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. Author manuscript; available in PMC: 2024 Jul 18.
Published in final edited form as: Contemp Educ Psychol. 2023 Jul 18;74:102209. doi: 10.1016/j.cedpsych.2023.102209

Feelings on feedback: Children’s emotional responses during mathematics problem solving

Megan Merrick 1, Emily R Fyfe 2
PMCID: PMC10420002  NIHMSID: NIHMS1921449  PMID: 37576469

Abstract

Theories of learning emphasize the importance of both the cognitive and affective state of the learner. The current study focused on children’s affective reactions to corrective feedback during mathematics problem solving. Eighty-seven elementary school children (M age = 7.6 years, 41% female, 68% White) solved mathematical equivalence problems during an online video call and received trial-by-trial feedback on their answers. Trained researchers used children’s facial expressions, tone of voice, and verbal statements to quantify their positive and negative affect on each trial. Overall, children tended to express more positive affect than negative affect. However, negative affect was more prominent when the child was incorrect and received negative feedback, and higher negative affect was associated with lower accuracy and lower persistence on the task. These results provide novel empirical evidence for the role of emotions during children’s STEM learning in a non-evaluative context.

Keywords: Achievement Emotions, Affect, Feedback, Mathematical Equivalence

Imagine a young child solving an equation and then receiving feedback that the answer is wrong. Do you think they will feel sad and disappointed or perhaps energized and excited by the challenge? And do these emotional responses matter for their ability or desire to solve another equation? Theories of learning have emphasized the critical role that emotion plays in academic achievement (e.g., Harley et al., 2019; Pekrun & Linnenbrink-Garcia, 2012), and some evidence suggests that experiencing positive versus negative emotional states can differentially relate to performance in school (e.g., Goetz & Hall, 2013; Pekrun et al., 2017). However, few studies have directly assessed children’s in-the-moment affective responses during problem solving and their associations with performance and motivational outcomes. The goal of the current study was to quantify children’s in-the-moment emotional experiences as they process trial-by-trial corrective feedback during mathematics problem solving and to explore how these emotional states relate to their task accuracy and persistence.

Achievement Emotions and Academic Achievement

Emotional experiences can be common in learning situations as students form expectations about achievement, like wanting to ace an exam or learn a new strategy. Several theories suggest the type of achievement emotion can influence whether they ultimately help (e.g., by motivating a student to study more) or hurt (e.g., by leading the student to quit; Gross, 2015; Harley et al., 2019; Pekrun & Linnenbrink-Garcia, 2012). These emotions can vary along multiple dimensions, but here we focus on one critical distinction in valence, whether the emotion is positive (e.g., joy, relief) or negative (e.g., boredom, shame; see Pekrun, 2006).

Previous research focused on the valence of achievement emotions suggests unique associations between positive emotions, negative emotions, and achievement (e.g., Arsenio & Loria, 2014). For example, one longitudinal study tracked children from Grade 5 to Grade 10 and measured their trait-like stable emotions related to math using self-report likert scale items (e.g., “after a math test I am proud of myself,” “I am annoyed during my math class,” Pekrun et al., 2017). Positive emotions like enjoyment and pride were associated with higher math grades in subsequent years, but negative emotions like anxiety, shame, and boredom were associated with lower math grades. Although informative, these analyses often focus on global trait-like emotions, like how students generally feel about math. But research is needed to assess learners’ in-the-moment state-like emotions in response to specific experiences. Thus, our goal is to focus on the presence of these state-like emotions when experiencing corrective feedback.

Achievement Emotions and Processing Feedback: Theoretical Frameworks

We opted to focus on corrective feedback because emotional responses may be particularly salient in this context (e.g., Goetz et al., 2018; Lipnevich et al., 2016). Feedback is any information about a person’s performance on a task, which ideally is used for attaining a goal. Meta-analyses often demonstrate positive, but highly variable effects of feedback on learning outcomes (e.g., Hattie & Timperley, 2007; Wisniewski et al, 2020). Some of this variability is explained by factors in the external environment – like the task instructions (Fyfe & Brown, 2020) or the content of the feedback message (Butler et al., 2013). Yet, several theories suggest that the learner’s internal environment – including their affective states – may also play a role in explaining these variable effects of corrective feedback.

For example, Feedback Intervention Theory suggests that feedback can direct the learner’s attention in different ways (Kluger & DeNisi, 1996), sometimes toward the task (e.g., What is a different strategy?) and sometimes toward the self (e.g., I am not that smart). When attention is directed toward the self, the feedback can “produce affective reactions that may interfere with task performance” (Kluger & DeNisi, 1998, p. 69). Others have similarly argued that processing emotions (whether positive or negative) can demand cognitive resources in ways that disrupt accuracy on a target task (e.g., Beal et al., 2005).

Some theories focus more specifically on negative feedback, which refers to feedback on an incorrect response or undesirable behavior. Negative feedback has an inherent dilemma – people need to receive negative feedback to know when they are not meeting a goal, but it often produces undesirable consequences (Eskreis-Winkler & Fishbach, 2019). According to one model, negative emotions in response to negative feedback are nearly unavoidable (Ilgen & Davis, 2000). And after experiencing these negative emotions, the learner is faced with the decision to avoid the task or to continue the task with more effort or a different approach. The model suggests that avoidance may be more likely when learners assume the error is due to a stable internal trait, like the lack of ability, or when their goal is to demonstrate competence.

A more recent theory, called the Model of Motivated Feedback Disengagement, builds on this work (Grundmann et al., 2021). It also suggests that negative feedback will produce negative affect. In turn, the model suggests this negative affect will increase the salience of hedonic goals (e.g., the desire to feel good), which can lead to disengagement strategies, like quitting the task or using distraction, in order to avoid more experiences of negative affect. These theories provide excellent frameworks for thinking about the constellation of feedback, affect, and learning. However, they are fairly broad in scope, intending to capture these relations for multiple types of learners (e.g., children and adults) in multiple contexts (e.g., school and the workplace). Empirical evidence is needed to verify these theoretical assumptions.

Achievement Emotions and Processing Feedback: Empirical Research

What empirical research exists on learner’s experience of affect in response to feedback? A fairly large literature has examined how students perceive the value of assessments and feedback, and has sometimes had them reflect on their emotional responses to different forms of assessment (e.g., Lipnevich & Smith, 2009; Rowe & Fitness, 2018; Ryan & Henderson, 2018). However, little work has directly measured learner’s affect in response to in-the-moment corrective feedback messages and compared it to their affect during general problem solving. Here, we outline the four existing studies that most closely resemble this approach, but note that all of them relied on self-reported measures of emotional experiences.

Comer (2007) had undergraduate students engage in problem-solving using a computer simulation program (e.g., you are a Fire Chief needing to put out fires). The students received feedback based on their performance (e.g., “You are at 59% and that is below the goal”) and then self-reported their mood. This feedback from a person influenced mood; the more negative the feedback message, the more students reported being sad. Two other studies focused more directly on enjoyment. In one study, kindergarten students completed literacy games on a tablet – once with immediate corrective feedback and once without (Muis et al., 2015). After playing each version, students self-reported their enjoyment. For one sample, feedback decreased children’s enjoyment and for a second sample it had no effect. In contrast, a different study with fifth and sixth grade children found that feedback increased students’ enjoyment (Kuklick & Lindner, 2021). These students answered science questions with or without corrective feedback. Ratings of enjoyment were higher when feedback was provided, but only for students with high levels of performance who tended to receive positive feedback. These studies suggest that feedback can influence affect (e.g., experiencing more sadness or less enjoyment), but they fail to correlate these emotional experiences to any learning outcomes.

A fairly recent report also found that feedback can enhance negative emotions, but suggested these emotions were motivating (Lipnevich et al., 2021). In this study, undergraduate students completed a writing assignment, and one week later they received feedback, rated their emotions, and then revised and resubmitted the assignment. The feedback always included written comments, but for some the comments were accompanied by an explicit numerical score. Receiving the numerical score feedback increased students’ negative emotions, though the indirect effect of negative emotion and subsequent performance was positive. Thus, in some cases, the experience of negative emotions may be motivating for students to improve.

These four studies provide a foundation for the importance of examining emotions in response to corrective feedback. However, the associations between these emotions and performance remain largely elusive. Previous work tends to rely on indirect, self-report measures of emotional reactions, and only rarely correlates the emotions with direct measures of learning and motivation. Several researchers have noted this gap and have called for future research in this area (e.g., Fyfe et al., 2022; Shute, 2008). For example, Lipnevich and colleagues (2021) note: “It is even more important to find out how these affective responses link to student performance on a task. In other words, more research is needed to establish the relation between these two constructs; in particular, understanding how different forms of feedback affect emotional responses in students can be particularly useful, with subsequent examination of links to performance outcomes” (p. 2). Our general aim is to help fill these gaps and provide an empirical test for theoretical claims about the role of affect in learning from feedback.

The Current Study

The specific goal of the current study was to quantify children’s in-the-moment emotional experiences as they process trial-by-trial corrective feedback during mathematics problem solving and to explore how these emotional states relate to their accuracy on the task and their persistence to keep going. To better isolate how feedback influences affect, we (a) directly measured children’s emotional responses using their tone of voice, verbal statements, and facial expressions rather than relying on self-report measures, and (b) compared their affect during the problem-solving process to their affect in response to the feedback.

During an online video-call, elementary school aged children solved a series of mathematical equivalence problems (e.g., 5 + 4 = 2 + __) in a fairly non-evaluative learning context. They received corrective feedback after each problem and we reliably rated their positive and negative affect throughout the activity. We also examined the associations between their expressions of affect with their accuracy and their persistence. We selected each of these design features with intention. We opted to work with elementary school children because previous research suggest they are sensitive to the effects of corrective feedback even in brief training sessions (e.g., Fyfe et al., 2012) and because children self-report experiencing emotion in response to math more generally (Ganley & McGraw, 2016). We chose the topic of mathematical equivalence because previous research documents children’s difficulties with these problems (see McNeil, 2014), and we wanted to ensure a mix of positive and negative feedback. We chose to independently rate children’s positive and negative affect, because most theories of feedback focus more centrally on the role of negative affect, and we wanted to provide evidence on the role of positive affect as well. Finally, we created a fairly non-evaluative learning context to mimic some educational experiences (e.g., practicing problems on an e-learning app) and to examine whether feedback elicits emotional responses even when the stakes are low.

This study allowed us to answer four research questions: (1) How much affect do children express during mathematics problem solving? (2) Does feedback increase affective responses for children solving mathematics problems? (3) Do affective responses differ after receiving positive versus negative feedback? (4) Do affective responses relate to accuracy and persistence? We expected children to experience greater emotions while processing feedback than while solving the problems. Further, we predicted that children’s emotional states would match the valence of the feedback they received, exhibiting more positive emotions with positive feedback and exhibiting more negative emotions with negative feedback. Finally, we tentatively expected increased negative emotions to negatively relate to learning outcomes.

Method

Participants

Participants were 87 children with parent consent. Their average age was 7.61 years (SD = 0.91, range = 6.13–8.99). Using optional open-ended questions, 83 parents provided gender information for their child and 79 parents provided race information. Based on this data, the sample was 41% female and 59% male, and 68% White, 16% Multiracial, 11% Asian, 3% Black, and 1% Hispanic. Children were primarily recruited from a mid-sized city in the Midwestern U.S. using a database of information for local families. Some participants also signed up via ChildrenHelpingScience.com, a website with a list of studies that families can opt into.

Children were recruited for a project focused on the effects of feedback on problem solving and 102 children completed a single online video-call session. The 87 children in the current sample represent participants who completed the online session in full and had sufficiently high-quality video data to reliably code their affect1. Given our focus on within-subject comparisons (e.g., a child’s negative affect vs. positive affect), power analyses indicated that our sample size was more than sufficient to detect effects. For example, a sample of just 26 children would provide approximately 80% power to detect a medium effect (f = .25, alpha = .05) for a 2 × 5 repeated measures ANOVA (which would allow us to examine positive and negative affect across the five levels of the game that the children completed). For transparency, we also report observed power for our primary analyses in the supplemental file.

Design

Each participant completed a single online video call session via Zoom with a trained researcher that lasted approximately 30 minutes. The primary task was to complete a training game in which children solved a set of mathematical equivalence problems and received corrective feedback after each problem. The 30-minute session included three other brief measures that are not relevant to the current research questions; these are described in the supplemental materials. The analyses presented in this paper focus on novel questions related to children’s affective states in response to feedback and their association with learning outcomes including children’s accuracy and persistence during the task.

Materials

Given that the study session occurred as an online video call, all the materials were presented on a computer screen. Presentation slides were prepared and then screen-sharing was used so that the participant could view all the stimuli on their own digital device.

The training game included five levels and each level included four mathematical equivalence problems (e.g., 3 + 5 = 4 + __). The full set of 20 problems is provided in the supplemental file. The four items within each set were designed to be coherent (e.g., having similar sums) and the five levels were designed to increase in difficulty (e.g., higher sums and more addends in Level 5 relative to Level 1). Each problem was presented one at a time in the center of the screen in black font with a light gray background (see Figure 1).

Figure 1. Screenshot of the Presentation of a Mathematical Equivalence Problem.

Figure 1

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Note. The stars on the bottom of the screen indicate progress through the level. Here, the child has completed two problems in Level 2 and is seeing the third problem.

Procedure

Each video call lasted approximately 30 minutes and included a trained researcher using a lab-based computer and a child participant using a digital device typically in their homes. After parent consent and child assent were obtained, the researcher provided brief instructions to ensure screen-sharing was functional and the child could see the presentation slides. The researcher completed several audio and video checks, and made sure that the child’s video was on and that the child was visible. For the primary training task, the researcher explained the math game and provided brief instructions. The goal was to create a fairly non-evaluative learning experience. The researcher expressed interest in “how kids your age think about number games,” and then said we are trying out a new game and we wanted the child’s opinion.

To begin the game, the researcher displayed an example screen in order to explain how the problems would appear and how the child could submit their answers to the problems by typing in the chat window. The researcher also explained that there were many levels of the game and the child could choose to continue the game or stop the game after each level. Once the child typed “go” the game began and the first problem appeared on the screen (Figure 1). The child was allowed as much time as needed and then typed their answer in the chat. On average, children spent 33 seconds (SD = 23, range = 7–116) solving each problem. Then, behind the scenes, the researcher clicked a button to ensure the appropriate feedback slide was displayed.

The feedback slide always included the problem in black font with the correct answer in blue font. Thus, all children received the correct answer as feedback and could determine whether their own answer was correct or incorrect. As part of a separate research question, children were randomly assigned to receive different types of feedback during the training game (see details in the supplemental materials). Thus, in addition to the correct answer, some children also received an explicit verification cue. The cue was presented visually on the computer screen (i.e., a green check mark for correct answers or a red x for incorrect answers) and auditorily, either with computer sounds (i.e., an ascending tone for correct answers or a descending tone for incorrect answers) or with words spoken by the experimenter (i.e., “That’s right” for a correct answer or “Uh oh that’s not right” for an incorrect answer). Thus, approximately half of the children received the correct answer alone as feedback, and the other half received the correct answer accompanied by explicit verification cues in both the visual and auditory modality. For all children, the feedback slide was displayed for 5 seconds (M = 5, SD = 1, range = 3–8), and then the next problem appeared. We decided on 5 seconds because initial pilot sessions indicated that children stopped attending after this period, and longer periods created confusion about game logistics (e.g., how to advance to the next problem).

This sequence of solving the problem and then receiving feedback repeated for the remainder of the game until the child typed “stop” at the end of a level or until they had completed all five levels of the game. At the end of the session, the researcher confirmed the parents’ consent for video sharing and then ended the video call.

Coding

Accuracy and persistence were objective measures based on children’s responses. For accuracy, children’s numerical solutions were scored as correct (1) or incorrect (0) and we calculated the proportion of items on which they provided a correct answer. For persistence, we calculated the number of questions children chose to complete (minimum 4, maximum 20).

For affect, two researchers were trained to use an existing coding scheme to rate children’s positive affect and negative affect using facial expressions, verbal statements, and tone of voice (adapted from Datler et al., 2012). Training included (a) becoming familiar with the written coding scheme, (b) watching children’s videos to differentiate key behaviors, and (c) using the coding scheme in tandem with the authors on an initial set of videos to ensure proper application. Once trained, one researcher watched each child’s video and for each problem, the researcher identified the problem-solving phase (i.e., the moment the problem appeared on the screen until the child entered a solution) and then identified the feedback phase (i.e., the moment the feedback slide appeared on the screen until the next problem was presented). Then, for each of those phases, the researcher rated the child’s global positive affect on a scale from 1 (not at all characteristic) to 5 (exceptionally characteristic) and also separately rated their global negative affect on a similar scale from 1 to 5. Thus, every child had four affect ratings for each item they solved: positive affect during problem solving, positive affect during feedback, negative affect during problem solving, and negative affect during feedback.

Table 1 provides example behaviors at each point on the rating scale and indicates that most ratings were based on differences in children’s facial expressions, though other behaviors were incorporated as well. Positive affect was indicted by behaviors like smiling, excited movements, affirming statements, and a positive tone of voice. Negative affect was indicated by behaviors like frowning, verbal frustration, moving away from the game, and whining. To establish the reliability of these measures, the second trained researcher independently watched videos for 20% of the sample and coded their affect blind to the original ratings. We compared the rating across researchers and calculated an intraclass correlation coefficient. Reliability was good: ICC = 0.79 for positive affect and ICC = 0.74 for negative affect.

Table 1.

Example Behaviors used to Code Positive and Negative Affect

Scale Positive Affect Example Negative Affect Example
1. Not at all characteristic Child has neutral facial expression, no visible reaction Child has neutral facial expression, no visible reaction
2. Minimally characteristic Child lifts head and half-smiles Child sighs and says “oh”
3. Moderately characteristic Child smiles with eyes wide, bounces in seat a little bit Child frowns and slumps over slightly in their chair
4. Highly characteristic Child dances in seat, says “ah yes” in happy but level tone Child whines and turns away from the screen
5. Exceptionally characteristic Child smiles big and very excitedly says “Yay!” Child stands, paces, and shouts “What!? No way!”
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Results

How much affect do children express during mathematics problem solving?

Descriptive statistics and correlations for all measures are provided in Table 1. On average, children were fairly modest in their expression of emotion. Across all trials, phases, and children, average positive affect was 1.60 (out of 5.00, SD = 0.60), which would correspond behaviorally to something like a small smile but no outright verbal expressions of excitement. Average negative affect was 1.26 (out of 5.00, SD = 0.37), which would correspond to something between a neutral face and a slight disappointed shrug. Both values were significantly greater than 1.00 (the minimum rating representing the lack of affect): positive affect, t(86) = 9.28, p < .001, d = .99, negative affect, t(86) = 6.59, p < .001, d = .71. At the individual child level, the vast majority of them experienced some emotion within this non-evaluative learning context, but not extreme levels. For example, 87% of children had average positive affect ratings greater than 1.00 (meaning they did not remain neutral the entire time, but experienced some positive emotion), but only 5% had an average positive affect rating of 3.00 or higher (out of 5.00). For negative affect, 74% of children had average ratings greater than 1.00, but only one child had an average negative affect rating of 3.00 or higher.

This trend was fairly consistent across the levels of the game, though average positive affect tended to decrease over time (see Figure 2). For example, we considered the 33 children who had affect data for all five levels, and conducted a 2 × 5 ANOVA with affect valence (positive, negative) and level (1, 2, 3, 4, 5) as within-subject factors. There were main effects of valence, F(1, 32) = 17.01, p < .001, ηp2 = .35, and level, F(4, 128) = 4.74, p = .001, ηp2 = .13, and also a valence by level interaction, F(4, 128) = 5.37, p < .001, ηp2 = .14. For positive affect, there was a main effect of level, F(4, 29) = 3.65, p = .016, ηp2 = .34, as positive affect during Level 1 (M = 1.68, SE = 0.11) was significantly higher than positive affect during Levels 2 through 5 (Ms = 1.38, 1.36, 1.35, 1.29 respectively), ps < .05. However, for negative affect there was not a main effect of level, F(4, 29) = 0.45, p = .772, ηp2 = .05, as negative affect was similarly low across Levels 1 to 5 (Ms = 1.08, 1.09, 1.07, 1.08, 1.09, respectively) ps > .05.

Figure 2. Positive and Negative Affect Ratings Across Game Levels.

Figure 2

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Note. Sample size decreases across levels as children choose to stop the game (N = 87, N = 68, N = 62, N = 47, N = 33 for Levels 1 to 5 respectively).

Binomial tests confirmed this as well; 23 out of 33 children who completed all five levels (70%) expressed higher positive affect in Level 1 than Level 5 which is greater than expected by chance, p = .035. For negative affect, fewer children (15%) expressed higher negative affect in Level 1 than Level 5 compared to chance levels, p < .001, because most children (58%) exhibited identical negative affect ratings in Levels 1 and 5. The takeaway is that most children experienced some, albeit modest affect2, with a slight decrease in positive affect over time.

Does feedback increase affective responses for children solving mathematics problems?

To determine whether feedback altered children’s affective states, we compared their affect ratings during the problem-solving phase with their affect ratings during the feedback phase. We conducted a 2 × 2 repeated measures ANOVA with affect valence (positive, negative) and phase (problem solving, feedback) as within-subject factors. This analysis was based on all 87 children and their average affect ratings across all the trials they opted to complete. There was a main effect of affect valence, F(1, 86) = 23.84, p < .001, ηp2 = .22, and a main effect of phase, F(1, 86) = 36.97, p < .001, ηp2 = .30. However, these were qualified by a significant valence by phase interaction, F(1, 86) = 19.16, p < .001, ηp2 = .18. For positive affect, children expressed more emotion during the feedback phase (M = 1.83, SE = 0.09) than during the problem-solving phase (M = 1.36, SE = 0.05), F(1, 86) = 46.02, p < .001, ηp2 = .35. But for negative affect, there was no significant difference in emotion during the feedback phase (M = 1.27, SE = 0.04) than during the problem-solving phase (M = 1.25, SE = 0.06), F(1, 86) = 0.04, p = .835, ηp2 = .00.

Binomial tests confirmed this as well; 62 out of 87 children (71%) expressed higher positive affect during the feedback phase than during the problem-solving phase, which is greater than expected by chance, p < .001. However, for negative affect, only 31 out of 87 children (36%) expressed higher negative affect during the feedback phase than during the problem-solving phase, which is lower than chance, p = .010, because a fairly large portion (35%) exhibited identical negative affect ratings across the feedback and problem-solving phases. In general, feedback tended to enhance children’s positive affect, but not their negative affect.

Do affective responses differ after receiving positive versus negative feedback?

To determine whether affect depended on the type of feedback provided, we compared their affect ratings on items solved correctly (resulting in positive feedback) to items solved incorrectly (resulting in negative feedback). We conducted a 2 × 2 repeated measures ANOVA with affect valence (positive, negative) and item accuracy (correct, incorrect) as within-subject factors. This analysis was based on the 66 children who solved at least one item correctly and at least one item incorrectly, and it reflected their affect ratings during the feedback phases. There was a main effect of affect valence, F(1, 65) = 39.32, p < .001, ηp2 = .38, and a main effect of accuracy, F(1, 65) = 4.56, p = .037, ηp2 = .07. But these were qualified by a significant valence by accuracy interaction, F(1, 65) = 44.23, p < .001, ηp2 = .41 (see Figure 3). For positive affect, children expressed more positive affect after correct trials (M = 2.31, SE = 0.16) than after incorrect trials (M = 1.42, SE = 0.08), F(1, 65) = 30.16, p < .001, ηp2 = .32. In contrast, children expressed more negative affect after incorrect trials (M = 1.61, SE = 0.09) than after correct trials (M = 1.01, SE = 0.01), F(1, 65) = 45.13, p < .001, ηp2 = .41, indicating that negative feedback leads to higher negative emotions than positive feedback.

Figure 3. Positive and Negative Affect Ratings During Problem Solving and During Feedback.

Figure 3

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Note. Sample size for these average affect ratings is 87.

Binomial tests confirmed this as well; 48 out of 66 children (73%) had higher positive affect on correct trials than on incorrect trials, which is greater than expected by chance, p < .001. However, for negative affect, only 1 child out of 66 (2%) had higher negative affect on correct than on incorrect trials, which is lower than what is expected by chance, p < .001. One interesting caveat, shown in Figure 3, is that children only expressed negative emotions in response to negative feedback; however, children expressed positive emotions in response to both positive and negative feedback. Put differently, when children solved an item incorrectly and received feedback, on average they expressed both positive and negative emotions.

Do affective responses relate to accuracy and persistence?

To examine the associations between affect and learning outcomes, we calculated bivariate correlations between children’s affect ratings and their accuracy (i.e., percentage of items solved correctly) and persistence (i.e., number of questions they opted to complete). We examined these correlations separately for the problem-solving phases and the feedback phases to determine whether these relations were specific to feedback. With eight correlations, we set the alpha level to .006. As shown in Table 1, both positive and negative affect were negatively associated with our measure of persistence, rs = −.29 to −.46 (and these correlations remained negative and significant after controlling for accuracy). However, only negative affect in response to feedback was negatively associated with accuracy, r(85) = −.63, p < .001 (and this correlation remained negative and significant after controlling for persistence).

The fact that higher levels of positive affect were associated with lower persistence was surprising, so we ran several exploratory analyses to further examine these effects. First, we expanded these results using two regression models with all four affect variables entered simultaneously. For predicting accuracy, the model was significant, F(4, 82) = 14.45, p < .001, R2 = .41, and the lone unique predictor was negative affect during feedback, β = −.64, p < .001. For predicting persistence, the model was also significant, F(4, 82) = 11.96, p < .001, R2 = .37, and two significant predictors emerged: negative affect during problem solving, β = −.36, p < .001, and negative affect during feedback, β = −.30, p < .001. Thus, when positive and negative affect are considered simultaneously, only negative affect relates to outcomes.

Second, we explored whether affect experienced early in the game (i.e., during Level 1) related to subsequent accuracy and persistence in Levels 2 to 5. These analyses were limited to the 68 children who opted to continue past Level 1, and with eight correlations we set alpha to .006. Accuracy during Levels 2 to 5 was significantly and negatively associated with children’s experience of negative affect in response to feedback during Level 1, r(66) = −.38, p = .001. Persistence during Levels 2 to 5 was negatively associated with negative affect during Level 1, both during problem solving, r(66) = −.48, p < .001, and during feedback, r(66) = −.33, p = .005. The key takeaway is that children who experienced more negative emotions early in the activity (but not more positive emotions), were likely to have lower scores and persistence later on.

Third, we explored differences in affect as a function of persistence – comparing children who chose to stop the game and those who chose to keep going. We provide statistical analyses but acknowledge that these are exploratory models and likely best interpreted at the descriptive level. We focus here on Level 1 (the earliest time to leave the game) and Level 4 (the latest time to leave the game). Eighty-seven children completed Level 1; 68 decided to persist to Level 2 and 19 decided to stop. These 19 children had lower accuracy than those who continued (Ms = 54% vs. 71%), F(1, 85) = 3.96, p = .049, ηp2 = .04, higher negative affect (Ms = 1.57 vs. 1.20), F(1, 85) = 14.93, p < .001, ηp2 = .15, and similar positive affect (Ms = 1.84 vs. 1.73), F(1, 85) = 0.40, p = .529, ηp2 = .01. So, the “leavers” generally seemed to experience a fair amount of emotion regardless of valence, but more negative affect relative to others. Later in the game, 47 children completed Level 4; 33 decided to persist to Level 5 and 14 decided to stop. These 14 children did not differ on our metrics relative to those who stayed; they had similar accuracy (Ms = 73% vs. 71%), F(1, 45) = 0.03 p = .873, ηp2 = .00, similar negative affect (Ms = 1.17 vs. 1.08), F(1, 45) = 1.91 p = .174, ηp2 = .04, and similar positive affect (Ms = 1.28 vs. 1.35), F(1, 45) = 0.15 p = .697, ηp2 = .00. At this late stage, some other factor may relate to dropping out.

Discussion

We documented children’s emotional responses during mathematics problem solving and how they reacted to corrective feedback. The problem solving was modestly difficult for this sample and occurred in a fairly non-evaluative, one-on-one environment. Also, our measure of affect was based on ratings of direct, in-the-moment expressions and statements (e.g., smiles, frowns, tone of voice). Several key findings emerged related to our four research questions. First, children expressed modest levels of emotion overall, with some children remaining fairly neutral throughout this non-evaluative context. Second, most children expressed more positive affect than negative affect, and this was especially true when processing the feedback message compared to problem solving. Third, the type of feedback message changed children’s affect; children expressed positive affect in response to both positive feedback and negative feedback, but more so in response to positive feedback; in contrast, they only expressed negative affect when they solved the problem incorrectly and received negative feedback. Fourth, children’s affect related to their performance; both positive affect and negative affect were negatively correlated with persistence, but negative emotions in response to feedback were uniquely and negatively associated with children’s accuracy. We discuss these findings in light of existing learning theories and outline limitations and future directions.

Quantifying Children’s Emotional Responses during Problem Solving

The results suggest that processing feedback in mathematics is not always a highly emotional activity. Children’s average affect was significantly but very modestly above the minimum, and a number of children remained neutral throughout the problem-solving and feedback phases. This modest expression of emotion may seem to contradict some previous theory and evidence. For example, several theories of feedback seem to assume that negative feedback will necessarily produce negative affect. Grundmann et al. (2021) write “…[negative feedback] is a mixed blessing because it elicits negative emotions” (p. 4). Similarly, Ilgen and Davis (2000) write, “since the model addresses only negative feedback, no matter how it is represented, it is unlikely to be positive” (p. 552). These statements assume the activation of negative affect when feedback is provided. Further, research in mathematics more generally suggests math often elicits negative emotions. Based on self-report measures, an international study indicated that 60% of students experienced some levels of math anxiety by the end of middle school (OECD, 2013), and other reports suggest that 25–40% of first through third grade students experience modest to high levels of worry in math (Ganley & McGraw, 2016).

We believe it is an important contribution to the literature to document the fact that mathematics problem solving with feedback does not automatically produce intense emotional experiences. We believe it is equally important to document the features of the context, as it is likely that some contexts produce more affective reactions than others. We speculate that two features of our study context played a role in children’s tempered expressions of emotion. First, the task difficulty was modest, but not too extreme. Across the sample, the average accuracy was 66%, and 94% of children solved at least one item correctly. Even though math equivalence problems can be quite challenging for elementary school students (see McNeil, 2014), we scaffolded their experience. The training game was preceded by four “warm-up” problems presented in a concrete contextualized format, and research suggests that solving equivalence problems in this concrete-then-abstract sequence can facilitate performance (Fyfe et al., 2015; Sherman & Bisanz, 2009. Also, the game levels started out easier and progressively got harder. The first two items in Level 1 only had operations on one side of the equal sign (e.g., 10 = 7 + __) and these items had higher accuracy rates (84% and 70%) than the next two items with operations on both sides of the equal sign (61% and 53%). Finally, we gave children the chance to stop after each level allowing them to regulate these emotional experiences (e.g., choosing to avoid more negative affect). This design choice likely increased the overall accuracy in this sample relative to others as low-performing children often stopped early. Thus, even in mathematics, children’s emotional experiences may remain modest overall when the task feels within reach or when the task can be stopped if and when emotional reactions occur.

Second, we created a fairly non-evaluative learning environment. Children generally enjoyed participating in the study, they were fully aware that our session was low-stakes and that their performance would not influence any external outcome, and we specifically told children that we were interested in how they thought about the game (not in how well they performed). And our exploratory analyses in the supplemental file indicated that children who received feedback in a non-evaluative manner (i.e., the correct answer only) expressed even less negative emotion than children who received feedback in a fairly evaluative manner (i.e., with an explicit verification cue of a green check mark or red x).

Other research in different non-evaluative settings also suggests that children may express modest levels of affect, even when more intensity may be expected. For example, six-year-olds played for five minutes with a novel peer in a toy room (Vallorani et al., 2022). Despite opportunities for joyful collaboration or frustrating conflict, children spent the vast majority of their time with neutral affect, and almost never expressed negative affect. Similarly, researchers coded toddlers’ affect during free play at childcare using a similar 1 to 5 scale as the current study; over 95% of observations were coded as 1 or 2 on the negative affect scale, and 80% of observations were coded as 1 or 2 on the positive affect scale. Thus, negative emotional reactions can be avoided in some learning contexts, and our results are in line with recommendations to provide feedback in a non-evaluative manner when possible (Shute, 2008).

We believe these results could have important implications for formal educational settings. Clearly, evaluative contexts in mathematics class cannot be avoided altogether, and we think it is unlikely that our results would generalize to those situations – for example, when children need to complete a math exam within a specified time limit that counts toward their grade. However, other situations can be created that are less evaluative – having children play a game on their tablet to practice math problems already introduced by the teacher or including “pretests” prior to a unit that are un-graded and allow for exploration of novel content. These tasks could be further structured to increase the chances that many students feel they are within reach – by including concrete formats first and sequencing the problems with more basic, familiar items at the beginning. Certainly, these represent our speculations and further research could examine children’s affect more directly in these formal educational settings.

How Feedback Changed Children’s Emotional Responses

Though children were modest in their expressions of affect, feedback did increase children’s positive emotions relative to the problem-solving phase. Feedback may be more likely to influence positive instead of negative emotions because of some quality of positive feedback; perhaps feedback on successes enhances children’s attention or desire to “tune in” relative to feedback on failures. Alternatively, it could be about quantity; children tended to experience more positive feedback than negative feedback in this study (on 66% of trials on average).

Also, not all feedback influenced affect in the same way. The valence of children’s affect tended to match the valence of the feedback message (see also Kuklick & Lindner, 2023). Positive affect was actually present in both cases (when children received positive feedback or negative feedback), but it was higher when positive feedback was provided. In contrast, negative affect was essentially only present when negative feedback was provided. Though intuitive, documenting this match is important for several reasons. It provides a sanity check that our participants were attending to the feedback message, it confirms that negative feedback and positive feedback influence the learner differently (e.g., Eskreis-Winkler & Fishbach, 2019), and it suggests that learners are attuned to the accuracy of their responses, even in a non-evaluative learning situation.

Associations Between Children’s Emotional Responses and Outcomes

Perhaps most critically, our results suggest that these affective responses matter, but in interesting ways. Though some research suggests that trait-like positive emotions relative to better learning outcomes (e.g., Pekrun et al., 2017), our results suggest that state-like positive emotions may have neutral or possibly negative associations with learning outcomes. Positive affect did not correlate with children’s accuracy, but it did correlate with children’s persistence such that expressing more positive emotion related to leaving the game earlier. These results were surprising as they go against an intuitive “positive emotions are good” sentiment. Our exploratory analyses indicated that children who decided to leave the game early generally had modest positive affect, modest negative affect, and low accuracy. Further, children who remained in the game for a long time generally expressed low levels of affect at all. These results lead us to speculate that some children tended to be more emotionally expressive overall – showing both positive and negative affect – and these children tended to stop the game. We think these speculations are somewhat consistent with Feedback Intervention Theory (Kluger & DeNisi, 1998), which suggests any form of emotional response to feedback may have consequences if it directs learners to think about themselves more than the task.

However, these associations between positive affect and persistence should be interpreted with caution. When we included both positive and negative affect as simultaneous predictors, only negative affect emerged as having a unique association with persistence. In fact, only negative affect in response to feedback (but not in response to problem solving) was associated with both lower persistence and lower accuracy on the task. Combined with previous research, this may suggest that both trait-like negative emotions (e.g., Pekrun et al., 2017) and state-like negative emotions (e.g., Jarrell et al., 2017) can lead learners to disengage with the feedback experience (see Grundmann et al., 2021) or interfere with learner’s task-relevant processing and decrease performance. Experiencing negative affect early in the task may matter the most; children in our study who had higher levels of negative affect during Level 1 had lower accuracy and lower persistence throughout the rest of the game in Levels 2 through 5.

Our study is unique in exploring the links between negative affect and performance outcomes with a young population (i.e., elementary school students) and with direct measures of affect expression (i.e., based on facial expressions, tone of voice). The findings confirm that learning from failure feedback can be difficult (e.g., Eskreis-Winkler & Fishbach, 2019), and they suggest that one reason may be the negative emotions that can accompany it. Given that children’s cognitive capacities are still developing (e.g., Gathercole et al., 2004), it may be especially difficult for them to simultaneously process their emotions and attempt to attend to and learn from the feedback message. Other research with older students has occasionally found that negative emotions can predict higher performance (assuming it motivates students to do better; Lipnevich et al., 2021) suggesting a need for future research to better delineate the situations in which in-the-moment negative affect will undermine students’ performance.

Limitations and Future Directions

Several limitations of the current study suggest additional directions for future research. Perhaps most critically, though we view our behavioral measure of affect as a strength, we did not also include self-report measures of affect. Our decision was merely a function of logistics and only including the measures we could in the 30-minute slot. However, previous research is encouraging in suggesting that observed behaviors may align well with self-report measures. For example, Casey (1993) had 7-year-old and 12-year-old children play a sorting game in a lab-setting and receive peer evaluations (e.g., I’d like to play with her because she seems nice vs. I don’t want to play with her because she doesn’t look nice). Their facial expressions in response to the evaluation were coded by trained researchers, and children self-reported their emotional responses retrospectively. The researchers concluded that “expression was consistent with children’s self-report of emotion” (p. 127). Of course, future research should continue to examine observed and self-reported measures in combination.

Further, our coders were able to reliably differentiate levels of global positive affect and levels of global negative affect, but we did not differentiate discrete emotion types (e.g., shame vs. anger). This is a major limitation as much research in the field of emotion regulation attempts to move beyond the simplistic “positive versus negative.” Indeed, theories of achievement emotion make important distinctions between discrete emotions that are activity-based (e.g., boredom, engagement) versus outcome-based (e.g., pride, shame), those that are future-oriented (e.g., anxiety) versus retrospective (e.g., disappointment), or even those that arise from expected versus unexpected events (e.g., Munzar et al., 2021; Pekrun & Linnenbrink-Garcia, 2012). And these discrete emotions – even if in the same broader category of negative – may relate to different regulation strategies, such as boredom leading to disengagement and disappointment leading to cognitive reframing (Webb et al., 2012). This is another reason for future research to consider employing multiple measures of affect in response to feedback.

In addition, we compared children’s emotional responses during problem solving to their emotional responses during feedback; however, feedback was provided on a trial-by-trial basis and could have influenced downstream affect during problem solving. Future research could include a no-feedback control condition to examine how children’s emotional responses do or do not change over the course of the activity when no explicit corrective feedback is provided.

Finally, our conclusions are based on a study with a specific sample of children solving a specific set of mathematical equivalence items in a one-on-one non-evaluative learning setting. Emotional responses in this context may be somewhat unique, especially as it relates to quantifying the intensity of children’s affect. Future research is needed with different samples, topics, and contexts to test the bounds of the generalizability of these results.

Conclusion

Emotions can play a significant role in how learners attend to and learn from feedback. Our study works to understand the connection between three key components of student learning: corrective feedback, affective responses, and learning outcomes. In our non-evaluative mathematics context, several surprising results emerged. Children expressed tempered levels of emotion despite a modestly difficult though manageable task and the presence of trial-by-trial corrective feedback. Also, across all trials, feedback tended to increase positive emotions relative to problem solving, despite many theories emphasizing negative emotions. Further, we did not find any evidence that positive emotions were “good” for students in terms of learning outcomes; instead, higher positive affect and higher negative affect were both associated with lower levels of persistence. And negative affect was also associated with lower accuracy. Clearly, affective states are important to consider during children’s STEM learning.

Supplementary Material

1

Figure 4. Positive and Negative Affect Ratings on Correct and Incorrect Trials.

Figure 4

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Note. The sample size for these average affect ratings is 66 as it excludes children who solved all the items correctly or all the items incorrectly.

Table 2.

Descriptive Statistics and Bivariate Correlations (N = 87)

M (SD) (1) (2) (3) (4) (5)
(1) Accuracy 66% (33%) --
(2) Persistence 13.63 (6.34) .27 --
(3) PS Positive Affect 1.36 (0.47) .04 −.29 --
(4) PS Negative Affect 1.25 (0.53) −.11 −.46 .06 --
(5) FB Positive Affect 1.83 (0.84) .11 .31 .64 .25 --
(6) FB Negative Affect 1.27 (0.39) .63 .40 .07 .23 .03
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Note. Accuracy is percent correct across all trials completed. Persistence is number of trials the child opted to complete (out of 20). Average affect ratings are on a scale from 1 to 5. PS = Problem Solving Phase. FB = Feedback Phase. All bolded correlations are significant at p < .05.

Highlights.

  • Researchers quantified children’s affect during mathematics problem solving.

  • Children expressed modest levels of emotion during problem solving and feedback.

  • Positive affect was higher than negative affect in response to feedback.

  • The valence of the feedback message (positive/negative) changed children’s affect.

  • Negative affect towards feedback was negatively associated with learning outcomes.

Acknowledgments

Megan Merrick and Emily R. Fyfe, Department of Psychological and Brain Sciences, Indiana University. Merrick was supported by a training grant from the Eunice Kennedy Shriver National Institute of Child Health and Human Development of the National Institutes of Health under Award Number T32 HD007475. The content is solely the responsibility of the authors and does not represent the official views of the National Institutes of Health. The authors thank Alex Bondi, Collin Byers, Elsie Gasaway, Jessica Ousterhout, Summer Smith, and Olivia Weed for their help with data collection and coding.

Footnotes

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1

The original sample included 102 children. Fifteen children were excluded from analyses because they were missing affect data on over 40% of the trials they completed. On average, those 15 children were missing 71% of possible affect data due to video-quality issues (e.g., face not visible). For the 87 included participants, missing data was rare (1.56% of all trials).

2

Though condition differences were not a central component of our research questions, children experienced one of four different feedback types. For transparency purposes, we report whether those feedback conditions influenced children’s experience of positive or negative affect in the supplemental material.

Contributor Information

Megan Merrick, Indiana University.

Emily R. Fyfe, Indiana University

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