Define “Textbooks”

Valerie Taylor asks good questions that get me thinking.

On Fri, August 12, 2011 I wrote:

Taking discussion to [IAEP] mailing list.

On Fri, August 12, 2011 6:26 am, Valerie Taylor wrote:
> I have been trying to piece together a Science “textbook” replacement.

Please bring your efforts into this public discussion. We would like to hear your ideas, which might help us in other projects, and we might have ideas that you can use. I hope that some of us can put your ideas to children and get their feedback also.

> I’m assuming that this should be learner-centered content – much like
> textbooks that are distributed to students. However, finding OERs for
> student use is challenging. Much of the information is for “teaching”
> – rather than for “learning”.

Exactly so. However, there are some teachers who “teach” physics primarily by asking questions for students to work on together, and occasionally providing hints. I suspect that we could teach physics using only questions commonly asked by children, but that would require a research project.

> Textbook “adoptions” normally come with vast amounts teacher
> materials, teacher’s guide, lesson plans, powerpoint slides, videos,
> training, resources, teaching strategies, references, even equipment
> in some cases.
> What’s the plan for Replacing Textbooks? How much of this
> infrastructure is required? What is “nice to have”?

None of it is absolutely required. All of it is nice to have. (Except no PowerPoint when we have Open Office/Libre Office Impress, Scratch, Turtle Art Portfolio, and so on.) One approach would be to collect and curate such materials from students, teachers, and volunteers. We must also, wherever we can, show how to link our approach with existing curriculum topics and sequences.

Here is a question that has been successfully asked of first-graders. Note that we are not requiring precision in the answers. A sphere is close enough. Any child who proposes an ellipsoid is well ahead of the game. Any first-grader who knows that the ellipsoid is inaccurate is either from a family of scientists, or is a genius.

How can you tell what shape the Earth is?

You should get at least five different answers back from any first-grade class that is exposed to TV and the Internet, preferably more. Here are ten of mine.

  1. The shadow of the Earth on the Moon in an eclipse is round.
  2. The Earth looks round from space.
  3. Things disappear below the horizon as they move farther away. The bottom disappears first.
  4. The horizon is further away the higher up you get. Thus crows’ nests on sailing ships, and broadcast antennae on the tops of the tallest buildings.
  5. Shadows are longer as you go further north or south from the equator. There is a band around the equator where the sun can be directly overhead twice a year. (Eratosthenes used that fact to measure the size of the Earth.)
  6. Every object in the Solar System above a certain size is round.
  7. Satellites going around the Earth in any direction can have circular orbits at nearly constant height.
  8. Laser measurements on the Golden Gate Bridge show that the tops of the towers are further apart than the bottoms.
  9. Gravity is perpendicular to the ground wherever it is level (not the same as flat), and to the surface of the ocean. The only surface which is perpendicular to all of the lines through its center is a sphere.
  10. If you put sticks of the same height into a straight canal a mile or more apart, and look from one end to the other, the line joining the tops of the two outer ones intersects the middle one well below the top. (This was done as a challenge to the Flat Earth Society in England. They denied that it had anything to do with the question.)

How much other math or physics do you have to know in order to understand each of these? The Earth’s shadow is the most direct, and was well known to Greek astronomers. Some of these require an understanding of geometric optics or of gravity. Number 9 uses a non-trivial mathematical fact.

It turns out that the Earth is not quite spherical, due to rotation, as was known to Newton. (Galileo observed the same phenomenon when looking at Jupiter.) It further turns out that the shape of the Earth varies very slightly with rock and ocean tides, and that there are a number of other factors involved. So here is a sequence of cross-disciplinary questions for high school students, involving deep issues of philosophy and psychology.

  • How much is known about the exact shape of the Earth?
  • How do we make such measurements?
  • How much is not known?
  • Can we get better information?
  • What are the sources for the answers to the above questions?
  • What ideas exist that contradict this knowledge, in addition to Flat Earthers? (Hollow Earthers, Inside-Out Earthers…)
  • Why do people believe such things? (along with UFOs, circle-squarers, angle trisectors, AIDS deniers, cold fusion, evolution deniers, Global Warming deniers…)
  • Can we refute these ideas? Is there anything to any of their objections? (A vital part of scientific method)
  • Will they accept your refutations?
  • Do you know anybody who believes something that is obviously not true?
  • Is there anything that everybody around you believes that you suspect isn’t so? (Plate tectonics was obviously nonsense when I was a child, because solid rock can’t move around, but became obviously true when mid-ocean volcanic spreading was discovered.)

It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.

Frequently attributed to Mark Twain, and often to Artemus Ward, Josh Billings, Will Rogers, Satchel Paige, as well as others.


About mokurai

Generalist; End poverty at a profit for all
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1 Response to Define “Textbooks”

  1. David says:

    It’s interesting that you mentioned plate tectonics, which became part of the standard school curriculum by the 1970s.

    Yet schools today teach few of the methods to even think about the mathematics of Galois, Minkowski, Turing or any other breakthroughs of the last two hundred years. I know our kids can only spare a few hours a week to learn math, but do we want to give our youth the impression that it is unimportant that such things not only transformed humanity’s understanding of pure thought, but revolutionized our influence on the natural world? Perhaps they don’t need to be ready for the new and unimagined applications of mathematical thinking that the next century will bring.

    (I fear the next generation will also get the impression that geographers and geophysicists are an order of magnitude more in touch and relevant than mathematicians.)

    I hope for yet more visionary teachers, and enlightened bureaucrats, who will ensure this is not so.

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