The effect of problem structure on problem-solving: an fMRI study of word versus number problems

The neuroscience basis and educational interventions of mathematical cognitive impairment and anxiety: a systematic literature review

Introduction

Mathematics is a fundamental subject with significant implications in education and neuroscience. Understanding the cognitive processes underlying mathematical cognition is crucial for enhancing educational practices. However, mathematical cognitive impairment and anxiety significantly hinder learning and application in this field. This systematic literature review aims to investigate the neuroscience basis and effective educational interventions for these challenges.

Methods

The review involved a comprehensive screening of 62 research articles that meet the ESSA evidence levels from multiple databases. The selection criteria focused on studies employing various methodologies, including behavioral experiments and neuroimaging techniques, to explore the neuroscience underpinnings and educational interventions related to mathematical cognitive impairment and anxiety.

Results

The review identified key themes and insights into the neuroscience basis of mathematical cognitive impairment and anxiety. It also examined their impact on educational practices, highlighting the interplay between cognitive processes and educational outcomes. The analysis of these studies revealed significant findings on how these impairments and anxieties manifest and can be addressed in educational settings.

Discussion

The review critically analyzes the shortcomings of existing research, noting gaps and limitations in current understanding and methodologies. It emphasizes the need for more comprehensive and diverse studies to better understand these phenomena. The discussion also suggests new directions and potential improvement strategies for future research, aiming to contribute to more effective educational interventions and enhanced learning experiences in mathematics.

Conclusion

This systematic review provides valuable insights into the neuroscience basis of mathematical cognitive impairment and anxiety, offering a foundation for developing more effective educational strategies. It underscores the importance of continued research in this area to improve educational outcomes and support learners facing these challenges.

Quantitative modelling demonstrates format-invariant representations of mathematical problems in the brain

Mathematical problems can be described in either symbolic form or natural language. Previous studies have reported that activation overlaps exist for these two types of mathematical problems, but it is unclear whether they are based on similar brain representations. Furthermore, quantitative modelling of mathematical problem solving has yet to be attempted. In the present study, subjects underwent 3 h of functional magnetic resonance experiments involving math word and math expression problems, and a read word condition without any calculations was used as a control. To evaluate the brain representations of mathematical problems quantitatively, we constructed voxel-wise encoding models. Both intra- and cross-format encoding modelling significantly predicted brain activity predominantly in the left intraparietal sulcus (IPS), even after subtraction of the control condition. Representational similarity analysis and principal component analysis revealed that mathematical problems with different formats had similar cortical organization in the IPS. These findings support the idea that mathematical problems are represented in the brain in a format-invariant manner.

Operation-Specific Lexical Consistency Effect in Fronto-Insular-Parietal Network During Word Problem Solving

The practice of mathematical word problem is ubiquitous and thought to impact academic achievement. However, the underlying neural mechanisms are still poorly understood. In this study, we investigate how lexical consistency of word problem description is modulated in adults' brain responses during word problem solution. Using functional magnetic resonance imaging methods, we examined compare word problems that included relational statements, such as "A dumpling costs 9 dollars. A wonton is 2 dollars less than a dumpling. How much does a wonton cost?" and manipulated lexical consistency (consistent: the relational term consistent with the operation to be performed, e.g., more-addition/inconsistent: e.g., less-addition) and problem operation (addition/subtraction). We found a consistency by operation interaction in the widespread fronto-insular-parietal activations, including the anterior insula, dorsoanterior cingulate cortex, middle frontal gyrus, and intraparietal sulcus, such that inconsistent problems engaged stronger activations than consistent problems for addition, whereas the consistency effect was inverse for subtraction. Critically, these results were more salient in the less successful problem solvers than their more successful peers. Our study is the first to demonstrate that lexical consistency effects on arithmetic neural networks are modulated during reading word problem that required distinct arithmetic operations. More broadly, our study has strong potentials to add linkage between neuroscience and education by remediating deficits and enhance instruction design in the school curriculum.

Neural representations of transitive relations predict current and future math calculation skills in children

A large body of evidence suggests that math learning in children is built upon innate mechanisms for representing numerical quantities in the intraparietal sulcus (IPS). Learning math, however, is about more than processing quantitative information. It is also about understanding relations between quantities and making inferences based on these relations. Consistent with this idea, recent behavioral studies suggest that the ability to process transitive relations (A > B, B > C, therefore A > C) may contribute to math skills in children. Here we used fMRI coupled with a longitudinal design to determine whether the neural processing of transitive relations in children could predict their current and future math skills. At baseline (T₁), children (n = 31) processed transitive relations in an MRI scanner. Math skills were measured at T₁ and again 1.5 years later (T₂). Using a machine learning approach with cross-validation, we found that activity associated with the representation of transitive relations in the IPS predicted math calculation skills at both T₁ and T₂. Our study highlights the potential of neurobiological measures of transitive reasoning for forecasting math skills in children, providing additional evidence for a link between this type of reasoning and math learning.

The Artery of Aphasia, A Uniquely Sensitive Posterior Temporal Middle Cerebral Artery Branch that Supplies Language Areas in the Brain: Anatomy and Report of Four Cases

BACKGROUND

Arterial disruption during brain surgery can cause devastating injuries to wide expanses of white and gray matter beyond the tumor resection cavity. Such damage may occur as a result of disrupting blood flow through en passage arteries. Identification of these arteries is critical to prevent unforeseen neurologic sequelae during brain tumor resection. In this study, we discuss one such artery, termed the artery of aphasia (AoA), which when disrupted can lead to receptive and expressive language deficits.

METHODS

We performed a retrospective review of all patients undergoing an awake craniotomy for resection of a glioma by the senior author from 2012 to 2018. Patients were included if they experienced language deficits secondary to postoperative infarction in the left posterior temporal lobe in the distribution of the AoA. The gross anatomy of the AoA was then compared with activation likelihood estimations of the auditory and semantic language networks using coordinate-based meta-analytic techniques.

RESULTS

We identified 4 patients with left-sided posterior temporal artery infarctions in the distribution of the AoA on diffusion-weighted magnetic resonance imaging. All 4 patients developed substantial expressive and receptive language deficits after surgery. Functional language improvement occurred in only 2/4 patients. Activation likelihood estimations localized parts of the auditory and semantic language networks in the distribution of the AoA.

CONCLUSIONS

The AoA is prone to blood flow disruption despite benign manipulation. Patients seem to have limited capacity for speech recovery after intraoperative ischemia in the distribution of this artery, which supplies parts of the auditory and semantic language networks.

Fronto-insular-parietal network engagement underlying arithmetic word problem solving

Mathematical word problems are ubiquitous and standard for teaching and evaluating generalization of mathematical knowledge for real-world contexts. It is therefore concerning that the neural mechanisms of word problem solving are not well understood, as these insights represent strong potential for improving education and remediating deficits in this domain. Here, we investigate neural response to word problems via functional magnetic resonance imaging (fMRI). Healthy adults performed sentence judgment tasks on word problems that either contained one-step mathematical operations, or nonarithmetic judgments on parallel narratives without any numerical information. Behavioral results suggested that the composite efficiency measurement of combining accuracy and RT did not differ between the two problem types. Arithmetic sentence judgments elicited greater activation in the fronto-insular-parietal network including intraparietal sulcus (IPS), dorsolateral prefrontal cortex (PFC), and anterior insula (AI) than narrative sentence judgment. Narrative sentence judgments, conversely, resulted in greater activation predominantly in the left ventral PFC, angular gyrus and perisylvian cortex compared with reading arithmetic sentences. Moreover, task-dependent functional connectivity analyses showed the AI circuits were more strongly coupled with IPS during arithmetic sentence judgments than nonarithmetic sentences. Finally, activations in the IPS during arithmetic were highly correlated with out-of-scanner performance on a distinct set of problems with the same characteristics. These results show arithmetic word problem performance differences may rely more heavily on fronto-insular-parietal circuits for mathematical model building than narrative text comprehension of similar difficulty. More broadly, our study suggests that quantitative measurements of brain mechanisms can provide pivotal role for uncovering crucial arithmetic skills.

Executive Functions Brain System: An Activation Likelihood Estimation Meta-analytic Study

Background and objective

To characterize commonalities and differences between two executive functions: reasoning and inhibitory control.

Methods

A total of 5,974 participants in 346 fMRI experiments of inhibition or reasoning were selected. First level analysis consisted of Analysis of Likelihood Estimation (ALE) studies performed in two pooled data groups: (a) brain areas involved in reasoning and (b) brain areas involved in inhibition. Second level analysis consisted of two contrasts: (i) brain areas involved in reasoning but not in inhibition and (ii) brain areas involved in inhibition but not in reasoning. Lateralization Indexes were calculated.

Results

Four brain areas appear as the most critical: the dorsolateral aspect of the frontal lobes, the superior parietal lobules, the mesial aspect of the premotor area (supplementary motor area), and some subcortical areas, particularly the putamen and the thalamus. ALE contrasts showed significant differentiation of the networks, with the reasoning > inhibition-contrast showing a predominantly leftward participation, and the inhibition > reasoning-contrast, a clear right advantage.

Conclusion

Executive functions are mediated by sizable brain areas including not only cortical, but also involving subcortical areas in both hemispheres. The strength of activation shows dissociation between the hemispheres for inhibition (rightward) and reasoning (leftward) functions.

Meta-analytic evidence for a core problem solving network across multiple representational domains

Problem solving is a complex skill engaging multi-stepped reasoning processes to find unknown solutions. The breadth of real-world contexts requiring problem solving is mirrored by a similarly broad, yet unfocused neuroimaging literature, and the domain-general or context-specific brain networks associated with problem solving are not well understood. To more fully characterize those brain networks, we performed activation likelihood estimation meta-analysis on 280 neuroimaging problem solving experiments reporting 3166 foci from 1919 individuals across 131 papers. The general map of problem solving revealed broad fronto-cingulo-parietal convergence, regions similarly identified when considering separate mathematical, verbal, and visuospatial problem solving domain-specific analyses. Conjunction analysis revealed a common network supporting problem solving across diverse contexts, and difference maps distinguished functionally-selective sub-networks specific to task type. Our results suggest cooperation between representationally specialized sub-network and whole-brain systems provide a neural basis for problem solving, with the core network contributing general purpose resources to perform cognitive operations and manage problem demand. Further characterization of cross-network dynamics could inform neuroeducational studies on problem solving skill development.

What Does "Being an Expert" Mean to the Brain? Functional Specificity and Connectivity in Expertise

To what extent is varying cognitive expertise reflected in the brain's functional specificity and connectivity? We addressed this question by examining expertise in mathematics based on the fact that mathematical skills are one of the most critical cognitive abilities known to be a good predictor of academic achievement. We investigated processing of hierarchical structures, which is a fundamental process for building complex cognitive architecture. Experts and nonexperts in mathematics participated in processing hierarchical structures using algebraic expressions. Results showed that a modulating effect depending on expertise was observed specifically in nonexperts in the left inferior frontal gyrus around pars triangularis and frontal sulcus, the left intraparietal sulcus, and the right inferior parietal lobule. This expertise-dependent pattern of activation led to a crucial dissociation within the left prefrontal cortex. More interestingly, task-related functional networks were also modulated differently in the frontoparietal network for relatively good performance and in the frontostriatal network for poor performance. The present study indicates that a high level of expertise is evident in a small number of specific brain regions, whereas a low level of expertise is reflected by broadly distributed brain areas, along with divergent functional connectivity between experts and nonexperts.

Amygdala real-time functional magnetic resonance imaging neurofeedback for major depressive disorder: A review

Advances in imaging technologies have allowed for the analysis of functional magnetic resonance imaging data in real-time (rtfMRI), leading to the development of neurofeedback (nf) training. This rtfMRI-nf training utilizes functional magnetic resonance imaging (fMRI) tomographic localization capacity to allow a person to see and regulate the localized hemodynamic signal from his or her own brain. In this review, we summarize the results of several studies that have developed and applied neurofeedback training to healthy and depressed individuals with the amygdala as the neurofeedback target and the goal to increase the hemodynamic response during positive autobiographical memory recall. We review these studies and highlight some of the challenges and advances in developing an rtfMRI-nf paradigm for broader use in psychiatric populations. The work described focuses on our line of research aiming to develop the rtfMRI-nf into an intervention, and includes a discussion of the selection of a region of interest for feedback, selecting a control condition, behavioral and cognitive effects of training, and predicting which participants are most likely to respond well to training. While the results of these studies are encouraging and suggest the clinical potential of amygdala rtfMRI-nf in alleviating symptoms of major depressive disorder, larger studies are warranted to confirm its efficacy.

Resting-state functional connectivity modulation and sustained changes after real-time functional magnetic resonance imaging neurofeedback training in depression

Amygdala hemodynamic responses to positive stimuli are attenuated in major depressive disorder (MDD) and normalize with remission. Real-time functional magnetic resonance imaging neurofeedback (rtfMRI-nf) training with the goal of upregulating amygdala activity during recall of happy autobiographical memories (AMs) has been suggested, and recently explored, as a novel therapeutic approach that resulted in improvement in self-reported mood in depressed subjects. In this study, we assessed the possibility of sustained brain changes as well as the neuromodulatory effects of rtfMRI-nf training of the amygdala during recall of positive AMs in MDD and matched healthy subjects. MDD and healthy subjects went through one visit of rtfMRI-nf training. Subjects were assigned to receive active neurofeedback from the left amygdale (LA) or from a control region putatively not modulated by AM recall or emotion regulation, that is, the left horizontal segment of the intraparietal sulcus. To assess lasting effects of neurofeedback in MDD, the resting-state functional connectivity before and after rtfMRI-nf in 27 depressed subjects, as well as in 27 matched healthy subjects before rtfMRI-nf was measured. Results show that abnormal hypo-connectivity with LA in MDD is reversed after rtfMRI-nf training by recalling positive AMs. Although such neuromodulatory changes are observed in both MDD groups receiving feedback from respective active and control brain regions, only in the active group are larger decreases of depression severity associated with larger increases of amygdala connectivity and a significant, positive correlation is found between the connectivity changes and the days after neurofeedback. In addition, active neurofeedback training of the amygdala enhances connectivity with temporal cortical regions, including the hippocampus. These results demonstrate lasting brain changes induced by amygdala rtfMRI-nf training and suggest the importance of reinforcement learning in rehabilitating emotion regulation in depression.

Brain activity associated with translation from a visual to a symbolic representation in algebra and geometry

This paper presents a small part of a larger interdisciplinary study that investigates brain activity (using event related potential methodology) of male adolescents when solving mathematical problems of different types. The study design links mathematics education research with neurocognitive studies. In this paper we performed a comparative analysis of brain activity associated with the translation from visual to symbolic representations of mathematical objects in algebra and geometry. Algebraic tasks require translation from graphical to symbolic representation of a function, whereas tasks in geometry require translation from a drawing of a geometric figure to a symbolic representation of its property. The findings demonstrate that electrical activity associated with the performance of geometrical tasks is stronger than that associated with solving algebraic tasks. Additionally, we found different scalp topography of the brain activity associated with algebraic and geometric tasks. Based on these results, we argue that problem solving in algebra and geometry is associated with different patterns of brain activity.

Real-time FMRI neurofeedback training of amygdala activity in patients with major depressive disorder

BACKGROUND

Amygdala hemodynamic responses to positive stimuli are attenuated in major depressive disorder (MDD), and normalize with remission. Real-time functional MRI neurofeedback (rtfMRI-nf) offers a non-invasive method to modulate this regional activity. We examined whether depressed participants can use rtfMRI-nf to enhance amygdala responses to positive autobiographical memories, and whether this ability alters symptom severity.

METHODS

Unmedicated MDD subjects were assigned to receive rtfMRI-nf from either left amygdala (LA; experimental group, n = 14) or the horizontal segment of the intraparietal sulcus (HIPS; control group, n = 7) and instructed to contemplate happy autobiographical memories (AMs) to raise the level of a bar representing the hemodynamic signal from the target region to a target level. This 40s Happy condition alternated with 40s blocks of rest and counting backwards. A final Transfer run without neurofeedback information was included.

RESULTS

Participants in the experimental group upregulated their amygdala responses during positive AM recall. Significant pre-post scan decreases in anxiety ratings and increases in happiness ratings were evident in the experimental versus control group. A whole brain analysis showed that during the transfer run, participants in the experimental group had increased activity compared to the control group in left superior temporal gyrus and temporal polar cortex, and right thalamus.

CONCLUSIONS

Using rtfMRI-nf from the left amygdala during recall of positive AMs, depressed subjects were able to self-regulate their amygdala response, resulting in improved mood. Results from this proof-of-concept study suggest that rtfMRI-nf training with positive AM recall holds potential as a novel therapeutic approach in the treatment of depression.

The impact of finger counting habits on arithmetic in adults and children

Here, we explored the impact of finger counting habits on arithmetic in both adults and children. Two groups of participants were examined, those that begin counting with their left hand (left-starters) and those that begin counting with their right hand (right-starters). For the adults, performance on an addition task in which participants added 2 two-digit numbers was compared. The results revealed that left-starters were slower than right-starters when adding and they had lower forward and backward digit-span scores. The children (aged 5-12) showed similar results on a single-digit timed addition task-right-starters outperformed left-starters. However, the children did not reveal differences in working memory or verbal and non-verbal intelligence as a function of finger counting habit. We argue that the motor act of finger counting influences how number is represented and suggest that left-starters may have a more bilateral representation that accounts for the slower processing.