A Tale of Two Metaphors: Storylines About Mathematics Education in Canadian National Media

Public perception about mathematics education is developed and sustained by the Canadian news media. Our goal is to understand better the nature of this public discourse by identifying what is being communicated and how it is presented. We examine a data corpus of 71 online national newspaper articles (published between 2013 and 2015, a period that included the release of the 2012 Programme for International Student Assessment [PISA] results) and use text-analytic tools to analyze how meaning is conveyed in them. Drawing on the social psychological theory of positioning, which focuses on a general study of the manufacturing and management of meanings, we identify storylines, positions, and communication acts that are at play in how Canadian mathematics education is depicted. The data reveal that there are two connected core metaphors in relation to mathematics education. One posits mathematics education as being at war, whereas the second suggests that the war is over territory marked by two ways of teaching school mathematics. Along with the strategic positioning of certain individuals, we identify storylines that are problematic, conveying fictitious meanings about mathematics teaching and learning.     

Encouraging Citizenship in Science Education: Continuing Questions and Hopeful Possibilities

Abstract

This special issue of the Canadian Journal of Science, Mathematics and Technology Education invokes questions intended to further the discourse of citizenship in science and mathematics education, such as, How do we define citizen and democracy? Is our call for student action hypocritical? Does positioning school science through the work of Rancière present a “straw man” argument for change? To what extent does the ghost of John Dewey animate and inform a “wild pedagogy” in science education? Challenging the view of the science and mathematics curriculum as a barrier to overcome, this article argues that possibilities for developing citizenship and critical thinking can be found and developed in existing curriculum formations and practices of school science and mathematics education.     

Trends in agent-based computational modeling of macroeconomics

Based on the 50 papers surveyed in Reference,²⁾ this paper addresses general research trends in agent-based macroeconomics. On the aspect ofagent engineering, we highlight two major developments: first, the extensive applications of computational intelligence tools in modeling adaptive behavior, and second the grounding of these applications in the cognitive sciences. Shu-Heng Chen, Ph.D.: He is a professor in the Department of Economics of the National Chengchi University. He now serves as the director of the AI-ECON Research Center, National Chengchi University, the editor-in-chief of the forthcoming journal “Fuzzy Mathematics and Natural Computing” (World Scientific) and a member of the Editorial Board of The Journal of Management and Economics. Dr. Chen holds a M.A. degree in mathematics and a Ph.D. in Economics from the University of California at Los Angeles. His research interests are mainly on the applications of computational intelligence to the agent-based computational economics and finance.     

Community building and knowledge sharing by individuals with disabilities using social media

The use of social media to share information, enhance learning, and connect with an online community has grown rapidly over the past 10 years. As social media becomes a more common tool in both formal and informal education, it is imperative to understand how it is used by individuals with disabilities. Through a systematic study of the literature, 215 articles on social media used by individuals with disabilities were selected and 29 selected for in-depth thematic analysis. Six major themes were identified: community, cyberbullying, self-esteem, self-determination, access to technology, and accessibility. To confirm these six categories, we expanded our search, yielding an additional 30 articles, for a total 59 articles reviewed in-depth. Interactions between individuals with disabilities within online communities often had the goal of acquiring knowledge or learning new information. A communities of practice theoretical framework is used to discuss interactions among the elements of social media design, learning, and the building of community by individuals with disabilities.     

A framework for intelligence analysis using spatio-temporal storytelling

Social media have ushered in alternative modalities to propagate news and developments rapidly. Just as traditional IR matured to modeling storylines from search results, we are now at a point to study how stories organize and evolve in additional mediums such as Twitter, a new frontier for intelligence analysis. This study takes as input news articles as well as social media feeds and extracts and connects entities into interesting storylines not explicitly stated in the underlying data. First, it proposes a novel method of spatio-temporal analysis on induced concept graphs that models storylines propagating through spatial regions in a time sequence. Second, it describes a method to control search space complexity by providing regions of exploration. And third, it describes ConceptRank as a ranking strategy that differentiates strongly-typed connections from weakly-bound ones. Extensive experiments on the Boston Marathon Bombings of April 15, 2013 as well as socio-political and medical events in Latin America, the Middle East, and the United States demonstrate storytelling’s high application potential, showcasing its use in event summarization and association analysis that identifies events before they hit the newswire.     

Social network,social trust and shared goals in organizational knowledge sharing

The aim of our study was to further develop an understanding of social capital in organizational-knowledge-sharing. We first developed a measurement tool and then a theoretical framework in which three social capital factors (social network, social trust, and shared goals) were combined with the theory of reasoned action; their relationships were then examined using confirmatory factoring analysis. We then surveyed of 190 managers from Hong Kong firms, we confirm that a social network and shared goals significantly contributed to a person's volition to share knowledge, and directly contributed to the perceived social pressure of the organization. The social trust has however showed no direct effect on the attitude and subjective norm of sharing knowledge.     

The Identification and Influence of Social Roles in a Social Media Product Community

This research focuses on the identification of social roles and an investigation of their influence in online context. Relying on a systemic approach for role conceptualization, we investigate member's activity, shared content and position in the network within a consumer to consumer social media‐based community (SMC) around a product. This investigation led to the identification of ten core roles, based on three key elements: object of interest (product, practice, and community), main contribution type (sharing information and seeking information), individual orientation (factual, emotional). We propose an explanation about how these roles, through their positioning, participate in the community dynamics and how they contribute to the creation and diffusion of cookery as a social practice, shaping the periphery around this practice.     

A Compendium of Continuous Lattices in MIZAR

This paper reports on the MIZAR formalization of the theory of continuous lattices as presented in Gierz et al.: A Compendium of Continuous Lattices, 1980. By a MIZAR formalization we mean a formulation of theorems, definitions, and proofs written in the MIZAR language whose correctness is verified by the MIZAR processor. This effort was originally motivated by the question of whether or not the MIZAR system was sufficiently developed for the task of expressing advanced mathematics. The current state of the formalization – 57 MIZAR articles written by 16 authors – indicates that in principle the MIZAR system has successfully met the challenge. To our knowledge it is the most sizable effort aimed at mechanically checking some substantial and relatively recent field of advanced mathematics. However, it does not mean that doing mathematics in MIZAR is as simple as doing mathematics traditionally (if doing mathematics is simple at all). The work of formalizing the material of the Gierz et al. compendium has (i) prompted many improvements of the MIZAR proof checking system, (ii) caused numerous revisions of the the MIZAR data base, and (iii) contributed to the to do list of further changes to the MIZAR system.     

Supporting students’ participation in authentic proof activities in computer supported collaborative learning (CSCL) environments

In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this conception of proving: a particular learning perspective promoted in reform documents and a genre of computer tools, namely dynamic geometry software, which affords this perspective of learning within the context of mathematical proof. Tracing the move from absolutism to fallibilism in the philosophy of mathematics, I highlight the vital role of community in the production of mathematical knowledge. This leads me to an examination of a certain CSCL tool whose design is guided by knowledge-building pedagogy. I argue that knowledge building is a suitable pedagogical approach for the proof model presented in this paper. Furthermore, I suggest software modifications that will better support learners’ participation in authentic proof tasks.     

Social Representations of High School Students About Mathematics Assessment

The perceptions of students about assessment in mathematics classes have been sparsely investigated. In order to fill this gap, this qualitative study aims to identify the social representations (understood as the system of values, ideas, and practices about a social object) of high school students regarding assessment in mathematics. We used semistructured focus group interviews to obtain data (N = 50). The data were examined using theoretical thematic analysis with the assistance of the specialized ATLAS.ti software. Eight themes or social representations emerged (e.g., assessment that measures the students' learning or assessment that measures the advances or what has been acquired). The results are consistent with literature that shows that students' representations about assessment in mathematics are closely linked to their representations of mathematics itself and the learning of it and also to their representation of what is fair and what is not.     

Clause Weighting Local Search for SAT

This paper investigates the necessary features of an effective clause weighting local search algorithm for propositional satisfiability testing. Using the recent history of clause weighting as evidence, we suggest that the best current algorithms have each discovered the same basic framework, that is, to increase weights on false clauses in local minima and then to periodically normalize these weights using a decay mechanism. Within this framework, we identify two basic classes of algorithm according to whether clause weight updates are performed additively or multiplicatively. Using a state-of-the-art multiplicative algorithm (SAPS) and our own pure additive weighting scheme (PAWS), we constructed an experimental study to isolate the effects of multiplicative in comparison to additive weighting, while controlling other key features of the two approaches, namely, the use of pure versus flat random moves, deterministic versus probabilistic weight smoothing and multiple versus single inclusion of literals in the local search neighbourhood. In addition, we examined the effects of adding a threshold feature to multiplicative weighting that makes it indifferent to similar cost moves. As a result of this investigation, we show that additive weighting can outperform multiplicative weighting on a range of difficult problems, while requiring considerably less effort in terms of parameter tuning. Our examination of the differences between SAPS and PAWS suggests that additive weighting does benefit from the random flat move and deterministic smoothing heuristics, whereas multiplicative weighting would benefit from a deterministic/probabilistic smoothing switch parameter that is set according to the problem instance. We further show that adding a threshold to multiplicative weighting produces a general deterioration in performance, contradicting our earlier conjecture that additive weighting has better performance due to having a larger selection of possible moves. This leads us to explain differences in performance as being mainly caused by the greater emphasis of additive weighting on penalizing clauses with relatively less weight.     

Visualizations for Mathematics Courses Based on a Computer Algebra System

This paper discusses the introduction of a computer-algebra system to perform visualizations in mathematics education.With theIllustrated Mathematicsproject, we provide a comprehensive collection of graphics and animations for various topics in mathematics, which can directly be used for teaching. Because the programs (written inMathematica) we used for the creation of this collection are included, it is easy to design new examples by modifying parameters in existing examples. Therefore,Illustrated Mathematicscan be used as a first step of the introduction of a computer-algebra system in mathematics education.In the second part, we report on the development of a workbench and learning environment, with which the students can discover the mathematical concepts by themselves. For that, the given examples have to be didactically enriched and processed. By creating their own visualizations of increasing complexity, the students improve their knowledge about the underlying computer-algebra system.     

Cross-Cultural Perspectives on Religion and Computer-Mediated Communication

Previous research on religion and CMC has focused primarily on Christianity and the Western world. The articles collected in this special theme section of the Journal of Computer-Mediated Communication examine a wide range of religions online through both quantitative and qualitative methodologies. The Abrahamic traditions of Judaism, Christianity, and Islam, as well as Hinduism, Shinto, Taoism, Chinese traditions, animism, Japan's New Religions, and diverse forms of Buddhism are examined, in an equally wide range of national cultures and traditions: Israel, Egypt and the Arab world more broadly, India, Japan, Malaysia, Singapore, and the United States. Individually and collectively, the articles highlight shared characteristics of religion cross-culturally that foster or hinder religions' migration online—a migration that most, although not all, religions undertake in varying degrees.     

Harnessing Lab Knowledge for Real-World Action Recognition

Much research on human action recognition has been oriented toward the performance gain on lab-collected datasets. Yet real-world videos are more diverse, with more complicated actions and often only a few of them are precisely labeled. Thus, recognizing actions from these videos is a tough mission. The paucity of labeled real-world videos motivates us to “borrow” strength from other resources. Specifically, considering that many lab datasets are available, we propose to harness lab datasets to facilitate the action recognition in real-world videos given that the lab and real-world datasets are related. As their action categories are usually inconsistent, we design a multi-task learning framework to jointly optimize the classifiers for both sides. The general Schatten \(p\) -norm is exerted on the two classifiers to explore the shared knowledge between them. In this way, our framework is able to mine the shared knowledge between two datasets even if the two have different action categories, which is a major virtue of our method. The shared knowledge is further used to improve the action recognition in the real-world videos. Extensive experiments are performed on real-world datasets with promising results.     

The big data of violent events: algorithms for association analysis using spatio-temporal storytelling

This paper proposes three methods of association analysis that address two challenges of Big Data: capturing relatedness among real-world events in high data volumes, and modeling similar events that are described disparately under high data variability. The proposed methods take as input a set of geotemporally-encoded text streams about violent events called “storylines”. These storylines are associated for two purposes: to investigate if an event could occur again, and to measure influence, i.e., how one event could help explain the occurrence of another. The first proposed method, Distance-based Bayesian Inference, uses spatial distance to relate similar events that are described differently, addressing the challenge of high variability. The second and third methods, Spatial Association Index and Spatio-logical Inference, measure the influence of storylines in different locations, dealing with the high-volume challenge. Extensive experiments on social unrest in Mexico and wars in the Middle East showed that these methods can achieve precision and recall as high as 80 % in retrieval tasks that use both keywords and geospatial information as search criteria. In addition, the experiments demonstrated high effectiveness in uncovering real-world storylines for exploratory analysis.     

The effectiveness of task-level parallelism for production systems

Large production systems (rule-based systems) continue to suffer from extremely slow execution which limits their utility in practical applications as well as in research settings. Most investigations in speeding up these systems have focused on match parallelism. These investigations have revealed that the total speed-up available from this source is insufficient to alleviate the problem of slow execution in large-scale production system implementations. In this paper, we focus on task-level parallelism, which is obtained by a high-level decomposition of the production system. Speed-ups obtained from task-level parallelism will multiply with the speed-ups obtained from match parallelism. The vehicle for our investigation of task-level parallelism is SPAM, a high-level vision system, implemented as a production system. SPAM is a mature research system with a typical run requiring between 50,000 and 400,000 production firings. We report very encouraging speed-ups from task-level parallelism in SPAM… -our parallel implementation shows near linear speed-ups of over 12-fold using 14 processors and points the way to substantial (50- to 100-fold) speed-ups. We present a characterization of task-level parallelism in production systems and describe our methodology for selecting and applying a particular approach to parallelize SPAM. Additionally, we report the speed-ups obtained from the use of virtual shared memory. Overall, task-level parallelism has not received much attention in the literature. Our experience illustrates that it is potentially a very important tool for speeding up large-scale production systems.     

Community detection via heterogeneous interaction analysis

The pervasiveness of Web 2.0 and social networking sites has enabled people to interact with each other easily through various social media. For instance, popular sites like Del.icio.us, Flickr, and YouTube allow users to comment on shared content (bookmarks, photos, videos), and users can tag their favorite content. Users can also connect with one another, and subscribe to or become a fan or a follower of others. These diverse activities result in a multi-dimensional network among actors, forming group structures with group members sharing similar interests or affiliations. This work systematically addresses two challenges. First, it is challenging to effectively integrate interactions over multiple dimensions to discover hidden community structures shared by heterogeneous interactions. We show that representative community detection methods for single-dimensional networks can be presented in a unified view. Based on this unified view, we present and analyze four possible integration strategies to extend community detection from single-dimensional to multi-dimensional networks. In particular, we propose a novel integration scheme based on structural features. Another challenge is the evaluation of different methods without ground truth information about community membership. We employ a novel cross-dimension network validation (CDNV) procedure to compare the performance of different methods. We use synthetic data to deepen our understanding, and real-world data to compare integration strategies as well as baseline methods in a large scale. We study further the computational time of different methods, normalization effect during integration, sensitivity to related parameters, and alternative community detection methods for integration.     

Caricature generation utilizing the notion of anti-face

The production of caricatures is a particularly interesting field of art, because it aims to highlight the very essence of a given face. Caricature generation systems traditionally rely on two approaches: they either follow extracted rules through learning algorithms, or follow rules that were directly programmed by experts. This paper attempts to reduce the reliance on heuristic methods, by proposing a novel method that provides a set of well-defined rules, which can be put to use for the purpose of caricature generation. The method is based on the notion of anti-face in conjunction with unbiased distortions. In addition, we indicate the usefulness of the anti-face as a means to perceive, for our own sake, the degree to which our face seems peculiar to others. Finally, we deploy a reverse variant of the method in order to attain beautification.

     

Learning About Ourselves: A Review of The Mathematics Teacher in the Digital Era

ABSTRACT

Mathematics Education in the Digital Era is a title that implies the ubiquity of digital technology in our everyday lives. In fact, it can be argued that digital technology is already ubiquitous for many stakeholders in mathematics education. Volume 2 of this series is titled The Mathematics Teacher in the Digital Era, which implies an exploration of the mathematics teacher as individual agent or actor in the experience of teaching and learning mathematics. What is exciting is the book editors' potentially unintended insights into teachers' affective sense, their beliefs, and their subsequent decisions for future pedagogical effort.     

A multimodal approach to coding discourse: Collaboration, distributed cognition, and geometric reasoning

Our research aims to identify children’s communicative strategies when faced with the task of solving a geometric puzzle in CSCL contexts. We investigated how to identify and trace distributed cognition in problem-solving interactions based on discursive cohesion to objects, participants, and prior discursive content, and geometric and cooperative concepts. We report on the development of a method of coding and representation of verbal and gestural content for multimodal interactional data and initial application of this framework to a microethnographic case study of two small groups of 7 and 8-year-old learners solving tangram manipulatives in physical and virtual desktop settings. We characterize the establishment of shared reference points as “coreferences” which cohere on object, para, and meta-levels through both gesture and speech. Our analysis foregrounds how participants establish common referential ground to facilitate collaborative problem solving with either computer-supported or physical puzzles. Using multimodal analysis and a theoretical framework we developed to study interactional dynamics, we identified patterns of focus, dominance, and coalition formation as they relate to coreferentiality on multiple levels. Initial findings indicate increased communication and cohesion to higher-level principles in the virtual tangram puzzle-solving setting. This work contributes to available models of multimodal analysis of distributed cognition using current manipulative technologies for early childhood mathematics education.