Kindergarten Geometry Challenge: What Shape Is This?


Don’t bother to count the sides.

Don’t try to think of what prefix to use.

I learned the “correct” answer from other parents who pulled their children out of school for homeschooling.

If you thought this was an octagon, I’m sorry to say that you were way off.

It’s a stop sign, of course.

Even though it’s not red.

Even though it doesn’t have the word STOP anywhere on it.

If your kids watched Mickey Mouse Clubhouse or Team UmiZoomi in preschool, this could be a little confusing, since those preschool shows actually use the technically correct words for these shapes (Mickey even teaches the names of 3D shapes).

Maybe those words become more challenging when the kids enter kindergarten.

All I can say is:

Please, oh please, octagon teaching our kids the wrong words!

Octagon it!

Between this and my previous post, I know we’ve said enough and have probably said too much.

Perhaps this merits a moment of silence instead…

Too Much Knowledge Should Be Punished, Right?

Too much knowledge

My daughter is 5 years old. She’s in kindergarten. Today she received her first report card.

One of the categories was shapes. The teacher assessed her knowledge of shapes for the past 9 weeks with a single 9-question test.

My daughter got 7 of the questions right, but somehow managed to earn a score of 2 out of 4.

Anyway, the two questions that she got wrong were box and can.

My daughter called the box a cube and she called the can a cylinder.

So instead of 4 out of 4, she has a score of 2 out of 4. Definitely, my daughter needs to improve her geometry skills.

It would be a shame if our students were to learn the precise terminology. How awful the world would be then.

The better thing, education seems to advocate, is for everyone to know just the material that will be taught on standardized exams. Let’s dare not learn something more or better, which may result in selecting incorrect answers on those precious multiple choice exams.

(It’s not a point I will debate with the teacher. It might make matters worse for my daughter in other ways. You have to be reasonable to be reasoned with. By the way, I am myself a teacher.)

* * *

This reminds me of another story. At the time, I was coach of a high school quiz bowl team at a math & science school for gifted juniors and seniors.

The team was competing in the state finals at the local university. The event was open to the public, and many parents and friends were in attendance.

One of the questions was a physics question. In case you don’t know, I have a Ph.D. in physics and I’ve been teaching physics for a dozen years. (I presently teach at the university.)

One of the students on the team was among the best students in my class. He answered the question promptly.

The question asked for the direction of centripetal acceleration.

My student answered, “Inward,” with a big smile, knowing that his answer was correct.

The judge said it was incorrect. The correct answer was “toward the center,” not “inward.” A little piece of paper with the words “toward the center” printed on it proved her point.

To complicate matters, the scorekeeper spoke up. It turns out that the scorekeeper was a math teacher. The scorekeeper indicated that she felt that inward and toward the center may both be correct answers.

But the judge decided that nothing was better than going by the exact answer printed on her sheet of paper, so inward was, in fact, incorrect.

What’s really funny is what happened immediately after the student said, “Inward.”

The judge stalled for a moment. After this silence, the student added to his answer, saying, “Negative r-hat.”

I just about slapped my forehead when I heard that. He was in the calculus-based physics class, where I had derived the equation for centripetal acceleration using polar coordinates and polar unit vectors. The mathematical way of expressing the acceleration vector in uniform circular motion is with “negative r-hat.”

He was right, but it probably didn’t help his cause.

(I kept my mouth shut the whole time because nothing good will come from complaining to a person who is in charge and showing signs of stubbornness. The last thing you want is to get disqualified, dismissed, not invited back, or to build a bad reputation for the school.)

* * *

Now for my peace of mind I shall have to read one of those treasured classics that foretell of a world that nearly succeeds in eliminating creative free thought, but, fortunately, doesn’t quite.

Please forgive my rant. If you’re familiar with my blog, you know that I prefer to write something that may be helpful and usually don’t rant. But tonight I could think of nothing else, so rant I did. 🙂

Chris McMullen

Which Came First: The Painting or the Artist?

It probably seems pretty obvious that the following evolution occurs:

  • The artist first conceives of the idea, perhaps in the artist’s mind’s eye.
  • The artist selects a suitable medium.
  • The artist creates the masterpiece.

In the previous ordering of events, the artist clearly came before the painting.

How can it possibly be any other way?

Please allow me to present a fascinating alternative. I’m not asking you to change your beliefs. You may consider this to be just for entertainment purposes, if you will. (However, if you want to incorporate this into your own philosophy, feel free.)

Consider this possibility (or impossibility, or whatever you may prefer to call it):

  • The Mona Lisa is transcendental. It always has been and always will be.
  • The Mona Lisa selected Leonardo Da Vinci as a suitable medium.
  • The Mona Lisa channeled itself through Leonardo Da Vinci, bringing the artist to life.

Is it really such a stretch?

Perhaps I worded it the wrong way. Using the word ‘channeled’ probably wasn’t the best idea. Let’s consider something simpler for a moment.

How about a triangle or a dodecahedron? These geometric shapes have always existed, right? They weren’t ‘invented’ by the first human to draw them.


A painting consists of shapes, colors, and textures put together. Can you insist that a triangle existed before geometricians, but that a painting doesn’t exist until the artist paints it? What if the artist paints a cube?

Another point to consider is that every artist has human experience. The ideas and visions that we have are very much shaped by our experience. So a painting is not a totally brand new vision, but a product of the artist’s human experience. Even if we paint something that seems out of this world, it’s inherently affected by our experience in this world. In a sense, the art has been developing within the painter for many years before it ever touches the canvas.

If I could paint, I would try to paint a picture of a Klein bottle in an Escher-like fashion such that it looks like both a chicken and an egg transforming into one another. It would have been the perfect image for this post. Instead, you’ll just have to envision that in your mind. Perhaps someday an artist will paint this picture. If so, remember that I already gave birth to the idea. Or has it always been there?

Chris McMullen, author of The Visual Guide to Extra Dimensions and A Visual Introduction to the Fourth Dimension (ironically, perhaps, these are conceptual geometry books, not philosophy books)