{
  "page_1": "Making failure desired during learning – A \nquasi-experimental study\nTanmay Sinha\nNational Institute of Education, Nanyang Technological University, Singapore 637616\nARTICLE INFO\nKeywords:\nfailure\ngrowth mindset\nutility value\nmixed-methods analysisABSTRACT\nOne hundred and nineteen ninth-grade students engaged in one of two preparatory interventions \n– growth mindset or utility value – aimed at increasing the desirability of failure in learning \nduring a quasi-experimental study. An additional fifty-one students participated in a control \ncondition that offered no such preparation. Everyone then underwent a standard productive \nfailure learning task where they ideated to solve an open-ended math problem prior to receiving a \nformal lecture on the targeted concept. Following mixed-methods analysis, my empirical results \nfor the growth mindset and utility value conditions showed improvements in students ’ beliefs \nabout failure and their math expectancies, and similar persistence behaviors during problem- \nsolving (compared to the control condition). Posttest performance following the lecture did not \ndiffer across the three conditions. With this work, I bring together complementary lines of \nresearch on low-cost and scalable motivational interventions in learning, typically applied to \nimprove engagement with learning content, to contemporary learning sciences pedagogies like \nproductive failure, in the novel service of making failure desired for students.\n1.Introduction\nHow can we encourage students to view failure within supportive learning environments positively? Such supportive learning \nenvironments are educational settings structured to promote psychological safety while encouraging risk-taking, destigmatize failure \nwhile acknowledging that not all forms of failure are desirable (Kapur, 2016 ; Bjork & Bjork, 2020 ). Current learning sciences research \nsuggests that intentionally incorporating task failures into the learning process that promote problem space exploration and draw \nattention to deep features of the task can be beneficial (e.g., Kapur & Bielaczyc, 2012 ; Sinha & Kapur, 2021a ; Fields et al., 2021 ; Wong \nand Lim, 2022 ; Sinha, 2022 ). However, there is increasing evidence that students are often reluctant to engage in activities that involve \nsuch kinds of potential failures (Pan et al., 2020 ; Zepeda et al., 2020 ), making this a complex challenge. One approach to address this \nissue is through growth mindset interventions (Yeager et al., 2019 ), which highlight the value of failure as a chance for learning. These \ninterventions can help students adopt goal-oriented behaviors, such as focusing on relevant information and accepting the discomfort \nthat comes with tackling difficult learning tasks. Similarly, motivational interventions that illustrate the benefits and reframing the \ncosts of failure via real-world exemplars offer a strong alternative approach to improving the utility value of engaging in failure-prone \ntasks. I",
  "page_2": "2.Theoretical background\n2.1. Productive failure learning context\nProductive failure, conceptualized by Kapur & Bielaczyc (2012) , is a constructivist two-phase learning design that engages novices \nin open-ended problem-solving on a yet-to-be-learned concept before providing canonical instruction. Students activate their prior \nknowledge to typically generate multiple suboptimal solutions, and during that exploratory process, begin recognizing gaps in their \nknowledge, which can make them more prepared to learn from follow-up instruction (Loibl et al., 2017 ). Supportive social norms and \nscaffolds such as motivation to persist without the fear of failing are commonplace during the initial problem-solving phase of \nwell-designed productive failure. Follow-up instruction typically builds on student-generated solutions to consolidate understanding \nof the targeted concept. Meta-analyses (Sinha & Kapur, 2021a ) shows that productive failure has a greater potential to improve \nconceptual understanding and transfer relative to instruction-first designs without compromising procedural knowledge.\nAt the core of the present study is the aim to make failure a more desirable aspect of learning by developing and validating two \ninnovative, low-cost, scalable and age-appropriate preparatory interventions for productive failure. Building on the established \ntheoretical and empirical foundations of desirable difficulties (Bjork & Bjork, 2020 ) and productive failure (Sinha & Kapur, 2021a ), I \nhypothesize that challenging situations, which may initially reduce performance but ultimately enhance future learning (Schwartz & \nBransford, 1998 ), may not be appealing to students (Zepeda et al., 2020 ). For instance, a large-scale survey conducted at three major \npublic universities in North America (Pan et al., 2020 ) revealed that even in higher education, students often hold unproductive beliefs \nabout actively engaging with failure-prone learning activities, despite acknowledging the importance and benefits of learning from \nfailures.\nWithout effective pedagogical approaches that promote resilience and highlight the value of learning from failure, students may be \nless inclined to engage fully with discomforting learning experiences, even when these approaches are implemented. While robust \nliterature on productive failure indicates its efficacy in enhancing learning (Sinha & Kapur, 2021a ), it is crucial to recognize that \nstudents’ initial reactions to failure-prone tasks can influence their long-term engagement and willingness to seek out similar chal-\nlenges in the future. Willingly seeking out discomforting experiences necessitates the adoption of a proactive student mindset to reap \nsustained learning benefits, which may not naturally occur without appropriate scaffolding. For instance, recent meta-analytic \nresearch indicates that mental effort is often perceived negatively, as it correlates with adverse feelings regardless of educational \nlevel or feedb",
  "page_3": "Previous student-focused growth mindset interventions in math (Bui et al., 2023 ) have exhibited the following limitations – \nspecifically, they have (i) utilized learning materials that are either entirely domain-general (e.g., information on brain function and \nthe strengthening of neural connections through failure) or domain-specific (e.g., how beliefs about math can influence perceptions of \nfailure), (ii) employed direct teaching and/or reading exercises to educate students on these topics, which may be detrimental to those \nwith low success expectations, (iii) focused primarily on quantitative measures to evaluate impact, leaving a gap in qualitatively \nunderstanding how these interventions shape students ’ mindsets towards failure, and (iv) been mainly implemented in American or \nEuropean contexts. More generally, the universal effectiveness of growth mindset interventions has also been questioned, owing to \nsignificant variability in their true effects across studies. For instance, despite achieving consistently small to moderately positive \neffects on expectancies (d ˆ0.18) and mindsets (d ˆ0.46), Burnette et al. (2023) found effects for achievement ranging from d ˆ-0.08 \nto 0.35. How may we design contextually appropriate pedagogies for administering growth mindset interventions to achieve stronger \nand more sustainable effects?\nIn the present work, I address these gaps by integrating the strengths of both domain-general and domain-specific approaches to \nhelp students reshape their beliefs about failure. Instead of direct instruction, we adopt a prediction followed by explanation cycle \n(Schwartz & Bransford, 1998 ) to enable students to develop an intuition about the key myths associated with a growth mindset and to \nintroduce elements of surprise into the learning process (Brod et al., 2018 ). To complement self-reports on general beliefs about ability \nand domain-specific expectancies, I encourage reflection on these myths and gather qualitative data to explore how our intervention \npromotes a constructive relationship with failure in mathematics.\n2.3. Utility value\nMy second preparatory intervention to make failure desired focuses on utility value, a class of motivational interventions (Lazowski \n& Hulleman, 2016 ) that are grounded in expectancy-value theory (Eccles-Parsons et al., 1983 ). This theoretical lens emphasizes that \nstudent motivation to pursue learning tasks is a factor of their expectancies for success and the perceived value of engagement – utility \nvalue, which focuses on beliefs about whether a learning task is useful, has been shown to be a critical predictor of performance in \nSTEM fields (e.g., see Harackiewicz & Priniski, 2018 for a meta-analytic review). The theory also posits that overall valuing of a task \ncan decrease when there are negative aspects associated with engagement (Wigfield et al., 2021 ) – within the context of learning \ndesigns like productive failure, such costs can stem from (i) student pe",
  "page_4": "must also be able to understand and manage emotions to succeed at school ” (MacCann et al., 2020 , p.174).\nEmotionally, engagement in problem-solving prior to instruction can result in students experiencing a wide palette of negatively \nvalenced emotions (e.g., shame, anger, confusion) as well as pleasurable emotions (e.g., happiness, interest, surprise) that drive \nlearning from failure (Sinha, 2022 ). Productive failure thus provides a ripe context to study how students appraise the usefulness of \n(and manage) such emotions, especially those that are unpleasurable – e.g., do they distance themselves from such emotions? do they \ntry to suppress them? do they reframe its instrumental quality? Existing literature on emotion regulation identifies a range of such \nempirically-supported strategies that can affect task persistence and problem-solving skills (Gross, 2015 ; Weidman & Kross, 2021 ). For \nexample, cognitive strategies like reappraisal – defined as reinterpreting a situation to alter its emotional impact – can enable students \nto view emotions evoked by challenging tasks as opportunities for growth, increasing motivation to stick with the task. Similarly, \ncognitive concentration , which refers to deliberate focusing of mental attention on a task, can facilitate deeper problem-solving insights \nin the midst of distractions. Behavioral strategies like situation selection and situation modification – defined as altering the choice of \nlearning environments or activities within them to elicit desired emotions – can allow students to shape their surroundings to evoke or \navoid particular emotions. Other strategies like venting , which involve behavioral expression of emotions by communicating feelings to \nseek emotional relief and/or outwardly express an intended emotion, while effective for enhancing the capacity to think clearly and \ncritically, may not always be normatively desired during problem-solving. Finally, strategies like distraction (defined as directing \nattention away from emotional triggers or distressing aspects of a situation towards neutral or unrelated stimuli) and distancing \n(defined as adopting a mentally detached or observer perspective to reduce the intensity of emotional responses) foster a \nnon-confrontational perspective when engaging with frustrating tasks – by isolating decision-making from the impact of emotions, \nsuch strategies run the risk of discrediting an emotional experience.\nUltimately, when students simply categorize their emotional experiences as positive (good) or negative (bad) based solely on \nvalence – rather than deliberately selecting regulation strategies that align with their instrumental task goals – they risk prematurely \ndisengaging from the learning experience (Tamir, 2009 ; Willroth et al., 2023 ; Sinha, 2025 ). After all, it is not always better to \nexperience more pleasurable and less unpleasurable emotions for academic and emotional well-being (Ford & Mauss, 2014 ) – for \nexample, empiric",
  "page_5": "with a challenging problem. Taken together, these pre-survey findings suggest room for implementing interventions that can foster a \nmore positive approach towards failure and evaluate their downstream learning impact.\n3.2. Study design\nI carried out a two-day between-subjects study where seven whole class sections were assigned to three conditions (see Figure 1),. \nThis was done at the school level by the teachers, who allocated each of their class sections to either a control (n ˆ51) or one of the two \ncomparison conditions (growth mindset – n ˆ66, utility value – n ˆ53). Consequently, students within each class section were \nassigned to the same condition. I recognize that while random assignment would have been preferable to mitigate class effects, this was \nnot feasible given the school ’s logistical and scheduling constraints, rendering the study quasi-experimental.\n3.3. Materials\nCustomized materials, administered via Qualtrics, were presented online depending on condition.\n3.3.1. Preparation phase materials\nGrowth mindset condition. A three-part interactive storyline intervention, drawing on and extending validated materials from \nYeager et al. (2019) , aimed to educate students about brain plasticity and growth mindsets in mathematics (25 minutes). However, \nwhile the materials from Yeager et al. (2019) focus solely on asking participants to read scientific evidence for neural plasticity, learn \nabout how students/celebrities have put a growth mindset in practice, and complete writing exercises to internalize key lessons, the \npresent online training materials were framed around myths, with their underlying sequencing and pedagogical delivery newly \ndeveloped to scaffold secondary school students about the importance of growth mindset within and outside mathematical contexts. In \npart I, everyone learned foundational knowledge about neurons and synaptic connections, making predictions about brain myths \nrelated to intelligence and failure, with customized feedback highlighting the brain ’s adaptability through failure-driven practice. Part \nII introduced domain-general growth and fixed mindsets, prompting students to predict perspectives on failure, effort, and mindset \ntypes while receiving tailored responses that emphasized persistence, effort, and strategies for improvement. Evidence from PISA ’s \n2018 assessment illustrated the benefits of a growth mindset in a local context. Part III focused on a domain-specific growth mindset in \nmathematics, where students made predictions about math-related myths, with customized responses using real-life examples to \ndemonstrate that anyone can enhance their math skills through effort and learning from failures. The intervention concluded with \nreflective questions prompting participants to justify a myth they were most interested in (or, surprised by), reconsider their past \nexperiences with failure in mathematics, and how they might approach such challenges differently. See supplementary mater",
  "page_6": "memorizing facts anymore; it was about using them creatively to solve problems. That ’s what truly sparked my interest in learning ”), (ii) failure \nas a motivator, (iii) failure facilitating deeper engagement with learning materials, (iv) failures as opportunities to rectify misinfor -\nmation, and finally, (v) the immediate process and delayed outcome benefits associated with failure. After reading all five quotes, \nstudents ranked them from most to least favorite and briefly justified their most favorite one. Following that, an animated video was \npresented to consolidate each quote. Finally, everyone wrote their quotations addressing future peers that demonstrated a revised \nunderstanding of how to tackle failures. All materials were newly developed. See supplementary materials for details.\nControl condition. Students in the control condition did not work through any online preparation materials but directly began \nwith the learning phase of productive failure.\n3.3.2. Learning phase materials\nDuring the learning phase of productive failure, the initial problem-solving task comprised generation of multiple solutions to \ndetermine which of two soccer players is more consistent based on their goal-scoring records. The follow-up lecture compared and \ncontrasted common suboptimal student answers before introducing the canonical solution, aligning with high-fidelity implementa -\ntions of productive failure (Sinha & Kapur, 2021a ). A standardized instruction worksheet comprising four problem-solution pairs \ncatering to different critical features of the canonical concept was used along with teacher facilitation of the topic – here, teachers were \ntasked with primarily managing time and clarifying any procedural study steps as students went through the worksheet in a self-paced \nmanner. Five teachers participated in facilitation across the seven class sections to ensure fidelity of the instruction phase in terms of all \nstudents being exposed to the four problem-solution pairs.\n3.4. Procedure\nThe study took place over two consecutive days and comprised two main phases.\n3.4.1. Preparation phase\nStudents in the growth mindset and utility value conditions first completed their respective online materials (up to 25 minutes, as \noutlined in section 3.3.1 ). Control group students did not receive preparation materials and proceeded directly to the learning phase.\n3.4.2. Learning phase\nAll students subsequently went through a productive failure design task, drawing on Kapur, 2014 (95 minutes) – here, they first \nsolved an open-ended problem on a yet-to-be-learned math concept of standard deviation by using their prior mathematical knowledge \n(problem-solving phase, 25 minutes), before being exposed to a formal lecture targeting that concept (instruction phase, 30 minutes). \nFinally, a posttest targeting procedural knowledge (max 2) and conceptual knowledge (max 15) of standard deviation, along with \ntransfer questions (max 5) targeting the topic of normaliza",
  "page_7": "3.5.2. Learning phase\nIn between the problem-solving and instruction phases (13 minutes), the following sets of measures were collected – students first \nself-reported learning mechanisms of productive failure via five-point Likert scales ranging from completely disagree to completely agree , \nwhich draw on recent measurement advances within this learning design (Sinha & Kapur, 2021b ) – (i) knowledge gap awareness \n(Cronbach ’s α ˆ0.77, e.g., “my knowledge was insufficient to carry out these tasks ”, “I felt that I did not manage to complete these tasks ”), \n(ii) state curiosity (α ˆ0.86, e.g., “I want to know more ”, “I feel like asking questions about what is happening ”), (iii) germane cognitive \nload (α ˆ0.88, e.g., “this activity improved my understanding of the content that was covered ”, “this activity improved my knowledge of how \nto deal with the problem covered ”), (iv) positive and negative affect (assessed via PANAS, Watson et al., 1988 ). Although not the focus of \nour present work, I report these measures for full transparency.\nAdditionally, I asked if students tried to change or manage how they were feeling when working through the math task. The \nmaterials provided examples of emotion regulation goals, such as trying to feel less negative (less anxious or frustrated), trying to feel \nmore positive (more happy or amused), or even trying to feel more negative or less positive). If students answered yes, I then asked \nthem to identify one or more emotion regulation strategies that they used drawing on evidence-backed self-reporting strategies to \nmanage emotions (Weidman & Kross, 2021 ). For instance, cognitive reappraisal (“I tried to think differently about the activity I was \ndoing ”), suppression (“I suppressed the outward expression of my current feelings ”), distancing (“I tried to adopt a more detached, objective \nperspective on the situation ”), etc. To further tap on metacognition about failing just after students had engaged in the problem-solving \ntask, I provoked reflection on whether students had succeeded or failed at the task (with three response options – failed, not sure, \nsucceeded). I further asked for descriptive open-ended accounts of their process of coming up with multiple solutions (using the \nquestion – how did you work through the problem-solving task to come up with multiple solutions? please explain briefly).\nSubsequently, everyone answered a brief intuitions assessment (max 12) that tapped on noticing of critical task features – the time \nwas kept intentionally low to discourage procedural computation, with items drawn from the conceptual understanding and transfer \ndimensions of the posttest. Between the instruction phase and posttest, students also rated the lecture quality using the shortened form \nof a validated questionnaire from Sinha & Kapur, 2021b (7 items, 5-point Likert scale ranging from completely disagree to completely \nagree , α ˆ0.79). This questionnaire tapped into facets like structure (",
  "page_8": "approach, with illustrative excerpts of participant verbalizations, and (iii) whether and how students engaged in emotion regulation to \nsoldier through the task, by using an ANOVA for the number of regulation strategies, along with a frequency comparison of self- \nreported strategy usage across conditions.\nFor RQ4, individual ANCOVAs and follow-up Tukey posthoc tests were used with intermediate / final learning outcomes (e.g., \nintuitions assessment, procedural knowledge posttest, conceptual knowledge posttest, transfer posttest) as dependent variables, \ncondition as a fixed factor, and prior mathematics knowledge as a covariate. Across RQ3 and RQ4, I did not use time on task (study \nduration) as a covariate for any reported analyses because it was not independent of our treatment effect, a critical assumption check \nwhen administering ANCOVA1. To complement null hypothesis significance testing (NHST) and counter the empirical critique that \nabsence of evidence is not evidence for absence, Bayes factor (BF01) was used to quantify strength of evidence favoring the null hy-\npothesis for comparisons with non-significant results from NHST. Based on Jarosz & Wiley (2014) , BF01 can be interpreted as evidence \nfor the null hypothesis with the following scale: 1–3 (weak/anecdotal), 3–10 (positive/substantial), 10 –20 (positive/strong), 20 –30 \n(strong), 30 –100 (strong/very strong), 100 –150 (strong/decisive), 150 (very strong/decisive). Given that I did not have leeway for \nincreasing the sample size (due to the maximum cohort size in the school where the study was conducted), an ANCOVA-based \nsensitivity power analysis suggested that I could reliably detect an effect of Cohen ’s d ˆ0.43 with 70% power (α error probability \n0.05). Cohen ’s d was used as the effect size measure to contextually interpret the practical significance of these results. JASP Team \n(2024) and GPT 4o-mini (OpenAI, 2024 ) were used for all reported data analyses. Because GPT 4o-mini was accessed via Azure OpenAI \nservice, all prompts (e.g., instructions, any anonymized student quotes) and completions (generative AI outputs) were unavailable \noutside the analysis context to the general public, and were not used to train, retrain or improve any underlying generative AI model, \nthus safeguarding participant privacy.\n4.Results\n4.1. Intervention fidelity\nDuring the online preparation phase of our intervention, I looked at the time taken (in seconds) along with the distribution of word \ncounts for various open-ended responses. For the growth mindset condition, I found that participants spent an increasingly greater \namount of time as they moved from part I – introduction to the brain (M ˆ74.4, SD ˆ26.88, max ˆ160.06), to part II – growth mindset \nand its associated myths (M ˆ106.90, SD ˆ44.95, max ˆ274.07), and finally to part III – relevance of growth mindset situated within \na mathematical learning context (M ˆ206.62, SD ˆ90.23, max ˆ375.32). This was in alignment with my expectati",
  "page_9": "4.2. Evidence for beliefs and expectancies change (growth mindset condition, RQ1)\nStudents in the growth mindset condition showed higher post-intervention domain-general beliefs (M ˆ3.65, SE ˆ0.09) relative to \npre-intervention beliefs (M ˆ3.42, SE ˆ0.08, z ˆ3.32, p D0.001, rrb ˆ0.52 / Cohen ’s d ˆ1.21, BF10 ˆ96.05), with very strong \nevidence disfavoring the null. Similarly, post-intervention domain-specific (math) expectancies (M ˆ3.68, SE ˆ0.11) were also re-\nported to be significantly higher than pre-intervention expectancies (M ˆ3.47, SE ˆ0.10, z ˆ3.67, p D0.001, rrb ˆ0.91 / Cohen ’s d ˆ\n4.39, BF10 ˆ61.56), again with strong evidence disfavoring the null.\n4.3. Evidence for the desirability of failure (growth mindset and utility value conditions, RQ2)\nMy AI-assisted thematic analysis method for the growth mindset and utility value conditions resulted in seven and four themes \nrespectively during the first two exploratory and focused refinement phases. Upon human evaluation of these AI-generated themes in \nthe subsequent collaborative refinement phase, the following changes were made – (i) expansion and renaming – the AI-generated \ntheme of ‘growth mindset and learning from failure ’ was adjusted to ’commitment to a proactive attitude towards personal \nimprovement ’ / ‘constructive perception of failure ’ to better capture the future-oriented aspect of students ’ responses, moving beyond \nmere passive acceptance of failure to active self-improvement, a vital distinction for the theoretical framing of this work, (ii) reframing \n– the AI-generated theme of ‘persistence and effort in problem-solving ’ was refined into ’recognition of the value of effective analytical \nand social learning strategies ’ / ‘practical strategies for success ’, which emphasized both analytical problem-solving and the strategic \nuse of social resources as a way to appraise failure better, and (iii) retaining and renaming – the theme of ‘changing perspectives on \nproblem-solving speed and learning outcomes ’ was retained for the growth mindset condition, given that students had made pre-\ndictions on an associated myth during the intervention and found it to be one of the more surprising myths. Finally, the theme of \n‘constructive outlook on emotional responses to failure ’ / ‘emotional growth through failure ’ was also retained across both conditions, \nowing to emotional processing being explicitly verbalized by students as a critical component of navigating failure. Note, though, that \nthe AI-generated themes had initially missed a critical nuance of students emphasizing their reframing of negative emotions into \nproductive learning experiences – discerning this subtle contextual meaning was an important sticking point that had to be navigated \nin the collaborative refinement phase.\n4.3.1. Growth mindset condition\nBased on these human-validated themes, students in the growth mindset condition articulated a revised understanding regarding \nthe desirability of failure in ",
  "page_10": "Fourth, constructive outlook on emotional responses to failure , where students shared how they might redirect failure-triggered \nfeelings of frustration, disappointment, etc into motivation for future efforts. For instance, reflections from the data such as “I used \nto give up easily when I got frustrated at hard math problems but that didn’t help me grow my mathematical knowledge. Now I try again until I \nnot only get the answer but also understand the concept and logic behind it” illustrate that although negative emotional responses initially \nsignaled defeat and prompted students to abandon the task altogether, reframing them as a cue to engage more deeply with the \nmaterial and developing constructive coping strategies potentially turned discouraging experiences into valuable lessons. Similarly, \nanother student described the shift in how they would emotionally revise their approach for working with mathematical concepts – \n“When working with polynomials, I once got really confused. I felt overwhelmed and kept reviewing my equation. If I could go back, I would stay \ncalm and strategically check every stage of my work or even seek help from my friend ”. Instead of succumbing to and ruminating over \nnegative emotional responses, students recognized that a calmer, more strategic approach may be a more plausible way to navigate \nfailure. Table 1summarizes these thematic exemplars.\n4.3.2. Utility value condition\nWhen looking at the quotations that students in the utility value condition wrote for a future student, I found that it reflected their \nability to apply the intervention ’s key messages, specifically around utilizing failures in new learning experiences. The thematic \ncategorization of these quotations mirrored evidence from the growth mindset condition – (i) constructive perception of failure , where \nstudents reframed failures as insights for identifying specific improvement areas and enhancing subject matter understanding, (ii) \npractical strategies for success , where students responded by providing examples of actionable advice for coping with failure, empha -\nsizing the importance of acceptance, reflection and finding alternative methods, (iii) resilience and perseverance , where continuing to \npush through and persist in the face of failures and challenges shone through student quotes, and finally, (iv) emotional growth through \nfailure , where student responses not only acknowledged feelings of stress, disappointment and demotivation but also articulated how \nthose experiences may contribute to personal growth. Table 2summarizes thematic exemplars.\n4.4. Evidence for persistence in the productive failure learning task (RQ3)\nIn terms of the diversity of mathematical idea generation in the productive failure learning task, there were no significant dif-\nferences across conditions – students in the growth mindset, utility value, and control conditions ideated at a similar frequency overall \n(BF01 ˆ4.83, signaling strong odds favoring",
  "page_11": "merge different concrete strategies or ideas, and creatively modify those approaches to suit the problem-solving task in the growth \nmindset and utility value conditions (37.4% of responses, n ˆ43) relative to the control condition (6% of responses, n ˆ3). The \nfollowing two exemplar quotes showcase verbalizations where students switched between different problem-solving strategies and \nimprovised – (i) “I tried to find ways to compare the largest difference in goals scored in consecutive seasons through using the mean, median \nand mode of the differences. I had also wanted to compare the difference between the median difference and largest difference in goal scored in \nconsecutive seasons to look out for one-off seasons. Overall, I was trying to compare the differences in goals scored and who had a smaller \ndifference ” (growth mindset condition), and (ii) “I used knowledge I had from my secondary 1of mean, median and mode and applied them \nto the tasks. I also tried different methods that I had never use before such as finding the smallest difference between mode and mean” (utility \nvalue condition). Second, in terms of problem decomposition and iterating through solution approach, there was relatively lower \nevidence of task disaggregation into manageable steps in the control condition (8% of responses, n ˆ4) – students in the growth \nmindset and utility value conditions, however, indicated relatively greater systematic breaking down of the problem – defined here as \nbreaking down complex problems into smaller, manageable parts (35.6% of responses, n ˆ41). For instance, one student in the growth \nmindset condition articulated that they “tried using existing definitions that I already knew to try to solve the problem and I tried to break the \nproblem down into simpler and sub parts so that I could solve these micro tasks more easily ”. Additionally, despite an overall low frequency \nof explicit references to iterative thinking across all conditions, which I define as the process of refining solutions through repeated \ncycles of evaluation and adjustment, I did see qualitative differences (0% of responses, n ˆ0 for control versus 7.8% of responses, n ˆ9 \nfor the two experimental conditions). For instance, a student in the utility value condition said that they “have rough idea then I try to \nwork on an idea, idea fail never mind, leave it there and try again, idea was found, checked and once happy move on then work on a new idea or \ngo back to the failed idea”. Finally, students often first focused on aptly defining consistency (e.g., “I defined what consistency could mean. \nI found different ways to find this ’consistency ’. I could have evaluated these methods further ”) – this tendency was, however similar when \ncomparing our two experimental conditions (28.7% of responses, n ˆ33) relative to the control (28% of responses, n ˆ14). Taken \ntogether, these results suggest intriguing preliminary trends in how the deployed problem-solving approach",
  "page_12": "Finally, the empirical evidence for students ’ emotion regulation profile, critical to persisting through the productive failure \nproblem-solving task, suggested that there were no differences in the number of students who tried to change or manage their emotions \nwhen generating solutions across conditions (χ² (2) ˆ0.32, p ˆ0.85). However, for the n ˆ65 (38.2%) students who self-reported \nreported proactively working on their emotions, their frequency of regulation strategy usage (max 9) was descriptively higher in \nthe growth mindset (M ˆ2.44, SE ˆ0.30, Cohen ’s d ˆ0.18, p ˆ0.81) and utility value (M ˆ3.84, SE ˆ0.35, Cohen ’s d ˆ0.75, p ˆ\n0.05‡) conditions relative to the control condition (M ˆ2.71, SE ˆ0.33). The corresponding ANOVA was significant (F (2, 62) ˆ5.01, \np ˆ0.01, η²p ˆ0.14), with only one of the three pairwise differences between the growth mindset and utility value conditions being \nstatistically significant (p ˆ0.009**).\nA further probe into the distribution of these emotion regulation strategies (see Figure 2) highlighted that cognitive reappraisal , \nwhich involves changing how one appraises a task to alter its emotional significance (e.g., a challenging problem can be reframed as an \nopportunity to learn something new and improve), was the most frequently self-reported strategy across conditions, despite a relatively \nlower non-judgmental focus of attention on the problem-solving process (cognitive concentration ). Further, students in the growth \nmindset condition had a higher prevalence of cognitive reappraisal compared to the utility value and control conditions (47.8% in-\ncrease). A similar percentage of students across conditions reported taking an emotionally detached perspective on the learning sit-\nuation (distancing ), actions to improve the quality of their problem-solving experience to alter its emotional impact (situation \nmodification ), and attempts to find meaning in the suboptimal idea generation process despite experiencing discomfort (reconstrual ). \nSometimes, students also resorted to relatively maladaptive strategies such as inhibiting their emotional reactions (suppression ) and \ndeploying attention away from the emotionally charged problem-solving process (distraction ). Behaviorally and/or physically \nexpressing emotions outwardly (venting, behavioral expression ) was scarce in the data sample.\n4.5. Evidence of performance during productive failure (RQ4)\nFor the intuitions assessment administered prior to the productive failure instruction on standard deviation, there were no sig-\nnificant differences across conditions (all p’s F0.05), with strong evidence for the null model (BF01 ˆ14.48). Similarly, there were no \nsignificant differences across conditions for posttest assessments of procedural knowledge (BF01 ˆ2.92), conceptual knowledge (BF01 \nˆ9.68), and transfer (BF01 ˆ13.43), with all p’s F0.05. Descriptively though, students in the control condition scored better on \nprocedural knowledge but rela",
  "page_13": "interventions can be impactful in making failure desired even for high-performing students and not just academically at-risk students \n(Paunesku et al., 2015 ). While this study did not find significant improvements in academic performance (as we will discuss later), the \nobserved shifts in attitude towards failure can still play a crucial role in gradually shaping students ’ perceptions. How can we induce \nand help our students internalize such non-normative perceptions to embrace failure? Designing authentic learning experiences where \nstudents can deliberately practice failing in a safe space may offer them the opportunity to gauge the relevance of critical factors like \nlearning strategy usage, speed, and emotional reactions in driving learning through failure. The designed productive failure learning \nphase offered precisely such an opportunity for students.\nAs results for RQ3 further show, empirical data from the productive failure learning phase suggested that students who underwent \nthe growth mindset and utility value preparatory interventions generated a similar number and diversity of generated ideas during \nopen-ended problem-solving as the control condition (see Table 3) – typically, this is taken as a proxy for prior knowledge activation in \nthe productive failure literature (Sinha & Kapur, 2021a ). As one critical mechanism underlying the learning design (Kapur & Bielaczyc, \n2012 ; Sinha & Kapur, 2021a ), prior knowledge activation has been conjectured to facilitate preparation for future learning by \nsurfacing knowledge gaps that can be addressed in the follow-up lecture (Loibl et al., 2017). Although I do not know of any empirical \nwork that has causally tested this assumption, running a mediation analysis with the present data sample supports this post hoc \nexplanation2. Despite students in the growth mindset and utility value conditions generating similar number of ideas, they did, \nhowever, demonstrate a more flexible and iterative problem-solving approach, creatively integrating their prior knowledge to develop \nthose ideas, relative to the control condition. Their persistence could be attributed both to a better cognitive approach as well as to a \nhealthier emotion regulation profile with greater prevalence of reappraisal (Weidman & Kross, 2021 ) – a strategy involving explicit \nFig. 2.Frequency of emotion regulation strategies used by students across the three conditions during the productive failure learning task \n(in percentage).\nTable 4 \nEvidence of performance during productive failure – Marginal means (standard errors) and effect sizes relative to control condition for intuitions \nassessment (pre-instruction) and posttest (post-instruction), controlling for prior math knowledge. All p’s F0.05.\nGrowth mindset Utility value Control\nIntuitions assessment (max 12) 6.95 (0.24) 6.65 (0.27) 7.10 (0.28)\n(F (2, 164) ˆ0.68, p ˆ0.51, η²p ˆ0.01) [Cohen ’s d -0.07] [Cohen ’s d -0.23]\nPosttest (procedural, max 2) 1.73 (0.06) 1.80 (0",
  "page_14": "reframing of the challenging productive failure learning situation (see section 4.4and Figure 2for more details).\nIt is crucial to recognize that the effects of this reframing, though, can differ based on whether it aims to lessen negatively valenced \nemotions by reframing discomfort positively or whether it embraces these emotions as a source of motivation to persist and/or seek \nassistance. The former approach undermines the emotional experience, while the latter can foster greater self-awareness and an \nincreased willingness to learn from failure (e.g., Leach & Cidam, 2015 ; Travis et al., 2020 ; Lench et al., 2024 ). More generally, the \ncurrent secondary school sample also showed that spontaneous emotion regulation to persist through failure-prone tasks was infre-\nquent, as only a small percentage (38.2%) indicated any attempts to proactively manage emotions. For educational practice, this \nimplicates a greater emphasis on teaching students adaptive emotion regulation strategies to help them cope with challenging learning \ncontexts.\nAs results for RQ4 show, students in the growth mindset and utility value condition demonstrated similar intuitions about the \ntargeted learning concept immediately following their problem-solving ideation, compared to the control condition. Such forms of \nintermediate knowledge, which reflect the extent to which students are able to notice critical task features, play an important role in \nlearning from the follow-up lecture in productive failure, as demonstrated both empirically (Trninic et al., 2022 ) and theoretically \n(Loibl et al., 2024 ). I further did not find any significant differences across the posttest learning outcomes of procedural knowledge, \nconceptual knowledge and transfer following the lecture (see Table 4for details). Descriptively though, it was interesting to note that \nthe control condition students scored better on the procedural knowledge posttest – why may that be case? One reason could be that \nthe lecture3, which was perceived as descriptively better by students in the control condition relative to the growth mindset and utility \nvalue conditions, may have had a normalizing effect on posttest scores – this could also be attributed, in part to the differences in \nteacher facilitation, despite our use of a standardized lecture worksheet (see supplementary materials for details) and clear facilitation \nguidelines across the different class sections. Another potential confounding factor could be the reduced task fatigue in the control \ncondition students, who engaged directly with the problem-solving task and lecture without the preceding 25-minute preparatory \nintervention. This could have resulted in heightened focus during the learning phase. However, I do not have evidence that the current \npreparatory interventions of growth mindset and utility value were perceived as challenging (nearly three-quarters of the students \nrated our designed material difficulty as 2 or lower on a 5-point",
  "page_15": "comprehensive design that includes all measures across all conditions, even when a direct effect is not theoretically predicted, to \nprovide a more complete picture of this intervention ’s impact.\nMethodologically, AI-assisted thematic data analysis is still an emerging area within educational research – despite improving \nefficiency, I acknowledge that it offers only one subjective lens to interpret the data and critically runs the risk of exacerbating biases \ndue to the integration of human and machine-based subjective judgments. Despite maintaining audit trails capturing the evolution of \nmy coding decisions with AI-assistance, rethinking about the validity of qualitative data coding in the age of generative AI seems \nworthwhile for future work. I further focused solely on the short-term effects of growth mindset and utility value interventions. \nConducting replication studies in various socio-cultural contexts with different age groups and gender distributions would enhance the \ngeneralizability of these findings. Maintaining the desirability of failure and related persistence behaviors over longer periods also \npresents an opportunity to develop distributed scaffolding that can build resilience in students and positively influence their academic \nperformance beyond mathematics.\nAuthor Note\nTanmay Sinha (ORCID id 0000-0003-3069-2899), Learning Sciences and Assessment Department, National Institute of Education, \nNanyang Technological University, Singapore. I appreciate the support of Nick Chan, Priscilla Lee, Deana Syazwani, Pamela Seah, \nAndy Chia and Nur Johari for facilitating classroom access. Thanks to Evadne Tanandika for implementing the learning materials on \nQualtrics and for data tabulation. Thanks to Dana Lim, Galvyn Goh, Nicky Loo for data collection assistance. The author is supported by \nthe National Institute of Education under a Start-up Grant (NIE-SUG 5-23 TS). Correspondence concerning this article should be \naddressed to Tanmay Sinha, National Institute of Education 2-02-14, 1 Nanyang Walk, Singapore 637616.\nCRediT authorship contribution statement\nTanmay Sinha: Writing – review & editing, Writing – original draft, Project administration, Methodology, Investigation, Funding \nacquisition, Formal analysis, Data curation, Conceptualization.\nSupplementary materials\nSupplementary material associated with this article can be found, in the online version, at doi:10.1016/j.tsc.2025.102094 .\nData availability\nData will be made available on request.\nReferences\nAronson, J., Fried, C. B., & Good, C. (2002). Reducing the effects of stereotype threat on African American college students by shaping theories of intelligence. Journal \nof Experimental Social Psychology, 38(2), 113–125. https://doi.org/10.1006/jesp.2001.1491\nBjork, R. A., & Bjork, E. L. (2020). Desirable difficulties in theory and practice. Journal of Applied Research in Memory and Cognition, 9(4), 475–479. https://doi.org/ \n10.1016/j.jarmac.2020.09.003\nBlackwell, L. S., Trze",
  "page_16": "Deslauriers, L., McCarty, L. S., Miller, K., Callaghan, K., & Kestin, G. (2019). Measuring actual learning versus feeling of learning in response to being actively engaged \nin the classroom. Proceedings of the National Academy of Sciences, 116(39), 19251 –19257. https://doi.org/10.1073/pnas.1821936116\nDommett, E. J., Devonshire, I. M., Sewter, E., & Greenfield, S. A. (2013). The impact of participation in a neuroscience course on motivational measures and academic \nperformance. Trends in Neuroscience and Education, 2(3-4), 122–138. https://doi.org/10.1016/j.tine.2013.05.002\nDweck, C. S. (2006). Mindset: The new psychology of success. Random House .\nEccles-Parsons, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In \nJ. T. Spence (Ed.), Achievement and achievement motivation (pp. 75–146). San Francisco, CA: W. H. \nFord, B. Q., & Mauss, I. B. (2014). The paradoxical effects of pursuing positive emotion: When and why wanting to feel happy backfires. In J. Gruber, & \nJ. T. Moskowitz (Eds.), Positive emotion: Integrating the light sides and dark sides (pp. 363–381). Oxford University Press. https://doi.org/10.1093/acprof:oso/ \n9780199926725.003.0020 . \nFields, Freeman., A, D., Kafai, Y. B., Morales-Navarro, L., & Walker, J. T (2021). Debugging by design: A constructionist approach to high school students ’ crafting and \ncoding of electronic textiles as failure artefacts. British Journal of Educational Technology, 52(3), 1078 –1092. https://doi.org/10.1111/bjet.13079\nFunder, D. C., & Ozer, D. J. (2019). Evaluating effect size in psychological research: Sense and nonsense. Advances in Methods and Practices in Psychological Science, 2 \n(2), 156–168. https://doi.org/10.1177/2515245919847202\nGaspard, H., Dicke, A.-L., Flunger, B., Brisson, B. M., Hafner, I., Nagengast, B., & Trautwein, U. (2015). Fostering adolescents ’ value beliefs for mathematics with a \nrelevance intervention in the classroom. Developmental Psychology, 51(9), 1226 –1240. https://doi.org/10.1037/dev0000028\nGaspard, H., Parrisius, C., Piesch, H., Kleinhansl, M., Wille, E., Nagengast, B., & Hulleman, C. S. (2021). The potential of relevance interventions for scaling up: A \ncluster-randomized trial testing the effectiveness of a relevance intervention in math classrooms. Journal of Educational Psychology, 113(8), 1507 –1528. https:// \ndoi.org/10.1037/edu0000663\nGrant, A. M., & Schwartz, B. (2011). Too much of a good thing: The challenge and opportunity of the inverted U. Perspectives on Psychological Science, 6(1), 61–76. \nhttps://doi.org/10.1177/1745691610393523\nGross, J. J. (2015). Emotion regulation: Current status and future prospects. Psychological Inquiry, 26(1), 1–26. https://doi.org/10.1080/1047840X.2014.940781\nHarackiewicz, J. M., & Priniski, S. J. (2018). Improving student outcomes in higher education: The science of targeted intervention. Annual Review of Psychology, 69, \n409–435. ",
  "page_17": "Trninic, D., Sinha, T., & Kapur, M. (2022). Comparing the effectiveness of preparatory activities that help undergraduate students learn from instruction. Learning and \nInstruction, 82, Article 101688. https://doi.org/10.1016/j.learninstruc.2022.101688\nWalkington, C., Bernacki, M. L., Vongkulluksn, V., Greene, M., Darwin, T., Leyva, E., Istas, B., Hunnicutt, J., Washington, J., & Wang, M. (2024). The effect of an \nintervention personalizing mathematics to students’ career and popular culture interests on mathematics interest and learning. Journal of Educational Psychology, \n116(4), 506–531. https://doi.org/10.1037/edu0000840\nWatson, D., Clark, L. A., & Tellegen, A. (1988). Development and validation of brief measures of positive and negative affect: the PANAS scales. Journal of Personality \nand Social Psychology, 54(6), 1063–1070. https://doi.org/10.1037/0022-3514.54.6.1063\nWeidman, A. C., & Kross, E. (2021). Examining emotional tool use in daily life. Journal of Personality and Social Psychology, 120(5), 1344–1366. https://doi.org/ \n10.1037/pspp0000292\nWigfield, A., Muenks, K., & Eccles, J. S. (2021). Achievement motivation: What we know and where we are going. Annual Review of Developmental Psychology, 3(1), \n87–111. https://doi.org/10.1146/annurev-devpsych-050720-103500\nWillroth, E. C., Young, G., Tamir, M., & Mauss, I. B. (2023). Judging emotions as good or bad: Individual differences and associations with psychological health. \nEmotion, 23(7), 1876–1890. https://doi.org/10.1037/emo0001220\nWong, S. S. H., & Lim, S. W. H. (2022). Deliberate errors promote meaningful learning. Journal of Educational Psychology, 114(8), 1817–1831. https://doi.org/ \n10.1037/edu0000720\nYeager, D. S., & Dweck, C. S. (2012). Mindsets that promote resilience: When students believe that personal characteristics can be developed. Educational Psychologist, \n47(4), 302–314. https://doi.org/10.1080/00461520.2012.722805\nYeager, D. S., Hanselman, P., Walton, G. M., Murray, J. S., Crosnoe, R., Muller, C., & Dweck, C. S. (2019). A national experiment reveals where a growth mindset \nimproves achievement. Nature, 573(7774), 364–369. https://doi.org/10.1038/s41586-019-1466-y\nYoucubed. (2018). Mathematical mindset teaching guide, teaching video, and additional resources. https://www.youcubed.org/mathematical-mindset-teaching- \nguide-teaching-video-and-additional-resources/ .\nZeeb, H., & Voss, T. (2024). Fostering preservice teachers’ research-related beliefs and motivation with growth mindset and utility value interventions. Motivation \nScience. Advance online publication. https://doi.org/10.1037/mot0000352 .\nZepeda, C. D., Martin, R. S., & Butler, A. C. (2020). Motivational strategies to engage learners in desirable difficulties. Journal of Applied Research in Memory and \nCognition, 9(4), 468–474. https://doi.org/10.1016/j.jarmac.2020.08.007T. Sinha                                                                                                                                    "
}