One of Jimmy’s favorite toys as a toddler was a simple little bucket of blocks. There were three shapes: a rectangular prism, a triangular prism, and a cylinder. The bucket’s lid had three holes: a square, a triangle, and a circle (The picture at right was the only one I could find online — this sort of toy has gotten much fancier in recent years).
For an adult, it’s a simple matter to properly sort the shapes by placing them into the corresponding holes, but for a toddler, it’s a real challenge. It took months before Jim was able to put any of the blocks through the holes, despite countless demonstrations by his parents. Maybe parents have a special sort of magic that kids just can’t do.
But eventually — perhaps by accident — Jimmy managed to get a cylinder through the round hole. Eureka! The puzzle was solved. He put another cylinder through the hole, and another. Aha! All you need to do is put the objects through the round hole. The others are decoys. Next he attempted to put a rectangular prism through the round hole. To his amazement, this didn’t work, even when he applied so much force that his little body shook from the effort. How about the triangular prism? This didn’t work either. He confirmed that indeed, the remainder of the cylinders fit through the hole. Apparently triangular and rectangular pieces required a different strategy. A smile of realization crossed his face.
Confidently, Jimmy tried his new solution. He removed the lid to the bucket and placed all the triangular and rectangular blocks into the bucket, one by one. Then he replaced the lid and looked to his parents for approval. He had finally solved the puzzle, hadn’t he?
It would be several weeks before Jimmy was able to properly sort all the blocks. Even after he had solved the puzzle once and for all, he still played with it for some time afterwards, as if to confirm that the rules of geometry he had carefully sorted out, hadn’t changed.
Perhaps surprisingly, it wasn’t until 2007 that a systematic study of this simple problem was undertaken. Helena Örnkloo and Claes von Hofsten presented 69 infants aged 14 to 26 months with a similar problem while carefully monitoring their attempts to solve it. Instead of just three shapes, they used seven, each progressively more difficult:
Their box was designed to accommodate just one shape at a time. The toddlers were given one block, along with the box and a lid with a hole shaped to match the block, and encouraged to insert it. First the block was oriented vertically, so all the child had to do was pick it up without re-orienting it and place it in the hole. Here are the results:
The 14-month-olds were only able to handle the cylinders with any regularity, and things didn’t improve much for the 18-month-olds. But somewhere between 18 and 22 months, nearly all the children showed a tremendous improvement. by 26 months, almost all the shapes were solved quite easily. But this was a relatively simple problem. Next the blocks were lain on their sides, so that some manipulation would be necessary in order to fit them in the box.
Now 14-month-olds did even worse, and there wasn’t much improvement at all by 18 months. Again there was a large leap in accuracy at 22 months, except for the triangle block with unequal sides. Even 26-month-olds weren’t able to fit this one through the hole. The unequal sides made the block especially challenging, because this meant that it would only go through the hole in one direction. Most kids simply didn’t get this concept, and just gave up after trying several times putting the first end they tried through the hole.
Örnkloo and von Hofsten took an even closer look at how the toddlers manipulated the blocks, and noticed some very interesting patterns:
- Kids rarely solved the problem by putting the block into the hole and moving it around. Instead they manipulated it in their hands prior to reaching the hole.
- 18-month-olds pre-manipulated some of the blocks and not others, as if in some cases they recognized that a manipulation was necessary and in others they just didn’t get it.
- If a block was pre-adjusted improperly, children of all ages rarely recovered from the error. They seemed to “get it” right away or not.
- Older children were more persistent, but persistence rarely paid off
Örnkloo and von Hofsten say that this all suggests that toddlers are solving the problem through mental rotation, not by physically manipulating the objects. Interestingly, they found no gender difference in the results. So though there is some evidence that older boys may be better mental-rotators than girls, it hasn’t emerged at this age. So this study finds no evidence that any difference in mental rotation ability between boys and girls is due to a genetic or hormonal difference.
Helena Örnkloo, Claes von Hofsten (2007). Fitting objects into holes: On the development of spatial cognition skills. Developmental Psychology, 43 (2), 404-416 DOI: 10.1037/0012-16126.96.36.1994