Tag: geometry

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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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Geometry from a Biblical Worldview (New eCourse Available)

mountain/stars

Despite how it often comes across to high school students, geometry is anything but meaningless. In fact, geometry means “earth measure.” It’s a branch of math that helps us measure God’s creation, from the microscopic to the vast distances of space.

I recently had the privilege to develop a geometry eCourse (available on MasterBooksAcademy.com). While it was the most challenging eCourse I’ve developed (creating slides to visually walk through proofs involving different shapes step by step required more than just walking through equations), it was also the most fun to work on. I was blown away over and over again by how geometry sings the Creator’s praises and proves a useful tool. Here are some examples, based on Harold Jacobs’ Geometry: Seeing, Doing, Understanding curriculum and the eCourse I developed to go alongside it (the eCourse both walks through the material and expands on the ideas in the textbook to really bring in the biblical worldview as well as to help students master the concepts without being overwhelmed by the challenges).

mountain/starsGeometry and God’s Creation

Did you know that geometry was used to find the circumference of the earth…and the distance to the nearest star? The distances of outer space are mind-blowing in themselves—yet how much more incredible the God who stretched out the heavens (Isaiah 42:5)! Geometry helps us describe the arrangement of molecules; did you know if the molecules in our bodies were just mirror images of what they are, life as we know it wouldn’t work? Geometry shouts out that life didn’t happen by accident. Geometry helps us see the design in our eyes, and how God gave us the ability to perceive both distance and depth. With geometry, we can measure the height of things we can’t physically stretch a measuring tape to measure—such as a mountain or a tree.

cell phoneGeometry and Real-Life Tasks

Not only does geometry help us explore God’s creation, but it helps us complete real-life tasks. It helps us design bridges, make beautiful art, and engineer chairs, to name a few. Geometry proves a wonderful course to talk about how God made man in His image and how we’re accountable to our Creator for how we use the intellect and abilities God gave us (a great theme to explore in high school as students are thinking through their futures). On a daily basis, we all experience the effects of geometry applied for both good and evil. Every time we use our cell phone, we’re using cell networks that are really a grid of “hexagonal cells” (Jacobs, p. 583)…and we’re using that device for either good or evil.

Geometry and Apologetics/Logical Thinking

While proofs are definitely a key part of geometry, they too are a useful tool. Proofs help us figure out if something applies just in one situation or in all, making them essential in describing God’s creation. After all, if we’re going to use geometry to measure distances in outer space where we can’t physically check our measurements, we need a way to think through those measurements logically. Deductive reasoning is thus a key piece of geometry—and it applies in other areas of life too. In the eCourse, students learn how in any proof, we start with assumptions—and the conclusions we reach are only as valid as the assumptions we begin with. This is key to understand when discerning through arguments people make (and when making them). For example, if you assume a uniformitarian perspective for how a canyon was made, you will reach different conclusions than if you assume a catastrophic global flood was the cause.

Conclusion

Don’t let geometry fool your students: it’s really an exciting journey through which we can behold God’s handiwork and get equipped to serve Him each step. While geometry can feel like a whole new world for students as it’s very different than arithmetic or algebra, understanding its purpose can help students push through the challenges to learn the key skills that really apply outside of math as well.

If you’d like to learn more or need a resource that teaches geometry from this perspective, check out the geometry eCourse I developed on the Master Books Academy. The first chapter is free to watch, and it will give you a greater glimpse into how geometry, far from being a meaningless exercise, is an incredible journey into measuring the earth.

 

Watch first chapter for free.

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Spiders, Math, & the Creator

It’s hard to watch a spider spinning its web without being awed at how carefully he engineers something so fragile, yet so strong.

When we look at spider webs using math, the awe simply compounds. Did you know that “the spider web is actually comprised of numerous radii, a logarithmic spiral (given by the polar equation r=ae^{bθ} ) and the arithmetic spiral (given by the polar equation r = a+bθ )”1?

(Video courtesy of Julie G.; used with permission.)

Nature worded it this way: “Spider webs themselves are characterized by a highly organized geometry that optimizes their function.”2

Spiders are yet one more example of how as we use math to explore God’s creation, we’re awed at the Creator’s wisdom and care. God designed spiders to spin these marvelous structures!

And we should be grateful He did. While spiders can certainly be spooky, they serve an incredible purpose. In his video Spiders! Ogres, Allies & Architects3, creation speaker Mike Snavely points out that if spiders were to take a vacation, the world would be overrun with insects. He actually uses math to better help us appreciate this fact.

In the video, Snavely looked with the viewer at the results of a study of how many ounces of insects one specific type of spider eats on average per day, and at another study done in Holland estimating the average number of spiders in each square yard. Then using basic arithmetic and some more facts (such as the size of Holland, the size of the world compared to Holland, the average weight of a person, etc.), he walks through how one could arrive at an estimate that spiders consume bugs that would equal the weight of 10,000,000 people per day! [Note: There’s no way to perfectly estimate something like this, but, as Snavely points out, “even if this number is exaggerated by a factor of 3 or even 4, that’s still a staggering number of bugs per day.” And other research indicates that the 10,000,000 number may even be a conservative estimate. It’s safe to say that spiders eat a LOT of bugs…and math helps us get a better idea of the magnitude of how much these little creatures eat!]

Now aren’t you glad God made spiders such incredible engineers? He knew that in a fallen world, we’d need these little creatures to keep the insect population down.

I loved how Snavely actually walked through the math (which was simple arithmetic) behind the estimate of how many bugs spiders eat. While many times science books or resources only quote a final number on a topic, know that math is involved in calculating the numbers you encounter in science. Math is truly the tool we use to explore God’s creation.

Here are a couple of ideas you can use to use math to explore God’s handiwork in spiders:

  • Have your student draw a spider web. (You can find various instructions online; here are 3 Ways to Draw a Spider Web.) As they draw, point out that we call what they’re drawing “line segments,” “angles,” etc. Depending on your student’s ages, you could also talk about the names we use to describe different types of angles (such as acute and right) that they are drawing. Math helps us name God’s creation. You could also have them pull out a protractor and measure some angles.
  • With older students, have them take a look at the spirals in many spider webs.
  • Head for a walk and find a spider web. Use a protractor to estimate some of the angles (being careful not to disrupt the web).
  • Read this article by Institute for Creation Research about God’s design on display in spider webs, and take a moment to thank God together for His wisdom and care over each detail.
  • Watch Mike Snavely’s Spiders!. You’ll be wowed by these amazing little creatures…and the even more amazing God Who created them. Plus, you’ll get to see an amazing example of math in action.

Reminder:  If you’re looking for a math curriculum that incorporates real life examples (including spiders!) so students see math in connection with God’s creation, be sure to check out Principles of Mathematics.
Principles of Mathematics

References:

[1] Alicia Bautista, “Spider Webs: Creepy or Cool?” (Math Projects, 2015), http://recursiveprocess.com/mathprojects/index.php/2015/06/09/spider-webs-creepy-or-cool/ (June 17, 2015 update).

[2] S.W. Cranford, et al., “Nonlinear Material Behaviour of Spider Silk Yields Robust Webs,” Nature. 482 (7383), 72-76. Quoted in Brian Thomas, “The Masterful Design of Spider Webs” Acts & Facts. 41 (4): 16. 2012, http://www.icr.org/article/masterful-design-spider-webs/

[3] Mike Snavely, Spiders! Ogres, Allies & Architects (Mission: Imperative!, 2015).

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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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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!