The Neuroscience of Mathematical Cognition and Learning

The synergistic potential of cognitive neuroscience and education for efficient learning has attracted considerable interest from the general public, teachers, parents, academics and policymakers alike. This review is aimed at providing 1) an accessible and general overview of the research progress made in cognitive neuroscience research in understanding mathematical learning and cognition, and 2) understanding whether there is sufficient evidence to suggest that neuroscience can inform mathematics education at this point. We also highlight outstanding questions with implications for education that remain to be explored in cognitive neuroscience. The field of cognitive neuroscience is growing rapidly. The findings that we are describing in this review should be evaluated critically to guide research communities, governments and funding bodies to optimise resources and address questions that will provide practical directions for short- and long-term impact on the education of future generations

Noninvasive brain stimulation techniques can modulate cognitive processing

Recent methods that allow a noninvasive modulation of brain activity are able to modulate human cognitive behavior. Among these methods are transcranial electric stimulation and transcranial magnetic stimulation that both come in multiple variants. A property of both types of brain stimulation is that they modulate brain activity and in turn modulate cognitive behavior. Here, we describe the methods with their assumed neural mechanisms for readers from the economic and social sciences and little prior knowledge of these techniques. Our emphasis is on available protocols and experimental parameters to choose from when designing a study. We also review a selection of recent studies that have successfully applied them in the respective field. We provide short pointers to limitations that need to be considered and refer to the relevant papers where appropriate

Winning versus losing during gambling and its neural correlates

Humans often make decisions which maximize an internal utility function. For example, humans often maximize their expected reward when gambling and this is considered as a "rational" decision. However, humans tend to change their betting strategies depending on how they "feel". If someone has experienced a losing streak, they may "feel" that they are more likely to win on the next hand even though the odds of the game have not changed. That is, their decisions are driven by their emotional state. In this paper, we investigate how the human brain responds to wins and losses during gambling. Using a combination of local field potential recordings in human subjects performing a financial decision-making task, spectral analyses, and non-parametric cluster statistics, we investigated whether neural responses in different cognitive and limbic brain areas differ between wins and losses after decisions are made. In eleven subjects, the neural activity modulated significantly between win and loss trials in one brain region: the anterior insula ($p=0.01$). In particular, gamma activity (30-70 Hz) increased in the anterior insula when subjects just realized that they won. Modulation of metabolic activity in the anterior insula has been observed previously in functional magnetic resonance imaging studies during decision making and when emotions are elicited. However, our study is able to characterize temporal dynamics of electrical activity in this brain region at the millisecond resolution while decisions are made and after outcomes are revealed

Verbal paired associates and the hippocampus: The role of scenes

It is widely agreed that patients with bilateral hippocampal damage are impaired at binding pairs of words together. Consequently, the verbal paired associates (VPA) task has become emblematic of hippocampal function. This VPA deficit is not well understood and is particularly difficult for hippocampal theories with a visuospatial bias to explain (e.g., cognitive map and scene construction theories). Resolving the tension among hippocampal theories concerning the VPA could be important for leveraging a fuller understanding of hippocampal function. Notably, VPA tasks typically use high imagery concrete words and so conflate imagery and binding. To determine why VPA engages the hippocampus, we devised an fMRI encoding task involving closely matched pairs of scene words, pairs of object words, and pairs of very low imagery abstract words. We found that the anterior hippocampus was engaged during processing of both scene and object word pairs in comparison to abstract word pairs, despite binding occurring in all conditions. This was also the case when just subsequently remembered stimuli were considered. Moreover, for object word pairs, fMRI activity patterns in anterior hippocampus were more similar to those for scene imagery than object imagery. This was especially evident in participants who were high imagery users and not in mid and low imagery users. Overall, our results show that hippocampal engagement during VPA, even when object word pairs are involved, seems to be evoked by scene imagery rather than binding. This may help to resolve the issue that visuospatial hippocampal theories have in accounting for verbal memory

From counting to retrieving: Neural networks underlying alphabet arithmetic learning

This fMRI study aimed at unraveling the neural basis of learning alphabet arithmetic facts, as a proxy of the transition from slow and effortful procedural counting-based processing to fast and effortless processing as it occurs in learning addition arithmetic facts. Neural changes were tracked while participants solved alphabet arithmetic problems in a verification task (e.g., F + 4 = J). Problems were repeated across four learning blocks. Two neural networks with opposed learning-related changes were identified. Activity in a network consisting of basal ganglia and parieto-frontal areas decreased with learning, which is in line with a reduction of the involvement of procedure-based processing. Conversely, activity in a network involving the left angular gyrus and, to a lesser extent, the hippocampus gradually increases with learning, evidencing the gradual involvement of retrieval-based processing. Connectivity analyses gave insight in the functional relationship between the two networks. Despite the opposing learning-related trajectories, it was found that both networks become more integrated. Taking alphabet arithmetic as a proxy for learning arithmetic, the present results have implications for current theories of learning arithmetic facts and can give direction to future developments

Neural circuits involved in mental arithmetic: Evidence from Customized Arithmetic Training

An arithmetic training study was conducted using a novel paradigm known as Customized Arithmetic Training (CAT). Using the CAT system, self-reports obtained from the participants were used to generate individually tailored problem sets. These problem sets balanced strategy use such that each participant started with an equal amount of problems solved by fact retrieval (e.g., 2 + 2 = 4) and an equal amount of problems solved by procedural calculation (e.g., 34 + 37). Following the training period, participants solved trained and untrained problems from their customized arithmetic sets while undergoing an fMRI scan, after which they again provided self-reported strategy. Through the use of the CAT paradigm, which tracks (for the first time) arithmetic strategy both pre- and post-training, the neural correlates of arithmetic learning were examined by separating calculated problems which became memorized through training from problems that were rehearsed but did not show a shift in strategy. This analysis produced results consistent with previous studies of arithmetic training, namely a shift from widespread fronto-parietal activation to focal activation of the angular gyrus. However, it also produced several novel findings relating to neural correlates of mental arithmetic, namely an association between right anterior hippocampus in fact retrieval as well as evidence of a temporal gradient which affected brain activity when comparing new vs old arithmetic facts. Furthermore, analysis of training effects on calculated problems (which did not become memorized) revealed a modulation of activity in the putamen, a structure commonly associated with the procedural memory system

A Conceptual Framework for Mathematical Ability Analysis through the Lens of Cultural Neuroscience

AbstractThis paper present a conceptual framework that will be used for analyzing divergence in mathematical thinking, skills, abilities, processes and achievements in mathematics through the lens of cultural neuroscience. The bidirectional interface between mathematical thinking and cultural neuroscience is used to explore different learning styles, cognition patterns and neural activities in response of mathematical thinking influenced by culture. Research questions are emerged as how do innate mathematical abilities, plasticity of the young brains and the mathematical cultural environment contribute to mathematical thinking? Why do a group of students from one ethnicity tend to achieve higher scores in mathematics than a group of students from another ethnicity? How does cultural neuroscience report the differences in mathematical thinking and learning trajectories? How does culture accelerate the mathematical thinking?

Comparative Study between Drill Skill and Concept Attainment Model towards Physics Learning Achievement

Alternative learning model that can be used in teaching physics to overcome the problems of lack of student learning achievement is a model of skill training (drill skills, and the concept attainment model. Drill skill model is a teaching technique in which students carry out training activities on what they have learned, so that the material already taught more embedded in the minds of students, and students will have the dexterity or higher, while the concept attainment is a model of achievement of learning model that is designed to help students to be more easily learn a concept. The purpose of this study was to compare the results between student who was teached with drill skill model and concept attainment model. The quasi-experimental type was used. Sampling was done randomly in order to obtain two classes one for the first experimental group with drill skill, and the second one for the second experimental group with concept attainment model. These results suggest that the science-physics learning achievement of students with drill skill model is better than using a concept attainment model

Emerging methods for conceptual modelling in neuroimaging

Some open theoretical questions are addressed on how the mind and brain represent and process concepts, particularly as they are instantiated in particular human languages. Recordings of neuroimaging data should provide a suitable empirical basis for investigating this topic, but the complexity and variety of language demands appropriate data-driven approaches. In this review we argue for a particular suite of methodologies, based on multivariate classification techniques which have proven to be powerful tools for distinguishing neural and cognitive states in fMRI. A combination of larger scale neuroimaging studies are introduced with different monolingual and bilingual populations, and hybrid computational analyses that use encoded implementations of existing theories of conceptual organisation to probe those data. We develop a suite of methodologies that holds the promise of being able to holistically elicit, record and model neural processing during language comprehension and production