Mathematical Cognition Research Articles

Research on the Application of Augmented Reality Technology into the Educational Activities of Kindergarten’s Number Concept

Augmented Reality (AR) is different from virtual reality (VR). It is an emerging technology that does not emphasize the creation of virtual feelings through virtual objects, but focuses on combining virtual objects with real environments. This article starts from the connotation interpretation and characteristic analysis of augmented reality technology, and examines the current kindergarten number concept education activities, and finds that there are the following problems in kindergarten number concept education activities: insufficient creation of mathematics environment, single learning methods for children, and lack of effective learning among children interactive. Combining the characteristics and functions of augmented reality technology, we propose optimization strategies for optimizing kindergarten math concept education activities, respectively creating a unity of “form” and “body” for the environment, rich game experience and dialogue-creating-meaning construction of children’s mathematics cognition.

Chapter 5 - Learning disabilities: Developmental dyscalculia

Developmental dyscalculia (DD) is a developmental learning disability that manifests as a persistent difficulty in comprehending even the most basic numeric and arithmetic concepts, despite normal intelligence and schooling opportunities. Given the predominant use of numbers in modern society, this condition can pose major challenges in the sufferer's everyday life, both in personal and professional development. Since, to date, we still lack a universally recognized and psychometrically driven definition of DD, its diagnosis has been applied to a wide variety of cognitive profiles. In this chapter, we review the behavioral and neural characterization of DD as well as the different neurocognitive and etiologic accounts of this neurodevelopmental disorder. We underline the multicomponential nature of this heterogeneous disability: different aspects of mathematical competence can be affected by both the suboptimal recruitment of general cognitive functions supporting mathematical cognition (such as attention, memory, and cognitive control) and specific deficits in mastering numeric concepts and operations. Accordingly, both intervention paradigms focused on core numeric abilities and more comprehensive protocols targeting multiple neurocognitive systems have provided evidence for effective positive outcomes.

표상과 연계한 수학활동이 유아의 수학능력, 인지처리능력, 언어능력에 미치는 효과 분석

표상과 연계한 수학활동이 유아의 수학능력, 인지처리능력, 언어능력에 미치는 효과 분석

Mathematical cognition and enculturation: introduction to the Synthese special issue

Mathematical cognition and enculturation: introduction to the Synthese special issue

Mathematics anxiety and cognition: an integrated neural network model.

Many students suffer from anxiety when performing numerical calculations. Mathematics anxiety is a condition that has a negative effect on educational outcomes and future employment prospects. While there are a multitude of behavioral studies on mathematics anxiety, its underlying cognitive and neural mechanism remain unclear. This article provides a systematic review of cognitive studies that investigated mathematics anxiety. As there are no prior neural network models of mathematics anxiety, this article discusses how previous neural network models of mathematical cognition could be adapted to simulate the neural and behavioral studies of mathematics anxiety. In other words, here we provide a novel integrative network theory on the links between mathematics anxiety, cognition, and brain substrates. This theoretical framework may explain the impact of mathematics anxiety on a range of cognitive and neuropsychological tests. Therefore, it could improve our understanding of the cognitive and neurological mechanisms underlying mathematics anxiety and also has important applications. Indeed, a better understanding of mathematics anxiety could inform more effective therapeutic techniques that in turn could lead to significant improvements in educational outcomes.

Realistic Mathematics Education (RME) Approach to Enhance Mathematical Cognition of Elementary School Students

Mathematical cognition is a fundamental skill in studying mathematics at the elementary school level. Teaching mathematics at school must aim to enhance mathematics cognition and can be used to solve real-life problems. This study observed the increase in students’ mathematics cognition after implementing RME approach in the classroom. This study used a quasi-experimental design. The subject is 58 elementary school students at Agam and Bukittinggi. Data analyzed using SPSS statistic program. The research showed that there is a significant difference in students’ mathematics cognition after learning with the Realistic Mathematics approach. It can be assumed that the use of Realistic Mathematics Education approach enhanced students’ mathematics cognition and encourage students to engage actively in the teaching and learning of mathematics. Thus, Realistic Mathematics Education approach is an appropriate method to enhance the quality of teaching and learning process.

RME Approach and Mind Map Methode to Enhance Mathematical Cognition of Elementary School Students

Early mathematics achievement has been found to be important for later mathematical development. Intelligence and other cognitive factors typically explain no more than half of the variability in mathematical variation. This study aimed to investigate the effect of applying a Realistic Mathematics Education approach and mind map method to enhance mathematic cognitive at elementary school students. The participants were recruited from elementary schools in Bukittinggi, West Sumatra, Indonesia. The constant comparative and grounded theory techniques were used for data analysis. The theoretical contribution of this study is a very detailed diagnosis of increasing at mathematical cognition resulting in a profile rather than in a single score. Practically, this profile enabled efficient intervention that resulted in students’ high mathematical cognition and achievement in students’ learning achievement.

Game-Based Training to Promote Arithmetic Fluency

The research team designed and evaluated a mobile game to promote rapid retrieval of arithmetic facts among a group of children aged 7-8 years (n=97). The design of the game was based on principles drawn from research literature in mathematical cognition, game-based learning, and game design. The game trains basic number knowledge within a motivating context. It tested an implication of theory of automatization of arithmetic facts that training of recognition of multiples of single-digit numbers should lead to greater fluency in solving multiplication and division problems. A quasi-experimental design was employed to test whether the game improves retrieval of arithmetic facts. Children played the game in their classrooms for 20 minutes a day for 2 weeks. Comparisons between pre- and post-tests showed that the game playing group outperformed controls with a medium to large effect size (> 0.6). These results suggest an improvement in arithmetic fluency equivalent to around 7 months’ progress and provide rare empirical evidence supporting transfer of game-based training to a pencil-and-paper test. The findings are consistent with a connectionist theory of arithmetic skill, by showing that improved recognition of multiples contributes to multiplication and division skill. The theoretical and practical implications of these findings are discussed.

P300 amplitude and latency reflect arithmetic skill: An ERP study of the problem size effect

The effect of arithmetic problem size is widespread in behavior (e.g., slower responses to 8 × 7 than 2 × 2). Here, we measure event related potentials (ERPs) to determine how the problem size effect unfolds under different conditions. Adults judged the correctness of simple multiplication problems (2 × 4 = 8 versus 9) that varied in size and operand number format (written digits versus spoken number words). The P300, an ERP component associated with stimulus categorization, was measured from solution onset. P300 amplitude was greatest for small and correct solutions, as expected for easily categorized stimuli. Large incorrect solutions elicited a disproportionately reduced P300, an interaction not measurable in verification behavior. Additionally, ERP measures revealed effects of operand format preceding, but not following, solution onset. The significance of these findings for theories of mathematical cognition are addressed.

Individual differences in numerical comparison is independent of numerical precision

Numeracy, as measured by performance on the non-symbolic numerical comparison task, is a key construct in numerical and mathematical cognition. The current study examines individual variation in performance on the numerical comparison task. We contrast the hypothesis that performance on the numerical comparison task is primarily due to more accurate representations of numbers with the hypothesis that performance dependent on decision-making factors. We present data from two behavioral experiments and a mathematical model. In both behavioral experiments we measure the precision of participant’s numerical value representation using a free response estimation task. Taken together, results suggest that individual variation in numerical comparison performance is not predicted by variation in the precision of participants’ numerical value representation.

Meanings that engineering students confer to the antiderivative

In this article, are presented the results of a questionnaire designed to evaluate college students’ understanding of the antiderivative. Specifically, by civil engineering students when answering the questionnaire tasks, in order to identify and characterize the meanings on the antiderivative that are developed by them. In order to analyse the answers given, were used some theoretical and methodological notions provided by the theoretical model known as the Onto-Semiotic Approach (OSA) of mathematics cognition and instruction. The results show the knowledge of antiderivative by the Civil Engineering students. Furthermore, the comparison between the mathematical activity of students provides information that allows concluding that the meanings that they mobilized might be shared among their communities

Numerical processing profiles in children with varying degrees of arithmetical achievement

Recent studies show basic cognitive abilities such as the rapid and precise apprehension of small numerosities in object sets (“subitizing”), verbal counting and numerical magnitude comparison significantly influence the acquisition of arithmetic and continues to modulate more advanced stages of mathematical cognition. Additionally, children with low arithmetic achievement (LAA) and Developmental Dyscalculia (DD) exhibit significant deficits in these cognitive processes. Nevertheless, the different cognitive profiles of children with varying degrees of numerical and arithmetic processing deficits have not been sufficiently characterized, despite its potential relevance to the stimulation of numerical cognition and the design of appropriate intervention strategies. Here, the cognitive profiles of groups of typically developing children, children with low arithmetical achievement and DD, exhibiting typical and atypical subitizing ability were contrasted. The results suggest that relatively independent neurocognitive mechanisms may produce distinct profiles at the behavioral level and suggest children with low arithmetic performance exhibiting atypical subitizing abilities are not only significantly slower, but rely on compensatory mechanisms and strategies compared to typical subitizers. The role of subitizing as a correlate of arithmetic fluency is revised in the light of the present findings.

Distinguishing between cognitive explanations of the problem size effect in mental arithmetic via representational similarity analysis of fMRI data

Not all researchers interested in human behavior remain convinced that modern neuroimaging techniques have much to contribute to distinguishing between competing cognitive models for explaining human behavior, especially if one removes reverse inference from the table. Here, we took up this challenge in an attempt to distinguish between two competing accounts of the problem size effect (PSE), a robust finding in investigations of mathematical cognition. The PSE occurs when people solve arithmetic problems and indicates that numerically large problems are solved more slowly and erroneously than small problems. Neurocognitive explanations for the PSE can be categorized into representation-based and process-based views. Behavioral and traditional univariate neural measures have struggled to distinguish between these accounts. By contrast, a representational similarity analysis (RSA) approach with fMRI data provides competing hypotheses that can distinguish between accounts without recourse to reverse inference. To that end, our RSA (but not univariate) results provided clear evidence in favor of the representation-based over the process-based account of the PSE in multiplication; for addition, the results were less clear. Post-hoc similarity analysis distinguished still further between competing representation-based theoretical accounts. Namely, data favored the notion that individual multiplication problems are stored as individual memory traces sensitive to input frequency over a strictly magnitude-based account of memory encoding. Together, these results provide an example of how human neuroimaging evidence can directly inform cognitive-level explanations of a common behavioral phenomenon, the problem size effect. More broadly, these data may expand our understanding of calculation and memory systems in general.

TRANSFORMATIVE PROFESSIONAL DEVELOPMENT FOR MATHEMATICS TEACHERS

This paper was an attempt to redesign the current professional development training for Mathematics teachers in the Philippines. Mathematics teachers claimed that most training and seminars they attended ignored their local work context; was routinely and was hardly applicable to their classroom milieu. By utilizing the transformative professional development training, the teachers identified the classroom issues that had confronted them; restructured their useful pedagogical ideas and instructional plans and materials; implemented these in their classrooms; and shared their reflections on the new teaching experiences. Qualitative data were gathered from focus group discussions and key informant interviews. University researchers (3), secondary Mathematics teachers (28), and students (250) from four rural public schools in the Hamiguitan Range participated. The teachers and students revealed that their lack of self and environmental understanding were the prevalent issues that led to critical behavior in Mathematical cognition and learning. By applying the transformative education in the classroom, promising results like better teacher performance, improved students' interest, and maximized student participation were evident. This transformative professional development training adequately responded to the teachers' work needs and was recommended to other areas of learning.

The Contribution of General Cognitive Abilities and Specific Number Skills toward Arithmetic Performance in Students with Mild Intellectual Disability

ABSTRACT General cognitive and specific number abilities that underlay arithmetic performance have been heavily investigated among typically developing students; however, the inquiry has rarely been applied to students with mild intellectual disability (MID). We examined whether domain-general cognitive abilities (i.e. working memory, processing speed, and long-term memory) and specific number skills (i.e. approximate and exact numerical systems) are related to arithmetic performance in 93 students with MID (mental age of 7.1 to 8.9 years) and if these relationships are similar to the ones found in 113 typically developing students with the same mental age. The results of our regression models indicated that, in both groups, the three general cognitive abilities independently explained the variance in arithmetic performance when entered in one step; however, none of them had an independent contribution to arithmetic skill in the presence of the specific number abilities. These findings supported those of Von Aster and Shale’s developmental model of mathematical cognition and reinforced the notion that specific number abilities constitute the basis for arithmetic skill, and it is possible with the support of the general cognitive abilities among both students with MID and typically developing students.

Collaborative gesture as a case of extended mathematical cognition

Gestures have been shown to play a key role in mathematical reasoning and to be an indicator that mathematical understanding is embodied – inherently linked to action, perception, and the physical body. As learners collaborate and engage in mathematical discussions, they use discourse practices like explaining, refuting, and building on each other’s reasoning. Here we examine how gestural embodied actions become distributed over multiple learners confronting mathematical tasks. We define collaborative gestures as gestural exchanges that take place as learners discuss and explore mathematical ideas, using their bodies in concert to accomplish a shared goal. We identify several ways in which learners’ gestures can be used collaboratively and explore patterns in how collaborative gestures arise while proving geometric conjectures. Learners use collaborative gestures to extend mathematical ideas over multiple bodies as they explore, refine, and extend each other’s mathematical reasoning. With this work, we seek to add to notions of important talk moves in mathematical discussions to also include a consideration of important gesture moves.

Emerging perspectives in mathematical cognition: contextualizing, complementizing, and complexifying

This article describes emerging perspectives on contextualizing, complementizing, and complexifying—three processes involved when individuals ascribe meaning to mathematical objects of their thinking. The article is oriented toward a dialectic between theory and empirical research and is structured in two parts. The first part focuses on an evolving theoretical framing that acknowledges the significance of these three processes in mathematical cognition. In the second part, the evolving theoretical framing is used to analyze one student’s knowing of the limit concept of a sequence. This analysis directs one’s attention to the emergence and function of this student’s knowledge resource, which was generic in usage and complex in structure, allowing the activation of productive ideas and contextual meaning-making as needed. Through this analysis, theoretical and interpretative possibilities were generated that inform research on mathematical cognition and elucidate the emerging theoretical perspectives of contextualizing, complementizing, and complexifying.

Extended mathematical cognition: external representations with non-derived content

Vehicle externalism maintains that the vehicles of our mental representations can be located outside of the head, that is, they need not be instantiated by neurons located inside the brain of the cogniser. But some disagree, insisting that ‘non-derived’, or ‘original’, content is the mark of the cognitive and that only biologically instantiated representational vehicles can have non-derived content, while the contents of all extra-neural representational vehicles are derived and thus lie outside the scope of the cognitive. In this paper we develop one aspect of Menary’s vehicle externalist theory of cognitive integration—the process of enculturation—to respond to this longstanding objection. We offer examples of how expert mathematicians introduce new symbols to represent new mathematical possibilities that are not yet understood, and we argue that these new symbols have genuine non-derived content, that is, content that is not dependent on an act of interpretation by a cognitive agent and that does not derive from conventional associations, as many linguistic representations do.

Coming Together: R&D and Children's Entertainment Company in Designing APPs for Learning Early Math.

Information and Communication Technologies (ICT) have an increasing influence on the way we interact, learn, and live. The increase in teaching and learning methodologies that are mediated by ICT in the field of education and in the domestic settings encourages the design of new effective technological tools, supported by scientific research and development to improve student learning. The challenge psychology is facing in the education field is to promote those technologies and make them available to the education community. Technologies also would produce attractive items for users and realistic commercial issues for businesses. This also allows an effective transfer for scientific work, providing visibility to Research and Development. In this context, the main aim of the article is to describe the process to get an agreement between Babyradio (a children’s entertainment company: https://babyradio.es/) and our research team, starting a collaborative work between two groups of people (Babyradio’s technical designer and Psychologist-Engineers software designer), in order to create several educative applications (APPs) in the field of early mathematics cognition. The institutional framework of the relationship of the R&D project and a children’s entertainment company is described. The article also focuses on experience in Psychology, Technological Innovation, and Entrepreneurship. In considering the efficiency of the agreement, we present different APPs designed for tablets and smartphone devices, adapted to the different operating systems (IOS, Android, Windows). APPs are designed to instill the cognitive fundamentals associated with early math learning for students aged 4 to 7 years. The study developed after this babyradio-university enterprise agreement contributes to the development of mathematics skills in children, aged 4–7 years, so that they can successfully meet the mathematics school requirements; it also contributes to encouraging a more positive attitude toward mathematics. This study also suggests how the education system and software and educational content developers’ companies would manage verified instructional APPs, with a more realistic commercial perspective.

What’s new: innovation and enculturation of arithmetical practices

One of the most important questions in the young field of numerical cognition studies is how humans bridge the gap between the quantity-related content produced by our evolutionarily ancient brains and the precise numerical content associated with numeration systems like Indo-Arabic numerals. This gap problem is the main focus of this paper. The aim here is to evaluate the extent to which cultural factors can help explain how we come to think about numbers beyond the subitizing range. To do this, I summarize Clark’s (Analysis 58:7–19, 1998) notion of a difference maker in explaining complex causation that criss-crosses between mind and world and apply it to Menary’s (In: Metzinger T, Windt JM (eds) Open MIND. MIND Group, Frankfurt, 2015a) discussion of mathematical cognition as a case of enculturation. I argue that while Menary’s views on enculturation can help explain what makes the difference between numerate and anumerate cultures, it cannot help specify what makes the difference between numerate and anumerate individuals. I argue that features of enculturation do not provide an account of innovation capable of explaining how individuals manage to improve and modify the practices of their cultural niche. This is because Menary’s construal of the role of enculturation in the development of mathematical cognition focuses mostly on the inheritance and transmission of practices, not on their origins, which involve individual-level understanding, rather than population-level practices and pressures. The upshot is that culture provides the necessary background conditions against which individuals can innovate. This role is crucial in the development of numerical abilities—crucial, but explanatorily limited.