Bridging cognitive neuroscience and education: Insights from EEG recording during mathematical proof evaluation.

BACKGROUND: Much of modern mathematics education prioritizes symbolic formalism even at the expense of non-symbolic intuition, we contextualize our study in the ongoing debates on the balance between symbolic and non-symbolic reasoning. We explore the dissociation of oscillatory dynamics between algebraic (symbolic) and geometric (non-symbolic) processing in advanced mathematical reasoning during a naturalistic design. METHOD: Employing mobile EEG technology, we investigated students' beta and gamma wave patterns over frontal and parietal regions while they engaged with mathematical demonstrations in symbolic and non-symbolic formats within a tutor-student framework. We used extended, naturalistic stimuli to approximate an authentic educational setting. CONCLUSION: Our findings reveal nuanced distinctions in neural processing, particularly in terms of gamma waves and activity in parietal regions. Furthermore, no clear overall format preference emerged from the neuroscientific perspective despite students rating symbolic demonstrations higher for understanding and familiarity.

Math on cortex-enhanced delta phase synchrony in math experts during long and complex math demonstrations.

Neural oscillations are important for working memory and reasoning and they are modulated during cognitively challenging tasks, like mathematics. Previous work has examined local cortical synchrony on theta (4-8 Hz) and alpha (8-13 Hz) bands over frontal and parietal electrodes during short mathematical tasks when sitting. However, it is unknown whether processing of long and complex math stimuli evokes inter-regional functional connectivity. We recorded cortical activity with EEG while math experts and novices watched long (13-68 seconds) and complex (bachelor-level) math demonstrations when sitting and standing. Fronto-parietal connectivity over the left hemisphere was stronger in math experts than novices reflected by enhanced delta (0.5-4 Hz) phase synchrony in experts. Processing of complex math tasks when standing extended the difference to right hemisphere, suggesting that other cognitive processes, such as maintenance of body balance when standing, may interfere with novice's internal concentration required during complex math tasks more than in experts. There were no groups differences in phase synchrony over theta or alpha frequencies. These results suggest that low-frequency oscillations modulate inter-regional connectivity during long and complex mathematical cognition and demonstrate one way in which the brain functions of math experts differ from those of novices: through enhanced fronto-parietal functional connectivity.

The effects of procedural and conceptual knowledge on visual learning.

Even though past research suggests that visual learning may benefit from conceptual knowledge, current interventions for medical image evaluation often focus on procedural knowledge, mainly by teaching classification algorithms. We compared the efficacy of pure procedural knowledge (three-point checklist for evaluating skin lesions) versus combined procedural plus conceptual knowledge (histological explanations for each of the three points). All students then trained their classification skills with a visual learning resource that included images of two types of pigmented skin lesions: benign nevi and malignant melanomas. Both treatments produced significant and long-lasting effects on diagnostic accuracy in transfer tasks. However, only students in the combined procedural plus conceptual knowledge condition significantly improved their diagnostic performance in classifying lesions they had seen before in the pre- and post-tests. Findings suggest that the provision of additional conceptual knowledge supported error correction mechanisms.

Factors related to the performance of laypersons diagnosing pigmented skin cancer: an explorative study.

It is important but challenging for prospective health professionals to learn the visual distinction between potentially harmful and harmless skin lesions, such as malignant melanomas and benign nevi. Knowledge about factors related to diagnostic performance is sparse but a prerequisite for designing and evaluating evidence-based educational interventions. Hence, this study explored how the characteristics of 240 skin lesions, the number of classified lesions and the response times of 137 laypeople were related to performance in diagnosing pigmented skin cancer. Our results showed large differences between the lesions, as some were classified correctly by more than 90% and others by less than 10% of the participants. A t-test showed that for melanomas, the correct diagnosis was provided significantly more often than for nevi. Furthermore, we found a significant Pearson correlation between the number of solved tasks and performance in the first 50 diagnostic tasks. Finally, t-tests for investigating the response times revealed that compared to true decisions, participants spent longer on false-negative but not on false-positive decisions. These results provide novel knowledge about performance-related factors that can be useful when designing diagnostic tests and learning interventions for melanoma detection.

Prior math achievement and inventive production predict learning from productive failure.

A frequent concern about constructivist instruction is that it works well, mainly for students with higher domain knowledge. We present findings from a set of two quasi-experimental pretest-intervention-posttest studies investigating the relationship between prior math achievement and learning in the context of a specific type of constructivist instruction, Productive Failure. Students from two Singapore public schools with significantly different prior math achievement profiles were asked to design solutions to complex problems prior to receiving instruction on the targeted concepts. Process results revealed that students who were significantly dissimilar in prior math achievement seemed to be strikingly similar in terms of their inventive production, that is, the variety of solutions they were able to design. Interestingly, it was inventive production that had a stronger association with learning from PF than pre-existing differences in math achievement. These findings, consistent across both topics, demonstrate the value of engaging students in opportunities for inventive production while learning math, regardless of prior math achievement.

Nonlinear and machine learning analyses on high-density EEG data of math experts and novices.

Current trend in neurosciences is to use naturalistic stimuli, such as cinema, class-room biology or video gaming, aiming to understand the brain functions during ecologically valid conditions. Naturalistic stimuli recruit complex and overlapping cognitive, emotional and sensory brain processes. Brain oscillations form underlying mechanisms for such processes, and further, these processes can be modified by expertise. Human cortical functions are often analyzed with linear methods despite brain as a biological system is highly nonlinear. This study applies a relatively robust nonlinear method, Higuchi fractal dimension (HFD), to classify cortical functions of math experts and novices when they solve long and complex math demonstrations in an EEG laboratory. Brain imaging data, which is collected over a long time span during naturalistic stimuli, enables the application of data-driven analyses. Therefore, we also explore the neural signature of math expertise with machine learning algorithms. There is a need for novel methodologies in analyzing naturalistic data because formulation of theories of the brain functions in the real world based on reductionist and simplified study designs is both challenging and questionable. Data-driven intelligent approaches may be helpful in developing and testing new theories on complex brain functions. Our results clarify the different neural signature, analyzed by HFD, of math experts and novices during complex math and suggest machine learning as a promising data-driven approach to understand the brain processes in expertise and mathematical cognition.

Physical inference of falling objects involves simulation of occluded trajectories in early visual areas.

Humans possess an intuitive understanding of the environment's physical properties and dynamics, which allows them to predict the outcomes of physical scenarios and successfully interact with the physical world. This predictive ability is thought to rely on mental simulations and has been shown to involve frontoparietal areas. Here, we investigate whether such mental simulations may be accompanied by visual imagery of the predicted physical scene. We designed an intuitive physical inference task requiring participants to infer the parabolic trajectory of an occluded ball falling in accordance with Newtonian physics. Participants underwent fMRI while (i) performing the physical inference task alternately with a visually matched control task, and (ii) passively observing falling balls depicting the trajectories that had to be inferred during the physical inference task. We found that performing the physical inference task activates early visual areas together with a frontoparietal network when compared with the control task. Using multivariate pattern analysis, we show that these regions contain information specific to the trajectory of the occluded ball (i.e., fall direction), despite the absence of visual inputs. Using a cross-classification approach, we further show that in early visual areas, trajectory-specific activity patterns evoked by the physical inference task resemble those evoked by the passive observation of falling balls. Together, our findings suggest that participants simulated the ball trajectory when solving the task, and that the outcome of these simulations may be represented in form of the perceivable sensory consequences in early visual areas.

Understanding Randomness on a Molecular Level: A Diagnostic Tool.

Undergraduate biology students' molecular-level understanding of stochastic (also referred to as random or noisy) processes found in biological systems is often limited to those examples discussed in class. Therefore, students frequently display little ability to accurately transfer their knowledge to other contexts. Furthermore, elaborate tools to assess students' understanding of these stochastic processes are missing, despite the fundamental nature of this concept and the increasing evidence demonstrating its importance in biology. Thus, we developed the Molecular Randomness Concept Inventory (MRCI), an instrument composed of nine multiple-choice questions based on students' most prevalent misconceptions, to quantify students' understanding of stochastic processes in biological systems. The MRCI was administered to 67 first-year natural science students in Switzerland. The psychometric properties of the inventory were analyzed using classical test theory and Rasch modeling. Moreover, think-aloud interviews were conducted to ensure response validity. Results indicate that the MRCI yields valid and reliable estimations of students' conceptual understanding of molecular randomness in the higher educational setting studied. Ultimately, the performance analysis sheds light on the extent and the limitations of students' understanding of the concept of stochasticity on a molecular level.

Problem-solving in virtual environment simulations prior to direct instruction for differential diagnosis in medical education: An experimental study.

Background: Despite acquiring vast content knowledge about the functioning of the human body through university teaching, medical students struggle to transfer that knowledge to one of the core disciplinary practices - differential diagnosis. The authors aimed to overcome this problem by implementing computer-based virtual environment simulations in medical education courses. Methods: In an experimental study, the authors compared problem-solving in medical computer-based virtual environment simulations prior to instruction with an instruction-first approach. They compared the effects on isomorphic testing and transfer performance of clinical knowledge and clinical reasoning skills as well as evoked learning mechanisms. The study took place in spring 2021 with undergraduate medical students in the scope of a medical trajectory course. Due to Corona-Virus-19 measures participants completed all study activities remotely from home. Results: The authors did not find any learning activity sequence to be superior to the other. However, when looking at the two learning activities individually, they found that problem-solving in computer-based virtual environment simulations and direct instruction might be equally effective for learning content knowledge. Nevertheless, problem-solving in computer-based virtual environment simulations with formative feedback might be more effective for learning clinical reasoning skills than mere instruction. Conclusions: The findings indicate that problem-solving in computer-based virtual environment simulations might be more effective for learning clinical reasoning skills than mere theoretical instruction. The present study has a high level of ecological validity because it took place in a realistic setting where students had to perform all learning and testing tasks autonomously.

The Disappearing "Advantage of Abstract Examples in Learning Math".

When teaching a novel mathematical concept, should we present learners with abstract or concrete examples? In this experiment, we conduct a critical replication and extension of a well-known study that argued for the general advantage of abstract examples (Kaminski, Sloutsky, & Heckler, 2008a). We demonstrate that theoretically motivated yet minor modifications of the learning design put this argument in question. A key finding from this study is that participants who trained with improved concrete examples performed as well as, or better than, participants who trained with abstract examples. We argue that the previously reported "advantage of abstract examples" manifested not because abstract examples are advantageous in general, but because the concrete condition employed suboptimal examples.

Productive failure in learning math.

When learning a new math concept, should learners be first taught the concept and its associated procedures and then solve problems, or solve problems first even if it leads to failure and then be taught the concept and the procedures? Two randomized-controlled studies found that both methods lead to high levels of procedural knowledge. However, students who engaged in problem solving before being taught demonstrated significantly greater conceptual understanding and ability to transfer to novel problems than those who were taught first. The second study further showed that when given an opportunity to learn from the failed problem-solving attempts of their peers, students outperformed those who were taught first, but not those who engaged in problem solving first. Process findings showed that the number of student-generated solutions significantly predicted learning outcomes. These results challenge the conventional practice of direct instruction to teach new math concepts and procedures, and propose the possibility of learning from one's own failed problem-solving attempts or those of others before receiving instruction as alternatives for better math learning.

Cognitive consistency and math-gender stereotypes in Singaporean children.

In social psychology, cognitive consistency is a powerful principle for organizing psychological concepts. There have been few tests of cognitive consistency in children and no research about cognitive consistency in children from Asian cultures, who pose an interesting developmental case. A sample of 172 Singaporean elementary school children completed implicit and explicit measures of math-gender stereotype (male=math), gender identity (me=male), and math self-concept (me=math). Results showed strong evidence for cognitive consistency; the strength of children's math-gender stereotypes, together with their gender identity, significantly predicted their math self-concepts. Cognitive consistency may be culturally universal and a key mechanism for developmental change in social cognition. We also discovered that Singaporean children's math-gender stereotypes increased as a function of age and that boys identified with math more strongly than did girls despite Singaporean girls' excelling in math. The results reveal both cultural universals and cultural variation in developing social cognition.