Literature Index

Displaying 561 - 570 of 3326
  • Author(s):
    Truran, J., & Begg, A.
    Year:
    1994
    Abstract:
    This paper discusses the important pedagogical question of by how much experimental probabilities need to deviate from subjective or symmetric probabilities before children consider revising their subjective probabilities. Many children believe that common random generators like coins and dice are subject to mystical or physical powers, or to be inherently opposed to a child's wishes. Even 9% of Year 11 students have been found to believe that a six is the least likely outcome from tossing a die. Providing experiences which encourage children to revise their opinions is difficult. One reason for this difficulty arises from the mathematics of the situation. There are 2500 tosses of a coin necessary to obtain a relative frequency of between 0.48 and 0.52 with 95% confidence. This makes it very difficult to attempt a classroom confirmation of any theory.
  • Author(s):
    Drier, H. S.
    Editors:
    Garofalo, J.
    Year:
    2000
    Abstract:
    This dissertation investigated children's probabilistic reasoning during a twomonth<br>teaching experiment. As part of the research process, the researcher developed a<br>computer microworld environment, Probability Explorer, for children's explorations with<br>probability experiments. The design of the microworld is based on a constructivist theory<br>of learning, design of mathematical computer microworlds, and research on students'<br>understanding of probability and rational number concepts. Two major features in the<br>microworld include a dynamic link between numerical, graphical and iconic<br>representations of data that are updated simultaneously during a simulation, and the<br>ability to design experiments and assign probabilities to the possible outcomes.<br>The teaching experiment was conducted with three nine-year-old children. The<br>children participated in 10 hours of teaching sessions using the microworld. Each child<br>also participated in pre- and post- task-based interviews to assess their reasoning in<br>probabilistic situations. Each teaching session was videotaped, and computer interactions were recorded through internal mechanisms to create a video, including children's audio, of all actions in the microworld. These tapes provided the basis for analysis and interpretation of the children's development of probabilistic reasoning while using the microworld tools.<br>The individual case studies detail the children's probabilistic reasoning during the<br>pre-interview, teaching experiment, and post-interview. After extensive coding, several<br>themes were identified and discussed in each case study. Some of the major themes<br>included: understanding and interpretation of theoretical probability in equiprobable and<br>unequiproable situations; theories-in-action about the law of large numbers; and<br>development of part-whole reasoning as it relates to probability comparisons, a priori<br>predictions, and analysis of relative frequencies.<br>The children's development of probabilistic reasoning and their interactions with<br>the computer tools varied during the study. The children employed different strategies<br>and utilized different combinations of representations (e.g., numerical, graphical, iconic)<br>to make sense of the random data to enact their own theories-in-action. The results from<br>this study imply that open-ended microworld tools have the potential to act as agents for<br>children's development of intuitive-based probability conceptions. Dynamically linked<br>multiple representations and flexibility in designing experiments can facilitate an<br>exploratory approach to probability instruction and enhance children's meaning-making<br>activity and probabilistic reasoning.
  • Author(s):
    Ben-Zvi, D., Makar, K., Bakker, A., & Aridor, K.
    Editors:
    A. Bakker
    Year:
    2011
    Abstract:
    Research on informal statistical inference has so far attended little to developing students' reasoning about samples and sampling. This SRTL-7 pre-paper will prepare the ground for analyzing children’s reasoning about sampling when making informal statistical inferences in a collaborative, project- and inquirybased learning environment. Using data from a design experiment in Israeli Grade 5 (age 11) classrooms, we focus on the emergent reasoning of two boys working with TinkerPlots on investigations with growing sample size.   
  • Author(s):
    Kapadia, R., &amp; Ibbott, J.
    Year:
    1987
    Abstract:
    This paper presents the results of an instrument designed to probe children's intuitive notions of probability. The test consists of 16 questions, a few of which are analyzed in depth either qualitatively or quantitatively. A good selection of pupils' responses are included to illuminate children's intuitions. It is suggested that a mixture of teaching approaches should be used to help children develop probabilistic concepts coherently.
  • Author(s):
    Hoemann, H., &amp; Ross, B. M.
    Year:
    1971
    Abstract:
    4 experiments administering probability judgment tasks are reported using child Ss ranging in age from preschool to early adolescence. Experiment 1 showed equivalent results with probability and proportionality instructions when judgments were performed between 2 circles with different black and white proportions. Experiment 2 showed that fewer correct probability than proportionality judgments occurred when Ss judged a single circle. It was concluded that the 2-circle task does not require probability concepts, since Ss need not construct probability ratios to succeed. These results confirm those of Piaget and Inhelder. Experiments 3 and 4 modified the 2-circle task to require use of probability concepts and administered a probability task with double arrays of discrete objects. Results were comparable to those found for the single-circle task. Researchers who have claimed that preschool children use probability concepts are criticized since their experimental tasks have been similar to the unmodified 2-circle task of Experiment 1.
  • Author(s):
    Truran, K.
    Year:
    1994
    Abstract:
    This paper discusses the premise that young children do not perceive accurate relationships between the behavior of different, but related random generators. Data for this preliminary study has been collected from suburban primary school students aged from 7 - 12 years, who were questioned about their perceptions of the behavior of dice, coins, raffle tickets and a range of different and unusual random generators in identical situations. The findings indicate that children predict different result depending for example, on whether tickets rather than dice are used in a game. Their predictions appears to be based on the observation of the physical differences between dice and raffle tickets. Owing to the size of the preliminary study no tests of significance have been carried out and results are given in simple percentages.
  • Author(s):
    Green, D. R.
    Editors:
    Davidson, R., &amp; Swift, J.
    Year:
    1986
    Abstract:
    This paper reports on some aspects of research carried out in 1986 using 1600 Primary school children in mixed ability classes in state schools in a small Leicestershire town. The subjects, aged between 7:9 and 11:9 were give two untimed class tests which together took from 40 to 55 minutes to administer. All questions were read out to the subjects. The first test was concerned with concepts of randomness, the second with comparison of odds. Results indicate that young children do have a sound conceptual awareness of randomness.
  • Author(s):
    Jacobs, V. R.
    Year:
    1997
    Abstract:
    Two studies investigated upper elementary school students' informal understanding of sampling issues in the context of interpreting and evaluating survey results. The specific focus was on the children's evaluation of sampling methods and means of drawing conclusions from multiple surveys. In Study 1, 17 children were individually interviewed to categorize children's conceptions. In Study 2, 110 children completed paper-and-pencil tasks to confirm the response categories identified in Study 1 and to determine the prevalence of the response categories in a larger sample. Children evaluated sampling methods focusing on potential for bias, fairness, practical issues, or results. All children used multiple types of evaluation rationales, and the focus of their evaluations varied somewhat by context and type of sampling method (restricted, self-selected, or random). Children used affective (fairness) rationales more often in school contexts and rationales focused on results more often in out-of-school contexts. Children had more difficulty detecting bias with self-selected sampling methods than with restricted sampling methods because self-selection was initially the most fair (i.e., everyone had a chance to participate). Children preferred stratified random sampling to simple random sampling because they wanted to ensure that all types of individuals were included. When drawing conclusions from multiple surveys, children: (1) considered survey quality; (2) aggregated all surveys regardless of quality; (3) used their own opinions and ignored all survey data; or (4) refused to draw conclusions. Even when children were able to identify potential bias, they often ignored survey quality when drawing conclusions from multiple surveys.
  • Author(s):
    Falk, R.
    Abstract:
    Freudenthal (1982) has observed that Symmetry as a source of stochastic understanding is a virtually unknown and badly neglected intuitive and didactic tool. Saying this should be a platitude, but didacticians appear to be no faster learners than their students. In the teaching of probability three common aids which assume symmetry are frequently used: coins, dice and urns. This paper will discuss some aspects of children's understanding of the first two of these aids.
  • Author(s):
    Ben-Zvi, D., & Aridor, K.
    Year:
    2013
    Abstract:
    The knowledge and application of the problem context and its relation to data analysis is a key component in the development of students' informal inferential reasoning. This case study analyzes children's emergent understanding of the relationship between the context world and the data world while making informal statistical inferences in an inquiry-based learning environment using TinkerPlots. We focus on two fifth grade students (aged 11) who participated in the 2010 Connections design experiment in Israel. We observe and analyze their first steps in the two worlds – data and context – in growing samples investigations. They developed gradually and inconsistently an understanding of making informal inferences considering both context and data. They moved from an initial conception of context and data as separate entities to two interconnected and relevant dimensions. We finally discuss this development and what might have supported it. 

Pages

The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education