When you can’t count on arithmetic density, why not?
From the ABC’s Math and Science blog: A new study from the University of NSW, published today, suggests that in certain situations, counting is easier than counting in mathematics.
The team, led by Professor Ian C. White, used mathematical models to test how well an individual could compute the number of times they had counted, in addition to how well they could remember how many times they have done the calculation.
The result is that people can be counted more accurately on average than mathematicians have been able to predict.
“A lot of people have looked at the mathematical results of a person counting or counting in their head, and they’ve found that they’re better at doing it, but we’re not always able to accurately predict that individual’s ability,” said Professor White.
“So we thought we’d try to figure out whether that was true for people who were not being counted.”
The researchers used a mathematical model to test the ability of participants to perform a series of arithmetic tasks.
The mathematical model involved three sets of arithmetic rules, which they used to determine how well each participant was able to compute the numbers.
For example, they used a set of rules to calculate how many numbers there were in an array of integers and the sum of the integers in that array.
They also used a model to calculate the number 1 in an integer array and the number 0 in a list of integers.
“In this way, it was possible to take the individual performance measures and compare them to the average performance of mathematicians in a series that were used to measure a person’s mathematical ability,” Professor White said.
“We found that people who are very good at performing these arithmetic tasks tend to perform better than average in mathematics.”
The study was published in the Journal of Mathematical Psychology.