Purposeful Learning

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God’s Perfection in Mathematics

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One evening about a month ago, my six-year-old brother asked a question that was designed to stump the oldest of us. “What’s fifty times fifty?” He loves starting with the hardest number to multiply that he can fathom, and then multiply that by itself, the new number by itself again, and keep going—until even the calculator groans and returns an E+, ‘Overflow’, or simply starts showing uninterpretable decimals.

Squares 01

But since fifty times fifty isn’t too big, I set it up on the whiteboard for him and gave him the answer. “Two thousand five hundred.”

“So…what’s forty times forty?”

I can’t remember exactly how the conversation went from there, but we ended up calculating several squares in the 47-52 range. After looking at the ones on the board, I suddenly wondered if there was a pattern. If we could possibly predict the next one.

472 = 2,209
482 = 2,304 (difference from 472: 95)
492 = 2,401 (difference from 482: 97)
502 = 2,500 (difference from 492: 99)
512 = 2,601 (difference from 502: 101)
522 = 2,704 (difference from 512: 103)

If there is a pattern, 532 should be 522 plus 105. It is—2,809.

After this, Mom went back to 1 and wrote down the squares of the first 12 numbers, to see if they followed the same pattern.

Squares 02
Should give you an idea of what she did. The differences are the bottom row of numbers.

They do. Each difference is precisely two numbers greater than the last one. Incredible, isn’t it? And while it’s amazing, we also realize that God has known all along and He made it that way for a reason.

So there’s your math lesson for the day. A terribly impractical, but undeniably fascinating pattern.

The Flow of History

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If there’s one thing I remember doing in my earliest memories, it would be having our family worship time. Although the times of day when we do it has changed over the years, it’s an every day occurrence aside from Sundays. I only remember one time when we’ve actually missed having it, and that was not on purpose, believe me! This is a long-standing tradition, one that I’m sure will never stop, even after all of us children eventually leave home.

01: Flow of History

I really respect my dad for keeping it up all these years. It can’t be easy for him; often he’s had long days at work and he’s physically drained, but he always makes sure that we have our Bible time.Over the years, we’ve done at least two almost cover-to-cover read-throughs of the Bible (we’ve skipped some of the genealogies—the younger children have a hard time reading, let alone understanding, all the names!). I can’t remember exactly when we started the last read-through, but it was probably a year or two ago. We got up to 1 Kings 7 by October last year, then Dad decided to switch to Blue Letter Bible’s Chronological reading plan. Reading the Bible this way adds a whole new dimension to the stories and context, which makes it quite interesting! Currently, we’re reading in 2 Kings, 2 Chronicles, and Isaiah.

As we’ve been reading through Kings and Chronicles, I’ve noticed some interesting “threads” of history. I’m keeping track of those findings on slips of paper, and eventually I’ll transfer them into my journal for safe keeping. I thought I’d share them here today, since I find the similarities so interesting.

The Flow of History #1:

Taken from: II Kings 15, especially verses 9, 18, 24, and 28.

Zachariah, son of Jeroboam, king of Israel (not related to the first king of Israel; he was Jehu’s great-great grandson, according to the word of the Lord—see II Kings 10:30)

  • Departed not from Jeroboam’s sins (Jeroboam the son of Nebat was the first king of Israel, and this is who it is referring to)
  • Was conspired against and killed by Shallum (vs. 10; who was in turn killed a month later by Menahem)

Menahem, son of Gadi, king of Israel

  • Killed Shallum (who had killed Zachariah)
  • Died a natural death
  • Departed not from Jeroboam’s sins

Pekahiah, son of Menahem, king of Israel

  • Departed not from Jeroboam’s sins
  • Conspired against and killed (vs. 25)

Pekah, son of Remaliah, king of Israel

  • Killed Pekahiah
  • Departed not from Jeroboam’s sins
  • Conspired against and killed by Hoshea the son of Elah (vs. 30)

IN CONCLUSION:

Jeroboam the son of Nebat set a precedent that was never overturned. He went down in history as the “man who made Israel to sin.” What precedent are YOU setting?

I found it fascinating that of the five kings in this chapter, all followed the sins of Jeroboam and four out of the five were conspired against and killed. Isn’t that interesting? Reminds me of Romans 6:23: “For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.”

02: Flow of History

The Flow of History #2

Taken from: II Chronicles 21-29

Chapter 21: Jehoram, son of Jehoshaphat, who was the son of Asa, king of Judah (the latter two followed the Lord)

  • His mother’s name is not mentioned
  • Married Ahab’s daughter (21:6)
  • Compelled Judah to sin (21:11)

Chapter 22: Ahaziah, youngest son of Jehoram, king of Judah

  • Mother’s name was Athaliah (22:2; we find out later in the chapter that she killed all her grandsons so she could reign over Judah)
  • Walked in the ways of Ahab (an evil king of Israel; 22:3)

Chapter 24: Joash, son of Ahaziah, king of Judah

  • Mother’s name was Zibiah (24:1)
  • Did that which was right all the years that Jehoiada the priest was alive (24:2)

Chapter 25: Amaziah, son of Joash, king of Judah

  • Mother’s name was Jehoaddan (25:1)
  • Did that which was right in the eyes of the Lord, but not perfectly (25:2)

Chapter 26: Uzziah, son of Amaziah, king of Judah

  • Mother’s name was Jecoliah (26:3)
  • Did that which was right in the eyes of the Lord, but not perfectly (26:4-5)

Chapter 27: Jotham, son of Uzziah, king of Judah

  • Mother was Jerushah (27:1)
  • Did that which was right in the eyes of the Lord, but not perfectly (27:2)

Chapter 28: Ahaz, son of Jotham, king of Judah

  • No mother named
  • Provoked the Lord God to anger (28:25)

Chapter 29: Hezekiah, son of Ahaz, king of Judah (one of the most righteous kings in Judaean king history; he prayed for deliverance from the Assyrians and the Lord defeated the army)

  • Mother’s name was Abijah (29:1)
  • Did that which was right in the eyes of the Lord, according to all that king David had done (29:2)

IN CONCLUSION:

The Godly mothers are named for the kings that followed the Lord. Only one evil king out of the three mentioned had his mother named, and that was because everyone knew how evil she was. We are all examples to someone, just as these mothers were to their sons. What kind of example are you setting before your coworkers, your siblings, your children, or others that you come in contact with on a frequent basis? What kind of Godly influence are YOU?

Indeed, “Blessed is the nation whose God is the Lord; and the people whom he hath chosen for his own inheritance.” Psalm 33:12

Be blessed, friend. Live for Jesus today.
-Esther

The Mystery Object: Can You Help?

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One evening this week, my ten year old brother was searching through my sixteen year old brother’s things, trying to find a lost wallet. I don’t know if he ended up finding the wallet or not, but he did discover something fascinating—an old metal thing, with the name “Nat” inscribed on the outside, and a tiny picture of a man on the inside. It is about 15 mm in diameter, so pretty tiny!

Mystery Object 01

There is nothing on the outside edge that would have made it possible to put on a necklace (no little loops or anything), and it wasn’t made to snap onto clothing as a button—we tried that out, and it didn’t work.

Mystery Object 02

I asked my brothers how they had found it, and the older brother said he had seen something shiny in the garden while he was cultivating, and picked it up. It was covered in dirt, so he soaked it in water and then cleaned it off. Afterward, he put it in with his other odds and ends, and forgot about it.

Then our younger brother was looking for his wallet, and found it—and seeing that it was made up of two different pieces, tried to open it! After prying it apart, this is what he found. In an attempt to find out who the man was, the boys popped his picture out to see if there were words underneath, but there were none—and in the process of putting it back in, some of the picture flaked off. They decided we ought to take a photograph of it before it gets any worse!

Mystery Object 03

Have you seen anything like this before? Do you know what it could be? None of us can figure any more out than what has already been stated.

In other news, I’m working on writing a guest post for my cousin Kendra Stamy at A Proverbs 31 Wife. So far, the task has proven challenging, but I’m enjoying it. Lots of interesting thoughts coming out about books and why we read what we read. Praying that I’ll be able to encourage someone through this opportunity! I’ll share the link on here once the post is published.

Also, I’ve been working on memorizing Psalm 67 the last two weeks. So far, so good—almost through the chapter now. I did get a little stuck on verse four, but I think I’m getting it. Just need to remember that verses three and five are exactly the same, and get six and seven down pat yet. I’m getting there!

Memorising Psalm 67:4
I decided to put the verse on my computer desktop until I get it memorized, so I won’t forget to practice it.

I also need to get this month’s newsletter written and sent. AFTER the guest post is written! I need to send out the last giveaway prize today—just heard back from the last winner this morning—and then that job will be done. 🙂 There are a couple other emails related to the giveaway that need replies yet, but they’ll be taken care of soon.

And along with all of that, I’m trying to ignore the insistent summons from a recent fascinating story, The Destiny of a Few by Sarah Holman, to finish reading it. Hey, I just got on Amazon to get a link for you, and I see that the Kindle version is currently free! Get it now if you can! I’m about halfway through the book, and thoroughly enjoying the adventure, even though I don’t completely agree with some of the views put forward in the book. If I can hold out until my work for today is done, then I can indulge in reading. I think.

Hope you’re having a great day, and if you have any ideas about what this mystery object is, my brothers and I would be glad to hear your thoughts.

Hello, Winter! (and Giveaway Winners)

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Hello, winter, what a surprise!
Icicles blooming before our eyes!

Well, not quite like that. But the heavy frost did come as a surprise to me yesterday morning.

Hello, Winter! 01

We’ve had skirmishes with frost the last couple weeks, little touches announcing that the hard one is on the way, but up until now we haven’t had anything serious. It’s been chilly, yes, but not quite to the point of freezing.

Hello, Winter! 02
The grass close to the sprinkler was heavily iced over. It made the most delightful crunch when stepped on!

Well, two nights ago it arrived. Mom woke up around 12:30, noticed that the air was pretty cold, and turned the sprinkler on. I woke up at 6, realized that my room felt like a freezer, turned my fan heater on, and went back to bed. I got up around 7 when the room was nice and toasty.

Hello, Winter! 03
The pumpkin leaves, beautifully encased in ice, looked almost like the plastic food look-a-likes you can buy at some stores.

Then came my morning routine–go in the house to get some hot coffee, and grab the overnight oatmeal with peaches that I had made the night before (you can’t beat pre-made breakfast!). After hearing how the water had been on for about seven hours, and seeing a sample of the icy coating on a pumpkin leaf someone had brought up, I decided that despite the fact that my coffee would get cold, I had to get a few pictures of the beauty out in our ice-encased garden.

Hello, Winter! 04

It was more beautiful than words or pictures can describe. I guess God’s creation is normally like that, but I rarely stop to just look and stand in awe.

Hello, Winter! 05

Hello, Winter! 06

Hello, Winter! 08

The most beautiful thing I saw in that half-hour out in God’s beautiful frozen paradise was the thistle flower. Showcased in a perfect sphere of ice.

Hello, Winter! 09

Hello, Winter! 10

The hollyhock was another favorite specimen.

Hello, Winter! 11

Hello, Winter! 12

I just have to wonder, looking at this…why does God choose to use cold to make such beauty? I don’t enjoy being cold. But yet, perhaps, sometimes He uses things like cold to draw us to Himself.

Hello, Winter! 13

The really interesting thing was–once the sun came out and melted away the ice, the plants looked perfectly fine. They hadn’t been frosted. The ice itself kept the plants from dying. There’s a scientific explanation for why this works under certain conditions, and I won’t go into it now. Suffice to say that for us, this was a fascinating experiment, and it was successful this time. If you want to read up on the technical side of why this works, go here.

Hello, Winter! 07

Last night, the sprinkler didn’t get turned on early enough, so we did get a little frost damage–it was almost as cold last night as the night before. And from the looks of it, we’ll be getting another good one tonight. But for now, I feel privileged to have been able to see the beauty in our garden, and ponder the spiritual allegories that could be derived from the experience.

And yes, by the time I was finished taking pictures about half an hour later, my coffee was quite cold. It did still taste good, though!

Hello, Winter! 14

The intricate ways God made this world are truly incredible!

And for the giveaway winners: Please join me in congratulating Bonnie S, Ashley S, Nancy T, Ross T, and Camy L for winning the One Year Celebration Giveaway! Congratulations, friends–and thank you, all of you, for participating. I wish I could send a prize to each of you, but I can’t. I am planning to host more giveaways just because they’re so fun, so hopefully if you didn’t win this time you can later. 🙂

What was your most memorable experience with ice?

God’s Surprises

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This morning, I saw that this week’s five minute Friday prompt was the word “surprise”. Even though I’ve never done it before, I thought this would be a fun challenge, so below is my piece on the topic.

The rules: Write for five minutes straight, with no editing, on the topic given. Share online.

Easy enough . . . hopefully!

Bee on the Goldenrod

GO!

Surprises come in many different packages. Whether it’s your boss at work playing a prank on you, you sharing in a friends’ surprise party, or simply reading the Word and being surprised at its contents.

There are so many surprises in the world, and one thing that is often connected in my brain is the word surprise with the word mystery. Both are talked about in relation to God, and there’s that really fascinating verse by Paul, I think, that says the mysteries of God are now clearly seen—that’s butchered, I know, but you should get the drift.

I love that facet of His character. I love how there were (well, still are) mysteries about Him, but through Jesus coming here, living among us, Emmanuel, many mysteries have been cleared up. We can now understand the heart behind the old law, and yet there are so many things—threads—connecting both the old law and the new law.
Such as the oft-repeated command: “Obey my commandments, and you will have My blessing”—I’ve been noticing a lot of those in Numbers and Deuteronomy, and I know Jesus said that several times in John as well. That’s just one of the threads. The threads in His Word are fascinating! And there’s so many others, too!

STOP.

Beautiful flowers!

I didn’t quite finish the thought, so here it is—God’s surprises and mysteries come in many ways. Many mysteries are made understandable through the Word. And many of His surprises come through His Word (wow; I didn’t know this verse/that meaning was there!).

Another interesting related thought is that He promises we will be blessed if we follow His commands (John 14:15—“If ye love me, keep my commandments.”) His blessings come in many forms. Perhaps it isn’t even very obvious at times, but I’ve found that in genuinely trying to care for others—through His strength, because I can’t on my own!—I get blessed in return.

Well, I enjoyed that. I’ll have to do it again.

In more down-to-earth daily life, we’ve had a coolish week this last week. We’ve had some beautiful days, a couple rain days, and today was a bit of a hot day. Praise the Lord, we got about 40 mm of rain (1 ½ inches) about three days ago—much needed, and much prayed for!

Last evening, as we were preparing to have Bible time, I noticed the beautiful sunshine coming through the trees. This picture doesn’t do it justice, but that combined with the ever-sunny Jerusalem artichoke flowers was a gorgeous sight!

As I near the end of this week, I want to pause and take in the beauty around me, all the little surprises God has packed into each day. Whether it’s the sunset, the heart-melting grin of my little sister, or the little brother that wants a cuddle and a story. I want to take it in, and in return thank Him for each one.

I also want to continue to delve deeper, learn more, study Him—and ask Him to make me more like the daughter of God, the “moon” of His Son, that He wants me to be.

Do you have anything you’re wanting to focus on this weekend, and the coming week as we approach the Easter season?

P. S. Yes, I’m on Instagram now. Follow me here, if you like. 🙂

Where This Blog is Headed

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(To change things up a bit and make it easier for you, I’ll start with the conclusion so you can get the gist of why I’m writing this post—and if you don’t have time for the other 1,000-some words, you’ll still know what’s going on.)

From now on, I’m going to be writing about the stuff that I find interesting. It might be my goals for the week, it might be what we’ve been doing lately, it might be just a random thought from the morning’s Bible study. And, perhaps sometimes, I’ll share a tip or resource I’ve recently found.

I’m not going to try to write for a particular audience. It will end up being mostly applicable to homeschool students/graduates, and maybe Moms at times. I just don’t want to keep writing about something I’m not 100% interested in—there are plenty of other things in my life that I do that I’m not putting my all into, and I don’t want to have to do that with this blog as well.

Where This Blog is Headed

Alright, here’s the reasoning behind this change:

If you haven’t figured this out already, I’ll tell you now: I love to think. Therefore, a lot of what I want to share on my blog is random thoughts I’ve had. And recently while thinking about this blog, I realized something needs to change. I’ve hinted at changes several times (in February’s newsletter, and perhaps once or twice here), but as yet I haven’t come to any conclusive thoughts on the matter.

The purpose of this post today is to sort out all the thoughts I’ve had about this blog, what I don’t like about it and what I want to do in the future. If you don’t want to read it, that’s fine—I just need to process everything somewhere and this seems to be the best place to do it.

Peas
Can’t pull the pea off? Go ahead and eat it while it’s still attached to the vine–it won’t hurt you.

Before I begin, I’d like to go back to when I first started this blog. Back in May and June last year, as I was preparing to launch Learning Resource Directory, I decided I wanted something to go along with the website. Something with fresh content that was updated frequently, as opposed to the almost-static book reviews. Yes, they’re fresh and 5-7 new ones are posted a week, but they aren’t as engaging as a blog. Once posted, they’re basically static content.

I decided a blog would be the best option. Since I was interested in writing, and since writing is very involved with books, and since books are also very involved in homeschool, I decided to have a blog designed to encourage homeschoolers and writers. Purposeful Learning was created.

However, over the past few months I’ve come to realize that I’m not always thinking about or interested in writing or homeschooling. Therefore the posts I posted felt forced—I was writing about the topic of the blog, even though my heart wasn’t in it. Sometimes, there are other things that are much more interesting to me.

Salt Mountains
Mountains of salt at a factory north of us—spotted on a recent family trip.

Then I read a blog post on Noveltea. And the wheels really started turning. (Please, do read that post—I’ll try not to copy Lydia’s thoughts, but I do agree with her on every point!)

There are some things I really don’t like in different people’s blogs…and yet I write the same way myself. There are some popular guidelines that mainstream bloggers give as to how to be a successful blogger. But yet some of those are not appealing to me. From the very beginning, I wanted a way to share my life, my concerns about the world around me, and my random thoughts, in a place that people—even just one or two—could read it, be encouraged, and possibly allow that to change their lives. Or, if I have the wrong idea about something, that they could show me how I’m wrong, and I can change (Matthew 18 in action, to some extent).

Just so I can sum this up in my head, and since I have a thing for numbered lists and bullet points, here are a few things I’ve considered when mulling this topic over.

Some things I don’t like in blogs:

  • Posts that don’t resonate with me or my situation right now. A lot of advice given is to find your niche and write for that niche. However, there are some flaws in that idea—I’ll address them later. Suffice to say for now, if a blog I follow mostly shares posts that I don’t find interesting, I’ll rarely read the blog. The only reason I follow it is because I know the person and/or they sometimes share something that I find very helpful.
  • Posts that are all about the same thing. Also relating to the first point—there are some major downfalls to blogs like this. No, I’m really not interested in your book right now, no matter how much you talk about it. Does your life really completely revolve around that book?
  • Pictures that are used…and reused. I know I’m guilty of this myself, but really—I’ve already seen that picture. Yes, it’s a nice one, but don’t you take new ones on occasion?
  • Blogging just for the sake of gaining attention. I’m highly guilty of this, but I want it to change! Yes, it’s pretty obvious that the only reason you write is because you want to attract big numbers and/or attention from those in the publishing world. Sorry, but I’m not interested in being part of a fanbase like that.
Boating
Big brother taking little sis for a boat ride.

Some things I do like in blogs:

  • Posts sharing ordinary life. Ones that contain the nittie-grittiness of life, such as telling how you failed (again) at completing that goal. Of course, if you’re always failing and never ever get it right, then that can be over-the-top too, but I love hearing how you are failing and then experiencing the win with you. Pictures showing your life also are really fun.
  • Random thoughts. I love getting in other people’s heads, and when they share the random pieces of information they’ve picked up lately, I really enjoy that glimpse into their lives.
  • Goal posts or reading lately/doing lately posts. Kind of the same idea as the first point, but I love seeing what things other people are trying to achieve in their lives, and then following their progress. I also love seeing what they’re reading, listening to, etc. as well.
Split Apple Rock
Split Apple Rock, a beautiful piece of New Zealand coast north of us.

Why I think writing for a niche is faulty:

The reasoning you get is, if you write for a niche, then you’ll attract fans that are especially interested in the things that you’re interested in. People will know what they’ll get when they come to visit, which provides some reason for them to come by. They’ll know when they see your name what you represent, which provides some form of security.

While I can see the logic behind that (that is, if I’m understanding the advice right), and the value in branding yourself, I see one little problem that could potentially be huge:

What about all the other things that we’re interested in, but we can’t share because we’re trying to write for our target audience?

I explored the thought in a comment on Lydia’s post, but basically it boiled down to: We’re all three-dimensional characters. We’re all interested in a lot of different things. And it’s really hard to connect to a one-dimensional person. Maybe I should just quote my comment:

“Having a blog that doesn’t have a particular “niche” means that we share whatever comes to mind at any particular time. To say it in writing terms, our blogs become dynamic, well-rounded characters, instead of being flat one-dimensional characters. Just about everyone has their own wide range of interests, and when that is shown through the blog, we can connect a lot better. Just as we don’t connect very well to one-dimensional characters in books, we also can’t connect as well to one-dimensional blogs.”

In conclusion, I want to be genuinely me, and I think changing is the best way to do it. I’ll be writing about what I find interesting, and hopefully you’ll find interesting as well. So…welcome to my brain!

By the way, if you managed to read all the way to the end—all 1,300+ words, I congratulate you. Great job.

Now go do something worth doing!

Over to you: What kind of blog posts and blogs do you enjoy reading? Do you have any tips for how I (or other people!) could do this whole blogging thing better?