Marci S. DeCaro

Diagnosing and alleviating the impact of performance pressure on mathematical problem solving

High-pressure academic testing situations can lead people to perform below their actual ability levels by co-opting working memory (WM) resources needed for the task at hand (Beilock, 2008). In the current work we examine how performance pressure impacts WM and design an intervention to alleviate pressures negative impact. Specifically, we explore the hypothesis that high-pressure situations trigger distracting thoughts and worries that rely heavily on verbal WM. Individuals performed verbally based and spatially based mathematics problems in a low-pressure or high-pressure testing situation. Results demonstrated that performance on problems that rely heavily on verbal WM resources was less accurate under high-pressure than under low-pressure tests. Performance on spatially based problems that do not rely heavily on verbal WM was not affected by pressure. Moreover, the more people reported worrying during test performance, the worse they performed on the verbally based (but not spatially based) maths problems. Asking some individuals to focus on the problem steps by talking aloud helped to keep pressure-induced worries at bay and eliminated pressures negative impact on performance.

When higher working memory capacity hinders insight.

Higher working memory capacity (WMC) improves performance on a range of cognitive and academic tasks. However, a greater ability to control attention sometimes leads individuals with higher WMC to persist in using complex, attention-demanding approaches that are suboptimal for a given task. We examined whether higher WMC would hinder insight problem solving, which is thought to rely on associative processes that operate largely outside of close attentional control. In addition, we examined whether characteristics of the insight problems influence whether this negative relationship will be revealed. In Experiment 1, participants completed matchstick arithmetic problems, which require a similar initial problem representation for all problems. Higher WMC was associated with less accurate insight problem solving. In Experiment 2, participants completed insight word problems, which require substantially different representations for each problem. Higher WMC was again negatively associated with insight, but only after statistically controlling for shared variance between insight and incremental problem-solving accuracy. These findings suggest that WMC may benefit performance on fundamental processes common to both incremental and insight problem solving (e.g., initial problem representation), but hinder performance on the processes that are unique to insight (e.g., solution and restructuring). By considering the WMC of the individual, and the nature of the insight task, we may better understand the process of insight and how to best support it. (PsycINFO Database Record

An Alternative Time for Telling: When Conceptual Instruction Prior to Problem Solving Improves Mathematical Knowledge.

BACKGROUND The sequencing of learning materials greatly influences the knowledge that learners construct. Recently, learning theorists have focused on the sequencing of instruction in relation to solving related problems. The general consensus suggests explicit instruction should be provided; however, when to provide instruction remains unclear. AIMS We tested the impact of conceptual instruction preceding or following mathematics problem solving to determine when conceptual instruction should or should not be delayed. We also examined the learning processes supported to inform theories of learning more broadly. SAMPLE We worked with 122 second- and third-grade children. METHOD In a randomized experiment, children received instruction on the concept of math equivalence either before or after being asked to solve and explain challenging equivalence problems with feedback. RESULTS Providing conceptual instruction first resulted in greater procedural knowledge and conceptual knowledge of equation structures than delaying instruction until after problem solving. Prior conceptual instruction enhanced problem solving by increasing the quality of explanations and attempted procedures. CONCLUSIONS Providing conceptual instruction prior to problem solving was the more effective sequencing of activities than the reverse. We compare these results with previous, contrasting findings to outline a potential framework for understanding when instruction should or should not be delayed.

Enclothed Cognition and Controlled Attention during Insight Problem-Solving.

Individual differences in working memory capacity (WMC) increase the ability, and tendency, to devote greater attentional control to a task—improving performance on a wide range of skills. In addition, recent research on enclothed cognition demonstrates that the situational influence of wearing a white lab coat increases controlled attention, due to the symbolic meaning and physical experience of wearing the coat. We examined whether these positive influences on attentional control lead to negative performance outcomes on insight problem-solving, a task thought to rely on associative processes that operate largely outside of explicit attentional control. Participants completed matchstick arithmetic problems while either wearing a white lab coat or in a no-coat control condition. Higher WMC was associated with lower insight problem-solving accuracy in the no-coat condition. In the coat condition, the insight problem-solving accuracy of lower WMC individuals dropped to the level of those higher in WMC. These results indicate that wearing a white lab coat led individuals to increase attentional control towards problem solving, hindering even lower WMC individuals from engaging in more diffuse, associative problem-solving processes, at which they otherwise excel. Trait and state factors known to increase controlled attention and improve performance on more attention-demanding tasks interact to hinder insight problem-solving.

Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics

An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals’ ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth- and sixth-grade students (N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcut-first condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems.

Ego depletion improves insight

ABSTRACT Initial acts of self-control can reduce effort and performance on subsequent tasks – a phenomenon known as ego depletion. Ego depletion is thought to undermine the capacity or willingness to engage executive control, an important determinant of success for many tasks. We examined whether ego depletion improves performance on a task that favours less executive control: insight problem solving. In two experiments, participants completed an ego-depletion manipulation or a non-depleting control condition followed by an insight problem-solving task (i.e., matchstick arithmetic). Participants in the depleting condition demonstrated greater insight problem-solving accuracy than those in the non-depleting control condition. Priming theories of willpower did not impact these results. Although ego depletion is widely regarded as a “state of impairment”, attendant decreases in executive control may foster insightful thinking.

The lure of seductive details during lecture learning.

Research demonstrates that seductive details negatively impact learning from instructional materials such as textbooks and learning modules. Yet, anecdotally, teachers and students consider seductive details an enhancement to classroom lectures. We examined this apparent disconnect by exploring the impact of seductive details in mathematics lecture learning as a function of prior knowledge across 2 affective contexts: low-stakes learning and high-stakes learning. Undergraduate students viewed a video lecture on matrix algebra with or without seductive details either in a low-stakes or high-stakes learning environment. The high stakes were designed to mimic common classroom accountability for learning and were removed prior to the final test. On the final test, seductive details were generally detrimental in the low-stakes, but not high-stakes, learning environment. However, this effect was moderated by students’ prior knowledge. Students with higher prior knowledge were not impacted by seductive details in either high- or low-stakes learning environments. In contrast, students with lower prior knowledge—those most in need of pedagogical assistance—learned more when seductive details were included in a high-stakes lecture environment. These results suggest that seductive details may not be as detrimental as previously concluded, and may even be beneficial in an incentivized learning environment for students who have the most to learn.