Effects of Emotional Arousal on Mathematical Learning

Realistic “word” or “story” problems represent one of the most difficult areas of undergraduate mathematics learning (Bessant, 1995). The situation is unfortunate as story problems have the power to stimulate interest (De Bock et al., 2004) and connect academics with real issues (Frankenstein, 1990). Story problems may help students to learn high level analytical skills sought after by employers (Harvey, 2001). In a story problem, students decode a written description of a situation, create a mathematical model, and make calculations to answer realistic questions (Pollack, 1978). For example, students might read about a business, write down equations for the revenues and costs, and calculate the maximum profit. Story problems are very common in undergraduate mathematics courses (Ganter, 2001). The details of the story in a problem may affect students’ learning (Boaler, 1994). Winter and DeLong (2006) found that interesting stories led to enhanced recall of non-mathematical facts. In addition, under some circumstances students remembered the calculus significantly better than when learned through uninteresting applications. Winter (2007) found that students who learned algebra through deliberately inflammatory word problems focused on social justice gained significant knowledge of social justice issues and were significantly less likely to fail or withdraw from the course than students who learned through more conventional word problems. Some researchers have suggested that the underlying mechanism producing these gains in learning may be emotional arousal on the part of the learner (Winter & DeLong, 2009). Classic psychological studies have demonstrated that a moderate degree of arousal is associated with enhanced recall under some conditions (Kleinsmith & Kaplan, 1964). We suggest that the emotional arousal produced by certain kinds of story problems may be sufficient to enhance mathematical learning. We propose to carry out an experiment to test this hypothesis. We will use physiological measurements (galvanic skin response) to measure emotional arousal (Montagu & Coles, 1966) and written instruments to measure recall and mathematical performance. We will attempt to find correlations between these quantities. If emotional arousal is a factor in producing learning gains, we expect to see significant, positive correlations. We will employ a two period, randomized trial with cross over design. At the beginning of the experiment, all subjects will take a mathematics test to establish a baseline of mathematical skill and background. One randomly selected group of subjects will learn a mathematical concept through an emotionally arousing story problem. The other group will learn the same concept with no emotional arousal. During the learning phase we will measure galvanic skin response. After a delay, we will measure recall and mathematical learning. The process will be repeated with a second mathematical concept and two new stories, and the roles of the groups reversed. We will employ repeated measures analysis of variance to examine the effects of the nature of the story upon learning, and analysis of covariance to examine the relationships between arousal, mathematical learning and non-mathematical recall while controlling for variables such as baseline mathematical skill.