Confused, now what? A Cognitive-Emotional Strategy Training (CEST) intervention for elementary students during mathematics problem solving
Introduction
Mathematics problem solving is complex and can be challenging, both cognitively and emotionally. Cognitively, effectively solving mathematics problems involves various skills such as the ability to understand number sense, apply basic mathematics facts and mathematical reasoning, and activate relevant prior knowledge (Baroody and Dowker, 2013, Davidson and Sternberg, 1998). Because of the complexity of solving mathematics problems, students must also engage in self-regulated learning (De Corte et al., 2000, Pape and Smith, 2002). Self-regulated learning facilitates students’ ability to plan, monitor, and evaluate their work, and recruit from their executive functions to organize, sustain and shift attention, inhibit distractions, utilize working memory, and maintain an appropriate level of motivation (Cragg & Gilmore, 2014). Emotionally, as students solve complex mathematics problems, they can experience positive emotions, such as curiosity, enjoyment, and pride, and negative emotions, like frustration, anxiety, and boredom (Frenzel et al., 2007, Goldin, 2014, Op't Eynde et al., 2007, Raccanello et al., 2019). Of particular concern, Di Leo, Muis, Singh, and Psaradellis (2019) reported that confusion and frustration were the two most frequently expressed emotions by fifth-grade students during a complex mathematics problem-solving task. This is alarming given that negative emotions can have detrimental effects on self-regulated learning (Muis, Psaradellis, Lajoie, Di Leo, & Chevrier, 2015), and mathematics learning and achievement (Frenzel et al., 2007, Raccanello et al., 2019) if they are not appropriately regulated or resolved (Munzar, Muis, Denton, & Losenno, 2020).
Several interventions with elementary students exist in the literature that have been effective in fostering emotion regulation (see Quoidbach, Mikolajczak, & Gross, 2015) or self-regulated learning (see Dignath & Büttner, 2008). Although emotions and cognitive processes are interconnected and dynamically linked (Barrett, 2009, Blair, 2002, Pekrun, 2006, Pekrun, 2018, Scherer, 2009), to our knowledge, there are currently no interventions that take into consideration cognition-emotion relations to improve mathematics problem solving skills among elementary students. As such, using an explanatory mixed methods approach (McCrudden, Marchand, & Schutz, 2019), the goal of this study was to evaluate an intervention we designed to help elementary students resolve confusion during mathematics problem solving through promoting emotional awareness and self-regulated learning strategies. Prior to delineating the specific intervention, relevant theoretical and empirical work is reviewed.
Emotions are multifaceted phenomena that include components relating to cognition, affect, physiology, motivation, and expression (Scherer, 2000). For example, the anxiety that students experience about mathematics problem solving may consist of worrying about not accurately solving the problem (cognitive), feelings of nervousness (affective), increased cardiovascular activation (physiological), impulses to flee the situation (motivational), and anxious facial expression (expressive; Scherer, 2000). Emotions are typically organized into different categories along two dimensions: valence (positive or negative) and activation (activating or deactivating arousal; Shuman & Scherer, 2014). Emotions can be further classified by whether they are positive activating (e.g., curiosity, hope, enjoyment, pride), positive deactivating (e.g., relief), negative activating (e.g., anxiety, confusion, frustration, anger, shame), and negative deactivating (e.g., boredom, hopelessness, sadness; Linnenbrink, 2007, Pekrun, 2006). One additional emotion, surprise, is considered neutral in valence as it can elicit positive or negative arousal depending on the context (Mauss & Robinson, 2009).
During complex learning situations like mathematics problem solving, emotions such as surprise, confusion, and curiosity are often experienced as they are triggered by cognitive incongruity, novelty, and impasses (D’Mello and Graesser, 2012, D’Mello et al., 2014). For example, surprise is likely to be experienced when a student encounters unexpected information, curiosity when the student experiences something new and has the desire to learn more about it, and confusion when a student encounters information that is inconsistent with prior knowledge and judges that resolving the incongruity may be difficult (Graesser & D’Mello, 2012). Confusion may also arise when goals are blocked, or other discrepant events occur like impasses, contradictions, or unexpected feedback (Chinn & Brewer, 1993). As D’Mello et al. (2014) argued, these events trigger cognitive disequilibrium (incongruity, dissonance, conflict). When cognitive disequilibrium occurs, learning is disrupted, and emotions may then fluctuate and oscillate from one emotion to another during complex learning and problem solving (D’Mello & Graesser, 2012).
Dynamics of emotions. D’Mello and Graesser (2012) developed a model to explain the dynamic nature of emotional states that occur during complex learning. They proposed that a learner who is in the state of engagement/flow (i.e., a cognitive-affective state of positive valence and moderate level of arousal that elicits a high state of engagement in the learning task) will experience confusion when confronted with cognitive incongruities, contradictions, anomalies, or impasses. The learner will then implement cognitive and metacognitive learning strategies to overcome the incongruity. If the cognitive incongruity (confusion) has been resolved, the learner will return to a state of engagement/flow and may experience enjoyment or relief for having resolved the incongruity. However, if the learner has failed to resolve the incongruity, they might feel stuck and their confusion will transition to frustration, at which point the learner may oscillate between confusion and frustration. With persistent failure in resolving the incongruity, the learner’s frustration will eventually transition to boredom. D’Mello and Graesser's (2012) model illustrates that confusion can be productive when it is resolved and the learner transitions to engagement/flow. However, confusion can be unproductive when the learner has difficulty resolving the incongruity and will oscillate between confusion and frustration and then transition from frustration to boredom, which subsequently leads to disengagement from the task.
D’Mello and Graesser's (2012) model has been empirically supported among adult students (Craig et al., 2004, D’Mello and Graesser, 2012, D’Mello et al., 2014, Graesser et al., 2007) and more recently with elementary students in the fifth grade (Di Leo, Muis, Singh, & Psaradellis, 2019, Muis, Psaradellis, Lajoie, Di Leo, & Chevrier, 2015). For example, Di Leo et al. (2019) found that fifth grade students’ confusion during mathematics problem solving functioned in both productive and unproductive ways. Although confusion positively predicted metacognitive learning strategies, it also negatively predicted planning and cognitive learning strategies. Di Leo et al. (2019) also investigated the dynamics of emotions through emotional-state transitions. Using a think-aloud protocol, students’ thoughts and emotions were captured as they solved a complex mathematics problem. Concordant with D’Mello and Graesser's (2012) model, patterns of emotional-state transitions were observed. Confusion transitioned to negative emotions, including frustration and boredom, but also transitioned to curiosity. Frustration transitioned to hopelessness and confusion. Additionally, patterns were observed between emotions and learning strategies. In particular, confusion transitioned to cognitive and metacognitive learning strategies including help-seeking, planning, identifying important information, and monitoring. This evidence suggests that confusion can be both productive and unproductive for elementary students.
Di Leo et al.'s (2019) study further revealed that the most frequently expressed emotions that these fifth-grade students experienced during mathematics problem solving were confusion and frustration. This implies that the overall experience of solving mathematics problems might be unpleasant for elementary students, which may constrain the learning strategies they implement and thus their overall performance. That is, sufficient evidence reveals that experiencing confusion can be particularly detrimental for young students (Muis et al., 2015). Although confusion is commonly experienced for all students, young students may more frequently fall into a pattern of emotional-state transitions of confusion to frustration and thus remain in a negative emotional state. Persistent or unresolved confusion can lead to greater opportunities to experience boredom, use fewer self-regulated learning strategies, and eventually disengage from the task.
Frustration in younger students has also been shown to lead to disengagement (Earl, Taylor, Meijen, & Passfield, 2017). This suggests that young students need to be explicitly taught a set of strategies they can apply to overcome confusion when it arises during mathematics problem solving to avoid frustration and eventual disengagement from the task. Moreover, as Pekrun (2006) argued, confusion, frustration, and boredom might also arise from cognitive appraisals of control over the learning task and value in the learning activity. Indeed, research has shown that lower perceived control predicts higher levels of confusion during learning and problem solving (Dowd, Araujo, & Mazur, 2015), whereas higher perceived value predicts higher levels of curiosity, and lower levels of confusion and frustration during problem solving (Di Leo, Muis, Singh, & Psaradellis, 2019, Muis, Psaradellis, Lajoie, Di Leo, & Chevrier, 2015). This suggests that perceived control should be targeted in interventions designed to teach students cognitive and metacognitive strategies to resolve confusion when it occurs.
This underlines the importance, particularly for young students, to acquire a foundation of self-regulatory skills to have awareness of their cognitive processes, as well as emotional states, and to appropriately implement self-regulated learning strategies during mathematics problem solving. As such, it is critical to develop an intervention for elementary students that facilitates self-regulated learning while also taking into account the role that emotions play in self-regulated learning (Muis, Chevrier, & Singh, 2018).
Self-regulated learning refers to the complex, interactive, and self-directive processes involved in regulating, planning, directing, and evaluating one’s behavior, cognitions, and emotions for the purpose of goal attainment in a learning context (Schunk & Zimmerman, 1997). Several models have been developed to delineate how students engage in self-regulated learning. For example, Muis' (2007) model of self-regulated learning includes four phases of learning, namely, task definition, planning and goal setting, enactment, and evaluation, and five areas for regulation including cognition, motivation, affect, behavior, and context. In the first phase, students begin by defining the task, which is influenced by the five areas for regulation. Learning strategies that might be employed during the task definition phase include prior knowledge activation and identifying important information. For the second phase, learners may set goals and plans to establish what they will do to solve the problem, including selecting appropriate learning strategies.
The third phase, enactment, begins once learners implement the selected strategies to carry out the task. In the context of mathematics problem solving, the enactment phase may include hypothesizing, summarizing, help seeking, calculating/measuring, or re-reading (Muis et al., 2015). In the last phase, individuals may evaluate the successes or failures of each phase, products created for the task, and/or perceptions about the self or context. Critical to this phase is metacognitive monitoring and evaluation. Strategies implemented during this phase might include self-questioning, monitoring, judgments of learning, self-correcting, and evaluating (Muis et al., 2015). Muis (2007) further proposed that metacognitive processes can occur within all phases of self-regulated learning and can be ongoing throughout the learning and problem-solving process. As noted previously, the skills required for each phase, including metacognitive monitoring, are critical for successful mathematics problem solving (Fuchs et al., 2006, Jacobse and Harskamp, 2012, Schoenfeld, 1994). With empirically supported models of self-regulated learning that provide insight into how it functions, it is also important to understand how to promote self-regulated learning.
Promoting self-regulated learning. Teaching students how to self-regulate their learning and to master complex strategies can be accomplished through cognitive strategy instruction (MacArthur, 2012). Substantial evidence points to the effectiveness of cognitive strategy instruction to facilitate complex tasks (Rosenshine, 1997), to promote the monitoring of their thinking and progress as they engage in problem solving (Kramarski and Mevarech, 2003, Verschaffel et al., 1999), and to promote mathematics automaticity and problem-solving skills (Carnine, 1997, Kroesbergen and Van Luit, 2003, Maccini and Hughes, 2000, Montague et al., 2011). In cognitive strategy instruction, the explicit teaching, modeling, scaffolding, and coaching of the components and steps of the strategy are considered to be effective in promoting students’ achievement (Rosenshine, 1997, Schunk and Zimmerman, 1997). Rosenshine (1997) identified two important components of strategy instruction: concrete prompts (e.g., checklists, cue cards) and instructional scaffolds (e.g., model using the strategy, think aloud, begin with simplified material, anticipate difficult areas in the material, provide correction strategies, increase students’ responsibility).
Cognitive strategy instruction has been successful in promoting self-regulated learning to support mathematics achievement for young students with various learning profiles (e.g., Case et al., 1992, Cassel and Reid, 1996, Mastropieri et al., 1991, Mercer and Miller, 1992), with meta-analyses revealing an average effect size around 0.66 (Donker, de Boer, Kostons, Dignath van Ewijk, & van der Werf, 2014). However, such training programs have focused solely on strategies that emphasize cognitive, metacognitive, and motivational processes without consideration of the role of emotions in learning and problem solving. Given that emotions experienced during learning and problem solving can facilitate or constrain self-regulated learning and learning outcomes (Di Leo, Muis, Singh, & Psaradellis, 2019, Muis, Psaradellis, Lajoie, Di Leo, & Chevrier, 2015, Pekrun, 2006, Pekrun, 2018), there is a critical need to incorporate emotional components into training programs that aim to improve mathematics problem solving through strategy instruction. Furthermore, self-regulated learning also involves regulation of affective states. Therefore, it would be highly relevant and important to also train students emotion regulation strategies and to monitor their emotional states and engage such strategies to effectively manage their emotions and diminish the experience of negative emotions and increase positive emotions.
Emotional awareness and emotion regulation. Indeed, it is imperative that students manage and regulate their emotions in the classroom setting as they carry out academic tasks (Fried, 2010, Fried, 2011). Emotion regulation can be described as one’s ability to control and manage one’s experience and expression of emotions (Gross, 2002). It involves the attempt to increase or decrease the magnitude or duration of one’s emotions (Gross et al., 2006, Gross et al., 2011, Gross and Thompson, 2007) and to reduce the urgency of the emotions to have control over one’s behaviors (Melnick & Hinshaw, 2000) to maintain engagement with the task at hand (Fried, 2010).
Appropriate and effective emotion regulation depends on one’s emotional awareness and the ability to identify and appraise one’s emotions (e.g., Berking and Wupperman, 2012, Boden and Thompson, 2015). Emotional awareness is considered a part of emotion regulation (Gross & Thompson, 2007) and has been described as paying attention to one’s emotional state and having a clear understanding of one’s emotions (e.g., Boden and Thompson, 2015, Coffey et al., 2003, Gohm and Clore, 2002). Facets of emotional awareness, especially identifying the type of emotion, have been associated with emotional regulation, i.e., expressive suppression, acceptance of emotions, and cognitive reappraisal (Boden & Thompson, 2015). More specifically, individuals who identify the emotion type are more likely to select and implement appropriate emotion regulation strategies (Boden & Thompson, 2015).
Teaching students to develop emotional awareness and implement emotion regulation strategies can be done explicitly in the classroom (Boekaerts, 1997) whereby an instructor uses techniques such as modelling strategies, which can then be used by the student (Pincus & Friedman, 2004; Schunk & Zimmerman, 2007). Direct instruction can help bring students’ strategy use into conscious awareness as they use reflective thinking to become aware of the emotions they experience and understand their strategy use (Schraw, Crippen, & Hartley, 2006). Furthermore, it is possible that discussion of emotional experiences within the classroom setting can further develop students’ emotion regulation strategies (Weare, 2004) as this may increase students’ knowledge of emotional expression (Denham & Kochanoff, 2002). To incorporate emotional awareness and regulation during learning, we developed a cognitive-emotional strategy training intervention (CEST) by integrating cognitive strategy instruction with components of cognitive behavioral therapy (CBT). The CBT interventions we reviewed included those designed for children and adolescents with anxiety disorders given their specific focus on emotion and emotion regulation.
Cognitive behavioral therapy (CBT) programs that target anxiety, like Coping Cat (Kendall, 1994), Building Confidence (Galla, Wood, Chiu, Langer, & Jacobs, 2012), or Healthy Minds, Healthy Schools (Montreuil & Tilley, 2017) focus on helping the child to: (1) recognize feelings and bodily somatic reactions to anxiety, (2) clarify thoughts about anxiety-provoking situations (e.g., negative attributions), (3) develop coping skills (e.g., change negative self-talk to coping self-talk), and, (4) evaluate outcomes. Behavioral training strategies include modelling, role playing and relaxation training, and cognitive strategies include self-control, self-observation, self-modification, and self-evaluation. For example, in the STOP program (Silverman et al., 1999), children and adolescents are taught to identify when they are feeling anxious, to identify their anxious thoughts, then modify or restructure their anxious thoughts by generating alternative coping thoughts and behaviors, and then praise themselves for confronting their fears. These programs have been shown to be effective with students as young as six years of age (Hirshfeld-Becker et al., 2010).
Section snippets
The current study
Taking cognitive strategy instruction and CBT together, we developed a CEST intervention that targeted training of cognitive and metacognitive strategies over the four phases of self-regulated learning, and the regulation of confusion during mathematics problem solving.
Using a mixed-methods approach, the objective of this research was to evaluate the efficacy of our CEST intervention with a sample of fifth-grade students. We used cognitive strategy instruction and modeling techniques to provide
Participants
All grade 5 teachers (N = 3) from one urban school were invited to participate. All three teachers agreed. Parental consent and student assent forms were then distributed to all students in grade 5 from the three classrooms (N = 72). Sixty-seven students from the fifth grade (n = 28 girls) across the three classrooms agreed to participate (93% of all students invited). The mean age of the sample was 10.84 years (SD = 0.31). A total of 11 students were on an individualized education plan (IEP);
Preliminary analyses
Assumptions. Skewness and kurtosis values were examined for normality for prior mathematics knowledge, mathematics problem-solving outcome, macro-level learning strategies, and emotions. Prior mathematics knowledge, mathematics problem-solving outcome, and learning strategies were within the acceptable range for skewness and kurtosis (using Tabachnick and Fidell’s [2013] criteria of <|3| for skewness and <|8| for kurtosis). Emotions fell within the range of <|8| for kurtosis with a range from
Discussion
Confusion, a negative activating emotion, can be related to optimal achievement outcomes when students appropriately implement learning strategies to resolve the confusion (D’Mello et al., 2014). However, confusion can have detrimental effects on learning among elementary students (e.g., Di Leo, Muis, Singh, & Psaradellis, 2019, Muis, Psaradellis, Lajoie, Di Leo, & Chevrier, 2015). Given this, research calls have been made to teach elementary students appropriate skills to resolve their
Conclusion
Collectively, these findings provide insight into cognitive-emotional strategy instruction and the need for explicitly teaching young students self-regulated learning strategies to overcome their confusion. Previous interventions focused solely on the cognitive component of problem solving and excluded the emotional components. This study is the first to include emotions and target confusion within an intervention for mathematics problem solving among elementary students. However, given that
Funding
Funding for this work was provided by a grant to Krista R. Muis from the Social Sciences and Humanities Research Council of Canada (435-2014-0155), and from the Canada Research Chair program. Correspondence concerning this article can be addressed to Krista R. Muis, Department of Educational and Counselling Psychology, Faculty of Education, McGill University, 3700 McTavish Street, Montreal, QC, H3A 1Y2, or via email at [email protected].
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