period through the dashed line, the bottom purple wave passes through twice, thus it has twice the frequency.

We can also look at the wavelength—at how long each of the repeated wave structures are.

Again, we can use a number to describe the wavelength!

Figure 1.3 The marked distance between the peak of each wave is the wavelength. Notice that the top wave has a greater wavelength than the bottom one.

Now, in real life, it’s not easy to measure the frequency of a light wave—it corresponds to a really short amount of time. But it is easier to measure the wavelength. And then—you guessed it!—we can use math to help us find the frequency. Let’s take a look at how.

Using Math to Find the Frequency

Because of the consistent way God governs all things, there is a consistent relationship between the velocity, frequency, and wavelength of a wave:

velocity = frequency • wavelength

Since in math we tend to use letters instead of writing out the whole words (it saves time and makes it a lot easier to work with the equation!), we’ll use symbols to represent this same relationship (the v represents the velocity, the f the frequency, and the λ the wavelength):

v = f λ

Now that we know the relationship between the velocity, frequency, and wavelength [1], we can use math to help us figure out the frequency. In a light wave, the velocity is the speed of light, which, because of the consistent way God governs all things, is always constant 670,616,629 miles per hour (or roughly 3.00 x 1017nm/sec). Note: The “sec” stands for “second,” and the nm stands for nanometers or 1 billionth the length of a meter—it’s very small! Thus, we can write that amount for the velocity (which we represented with a v) in the equation, giving us this:

3.00 x 1017 nm/sec = f λ

And now if we know the wavelength, we can easily find the frequency!

Example: If the wavelength (λ) of a light wave is 650 nm, what is its frequency?

We know this relationship: 3.00 x 1017 nm/sec = f λ

Substituting in 650 nm for the wavelength (λ) gives us this: 3.00 x 1017 nm/sec = f(650 nm)

If we now divide both sides by 650 nm, we’ll find the frequency.

frequency equation

Note: Notice that we divided both sides by the same amount to simplify the answer—we’re able to do that because of the consistent way God governs creation.

The THz stands for Terahertz. Tera means a trillion. We just saw that a 650 nm light wave has a frequency of 462 Terahertz; in other words, it is repeating the wave-like pattern 462 trillion times per second! Can you imagine something happening a trillion times over and over again in a single second!?

Discovering the Colors of Light—and Invisible Light

One of the neat things we discover as we use math to explore light is that different wavelengths result in different colors.

While we are used to white light, we also encounter colored lights, such as the red light in a small laser pointer. Notice how the color varies as the wavelength varies.

 

Figure 1.4: Approximate wavelengths of different colored lights.[2]

Some light, though, is invisible. It turns out that there are more to light waves than just what we think of as “light”! There are kinds of light waves with smaller and larger wavelengths that we can consider as invisible light. These different invisible light waves along with visible light are all called electromagnetic waves and make up a whole spectrum as shown in the figure below.

Electromagnetic Spectrum

Figure 1.5: Schematic of the electromagnetic spectrum. Going from left to right goes from longer wavelengths to shorter wavelengths.

Just think of the fact we can also only see a small portion of the electromagnetic spectrum—what beauty must exist to God who can see in the entire spectrum!

We are literally “in the dark” to most of the light waves around us—we only know much about them because we can use tools and equipment to detect them.

Applying What We Learn About Light

Not only does math help us appreciate the amazing beauty God put in light, but math helps us apply what we learn to build technology.

For example, take CDs, DVDs, and “Blue-Ray” discs. Did you know that the CD/DVD/Blue-Ray player reads the data off these disks using light, and that each of them use light with different wavelengths (and thus different colors)[3]?

  • CDs – 780 nm wavelength (infrared)
  • DVDs – 650 nm wavelength (red)
  • Blue-ray – 405 nm wavelength (indigo…somebody named that wrong!)

Every time you use a CD/DVD/Blue-ray disc, you’re reaping the benefits of math in action.

Let There Be Light

That’s just a glimpse into how math reveals design and beauty in the very light around us—the light God created by the simple command, “Let there be light” (Genesis 1:3 KJV).

As you enjoy the bright summer light today, pause and reflect on the Creator’s power and might Who simply spoke light into existence.

He is the same Creator who shone into the darkness of our sin with the Light—Jesus Christ.

“In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not…. But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:” John 1:3-4, 12 (KJV)

Note: Stay tuned for the final blog in the Waves, Math, and the Creator series. In it, we’ll explore sound waves.


[1] Equation from David J. Griffiths, Introduction to Electrodynamics, 3rd ed. (USA: Upper Saddle River, NJ: Prentice Hall, 1999), p. 368.
[2] The exact colors given for different lights varies by source, as the there are a range of hues within red, orange, etc., and the borders are hard to concretely define since what may be orange to one person might still be red to another (see this Live Physics page for one list of approximate ranges). The point is that different colors of light do have different wavelengths. These values came from those given in Griffiths, p. 377. The figure was adapted with those numbers from one by Gringer.
[3] Values from Kumar, T. Ravi, and R. V. Krishnaiah. “Optical Disk with Blu-Ray Technologoy.” International Journal of Computer Engineering & Applications III, no. II/III (July-September 2013), p. 160. https://arxiv.org/ftp/arxiv/papers/1310/1310.1551.pdf.

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Why, Oh, Why Must I Learn Math?

I recently asked some folks this question:

What are you/your children’s biggest struggles in math?

The responses varied (stay tuned for others in future blogs), but several voiced the same struggle: why.

Knowing why you need to learn something certainly doesn’t seem like too much to expect. It’s actually a very reasonable question. As Alfred North Whitehead said, “There can be nothing more destructive of true education than to spend long hours in the acquirement of ideas and methods that lead nowhere.”

So why math? Well, math is a way of describing the consistent manner in which God holds His creation together. Thus it helps us work with the world around us—from everyday tasks to sending men to the moon. It helps us complete various tasks that God gives us to do here on earth.

For example, fractions give us a handy way of describing division, helping us work with real-life relationships. Oh, and don’t forget that music notes, sewing, and cooking all use fractions! (There’s more on the why of fractions in my previous post “Why Learn Fractions?”)

One mother shared that her child wondered why finding the area of triangles matters. While triangles might not at first appear to be the most practical shape, they can actually help us measure such real-life distances as the height of a building and the distance across a stream. (In fact, that’s exactly what students learn to do in Principles of Mathematics while studying triangles.) As for finding their area, triangles also help us measure other shapes. For example, if we want to find the area of a hexagon (which is what bees make their honeycombs out of), we would use triangles to do it. Triangles—along with the rest of geometry—are incredibly practical!

For those of you wondering the “why” of high school math, I recently had an article published in The Old Schoolhouse magazine on that exact topic. You can read “What’s the Purpose of High School Math?” online (note: it may take a minute to load)…and I’d love if you’d then leave a comment here and let me know what you think.

And for those wondering how to teach math in such a way that your students will understand why they’re learning each skill they study, check out the math resources I wrote specifically to help students understand math’s true purpose…and to praise the Creator of all as they study. After all, math applies because Jesus is upholding all things by the power of His Word (Hebrews 1:3) in such a predictable way that we can describe it mathematically! Math, when properly taught, should encourage us to trust Him more and more.

Have a specific math topic you’d like to know the “why” of? Leave it as a comment!