FeedsThinking in a logarithmic scale
In a recent study published in Cognitive Psychology, John Opfer and Robert Siegler conducted experiments on how children place numbers on a number line from 0 to 1,000, with only 0, 500, and 1,000 marked on it ahead of time. The children were asked to place several numbers on the line, each time with a new, blank number line in front of them. The perhaps not too surprising result was that second graders are wildly wrong, while fourth graders are fairly spot on. This probably has a lot to do with experience, more advanced abstract reasoning abilities, and so on.
The surprise, however, is how well the second graders' answers fit a logarithmic scale, such that the distance between numbers decreases as the numbers increase. In fact, the best fit logarithmic estimate of the median values explained 95% of the variance between numbers. The interesting thing about this result is that such a structured approach to number placement must be innate, since it was definitely not taught to the children. If anything, one would expect them to have already been taught to structure numbers linearly.
The study did not end there, however. The scientists took those second graders who best fit a logarithmic scale and attempted to teach them to place numbers linearly. They did this by showing the correct position when they were off by a large enough margin. When there was a large variance, something seemed to have clicked in the child's brains and they almost immediately started placing numbers linearly, and the change was effectively permanent, causing the students to place the numbers correctly thereafter without additional coaching needed.
All in all, a fascinating study.
(via Cognitive Daily)
Stumble It!We use Markdown to style our comments. **This is bolded.** *This is italic.* [This is a link](url)
For more options,
try reading the
wikipedia article or the
official style guide.
Comments
Comments from site editors have a darker background than comments from everybody else.That correlation way cool. It also makes a lot of sense if you look at the way that a kid will categorize things into "small" "medium" "large" and "way large" groups -- if they've never seen them laid out linearly before it doesn't make a whole lot of sense to think of it that way. I'm surprised they learned so quickly, actually. I wonder if they would have forgotten it and gone back (at least partway) to the log. model if they were tested again the next week.
Also it doesn't say and I can't read the original article but did they give them different numbers to place every time? just checking.
We use Markdown to style our comments. **This is bolded.** *This is italic.* [This is a link](url)
For more options, try reading the wikipedia article or the official style guide.
Another thing about how quickly they learned. I remembered (ok, with the help of my developmental psych textbook) that kids around 7-8 years old are capable of judging strategies before they can implement them -- so it may occur to a kid that linear ordering makes just as much sense as the grouping they were using before, but that's part of the reason I'm curious if a second test phase would show the same results.
We use Markdown to style our comments. **This is bolded.** *This is italic.* [This is a link](url)
For more options, try reading the wikipedia article or the official style guide.
Each child was asked to place the numbers 2, 5, 18, 34, 56, 78, 100, 122, 147, 150, 163, 179, 246, 366, 486, 606, 722, 725, 738, 754, 818, and 938. These numbers were presented above the number line, each on a separate page of a workbook.
The scientists who wrote up the article speculate that the children created an analogy between the 0-100 line (which according to previous research children represent linearly) and the 0-1000 line.
I also would like to see how long the change in approach lasts. Unfortunately, the paper doesn't discuss this option at all.
We use Markdown to style our comments. **This is bolded.** *This is italic.* [This is a link](url)
For more options, try reading the wikipedia article or the official style guide.
If they placed the same numbers post-teaching-phase, that's pretty crappy. They might have just memorized the numbers. They should have used different numbers... ahh nitpicking
We use Markdown to style our comments. **This is bolded.** *This is italic.* [This is a link](url)
For more options, try reading the wikipedia article or the official style guide.