Success at mental arithmetic isn't purely a question of mathematical skill and knowledge - people's belief in their own ability, known as "self-efficacy", plays a key part too. Bobby Hoffman and Alexandru Spatariu who made the new finding say 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."
Hoffman and Spatariu tested the basic addition and multiplication abilities of 81 undergrad students, as well as their confidence in performing mental multiplication. Next, the researchers gave the students twenty easy (single digit X single digit) and twenty difficult (double digit X double digit) multiplication problems to perform in their heads, in a "reasonable amount of time". In a final twist, half the students were also 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?"
Self-efficacy and general ability each made a unique contribution to the students' success at the easy and difficult multiplication task, in terms of overall accuracy and efficiency. Those students with higher ability and greater self-belief performed more quickly and more accurately. For the harder multiplication task only, metacognitive prompting also boosted accuracy. It sped efficiency too, if the time taken for the prompts to appear and be cleared was not counted.
Lead researcher Dr Bobby Hoffman told the Digest that effective problem-solving requires a unique blend of skills and strategies. "In learning situations there is a natural tendency to build basic skills," he said, "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."
B HOFFMAN, A SPATARIU (2008). The influence of self-efficacy and metacognitive prompting on math problem-solving efficiency Contemporary Educational Psychology, 33 (4), 875-893 DOI: 10.1016/j.cedpsych.2007.07.002