Hello Fellow Hedonists,
On one hand, recently, it has been demonstrated that success at mental arithmetic isn't just a question of mathematical skill and knowledge. Self-efficacy, your belief that you have the ability to attain certain goals, plays an important role as well. Bobby Hoffman and Alexandru Spatariu claim that their research is the "first study that we know of to demonstrate the effect of self-efficacy on problem-solving efficiency when controlling for background knowledge."
Study: Hoffman and Spatariu tested the basic multiplication abilities of 81 subjects, as well as their confidence in performing mental multiplication. They gave the subjects twenty easy and twenty difficult multiplication problems to perform in their heads. Half the subjects were given so-called "metacognitive prompts" during the testing (for example, the computer screen on which they were being tested would flash up prompts like "What steps are you using to solve these problems?").
Conclusion: Self-efficacy and general ability made unique contributions to success at the easy and difficult multiplication tasks, in terms of overall accuracy and efficiency. Subjects with higher ability and greater self-belief performed more quickly and more accurately. For the harder multiplication task metacognitive prompting actually boosted accuracy and efficiency!
Hoffman argues that this data provides us with reason to believe that "In learning situations there is a natural tendency to build basic skills, but that is only part of the formula. Instructors that focus on building the confidence of students, providing strategic instruction, and giving relevant feedback can enhance performance outcomes."
Burton points out that the reward system responsible for addiction also provides the positive feedback necessary for us to learn: "the brain has provided us with a wide variety of subjective feelings of reward ranging from hunches, gut feelings, intuitions, suspicions that we are on the right track to a profound sense of certainty and utter conviction. And yes, these feelings are qualitatively as powerful as those involved in sex and gambling. One need only look at the self-satisfied smugness of a 'know it all' to suspect that the feeling of certainty can approach the power of addiction."
Burton argues that we need to recognize that the feelings of certainty and conviction don't reliably indicate whether our beliefs are accurate. Intuitions, gut feelings and hunches are neither right nor wrong a priori: they must ultimately be submitted to a posteriori empirical testing. If such testing isn't possible, then we should think of an intuition as an opinion rather than fact.
Burton gives a great example to illustrate his point: "Perhaps one of my favorite examples of how certainty is often misleading is the great mathematician Srinivasava Ramanujan. At his death, his notebook was filled with theorems that he was certain were correct. Some were subsequently proven correct; others turned out to be dead wrong. Ramanujan’s lines of reasoning lead to correct and incorrect answers, but he couldn’t tell the difference. Only the resultant theorems were testable."