Show the following five sentences to one group of students:
- A newly-wed bride had made clam chowder soup for dinner and was waiting for her husband to come home.
- Although she was not an experienced cook she had put everything into making the soup.
- Finally, her husband came home, sat down to dinner and tried some of the soup.
- He was totally unappreciative of her efforts and even lost his temper about how bad it tasted.
- The poor woman swore she would never cook for her husband again.
Then show all those sentences except the fourth, italicized sentence to another identical group of students.
Which group of students will rate their passage as more interesting?
For Greg Ashman, advocate of explicit instruction, the question is either a) moot, because learning matters more than interest, or b) answered in favor of the explicit version. Greg has claimed that knowledge breeds competence and competence breeds interest.
I don’t disagree with that first claim, that disinterested learning is better than interested ignorance. (Mercifully, that’s a false choice.) But that second claim is too strong. It fails to imagine a student who is competent and disinterested simultaneously. It fails to imagine that the very process of generating competence could be the cause of disinterest. It fails to imagine PISA where some of the highest achieving countries look forward to math the least.
That second claim is also belied by the participants in Sung-Il Kim’s 1999 study who rated the implicit passage as more interesting than the explicit one and who fared no worse in a test of recall. Kim performed two follow-up experiments to determine why the implicit version was more interesting. Kim’s determination: incongruity and causal bridging inferences.
That fifth sentence surprises you without the context of the fourth (incongruity) and your brain starts working to understand its cause and connect the third sentence to the fifth (casual bridging inference).
Kim concludes that “stories are interesting to the extent that they force challenging but resolvable inferences on the reader” (p. 67).
So consider a design principle for your math classes or math curriculum:
“Ask students to make challenging but resolvable inferences before offering them those resolutions.”
Start with estimation and invention, both of which offer cognitive benefits over and above interest.
[via Daniel Willingham’s article on the brain’s bias towards stories, which you should read]
2015 Jan 11. John Golden attempts to map Willingham’s research summary onto mathematics instruction.