Literature Index

Displaying 3281 - 3290 of 3326
  • Author(s):
    Jolliffe, F.
    Editors:
    The National Organizing Committee of the ICOTS 4
    Year:
    1994
    Abstract:
    This paper concentrates on the "Why?" parts of some of the simpler questions and discusses the usefulness of asking students to give a brief reason as to why they had chosen the answer they gave. Responses given by the UK students are used to illustrate points.
  • Author(s):
    Borovcnik, M. G.
    Editors:
    Bell, A., Low, B., & Kilpatrick, J.
    Year:
    1984
    Abstract:
    Some standard probability distributions (like the binomial or Poisson) are especially attractive for teaching. They can be decomposed into smaller "moduls". These moduls are much easier to handle, a check of them could be a statistical test, but a judgement by mere reflection of the situation is also possible. It is argued that the process of decomposing into moduls and synthesizing them to the original situation enables insight into the stochastic structure of the standard situations.
  • Author(s):
    Scheaffer, R. L.
    Year:
    1990
    Abstract:
    Recent years have witnessed a strong movement away from what might be termed classical statistics to a more empirical, data-oriented approach to statistics, sometimes termed exploratory data analysis, or EDA. This movement has been active among professional statisticians for twenty or twenty-five years but has begun permeating the area of statistical education for non-statisticians only in the past five to ten years. At this point, there seems to be little doubt that EDA approaches to applied statistics will gain support over classical approaches in the years to come. That is not to say that classical statistics will disappear. The two approaches begin with different assumptions and have different objectives, but both are important. These differences will be outlined in this article.
  • Author(s):
    Sue Gordon and Jackie Nicholas
    Year:
    2008
    Abstract:
    Examples have long been an integral component of statistics teachers' instructional repertoires<br>but tend to be in the background of pedagogical knowledge. We explore the diverse ways that<br>university statistics educators use examples, drawing on data from recent research (Gordon, Reid<br>&amp; Petocz, 2007). Three overlapping categories are proposed: examples are developed and<br>presented by educators in basic instruction, examples are generated by students, under teacher<br>direction, to aid learning and examples connect statistics with students' future professional work.<br>Expressions in the second category were sparse suggesting an opportunity for statistics educators<br>to develop teaching. We review models of exemplification in mathematics education and relate<br>these to the empirical findings to begin the development of a framework for characterising<br>examples in statistics education. We conclude that examples help promote statistical literacy.
  • Author(s):
    Engel, A.
    Year:
    1976
    Abstract:
    In the article "The Probabilistic Abacus", by A. Engel (Educational Studies in Mathematics 6, 1975, p. 1 - 22), we have introduced the probabilistic abacus and we have applied it to absorbing Markov chains. We have explained in detail how to compute absorption probabilities and expected times to absorption, but we gave no proofs. In this paper we give more applications of the abacus and we supply proofs for most of its properties.
  • Author(s):
    Ruma Falk
    Year:
    2009
    Abstract:
    The older one gets, the more one's life expectancy exceeds the population's given expectancy (at birth). Yet longevity is finite. This apparent paradox is analysed probabilistically with reference to empirical demographic data.
  • Author(s):
    Watts, D. G.
    Year:
    1991
    Abstract:
    The author states that the reason why students have major difficulty in learning statistics and that distinguishes statistics from other disciplines is that the important fundamental concepts of statistics are quintessentially abstract. In his view, concepts that are fundamental in statistics cannot be directly demonstrated, experienced, or drawn. Other factors are listed as making the problem worse: 1) intro stats courses involve more abstract concepts which are used frequently; 2) students must deal with truly abstract concepts AND immediately relate and apply these concepts to reality; 3) problems in statistics are always open to interpretation and have several solutions, none of which are truly known as being the correct ones; 4) the difference between statistics and mathematics lies in the type of numbers that are obtained- in mathematics, the numbers are obtained from calculations whereas in statistics, numbers are obtained from experiments; and 5) statistical notation and terminology are ambiguous and confusing. Watt's solution to the above problem is for statisticians to improve the notation and terminology by making the terms more meaningful and removing ambiguities.
  • Author(s):
    Kirschner, P. A., Sweller, J., Clark, R. E.
    Year:
    2006
    Abstract:
    Evidence for the superiority of guided instruction is explained in the context of our knowledge of human cognitive architecture, expert-notvice differences, and cognitive load. Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures that constitute human human cognitive architecture and evidence from empirical studeis over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient that instructional approaches that place a strong emphasis on guidance of the student learning process. The advantage of guidanc ebegins to recede only when learners have sufficiently high prior knowledge to provide "internal" guidance. Recent developments in instructional research and instructional design models that support guidance during instruction are briefly described.
  • Author(s):
    Stanek, E. J., Well, A. D., &amp; Ockene, I.
    Year:
    1999
    Abstract:
    Measures of biologic and behavioural variables on a patient often estimate longer term latent values, with the two connected by a simple response error model. For example, a subject's measured total cholesterol is an estimate (equal to the best linear unbiased estimate (BLUE)) of a subject's latent total cholesterol. With known (or estimated) variances, an alternative estimate is the best linear unbiased predictor (BLUP). We illustrate and discuss when the BLUE or BLUP will be a better estimate of a subject's latent value given a single measure on a subject, concluding that the BLUP estimator should be routinely used for total cholesterol and per cent kcal from fat, with a modified BLUP estimator used for large observed values of leisure time activity. Data from a large longitudinal study of seasonal variation in serum cholesterol forms the backdrop for the illustrations. Simulations which mimic the empirical and response error distributions are used to guide choice of an estimator. We use the simulations to describe criteria for estimator choice, to identify parameter ranges where BLUE or BLUP estimates are superior, and discuss key ideas that underlie the results.
  • Author(s):
    Sutton, S.
    Year:
    1998
    Abstract:
    The teaching of mathematics is not confined to a single approach. Because of the increasing diversity of knowledge and the quantitative data involved, students must make sense of the numerical data they are constantly facing. Seventeen people offer their ideas on how to teach numbers to students. Some espouse relating science teaching to mathematics. Otheres propose math education in relation to the work place. The value of logical thinking and analysis is also upheld as essential to the learning of numbers.

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