Literature Index

Displaying 951 - 960 of 3326
  • Author(s):
    Metz, K. E.
    Editors:
    LaJoie, S. P.
    Year:
    1998
    Abstract:
    The National Council of Teachers of Mathematics has recommended that we incorporate chance and probability as a thematic strand throughout children's formal schooling, beginning at the kindergarten level. This recommendation comes at a time when there is little agreement concerning the psychology of chance and probability. This is particularly disconcerting, given the importance now given to building on children's intuitions in the instructional process. The chapter addresses these issues as they involve the successful implementation of the K-4 statistics and probability standard, through an analysis of releveant research literatures. These literatures indicate that primary grade children have a number of intuitions that are directly relevant to statistical instruction. These include intuitions about relative magnitude and part/whole relations, incertitude and indeterminancy, the likelihood of a given event and, much more limited, intuitions about expected distrubutions of outcomes. The chapter also considers challenges to primary grade children's reasoning in this sphere that instruction needs to address, including conceptual gaps such as the idea of patterns in outcomes over the long haul, the restructuration and elaboration of children's intuitions, raising the meta-level of children's knowledge, and the issue of appropriate application.
  • Author(s):
    Gravemeijer, K.
    Editors:
    Phillips, B.
    Year:
    2002
    Abstract:
    This paper discusses an instructional design heuristic called "emergent modeling", with an instructional sequence on data analysis as an example. The emergent modeling approach is presented as an alternative for instructional approaches that focus on teaching ready-made representations. In relation to this, a distinction is made between modeling as "translation" and modeling as "organizing". Emergent modeling fits the latter. Within this perspective, the model and the situation modeled are mutually constituted in the course of modeling activity. This gives the label "emergent" a dual meaning. It refers to both the process by which models emerge, and the process by which these models support the emergence of more formal mathematical knowledge. This is reflected in the exemplary instructional sequence, in which the model co-evolves with the notion of distribution as an entity.
  • Author(s):
    Metz, K. E.
    Abstract:
    Compared kindergartners', third graders', and undergraduates' understanding and attribution of randomness. Found that kindergartners' interpretations were deterministic or outside the determinancy-indeterminancy frame. Most third graders had some grasp of randomness; their interpretations were less dominated by false attribution of determinism than kindergartners'. Undergraduates also showed performance deficiencies, suggesting that interpreting random phenomena constitutes a nontrivial challenge even for adults.
  • Author(s):
    Borovcnik, M., & Bentz, H. J.
    Editors:
    Kapadia, R., & Borovcnik, M.
    Year:
    1991
    Abstract:
    The analysis of historical development and philosophical ideas has shown the multifaceted character of probability. Kolmogorov's axiomatic structure does not reflect the complexity of ideas. The abundance of paradoxes not only occurred in the historical development of the discipline, it is also apparent in the individual learning process. Misconceptions are obstacles to comprehending and accepting theoretical ideas. Empirical research on probabilistic thinking aims to clarify and classify such misconceptions from both the theoretical as well as the individual's perspective. We present major research ideas of psychology and didactics of mathematics from a critical perspective. Our method of interpreting subjects' responses to experimental situations will be a complementarity of intuitions and official mathematics which is especially helpful for transferring ideas to actual teaching.
  • Author(s):
    Bentz, H. J., & Borovcnik, M. G.
    Year:
    1988
    Abstract:
    A frame of an interplay between intuitions of individuals and abstract theories is developed. Within this frame difficulties in learning/understanding a theory may be described by a breakdown in communication between the intuitive level of individuals and the "official" language of theory (used in class). It is, however, the scope of pertaining empirical research on probability concepts to investigate such intuitive imaginations. We will show that the interpretation of results is a precarious task and cannot successfully be done without regarding this interplay between intuitions and mathematics frame. Among the major problems are: Understanding of concepts and problem solving strategies are on different levels. It is hard to get information about the concept level in probands. The spectrum of intuitions covered be the investigations so far is very narrow, a huge percentage of diagnosing items referring to the symmetry view, few being related to the frequency aspect, hardly any to subjectivist ideas. The narrowness of the view on probability leads you inextricably into puzzles and troubles and may cause a breakdown in communication between interviewer and interviewed. The results of the discussion are directly transferred to the teaching situation. Some clues for improving teaching in class may be drawn from it.
    Location:
  • Author(s):
    Lajoie, S. P., Jacobs, V. R., & Lavigne, N. C.
    Year:
    1995
    Abstract:
    Statistics pervade our society, yet the understanding of statistics has remained the domain of a select few. Although the majority of the literature has focused on the adult learner, there is a movement toward teaching statistics to children. This article addresses the ways in which the study of statistics has been examined in the elementary and secondary schools in terms of content, readiness of children to learn, pedagogy, and assessment. A proposal is presented of how a cognitive apprenticeship model can be developed from the empirical research findings in order to build more effective instructional and assessment methods for statistics education.
  • Author(s):
    Paige A. Barnes
    Year:
    2009
    Abstract:
    This article describes an activity that helps students understand data analysis concepts while learning how to take control of their learning.
  • Author(s):
    BILGIN, Ayse and FRASER, Sharon
    Year:
    2007
    Abstract:
    Alternative assessment methods are becoming increasingly common in higher education with the aim of increasing the potential learning of students. This paper presents an application of an alternative assessment method: peer assessment of oral presentations for postgraduate students within a statistics department. Even though the assessment of peers is a valuable workplace skill, such an activity is rarely an integrated part of university education. With a new emphasis in universities on the development of generic skills, it is appropriate to explore means of assessment that are valued in the marketplace. The aim of the peer assessment intervention reported here was to increase the critical thinking skills of students and enable them to develop their ability as independent decision makers. The advantages and disadvantages of the intervention and peer assessment in general, are discussed and suggestions are made for possible improvements.
  • Author(s):
    Konold, C., & Falk, R.
    Editors:
    Geeslin W., & Graham K.
    Year:
    1992
    Abstract:
    Subjects' ratings of the apparent randomness of ten binary sequences were compared to the time required to memorize those same sequences. Memorization time proved a better predictor of the subjective randomness ratings than measures of the "objective" randomness of the sequences. This result is interpreted as supporting the hypothesis that randomness judgments are mediated by subjective assessments of encoding difficult. Such assessments are seen as compatible with the information theorists' interpretation of randomness as complexity.
  • Author(s):
    Robert J. Quinn, Tom S. Ball, Zhixia You
    Year:
    2010
    Abstract:
    We present a simple card game whose payout depends on a player's strategy, as well as on chance. Solutions require the use of conditional analysis and the computation of expected values.

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