Posted by: Alexandre Borovik | April 16, 2010

Some pre-school proto-mathematics

I already knew I was dumber than the fifth graders…but now it’s the preschoolers


Which way is the bus below traveling?

To the left or to the right?

Can’t make up your mind? Look carefully at the picture again.

Still don’t know?

Pre-schoolers all over the United States were shown this picture and asked the same question
90% of the pre-schoolers gave this answer.

“The bus is traveling to the left.”

When asked, “Why do you think the bus is traveling to the left?”

They answered:

“Because you can’t see the door to get on the bus.”
How do you feel now ???

I know, me too.

Have a nice day!



  1. Sadly the images are missing from this post for me.

  2. Gareth, can you see it now? I tried to fix.

  3. Damit xD I feel ashamed ^^
    Maybe it’s because of our age or let’s call it “experience” that we simply think too complex.
    Preschoolers are more simple minded or don’t think at last so far as we, so they’re seeing this trivial thing, while most of us simply trying to search for something more complex to solve this problem.

    I hope I’m right xD

  4. Ha-ha-ha-ha!

  5. Yes, images working now. Thanks. Haha!

  6. Nice one:-)
    But you live in UK, don’t you? So for you the US answer is obviously wrong.

    • A very good point. But what is left and what is right is irrelevant here. What is important is that children see the difference. For them, left and right are not absolute, they are logical constructs anchored to a wider context. Preschool children still remember how they were taught to tell a left boot from the right one.

      • I have seen this puzzle before, but I remain somewhat skeptical of the notion that for children “left and right are not absolute, they are logical constructs anchored to a wider context.” Such a notion might well explain why 90% of American preschoolers were able to answer the question correctly – by the way, is there a reliable source for that figure? – but there is a much simpler explanation at hand: preschoolers travel by school buses five days of the week, and therefore, the routine of getting on and off a bus is quite firmly imprinted on their minds. Thus, they can answer the question almost reflexively. On the other hand, how many adults really use buses in the US? A small proportion, I believe. No wonder, whatever imprinting happened during their preschool years fade away with the passage of time.

  7. Indeed, I would be most happy to see any confirmation of the statistics claimed — it looks slightly fishy to me. And I agree with Vishal — American children could perhaps answer the question on an instinctive level. And when I am talking about “wider context” I of course refer to everyday experiences of children — I lived in America, and my children were taking school bus, and this very obviously was an important part of their lives.

    As I have already said in I need your stories I collect childhood stories of mathematics; a whole chapter in my book is devoted to the problem of telling left from right. It appears to be a difficult task.

  8. I looked at I need your stories and discovered this comment:

    When I read your request, I thought I’d never had problems with math when I was young. But, like Tommi, I couldn’t remember which way division went. Of course, it’s made harder by the fact that it goes either way, depending on the symbol: 6 divided by 3 is the same as 3 gazinta 6.

    But my inability to remember that didn’t get in my way. If I saw a division problem with harder numbers, I just put 3 and 6 in their place for a moment, to orient me, and then I knew what was being asked.

  9. think like preschoolers. don’t think too much! hahaha..

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