TL;DR: In this paper, a classification of the various registers of semiotic representations that are mobilized in mathematical processes is presented, revealing two types of transformation of semio-semiotic representations: treatment and conversion.
Abstract: To understand the difficulties that many students have with comprehension of mathematics, we must determine the cognitive functioning underlying the diversity of mathematical processes. What are the cognitive systems that are required to give access to mathematical objects? Are these systems common to all processes of knowledge or, on the contrary, some of them are specific to mathematical activity? Starting from the paramount importance of semiotic representation for any mathematical activity, we put forward a classification of the various registers of semiotic representations that are mobilized in mathematical processes. Thus, we can reveal two types of transformation of semiotic representations: treatment and conversion. These two types correspond to quite different cognitive processes. They are two separate sources of incomprehension in the learning of mathematics. If treatment is the more important from a mathematical point of view, conversion is basically the deciding factor for learning. Supporting empirical data, at any level of curriculum and for any area of mathematics, can be widely and methodologically gathered: some empirical evidence is presented in this paper.
TL;DR: Part I: Introduction 1. Research as an important way of knowing 2. Essentials of research 3. Philosophical foundations 4. Framing the problem 5. Developing a knowledge base through review of the literature 6. Theory in research 7. Formulating research questions and queries
Abstract: Part I: Introduction 1. Research as an important way of knowing 2. Essentials of research Part II: Thinking Processes 3. Philosophical foundations 4. Framing the problem 5. Developing a knowledge base through review of the literature 6. Theory in research 7. Formulating research questions and queries 8. Language and thinking processes Part III: Design approaches 9. Experimental-type designs 10. Naturalistic inquiry designs Part IV: Action processes 11. Setting the boundaries of a study 12. Protecting the boundaries 13. Boundary setting in experimental-type designs 14. Boundary setting in naturalistic designs 15. Collecting information 16. Measurement in experimental-type research 17. Gathering information in naturalistic inquiry 18. Preparing and organizing data 19. Statistical analysis for experimental-type research 20. Analysis in naturalistic inquiry 21. Sharing research knowledge before the study 22. Sharing research knowledge during and after the study Part V: Improving practice through inquiry 23. Case study designs 24. Reciprocal role of research & practice 25. Stories from the field Appendix: Informed consent documents Glossary
TL;DR: The Creative Cognition Approach as mentioned in this paper extends this particular view of creativity to the programs and theoretical views of some of the most prominent researchers in the areas of problem solving, concept formation, and thinking.
Abstract: Mental processes are the essence of creative endeavor. The Creative Cognition Approach extends this particular view of creativity, first proposed and developed by the editors in their earlier book Creative Cognition, to the programs and theoretical views of some of the most prominent researchers in the areas of problem solving, concept formation, and thinking. Chapters cover a wide range of approaches and processes that play a role in creative cognition, from those that have their roots in associationism (the notion that creative ideas are produced incrementally), to the Gestalt point of view (particularly insight), to current computational approaches. Each chapter deals with central issues in cognition and creativity, and many consider new ways in which creativity can be studied under controlled conditions. The Creative Cognition Approach begins with a new look at an ancient subject, dreams. It then takes up intuition and insight from a contemporary cognitive perspective, and the importance of using prior knowledge in the incremental view of creative problem solving, which is contrasted with the importance of various forms of fixation and sudden insight. Studies are presented that provide new methods for distinguishing insight problem solving from analytic problem solving, and a general description of recall, problem solving, and creative thinking is provided along with relevant experimental evidence. Numerous laboratory studies of creative idea generation are described that reveal the conceptual structures that give rise to imaginative thinking. Visual representations are considered in the context of memory distortions, and in the use of diagrams in scientific discovery. Models that help clarify the relation between comprehension and creativity are discussed, and a novel integration of ideas (primary and secondary process thinking, conditioning, genetic algorithms, chaos theory, the thermodynamics of crystallography) are brought together in a connectionist framework. A multivariate investment approach is used to study creative performance, and criteria for assessing and enhancing creative realism are detailed. A Bradford Book
TL;DR: The authors assesses the political consequences of news presented to the public and how the public processes the news based on monitoring of 16 adults and the news content that reached them, focusing on the thinking processes that come into play when people cope with political information.
Abstract: This work assesses the political consequences of news presented to the public and how the public processes the news. Based on monitoring of 16 adults and the news content that reached them, it focuses on the thinking processes that come into play when people cope with political information.
TL;DR: In this paper, the authors focus on the thinking processes of the intimate dyad, as they influence and are influenced by the relationship with another person, and their focus is on thinking as it occurs at the dyadic level.
Abstract: This chapter is concerned with the thinking processes of the intimate dyad. So, although we will focus from time to time on the thinking processes of the individual—as they influence and are influenced by the relationship with another person—our prime interest is in thinking as it occurs at the dyadic level. This may be dangerous territory for inquiry. After all, this topic resembles one that has, for many years now, represented something of a “black hole” in the social sciences—the study of the group mind. For good reasons, the early practice of drawing an analogy between the mind of the individual and the cognitive operations of the group has long been avoided, and references to the group mind in contemporary literature have dwindled to a smattering of wisecracks.