Fact Retrieval Research Articles

The Efficacy of Mnemonic Strategies in Improving the Basic Multiplication Facts Retrieval

The current quasi-experimental study aims to investigate the efficacy of mnemonic strategies (Visual imagery and Story-linking) to improve the basic multiplication fact retrieval of grade 3 students with mathematics difficulties. The authors employed a quantitative approach within the matching-only pretest-post-test control group design to analyze the data on 206 subjects, of whom 78 exhibited mathematical difficulties. The study was conducted in eight inclusive primary schools in Purwakarta City, Indonesia. The research findings indicated that the N-gain acquisition of students in the experimental group (0.38) outperformed students in the control group (0.11). Similarly, the N-gain acquisition of students with mathematics difficulties in the experimental group (0.26) indicated a higher enhancement than those in the control group (0.08). Overall, the mnemonic strategies improved the students’ retrieval of basic multiplication facts on students with and without mathematics difficulties. However, mnemonic strategies have successfully achieved two of the Sustainable Development Goals 4 (SDG 4) by the 2030 Agenda for Sustainable Development on ensuring students with disabilities as one of the vulnerable groups, have equal access to education and guaranteeing both male and females are literate and numerically literate. These findings have practical implications for educators, providing them with actionable insights to develop effective teaching strategies for students with mathematics difficulties.

Teaching K–3 Multi-Digit Arithmetic Computation to Students with Slow Language Processing

The purpose of this article is to present three related studies that build on each other to demonstrate first the need and then the efficacy of the Blended Arithmetic Curriculum (BAC) to help students overcome both slow language processing and the environmental effects of being a student in an urban school district. The author’s underlying theory is that K–3 students with slow language processing may be good at complex reasoning, but still struggle with retrieving basic computational facts. Nonetheless, if they did not learn their facts, these students would struggle with K–3 multi-digit arithmetic computation, and ultimately struggle with their hypothesized strength: seeing numeric patterns as would be needed in university level computation. To teach arithmetic facts conceptually, the author developed a paper and pencil curriculum that first teaches complex multi-digit addition with regrouping using a limited number of facts such as 5 + 5, 9 + 1, 1 + 9; 7 + 7, 7 + 8, 8 + 7, and 8 + 8 in problems such as 197 + 108 = 305 so that fact retrieval and computation are fast and accurate. At the end of 2nd grade, urban students with learning disabilities solved 42 two-digit by two-digit problems with 92 percent accuracy in an average of 7 min. The results matched those of suburban students and were significantly faster and more accurate than general education students in the same urban school.

Large language models for air transportation: A critical review

In the past decade, Artificial Intelligence (AI) has contributed to the improvement of various aviation aspects, including flight plan optimization, the development of autonomous systems, performing predictive analytics, as well as in passenger / crew assistance systems. The latest AI technology to potentially revolutionize air transportation are so-called Large Language Models (LLMs), which have an outstanding ability to process and generate human-like text. The application areas for LLMs cover nearly all aspects of air transportation, through language processing, content generation, and problem solving. In this study, we discuss the potential of this impact with two major contributions. First, we have performed an experimental evaluation of twelve commonly-used LLMs concerning their performance of air transportation related subjects, covering fact retrieval, complex reasoning abilities, and explanation tasks. Second, we have performed a survey among graduate students at Beihang University, a leading aviation university in China, to explore the experiences and uses of LLMs. We believe that our study makes a significant contribution towards the dissemination and application of LLMs in the air transportation domain.

Profiles of mathematical deficits in children with dyslexia

Despite a high rate of concurrent mathematical difficulties among children with dyslexia, we still have limited information regarding the prevalence and severity of mathematical deficits in this population. To address this gap, we developed a comprehensive battery of cognitive tests, known as the UCSF Mathematical Cognition Battery (MCB), with the aim of identifying deficits in four distinct mathematical domains: number processing, arithmetical procedures, arithmetic facts retrieval, and geometrical abilities. The mathematical abilities of a cohort of 75 children referred to the UCSF Dyslexia Center with a diagnosis of dyslexia, along with 18 typically developing controls aged 7 to 16, were initially evaluated using a behavioral neurology approach. A team of professional clinicians classified the 75 children with dyslexia into five groups, based on parents’ and teachers’ reported symptoms and clinical history. These groups included children with no mathematical deficits and children with mathematical deficits in number processing, arithmetical procedures, arithmetic facts retrieval, or geometrical abilities. Subsequently, the children underwent evaluation using the MCB to determine concordance with the clinicians’ impressions. Additionally, neuropsychological and cognitive standardized tests were administered. Our study reveals that within a cohort of children with dyslexia, 66% exhibit mathematical deficits, and among those with mathematical deficits, there is heterogeneity in the nature of these deficits. If these findings are confirmed in larger samples, they can potentially pave the way for new diagnostic approaches, consistent subtype classification, and, ultimately personalized interventions.

Resolving Zero-Shot and Fact-Based Visual Question Answering via Enhanced Fact Retrieval

Resolving Zero-Shot and Fact-Based Visual Question Answering via Enhanced Fact Retrieval

Formal model of multi-agent architecture of a software system based on knowledge interpretation

The use of agents across diverse domains within computer science and artificial intelligence is experiencing a notable surge in response to the imperatives of adaptability, efficiency, and scalability. The subject of this study is the application of formal methods to furnish a framework for knowledge interpretation with a specific focus on the agent-based paradigm in software engineering. This study aims to advance a formal approach to knowledge interpretation by leveraging the agent-based paradigm. The objectives are as follows: 1) to examine the current state of the agent-based paradigm in software engineering; 2) to describe the basic concepts of the knowledge interpretation approach; 3) to study the general structure of the rule extraction task; 4) to develop the reference structure of knowledge interpretation; 5) to develop a multi-agent system architecture; 6) and to discuss the research results. This study employs formal methods, including the use of closed path rules and predicate logic. Specifically, the integration of closed path rules contributes to the extraction and explication of facts from extensive knowledge bases. The obtained results encompass the following: 1) a rule mining approach grounded in closed path rules and tailored for processing extensive datasets; 2) a formalization of relevance that facilitates the scrutiny and automated exclusion of irrelevant fragments from the explanatory framework; and 3) the realization of a multi-agent system predicated on the synergy among five distinct types of agents, dedicated to rule extraction and the interpretation of acquired knowledge. This paper provides an example of the application of the proposed formal tenets, demonstrating their practical context. The conclusion underscores that the agent-based paradigm, with its emphasis on decentralized and autonomous entities, presents an innovative framework for handling the intricacies of knowledge processing. It extends to the retrieval of facts and rules. By distributing functions across multiple agents, the framework offers a dynamic and scalable solution to effectively interpret vast knowledge repositories. This approach is particularly valuable in scenarios where traditional methods may struggle to cope with the volume and complexity of information.

Brain Active Areas Associated with a Mental Arithmetic Task: An eLORETA Study.

The neural underpinnings of mental calculation, the fundamentals of arithmetic representations and processes, and the development of arithmetic abilities have been explored by researchers over the years. In the present work, we report a study that analyzes the brain-activated areas of a group of 35 healthy subjects (9 males, 26 females, mean age ± SD = 18.23 ± 2.20 years) who performed a serial subtraction arithmetic task. In contrast to most of the studies in the literature based on fMRI, we performed the brain active source reconstruction starting from EEG signals by means of the eLORETA method. In particular, the subjects were classified as bad counters or good counters, according to the results of the task, and the brain activity of the two groups was compared. The results were statistically significant only in the beta band, revealing that the left limbic lobe was found to be more active in people showing better performance. The limbic lobe is involved in visuospatial processing, memory, arithmetic fact retrieval, and emotions. However, the role of the limbic lobe in mental arithmetic has been barely explored, so these interesting findings could represent a starting point for future in-depth analyses. Since there is evidence in the literature that the motor system is affected by the execution of arithmetic tasks, a more extensive knowledge of the brain activation associated with arithmetic tasks could be exploited not only for the assessment of mathematical skills but also in the evaluation of motor impairments and, consequently, in rehabilitation for motor disorders.

The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia

Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.

Disconnection in a left-hemispheric temporo-parietal network impairs multiplication fact retrieval

Arithmetic fact retrieval has been suggested to recruit a left-lateralized network comprising perisylvian language areas, parietal areas such as the angular gyrus (AG), and non-neocortical structures such as the hippocampus. However, the underlying white matter connectivity of these areas has not been evaluated systematically so far. Using simple multiplication problems, we evaluated how disconnections in parietal brain areas affected arithmetic fact retrieval following stroke. We derived disconnectivity measures by jointly considering data from n = 73 patients with acute unilateral lesions in either hemisphere and a white-matter tractography atlas (HCP-842) using the Lesion Quantification Toolbox (LQT). Whole-brain voxel-based analysis indicated a left-hemispheric cluster of white matter fibers connecting the AG and superior temporal areas to be associated with a fact retrieval deficit. Subsequent analyses of direct gray-to-gray matter disconnections revealed that disconnections of additional left-hemispheric areas (e.g., between the superior temporal gyrus and parietal areas) were significantly associated with the observed fact retrieval deficit. Results imply that disconnections of parietal areas (i.e., the AG) with language-related areas (i.e., superior and middle temporal gyri) seem specifically detrimental to arithmetic fact retrieval. This suggests that arithmetic fact retrieval recruits a widespread left-hemispheric network and emphasizes the relevance of white matter connectivity for number processing.

The role of the angular gyrus in arithmetic processing: a literature review.

Since the pioneering work of the early 20th century neuropsychologists, the angular gyrus (AG), particularly in the left hemisphere, has been associated with numerical and mathematical processing. The association between the AG and numerical and mathematical processing has been substantiated by neuroimaging research. In the present review article, we will examine what is currently known about the role of the AG in numerical and mathematical processing with a particular focus on arithmetic. Specifically, we will examine the role of the AG in the retrieval of arithmetic facts in both typically developing children and adults. The review article will consider alternative accounts that posit that the involvement of the AG is not specific to arithmetic processing and will consider how numerical and mathematical processing and their association with the AG overlap with other neurocognitive processes. The review closes with a discussion of future directions to further characterize the relationship between the angular gyrus and arithmetic processing.

Developmental trajectories of symbolic magnitude and order processing and their relation with arithmetic development

Efficient processing of absolute magnitude and relative order of numbers is key for arithmetic development. This longitudinal study tested 1) whether there is a developmental shift in the contribution of symbolic magnitude and order processing to arithmetic between Grades 1 and 2, and 2) whether the development of symbolic numerical abilities is characterized by reciprocal predictive relations. In two independent samples (UK: N = 195, Austria: N = 161), order processing did not predict early developmental change in arithmetic, but emerged as a predictor in Grade 2. Symbolic magnitude processing in Grade 1 predicted subsequent developmental change in arithmetic, but not later on. Moreover, we observed cross-lagged relations between symbolic magnitude and order processing. Our findings confirm that the contributions of symbolic magnitude and order processing to arithmetic development are interactive and change across the first years of schooling. This may be driven by a developmental shift from procedural strategies to retrieval of arithmetic facts. • Symbolic magnitude processing was a predictor of arithmetic development in Grade 1, but not in Grade 2. • Order processing did not predict developmental change in Grade 1, emerging as a unique predictor of arithmetic in Grade 2. • Cross-lagged predictive relations between symbolic magnitude and order processing across the entire study period. • Interactive and changing contributions of symbolic magnitude and order processing to arithmetic development.

Decoding fact fluency and strategy flexibility in solving one-step algebra problems: An individual differences analysis

Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses ‘missing-operand’ problems (e.g., x – 7 = 2) solvable via two typical strategies: 1) direct retrieval of arithmetic facts (e.g., 9 – 7 = 2) and 2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study investigated the strategies people choose when solving these problems, and whether some people are more flexible in their choices than others. U.S. undergraduates (n = 59) solved missing-operand problems and made speeded verifications of arithmetic sentences corresponding to the direct- and inverse-matched facts. To ‘decode’ their strategy as direct or inverse, each participant’s response times (RTs) for missing-operand problems were regressed on their RTs for the corresponding direct and inverse facts. Our findings replicated the problem size effect for the arithmetic verification task and extended this effect to missing-operand (i.e., one-step) algebra problems, suggesting that the two tasks draw on common representations and processes in the addition (but not subtraction) context. We found individual differences in strategy choice and flexibility such that participants varied both in terms of fluency for retrieving the direct fact and sensitivity to the potential benefit of switching to the inverse fact, which was validated by self-report. We did not find a predicted relation between strategy flexibility and standardized mathematical achievement. These findings inform our understanding of the cognitive processes involved in strategy flexibility in algebra and establish an RT-decoding paradigm for future examination of individual differences in students’ learning of early algebra concepts.

The relationship between phonological processing and arithmetic in children with learning disabilities.

Phonological processing skills have not only been shown to be important for reading skills, but also for arithmetic skills. Specifically, previous research in typically developing children has suggested that phonological processing skills may be more closely related to arithmetic problems that are solved through fact retrieval (e.g., remembering the solution from memory) than procedural computation (e.g., counting). However, the relationship between phonological processing and arithmetic in children with learning disabilities (LDs) has not been investigated. Yet, understanding these relationships in children with LDs is especially important because it can help elucidate the cognitive underpinnings of math difficulties, explain why reading and math disabilities frequently co-occur, and provide information on which cognitive skills to target for interventions. In 63 children with LDs, we examined the relationship between different phonological processing skills (phonemic awareness, phonological memory, and rapid serial naming) and arithmetic. We distinguished between arithmetic problems that tend to be solved with fact retrieval versus procedural computation to determine whether phonological processing skills are differentially related to these two arithmetic processes. We found that phonemic awareness, but not phonological memory or rapid serial naming, was related to arithmetic fact retrieval. We also found no association between any phonological processing skills and procedural computation. These results converge with prior research in typically developing children and suggest that phonemic awareness is also related to arithmetic fact retrieval in children with LD. These results raise the possibility that phonemic awareness training might improve both reading and arithmetic fact retrieval skills. RESEARCH HIGHLIGHTS: Relationships between phonological processing and various arithmetic skills were investigated in children with learning disabilities (LDs) for the first time. We found phonemic awareness was related to arithmetic involving fact retrieval, but not to arithmetic involving procedural computation in LDs. The results suggest that phonemic awareness is not only important to skilled reading, but also to some aspects of arithmetic. These results raise the question of whether intervention in phonemic awareness might improve arithmetic fact retrieval skills.

Event-related brain potentials study of arithmetic fact retrieval in children with different math achievement levels

ABSTRACT Fact retrieval deficits have been documented in children with mathematical learning disabilities. We assessed the retrieval of arithmetic facts in neurotypical 9-to-10-year-old children with different mathematical achievement levels using event-related potential methods while performing an arithmetic verification task (addition, subtraction, and multiplication). Forty-eight participants were divided into High (H), Average (A), and Low (L) mathematics performance according to their scores on The Wide Range Achievement Test 4 (WRAT4). Children determined whether appearing digits matched or not the correct solution of the preceding problem. L group showed a lower number of correct responses, prolonged reaction times, and poorer performance on working memory (WM) tasks. P300 component showed significantly higher amplitudes for correct solutions in H, while N270 showed higher amplitudes for incorrect solutions. L children showed difficulty in recovering arithmetic facts and poorly modulated N270 and P300 components, probably reflecting WM processing problems affecting the construction and retrieval of numerical information.

Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data.

Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts.

On silences and the Ottoman Archives

This article explores the making of the National Palaces Privy Purse Archive, which later was conjoined with the State Archives of the Presidency of the Republic of Turkey (the Ottoman Archives), and investigates the silences in the Ottoman and Iraqi historiographies that were produced in this process. Building on Michel-Rolph Trouillot’s scholarship, I argue that the moment of fact assembly and the moment of fact retrieval should be highlighted in understanding historiographic shifts as well as their related silences. This article further elaborates on the archival material in the Privy Purse record group, now accessible through the State Archives of the Presidency of the Republic of Turkey in Istanbul, Turkey, and suggests ways in which the Privy Purse record group could inform Ottoman and Iraqi historiographies in the future.

Relational integration predicted numerical inductive reasoning: ERP Evidence from the N400 and LNC.

As relational integration performance can be used to predict reasoning ability, the present study aimed to provide electrophysiological evidence for numerical inductive reasoning. Number series with two levels of relational complexity were utilized, including simple and hierarchical problems (such as "15-16-17" versus "15-16-18"). Two tasks were adopted: a relational integration task that required to determine whether the numerical relations were changed across numbers; a number series task that required to determine whether a hidden rule was acquired (Experiment 1) or to predict the subsequent number (Experiment 2), whose phases were divided as rule searching, rule discovery, and rule following. The event-related potential (ERP) results of both experiments indicated that, in contrast to simple problems, hierarchical problems triggered enhanced N400 and late negative component (LNC), reflecting numerical fact retrieval, and generalizing novel hypotheses about the hidden rules by integrating adjacent numerical relations, respectively; relational integration showed similar N400 and LNC activation patterns to rule discovery (Experiment 1) or rule searching (Experiment 2). Additionally, the N400 and LNC elicited by relational integration showed strong positive correlations and even were able to predict the ones triggered by rule discovery (Experiment 1) or rule searching (Experiment 2). Therefore, the results supported the role of relational integration in numerical inductive reasoning and thereby in intelligence.

Self-derivation of new knowledge through memory integration varies as a function of prior knowledge

ABSTRACT The current research was an investigation of the effects of prior, domain-relevant knowledge on self-derivation of new, integrated knowledge. Adults were presented with novel “stem” facts and tested for self-derivation of new knowledge through integration of the facts in memory. To examine the effects of prior knowledge on memory integration, we tested participants under three within-subject conditions, in which in advance of stem encoding, they were provided with either: (1) no domain relevant information (No Knowledge control), (2) generally relevant information about the domain (General), or (3) generally relevant information about the domain along with a stem fact that was directly necessary for self-derivation (General + Stem). Prior exposure to both General and General + Stem knowledge facilitated memory for the novel, explicitly-taught stem facts. Moreover, for both prior knowledge conditions, the amount of domain-relevant knowledge retained in memory was associated with trial-by-trial self-derivation success. Importantly, the type of prior knowledge modulated memory integration in different ways. Whereas General + Stem knowledge enhanced selective retrieval and integration of the stem facts, General knowledge supported learning of the individual stem facts, but not their integration with one another. Together, the findings indicate how malleable, domain-specific experience shapes encoding, integration, and flexible extension of new, related information.

Laterality in simple multiplication: Assessing hemispheric specialization of arithmetic fact retrieval in a visual hemifield paradigm.

The prominent view in numerical cognition is that highly overlearned arithmetic facts are verbally mediated and unilaterally processed in a left-hemispheric network, including language areas. However, this view has recently been challenged. Here, we evaluated the hemispheric specialization of verbal arithmetic fact retrieval and number magnitude processing using two verification tasks (i.e., multiplication and number magnitude comparison) in a divided hemifield paradigm in healthy participants (n = 35). In the number comparison task, we replicated bilateral processing advantages for the unit-decade compatibility effect. Magnitude processing was facilitated after bilateral compared with a unilateral presentation. In the multiplication task, lateralized presentation to the left hemisphere yielded processing advantages in arithmetic fact retrieval when the required interhemispheric transitions from the input, processing, and output stages were considered. Crucially, we observed a systematic processing advantage in left visual hemifield stimuli presentation (i.e., initial right-hemisphere processing). Our findings corroborate the assumption that arithmetic fact retrieval is subserved by left-lateralized verbal/linguistic processing. Thereby, they suggest a distinction between unilateral left-hemispheric linguistic processing of arithmetic fact retrieval and bilateral number magnitude processing. Interestingly, however, our data present right-hemispheric processing advantages in identifying early processed visual symbolic numerical stimuli. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

No influence of masked priming on the multiplication fact retrieval in a result verification task

In three experiments, we used a masked prime in a verification task to investigate the processing stages occurring during multiplication fact retrieval. We aimed to investigate the retrieval process by overlapping its execution with the processing of a masked prime consisting of a number. Participants evaluated the correctness of multiplication equations, where the result was preceded by a masked prime (presented for 30 ms, with different stimulus onset asynchrony between the operands and the prime). Decade consistency and relatedness of the prime were manipulated. For example, given the equation 4 x 7 = 28, the prime could be: a neighbor either decade consistent (24) or inconsistent (32), or an unrelated number either decade consistent (23) or inconsistent (31). We expected that the feature of the prime (relatedness or decade consistency) that generates interference depends on the processing stage reached when the prime is processed. Although Experiment 1 showed promising results, Experiments 2 and 3 suggest that the pattern found in Experiment 1 was a false positive. Overall, the paradigm used in this study (i.e., masked prime with a verification ask) does not seem to produce a stable interference during the retrieval process.