Discovering the structure of mathematical problem solving

Effects of a Complex Physical Activity Program on Children's Arithmetic Problem Solving and Arithmetic Reasoning Abilities

Research has shown that higher levels of physical activity are associated with better cognitive performance in children. However, the benefits of physical activity on academic achievement and specifically on mathematics performance need to be further explored. Therefore, this study aimed to investigate the effects of a complex physical activity (CPA) intervention program, including cognitive involvement, on children’s mathematics performance. The participants were 128 children (aged 12−13 years) attending third grade in three middle schools. They were randomly allocated into a CPA intervention (n = 64) or a waitlist control group (n = 64), the latter of which was given a regular and easy-to-perform activity program. At baseline and after the intervention, students’ physical fitness was measured using a battery of standardized motor tests (20 m shuttle run test, curl-up test, push-up test, and sit and reach test). In addition, the AC-MT 11-14 test was administered to allow a standardized and comprehensive assessment of arithmetic problem-solving and arithmetic reasoning abilities. In comparison to the control, the intervention group showed significant improvements (p < 0.001) in comprehension and production (d = 1.88), arithmetic reasoning (d = 2.50), and problem solving (d = 1.32), as well as in 20 m shuttle run test (d = 1.81), push-up test (d = 1.88), curl-up (d = 3.52), and sit and reach (d = 2.52). No significant changes were found in the control group. In conclusion, findings showed that a 12-week CPA intervention program can improve mathematical performance in children in the third grade of middle school. CPA intervention may be an effective method to improve academic performance and avoid student failure.

Behavioral Studies Using Large-Scale Brain Networks – Methods and Validations

Mapping human behaviors to brain activity has become a key focus in modern cognitive neuroscience. As methods such as functional MRI (fMRI) advance cognitive scientists show an increasing interest in investigating neural activity in terms of functional connectivity and brain networks, rather than activation in a single brain region. Due to the noisy nature of neural activity, determining how behaviors are associated with specific neural signals is not well-established. Previous research has suggested graph theory techniques as a solution. Graph theory provides an opportunity to interpret human behaviors in terms of the topological organization of brain network architecture. Graph theory-based approaches, however, only scratch the surface of what neural connections relate to human behavior. Recently, the development of data-driven methods, e.g., machine learning and deep learning approaches, provide a new perspective to study the relationship between brain networks and human behaviors across the whole brain, expanding upon past literatures. In this review, we sought to revisit these data-driven approaches to facilitate our understanding of neural mechanisms and build models of human behaviors. We start with the popular graph theory approach and then discuss other data-driven approaches such as connectome-based predictive modeling, multivariate pattern analysis, network dynamic modeling, and deep learning techniques that quantify meaningful networks and connectivity related to cognition and behaviors. Importantly, for each topic, we discuss the pros and cons of the methods in addition to providing examples using our own data for each technique to describe how these methods can be applied to real-world neuroimaging data.

How the brain negotiates divergent executive processing demands: Evidence of network reorganization in fleeting brain states

During performance in everyday contexts, multiple networks draw from shared executive resources to maintain attention, regulate arousal, and solve problems. At times, requirements for attention and self-regulation appear to be in competition. How does the brain attempt to resolve conflicts arising from such divergent processing demands? Here we demonstrate that the brain is capable of managing multiple processes via rapidly cycling between functional brain states over time, as it is typically regarded. Treating the brain as a complex system, comprising relationships within and between functional networks, we implemented Hidden Markov Modeling (HMM) on electroencephalographic (EEG) data to identify nonlinear brain states in both intra and internetwork synchrony that produced better performance for women subjects who were tasked with solving difficult problems under autobiographically-relevant, evaluative stress. Prior work often found that emotion-regulation and default-mode network (ERN and DMN) activity conflicted with the frontoparietal network's (FPN) ability to facilitate executive functioning necessary for problem solving. Contrastingly, we discovered that fleeting, nonlinear states dominated by FPN and ERN internetwork synchrony supported optimum performance generally, while during stress, states dominated by ERN and DMN intranetwork synchrony were more important for performance. These results imply that the brain may be capable of resolving competing processes through networks' cooperative dynamics. Further, data suggests a novel role for DMN as a mechanism for integrating external threats with internal, self-referent processing during evaluative stress within the observed population.

Context Matters: Situational Stress Impedes Functional Reorganization of Intrinsic Brain Connectivity during Problem-Solving

Extensive research has established a relationship between individual differences in brain activity in a resting state and individual differences in behavior. Conversely, when individuals are engaged in various tasks, certain task-evoked reorganization occurs in brain functional connectivity, which can consequently influence individuals' performance as well. Here, we show that resting state and task-dependent state brain patterns interact as a function of contexts engendering stress. Findings revealed that when the resting state connectome was examined during performance, the relationship between connectome strength and performance only remained for participants under stress (who also performed worse than all other groups on the math task), suggesting that stress preserved brain patterns indicative of underperformance whereas non-stressed individuals spontaneously transitioned out of these patterns. Results imply that stress may impede the reorganization of a functional network in task-evoked brain states. This hypothesis was subsequently verified using graph theory measurements on a functional network, independent of behavior. For participants under stress, the functional network showed less topological alterations compared to non-stressed individuals during the transition from resting state to task-evoked state. Implications are discussed for network dynamics as a function of context.

Neural dynamics of sentiment processing during naturalistic sentence reading

When we read, our eyes move through the text in a series of fixations and high-velocity saccades to extract visual information. This process allows the brain to obtain meaning, e.g., about sentiment, or the emotional valence, expressed in the written text. How exactly the brain extracts the sentiment of single words during naturalistic reading is largely unknown. This is due to the challenges of naturalistic imaging, which has previously led researchers to employ highly controlled, timed word-by-word presentations of custom reading materials that lack ecological validity. Here, we aimed to assess the electrical neural correlates of word sentiment processing during naturalistic reading of English sentences. We used a publicly available dataset of simultaneous electroencephalography (EEG), eye-tracking recordings, and word-level semantic annotations from 7129 words in 400 sentences (Zurich Cognitive Language Processing Corpus; Hollenstein et al., 2018). We computed fixation-related potentials (FRPs), which are evoked electrical responses time-locked to the onset of fixations. A general linear mixed model analysis of FRPs cleaned from visual- and motor-evoked activity showed a topographical difference between the positive and negative sentiment condition in the 224-304 ​ms interval after fixation onset in left-central and right-posterior electrode clusters. An additional analysis that included word-, phrase-, and sentence-level sentiment predictors showed the same FRP differences for the word-level sentiment, but no additional FRP differences for phrase- and sentence-level sentiment. Furthermore, decoding analysis that classified word sentiment (positive or negative) from sentiment-matched 40-trial average FRPs showed a 0.60 average accuracy (95% confidence interval: [0.58, 0.61]). Control analyses ruled out that these results were based on differences in eye movements or linguistic features other than word sentiment. Our results extend previous research by showing that the emotional valence of lexico-semantic stimuli evoke a fast electrical neural response upon word fixation during naturalistic reading. These results provide an important step to identify the neural processes of lexico-semantic processing in ecologically valid conditions and can serve to improve computer algorithms for natural language processing.

Spatiotemporal analysis of event-related fMRI to reveal cognitive states

Cognitive science has a rich history of developing theories of processing that characterize the mental steps involved in performance of many tasks. Recent work in neuroimaging and machine learning has greatly improved our ability to link cognitive processes with what is happening in the brain. This article analyzes a hidden semi-Markov model-multivoxel pattern-analysis (HSMM-MVPA) methodology that we have developed for inferring the sequence of brain states one traverses in the performance of a cognitive task. The method is applied to a functional magnetic resonance imaging (fMRI) experiment where task boundaries are known that should separate states. The method is able to accurately identify those boundaries. Then, applying the method to synthetic data, we explore more fully those factors that influence performance of the method: signal-to-noise ratio, numbers of states, state sojourn times, and numbers of underlying experimental conditions. The results indicate the types of experimental tasks where applications of the HSMM-MVPA method are likely to yield accurate and insightful results.

Faster learners transfer their knowledge better: Behavioral, mnemonic, and neural mechanisms of individual differences in children's learning

Why some children learn, and transfer their knowledge to novel problems, better than others remains an important unresolved question in the science of learning. Here we developed an innovative tutoring program and data analysis approach to investigate individual differences in neurocognitive mechanisms that support math learning and "near" transfer to novel, but structurally related, problems in elementary school children. Following just five days of training, children performed recently trained math problems more efficiently, with greater use of memory-retrieval-based strategies. Crucially, children who learned faster during training performed better not only on trained problems but also on novel problems, and better discriminated trained and novel problems in a subsequent recognition memory task. Faster learners exhibited increased similarity of neural representations between trained and novel problems, and greater differentiation of functional brain circuits engaged by trained and novel problems. These results suggest that learning and near transfer are characterized by parallel learning-rate dependent local integration and large-scale segregation of functional brain circuits. Our findings demonstrate that speed of learning and near transfer are interrelated and identify the neural mechanisms by which faster learners transfer their knowledge better. Our study provides new insights into the behavioral, mnemonic, and neural mechanisms underlying children's learning.

Real World Problem-Solving

Real world problem-solving (RWPS) is what we do every day. It requires flexibility, resilience, resourcefulness, and a certain degree of creativity. A crucial feature of RWPS is that it involves continuous interaction with the environment during the problem-solving process. In this process, the environment can be seen as not only a source of inspiration for new ideas but also as a tool to facilitate creative thinking. The cognitive neuroscience literature in creativity and problem-solving is extensive, but it has largely focused on neural networks that are active when subjects are not focused on the outside world, i.e., not using their environment. In this paper, I attempt to combine the relevant literature on creativity and problem-solving with the scattered and nascent work in perceptually-driven learning from the environment. I present my synthesis as a potential new theory for real world problem-solving and map out its hypothesized neural basis. I outline some testable predictions made by the model and provide some considerations and ideas for experimental paradigms that could be used to evaluate the model more thoroughly.

On the Role of Situational Stressors in the Disruption of Global Neural Network Stability during Problem Solving

When individuals are placed in stressful situations, they are likely to exhibit deficits in cognitive capacity over and above situational demands. Despite this, individuals may still persevere and ultimately succeed in these situations. Little is known, however, about neural network properties that instantiate success or failure in both neutral and stressful situations, particularly with respect to regions integral for problem-solving processes that are necessary for optimal performance on more complex tasks. In this study, we outline how hidden Markov modeling based on multivoxel pattern analysis can be used to quantify unique brain states underlying complex network interactions that yield either successful or unsuccessful problem solving in more neutral or stressful situations. We provide evidence that brain network stability and states underlying synchronous interactions in regions integral for problem-solving processes are key predictors of whether individuals succeed or fail in stressful situations. Findings also suggested that individuals utilize discriminate neural patterns in successfully solving problems in stressful or neutral situations. Findings overall highlight how hidden Markov modeling can provide myriad possibilities for quantifying and better understanding the role of global network interactions in the problem-solving process and how the said interactions predict success or failure in different contexts.

Discovering Event Structure in Continuous Narrative Perception and Memory

During realistic, continuous perception, humans automatically segment experiences into discrete events. Using a novel model of cortical event dynamics, we investigate how cortical structures generate event representations during narrative perception and how these events are stored to and retrieved from memory. Our data-driven approach allows us to detect event boundaries as shifts between stable patterns of brain activity without relying on stimulus annotations and reveals a nested hierarchy from short events in sensory regions to long events in high-order areas (including angular gyrus and posterior medial cortex), which represent abstract, multimodal situation models. High-order event boundaries are coupled to increases in hippocampal activity, which predict pattern reinstatement during later free recall. These areas also show evidence of anticipatory reinstatement as subjects listen to a familiar narrative. Based on these results, we propose that brain activity is naturally structured into nested events, which form the basis of long-term memory representations.

The discovery of processing stages: Extension of Sternberg's method

We introduce a method for measuring the number and durations of processing stages from the electroencephalographic signal and apply it to the study of associative recognition. Using an extension of past research that combines multivariate pattern analysis with hidden semi-Markov models, the approach identifies on a trial-by-trial basis where brief sinusoidal peaks (called bumps) are added to the ongoing electroencephalographic signal. We propose that these bumps mark the onset of critical cognitive stages in processing. The results of the analysis can be used to guide the development of detailed process models. Applied to the associative recognition task, the hidden semi-Markov models multivariate pattern analysis method indicates that the effects of associative strength and probe type are localized to a memory retrieval stage and a decision stage. This is in line with a previously developed the adaptive control of thought-rational process model, called ACT-R, of the task. As a test of the generalization of our method we also apply it to a data set on the Sternberg working memory task collected by Jacobs, Hwang, Curran, and Kahana (2006). The analysis generalizes robustly, and localizes the typical set size effect in a late comparison/decision stage. In addition to providing information about the number and durations of stages in associative recognition, our analysis sheds light on the event-related potential components implicated in the study of recognition memory. (PsycINFO Database Record

Hidden Stages of Cognition Revealed in Patterns of Brain Activation

To advance cognitive theory, researchers must be able to parse the performance of a task into its significant mental stages. In this article, we describe a new method that uses functional MRI brain activation to identify when participants are engaged in different cognitive stages on individual trials. The method combines multivoxel pattern analysis to identify cognitive stages and hidden semi-Markov models to identify their durations. This method, applied to a problem-solving task, identified four distinct stages: encoding, planning, solving, and responding. We examined whether these stages corresponded to their ascribed functions by testing whether they are affected by appropriate factors. Planning-stage duration increased as the method for solving the problem became less obvious, whereas solving-stage duration increased as the number of calculations to produce the answer increased. Responding-stage duration increased with the difficulty of the motor actions required to produce the answer.

A statistical approach for segregating cognitive task stages from multivariate fMRI BOLD time series

Multivariate pattern analysis can reveal new information from neuroimaging data to illuminate human cognition and its disturbances. Here, we develop a methodological approach, based on multivariate statistical/machine learning and time series analysis, to discern cognitive processing stages from functional magnetic resonance imaging (fMRI) blood oxygenation level dependent (BOLD) time series. We apply this method to data recorded from a group of healthy adults whilst performing a virtual reality version of the delayed win-shift radial arm maze (RAM) task. This task has been frequently used to study working memory and decision making in rodents. Using linear classifiers and multivariate test statistics in conjunction with time series bootstraps, we show that different cognitive stages of the task, as defined by the experimenter, namely, the encoding/retrieval, choice, reward and delay stages, can be statistically discriminated from the BOLD time series in brain areas relevant for decision making and working memory. Discrimination of these task stages was significantly reduced during poor behavioral performance in dorsolateral prefrontal cortex (DLPFC), but not in the primary visual cortex (V1). Experimenter-defined dissection of time series into class labels based on task structure was confirmed by an unsupervised, bottom-up approach based on Hidden Markov Models. Furthermore, we show that different groupings of recorded time points into cognitive event classes can be used to test hypotheses about the specific cognitive role of a given brain region during task execution. We found that whilst the DLPFC strongly differentiated between task stages associated with different memory loads, but not between different visual-spatial aspects, the reverse was true for V1. Our methodology illustrates how different aspects of cognitive information processing during one and the same task can be separated and attributed to specific brain regions based on information contained in multivariate patterns of voxel activity.

Learning Problem-Solving Rules as Search Through a Hypothesis Space

Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem property such as computational difficulty of the rules biased the search process and so affected learning. Experiment 2 examined the impact of examples as instructional tools and found that their effectiveness was determined by whether they uniquely pointed to the correct rule. Experiment 3 compared verbal directions with examples and found that both could guide search. The final experiment tried to improve learning by using more explicit verbal directions or by adding scaffolding to the example. While both manipulations improved learning, learning still took the form of a search through a hypothesis space of possible rules. We describe a model that embodies two assumptions: (1) the instruction can bias the rules participants hypothesize rather than directly be encoded into a rule; (2) participants do not have memory for past wrong hypotheses and are likely to retry them. These assumptions are realized in a Markov model that fits all the data by estimating two sets of probabilities. First, the learning condition induced one set of Start probabilities of trying various rules. Second, should this first hypothesis prove wrong, the learning condition induced a second set of Choice probabilities of considering various rules. These findings broaden our understanding of effective instruction and provide implications for instructional design.

Not taking the easy road: When similarity hurts learning

Two experimental studies examined the effects of example format and example similarity on mathematical problem solving across different learning contexts. Participants were more successful inducing a correct problem-solving rule when they were provided with annotated examples rather than nonannotated examples. The effects of example similarity varied depending on learning context. In Experiment 1, by presenting an example and problem simultaneously, a direct comparison was possible between the cases. When the examples were similar, participants relied on superficial analogies that hurt learning. When an example was dissimilar from the given problem, participants appeared to study the example first to induce a solution procedure and then apply the rule to the problem, thus resulting in better learning and transfer. However, in Experiment 2 where the example and problem were presented in a sequential manner, the effect disappeared because the learning context did not support a direct comparison. We conclude that comparison is not inherently good for promoting learning and transfer, rather its effect depends on whether it supports relational mapping that is essential for schema acquisition.