The potential benefits of cognitive skills in enhancing mathematics ability have been claimed by numerous researchers. Since mathematics requires a complete understanding and grasp of abstract concepts, it is essential to explore how learning with metacognitive skills affects mathematics learning. Thus, the study investigates the students' metacognitive awareness and conceptual understanding of integers. A descriptive-correlational method approach was utilized, and it was carried out on 303 seventh-grade students. The data were obtained using a metacognitive awareness inventory and achievement test on (...) integers. It was further revealed that the students have average metacognitive awareness and performed well in the fundamental operation of integers. Follow-up qualitative analysis revealed that students who were high achievers had the best understanding, average achievers had corrected or incomplete understanding, and low achievers had a functional misconception of integers. Moreover, the student's metacognitive awareness was significantly related to their conceptual understanding of integers. This indicates that student's higher-order thinking skills, such as metacognition, are essential since they are associated with building conceptual skills. Thus, teachers should encourage students' metacognitive awareness to improve students' conceptual understanding of integers. The study provides relevant information for educational managers on the potential factors to be considered in improving mathematics education practices, particularly in promoting metacognition among high school students. (shrink)

A new layer of complexity, constituted of networks of information token recurrence, has been identified in socio-technical systems such as the Wikipedia online community and the Zooniverse citizen science platform. The identification of this complexity reveals that our current understanding of the actual structure of those systems, and consequently the structure of the entire World Wide Web, is incomplete, which raises novel questions for data science research but also from the perspective of social epistemology. Here we establish the principled foundations (...) and practical advantages of analyzing information diffusion within and across Web systems with Transcendental Information Cascades, and outline resulting directions for future study in the area of socio-technical systems. We also suggest that Transcendental Information Cascades may be applicable to any kind of time-evolving system that can be observed using digital technologies, and that the structures found in such systems comprise properties common to all naturally occurring complex systems. (shrink)

Motivated by the significant amount of successful collaborative problem solving activity on the Web, we ask: Can the accumulated information propagation behavior on the Web be conceived as a giant machine, and reasoned about accordingly? In this paper we elaborate a thesis about the computational capability embodied in information sharing activities that happen on the Web, which we term socio-technical computation, reflecting not only explicitly conditional activities but also the organic potential residing in information on the Web.

Robots as social companions in close proximity to humans have a strong potential of becoming more and more prevalent in the coming years, especially in the realms of elder day care, child rearing, and education. As human beings, we have the fascinating ability to emotionally bond with various counterparts, not exclusively with other human beings, but also with animals, plants, and sometimes even objects. Therefore, we need to answer the fundamental ethical questions that concern human-robot-interactions per se, and we need (...) to address how we conceive of »good lives«, as more and more of the aspects of our daily lives will be interwoven with social robots. (shrink)

This paper is an attempt to lay out foundations for a general theory of coincidence in information spaces such as the World Wide Web, expanding on existing work on bursty structures in document streams and information cascades. We elaborate on the hypothesis that every resource that is published in an information space, enters a temporary interaction with another resource once a unique explicit or implicit reference between the two is found. This thought is motivated by Erwin Shroedingers notion of entanglement (...) between quantum systems. We present a generic information cascade model that exploits only the temporal order of information sharing activities, combined with inherent properties of the shared information resources. The approach was applied to data from the world's largest online citizen science platform Zooniverse and we report about findings of this case study. (shrink)

In this paper, we investigate a method for constructing cascades of information co-occurrence, which is suitable to trace emergent structures in information in scenarios where rich contextual features are unavailable. Our method relies only on the temporal order of content-sharing activities, and intrinsic properties of the shared content itself. We apply this method to analyse information dissemination patterns across the active online citizen science project Planet Hunters, a part of the Zooniverse platform. Our results lend insight into both structural and (...) informational properties of different types of identifiers that can be used and combined to construct cascades. In particular, significant differences are found in the structural properties of information cascades when hashtags as used as cascade identifiers, compared with other content features. We also explain apparent local information losses in cascades in terms of information obsolescence and cascade divergence; e.g., when a cascade branches into multiple, divergent cascades with combined capacity equal to the original. (shrink)

“Filter bubble”, “echo chambers”, “information diet” – the metaphors to describe today’s information dynamics on social media platforms are fairly diverse. People use them to describe the impact of the viral spread of fake, biased or purposeless content online, as witnessed during the recent race for the US presidency or the latest outbreak of the Ebola virus (in the latter case a tasteless racist meme was drowning out any meaningful content). This unravels the potential envisioned to arise from emergent activities (...) of human collectives on the World Wide Web, as exemplified by the Arab Spring mass movements or digital disaster response supported by the Ushahidi tool suite. (shrink)

The ability to solve problems is a prerequisite in preparing mathematics preservice teachers. This study assessed preservice teachers’ problem-solving difficulties and performance, particularly in worded problems on number sense, measurement, geometry, algebra, and probability. Also, academic profile differences in the preservice teacher’s problem-solving performance and common errors were determined. A descriptive-comparative research design was employed with 158 random respondents. Data were gathered face-to-face during the first semester of the school year 2022-2023, and data were analyzed with the aid of jamovi (...) software, ensuring ethical measures. Overall findings revealed that the preservice teachers experienced average difficulty in solving problems. The low performance of the preservice teachers on the given problems was also demonstrated. Further analysis revealed a significant difference between the preservice teachers’ problem-solving performance based on their subject preference and program. Moreover, the error analysis revealed that the preservice teachers incurred comprehension errors in misrepresentation, misinterpretation, and miscalculation. These results will serve as a measure for policymakers and curriculum developers of the teacher education institution concerned to make relevant enhancements to the math courses offered in the elementary and secondary education programs. (shrink)

Mathematical confidence and critical thinking are essential in preparing preservice teachers. Thus, this study explored the perceived confidence and critical thinking levels in mathematics of elementary and secondary preservice teachers. A descriptive-correlational-comparative research design was employed, with a sample of 107 randomly selected preservice teachers enrolled in the Bachelor in Elementary and Secondary Education programs of a state university in West Philippines. The study used arithmetic mean, standard deviation, Spearman’s rank-order correlation, and independent samples t-test to analyze and draw conclusions (...) from the data. The findings revealed that the preservice teachers have high confidence and critical thinking skills. Their program significantly correlates with their perceived critical thinking and confidence level. Besides, the preservice teachers’ confidence levels and perceived critical thinking skills significantly correlate. Further analysis found significant confidence and critical thinking differences favoring the secondary over the elementary preservice teachers. These findings provide insights that would benefit mathematics educators in providing priority programs to enhance the preparation of future math teachers. (shrink)

In a reflective and richly entertaining piece from 1979, Doug Hofstadter playfully imagined a conversation between ‘Achilles’ and an anthill (the eponymous ‘Aunt Hillary’), in which he famously explored many ideas and themes related to cognition and consciousness. For Hofstadter, the anthill is able to carry on a conversation because the ants that compose it play roughly the same role that neurons play in human languaging; unfortunately, Hofstadter’s work is notably short on detail suggesting how this magic might be achieved1. (...) Conversely in this paper - finally reifying Hofstadter’s imagination - we demonstrate how populations of simple ant-like creatures can be organised to solve complex problems; problems that involve the use of forward planning and strategy. Specifically we will demonstrate that populations of such creatures can be configured to play a strategically strong - though tactically weak - game of HeX (a complex strategic game).We subsequently demonstrate how tactical play can be improved by introducing a form of forward planning instantiated via multiple populations of agents; a technique that can be compared to the dynamics of interacting populations of social insects via the concept of meta-population. In this way although, pace Hofstadter, we do not establish that a meta-population of ants could actually hold a conversation with Achilles, we do successfully introduce Aunt Hillary to the complex, seductive charms of HeX. (shrink)

In the recent philosophical literature on inquiry, epistemologists point out that their subject has often begun at the point at which you already have your evidence and then focussed on identifying the beliefs for which that evidence provides justification. But we are not mere passive recipients of evidence. While some comes to us unbidden, we often actively collect it. This has long been recognised, but typically epistemologists have taken the norms that govern inquiry to be practical, not epistemic. The recent (...) literature challenges this assumption and uncovers a rich range of questions about the epistemic normativity of inquiry. In this paper, I approach these questions from the formal side of epistemology. Developing out of the philosophy of science, as it did, this branch of epistemology has long discussed inquiry. And, building on the insights of Janina Hosiasson (1931), David Blackwell (1951), and I. J. Good (1967), it has produced a reasonably well-developed framework in which to understand norms of inquiry, both epistemic and practical. In the first half of the paper, I will present the pragmatic versions of this framework due to Hosiasson, Blackwell, and Good, and the epistemic version due to Graham Oddie (1997); in the second half of the paper, I put this framework to work, turning to some of the questions from the recent debate about inquiry and asking how the framework can help us answer them. Questions include: When should we initiate an inquiry, when should we continue it, when should we conclude it, and when should we reopen it? How do epistemic norms of inquiry relate to epistemic norms of belief or credence, and can they conflict, as Jane Friedman (2020) contends? How should we resolve the apparent puzzle raised by Friedman's example of counting the windows in the Chrysler Building? How should we direct our attention, as Georgi Gardiner (2022) asks? How should we choose and reason after receiving evidence we'd rather not have received? And how should we understand the epistemic error that occurs when someone is resistant to evidence in the way Mona Simion (2023) describes? (shrink)