# Appraisal of children's facial expressions while performing mathematics problems van Amelsvoort, Marije; Krahmer, Emiel

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5 Procedure Participants individually saw the film with 114 fragments on a laptop. They were told that the children on the film were solving an easy or a difficult math problem, and that they, as viewers, had to guess how much difficulty the children experienced with the math problem. Participants first saw a trial version of eight fragments, during which they could ask for clarifications. Then they saw the actual film with 114 fragments. Before each fragment, a number was shown together with a sound, to indicate a new fragment was starting. Immediately after each fragment, participants were asked to fill the question on the child s experience of difficulty-level on a seven-point scale. They had three seconds to score the fragment. After 57 fragments, participants were allowed a short break. Results The scores for the two versions of the film we made to prevent order effects did not differ significantly, so we combined the results of both versions. We found a significant difference between easy and difficult problems on the perceived difficulty level. This means that participants rated children s reactions to difficult problems indeed as indicating a high difficulty (M = 3.31, SD = 0.15), and their reactions to easy problems as indicating low difficulty (M = 6.44, SD = 0.07), F(1, 30) = , p <.001, ŋ 2 =.96. Results show a significant difference between grades on perception of difficulty level. According to the participants, group 7 children showed higher levels of difficulty in their expressions (M = 4.79, SD = 0.07) than group 4 children did (M = 4.96, SD = 0.08), F(1, 30) = 17.89, p <.001, ŋ 2 =.37. There was also a significant interaction between grade level and difficulty level, F(1, 30) = , p <.001, ŋ 2 =.91, indicating that the perceived differences between easy and difficult problems in facial expressions is higher in group 7 than in group 4 (see Figure 3). Analysis of Facial Expressions The results of the perception experiment suggest that adults can perceive whether children find a given math problem easy or difficult by watching their face. The results also suggest that facial expressions vary with age. To further investigate which facial expressions children show and whether these are related to the results of the perception experiment, we analyzed the facial expressions of the children in all 114 fragments. The 114 fragments of children s reactions to math problems were coded on five facial expressions: (1) smiling, (2) gaze, (3) frowning, (4) funny face (a marked facial expression, which diverts from a neutral expression, Swerts & Krahmer, 2005), and (5) visual delay in answering. Verbal clues were not included in the analysis. The features are loosely based on some of the Action Units (AUs) described by Ekman & Friesen (1978) to distinguish facial expressions and the facial muscles involved. Of the visual features under consideration here, smiling is related to AUs 12 and 13 and gaze to AUs Frowning is related to AUs 1 and 2. Funny faces typically consist of a combination of AUs such as lip corner depression (AU 15), lip stretching (AU 20) or lip pressing (AU 24), combined with eye widening (AU 5) and possibly brow movement as well. Representative examples of these facial expressions are displayed in Figure 2. For every fragment, the five expressions are scored as present (= 1) or not present (= 0). Each reaction to a math problem could thus score a minimum of 0 facial expressions and a maximum of 5 facial expressions. Results Table 1 shows the frequencies (114 fragments) of shown facial expressions, split by difficulty level of the math problem and group level. On average, children show significantly fewer expressions when they are faced with an easy problem (M =.32; SD =.51) than when faced with a difficult problem (M = 1.91, SD = 1.01), t(112) = , p <.001. Smiling occurs both when facing easy and difficult problems, t(112) = 1.25, p =.21, while all other facial expressions occur significantly more often when a problem is difficult than when it is easy (p <.001). There is no significant difference in amount of expressions shown between group 4 and group 7, t(112) = -.51, p =.61. A significant strong negative relation (r = -.81, p <.001) was found between the perceived level of difficulty and the facial expressions. This means that participants think that children are solving simpler problems when they show fewer facial expressions. Figure 3. Perception of difficulty level for easy and difficult math problems inferred from facial expressions in two group levels. High scores indicate the problems were easy, low scores indicate the problems were hard. 1701

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