Kids and The Importance of Ideas

In One World Schoolhouse, Sal Khan emphasizes that real learning–the kind you don’t forget five minutes after the test–requires integration of ideas.  His book focuses on applying this concept to group schools, but I think it has implications for homeschooling too.  He uses the example of math and science:

Genetics is taught in science while probability is taught in math, even though one is really an application of the other.  Physics is separate from algebra and calculus despite its being a direct application of them.  Chemistry is partitioned off from physics even though they study many of the same phenomena at different levels…the breaking up of concepts like these has profound and even crucial consequences for how deeply students learn and how well they remember.

I’d take it a step further:

All subjects are integrated.

History, political change, philosophy, science, math, art, and literature happen together in historical eras.  None of these disciplines exists in a vacuum.  And, I would venture to add, you can’t really  understand what was going on in one area without understanding what was happening in other areas.

Educational “subjects” are a modern invention.

Khan hits this point as well, and he’s correct.  In times past, it was common for mathematicians to write about metaphysics (beliefs about ultimate truth, good, and God, among other things).  Early scientists were also philosophers.  Artists and writers reflected on political and social changes and helped to shape ethics.  It wasn’t until fairly recently that we broke everything down into rigid “disciplines” and “subjects” and while it helps to break up a school day, I think it was a detrimental development.

Ideas link subjects – even for little kids.

While some classical educators believe that kids should be filled with facts as “pegs” to hang ideas on later, I think on the contrary kids should be given ideas as pegs for their facts.  That’s more of a Charlotte Mason idea, but I think it has bearing on classical education too.  Learning facts along with the ideas that link them together makes the information more easily understood and helps the child to retain it and build on it.  Obviously older kids can analyze and interact more deeply with ideas, but even preschoolers can begin to make astute connections between different events and subjects if you help them think through great ideas.

How can you teach with ideas and integrate subjects?

Basically, teaching with ideas involves giving kids context for what they learn, and not artificially stovepiping information.  One thing I love about Tapestry of Grace is how it organizes subjects chronologically–so you learn what was going on in government, economics, literature, art, and science in any given historical period.  Just learning a timeline has some value, but when you can add in discussions about what caused new developments, how one area of knowledge impacts another, and why historical figures acted as they did, you give some weight and context to dry dates and rote memorization.  I’ve found that my kids retain the timeline much better when we do this, and conversely that knowing a timeline helps them to put what we’re reading about in-depth into the context of the broader scope of history.

If you don’t homeschool…

No matter what sort of school your kids attend, you can still encourage them to find connections between subjects.  I think just talking about context goes a long way, but you can also often find fiction and non-fiction books that shed more light on what was happening and what life was like in different time periods.  A fabulous resource for all time periods are The Story of the World books (get them on audio and kids can listen by themselves or you can listen together in the car.  Worth every penny!).  Sal Khan had some great ideas in his book for how schools could foster idea-based subject integration too.

What do you think about ideas and integrating subjects?  Is it something you do with your kids, and how do you do it?


Disclosure: I’m a Tapestry of Grace affiliate because I love the program so much–if you purchase something through the link in this post, I do get a credit from the company.  Thanks for supporting A Spirited Mind!

2 thoughts on “Kids and The Importance of Ideas

  1. Having taught math, I find it easiest to integrate math and science. For example, conversions go hand-in-hand with concepts in Algebra. I think sometimes, however, it is best for a student to master the basics in math and then applying to science. I say this because as I was getting the students to understand how solving for equations worked (thus using more traditional methods to get those concepts mastered first), the science teacher jumped straight to cross-multiplying, which is a great method and often easier for a good number of students, but it jumped over the understanding of why it worked. Algebra is so easy to apply to everything though–Physics, Chemistry, even grocery shopping (comparing unit prices!). There goes my dorky excitement!

    From my own education, taking Calculus first and then taking Physics was a much better way to do it so that you could flow through the physics concepts and not waiting on mastery of a complicated math skill to continue on–I understood the math concept and how it worked, not just how to mechanically solve problems using them, and learning those skills did not distract from how they applied to Physics. But definitely pointing out that these skills are related is useful. I also think that our Calculus books had “challenge” or word problems that applied the concepts to scientific concepts. Not done particularly well probably, but we were always aware that you have to have a firm grasp on mathematical concepts to be able to apply them to the science. In any case, I am a bit biased as a former math teacher so really think many math topics require individual focus and then application after that point. But definitely agree that you need to call attention to the fact that you are not learning math for the sake of learning math but because it applies to so many different areas of science and life!

    I had a course in high school that integrated history, literature, art, and music. Each class was taught separately but moved chronologically together–we had 1 hour lecture on a different topic each day and then the 2nd period was in seminars. It was AWESOME. By far one of the best classes I have ever taken. There, you do not have to wait necessarily to master a topic before being able to apply it and understand it in the other context, so I can see a far more integrated approach. In fact, learning about, say, the Rococo period in all topics helped master and reinforce understanding of the concepts.

    1. Frances, you should definitely read Khan’s book–I would love to hear your thoughts on it.

      I think you’re right about learning an in-depth concept in math and then applying it, but I also think it’s really helpful to know the broader context of the idea, where it came from, and what it led to. Remember those Humanities classes I took for a couple of years with the over 1000 pages of reading a week? It’s not that we were sitting around working through the mathematical and scientific concepts, but it was AMAZING to see the way that math and science developments fit in with the larger scope of history. I think it would be very helpful for students to have a framework and a context for math and science, so that while they are focusing carefully on say, geometry or physics, they can have in mind the way that Euclid or Newton or whoever fit into time, the consequences and context of those ideas, what made them revolutionary, etc. It just makes for a much richer and more complete education, at least in my mind.

      So I don’t think that the in-depth study needs to happen at exactly the same time to be integrated, but integrating the history of science and math with other historical developments, and linking the eventual application to the in-depth study, would be helpful.

      But seriously, read the book. I’m really interested to know what you think of Khan’s ideas!

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