A Really Cool Math Fact About the Squares

My kids are in Classical Conversations (CC), which we love. This year they learned the squares (a number times itself) to 15, and they learned them to a song. The information in CC is wonderful. I wish I knew all this stuff. But apparently when I was in elementary school the “educational experts” had decided that it was cruel to kids (or something) to make them memorize “useless information.” Harumph!

Anyway, I mentioned to my wife that I wish I could learn this stuff, so she asked me at dinner what I wanted to learn. I said, “the squares.” So they taught me the song. You can get it here, and here are the numbers:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

As I was thinking about these numbers and trying to learn the song, I remembered something I read in a Princeton Review book when I was studying for the GRE (this is one of the things that makes me grateful that I had to take the GRE, by the way, and one of the reasons I encourage students to study for it and really try to learn!).

Look at those numbers. Do you notice the space between them?

Between 1 and 4 are 3 points on the number line, then between 4 and 9 there are 5, between 9 and 16 there are 7, and it continues up by odd numbers as follows:

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29

That is cool. God made the world in an orderly fashion, and he built elegance and beauty into it, as though he expected people to come along and search out all his wisdom to marvel at his glory.

“In the beginning was the Word, and the Word was with God, and the Word was God” (John 1:1).

“The heavens declare the glory of God, and the sky above proclaims his handiwork” (Psalm 19:1).

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  1. I did a great deal of memorization as a student and learned a significant amount of information. I also taught memorization as an important component of learning–one among many, truly, but a viable one, nonetheless. But I believe you’re stretching things a bit in implying that those who felt it improper to memorize “useless information” were “idiots.” Frankly, some information is largely useless, regardless of how impressive it might sound to possess the knowledge. It was much more important to me to teach the children how to think and reason, and the processes and resources to use to discover the answers than it was to accumulate facts merely through rote memorization. Call me an idiot if you must. I feel there’s a definite place to memorize, as long as what one memorizes is truly beneficial. There’s a larger place for the development of reasoning through logic and rhetoric. I hope your children are blessed greatly and learning much through the classical conversations program. I will say that I taught for the last three years of my career at a Christian school. While it had its strengths and I am thankful for its impact on young lives, the children were at times deprived of knowledge through an inordinate fear of exposing them to “the world.” Thus, if a government leader or philosopher, for instance, was not a Christian, information about the person was often limited and skewed in such a way that the portrayal of the person was negative on balance. As a language arts teacher, I was often dismayed at great writers who were not read by the children because they were not Christian and did not have a Christian world view. So…no Steinbeck, Faulkner, Fitzgerald…and at times, when a Christian writer was misunderstood or misinterpreted by the administrative staff, said writer–Flannery O’Connor leaps immediately to mind–was also forbidden. I wanted to have my eighth graders read “To Kill a Mockingbird,” but it was declared to be inappropriate because it was too indelicate and even offensive. I’m sorry if I’ve drifted far afield from your original article, and I hope Classical Conversations is rigorous, balanced, thought-provoking, and God-honoring. May it not be too inwardly-focused and detached, and may it be a program where the young people are taught to think.

    1. Thanks for your note. I deleted the line that descended into name calling, and I apologize about that. Please forgive me.

      I agree with you about the inappropriate sheltering. My kids learned about the theories of natural selection and evolution in CC this year, and they also learned about “catastrophism” and “uniformitarianism” as well as a definition of “good science.”

      I’m really grateful for the education they’re getting, and I wish mine had been like it.


      1. Dr. Hamilton, I wasn’t at all offended by the way you initially expressed yourself. Actually, it is I who ought most to apologize for going off tangentially onto another issue. My mind takes leaps and pursues rabbit trails at times. In retirement, I’m still quite passionate about education and the need for quality instruction, and I have prayerful hopes for excellence in Christian education. Christianity doesn’t need artificial crutches; the Truth can withstand any test. Going beyond speaking just about the education of children, I’d hearken back to your own recent posts and those of other brothers in Christ who’ve spoken about reading actively/interacting with powerful, thought-provoking literature by someone suchas Camus or McCarthy/
        Thank you for your blog. I’m always blessed and often challenged by what you share.

  2. Jim,

    My son is in Classical Conversations and we love it! He just finished his kindergarten year and I wish I learned as much on history as he and my wife learned.

    In Christ,

  3. Hi Jim, great debate with Sam Storms and Doug Wilson. I think you won in terms of just plain sensibility.

    I am wondering if the problem with your system (as asked by Piper –> rev 19 and 20) would be solved if raptured saints were taken into account. Yeah, I know you are historic premill, not dispensational, but would that get around the problem of saints in the millennial kingdom?

    Second thing re the spacing between numbers — well, could it have been otherwise (given atheism for instance)?

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