Literature Index

Displaying 1991 - 2000 of 3326
  • Author(s):
    Gick, M. L., & Holyoak, K. J.
    Year:
    1983
    Abstract:
    An analysis of the process of analogical thinking predicts that analogies will be noticed on the basis of semantic retrieval cues and that the induction of a general schema from concrete analogs will facilitate analogical transfer. These predictions were tested in experiments in which subjects first read one or more stories illustrating problems and their solutions and then attempted to solve a disparate but analagous transfer problem. The studies in Part I attempted to foster the abstraction of a problem schema from a single story analog by means of summarization instructions, a verbal statement of the underlying principle, or a diagrammatic representation of it. None of these devices achieved a notable degree of success. In contrast, the experiments in Part II demonstrated that if two prior analogs were given, subjects often derived a problem schema as an incidental product of describing the similarities of the analogs. The quality of the induced schema was highly predictive of subsequent transfer performance. Furthermore, the verbal statements and diagrams that had failed to facilitate transfer from one analog proved highly beneficial when paired with two. The function of examples in learning was discussed in light of the present study.
  • Author(s):
    Shaughnessy, J. M., Watson, J. M. Moritz, J. B. & Reading, C.
    Year:
    1999
    Abstract:
    Although research has been done on students' conceptions of centers (averages, means, medians), there has not been a corresponding line of research into students' conceptions of variability or spread. In this paper we describe several exploratory studies designed to investigate school students' conceptions of variability. A sampling task that was a variation of an item on the 1996 National Assessment of Educational Progress (NAEP) was given to 324 students in Grades 4 - 6, 9, and 12 from Oregon, Tasmania, and New South Wales. Three different versions of the task were presented in a Before, and in an After setting. The Before and After students did the task both before and after carrying out a simulation of the task. Responses to the sampling task were categorized according to their centers (Low, Five, High) and spreads (Narrow, Reasonable, Wide). Results show a steady growth across grades on the center criteria but no clear corresponding improvement on the spread criteria. There was considerable improvement on the task among the students who repeated it after the simulation. Students' growth on the center criteria may be due to the emphasis that instruction places on centers in school mathematics. Similarly, the lack of clear growth on spreads and variability, and the inability of many students to integrate the two concepts (centers and spreads) on this task, may be due to instructional neglect of variability concepts.
    Location:
  • Author(s):
    Goodchild, S.
    Year:
    1988
    Abstract:
    This article reports an exploratory study of what 13 to 14 year olds understand when confronted by the word average in the context of an everyday situation.
  • Author(s):
    Rouan, O.
    Editors:
    Phillips, B.
    Year:
    2002
    Abstract:
    The importance of statistical graphics, as well as their practical use in day-to-day scientific research, makes it worth assessing and appraising teachers' conceptions concerning this matter. Accordingly, we should shed some light on the most specific components of dealing with such graphics as understood by math secondary level teachers. At the end, we try to give some guidelines that could be useful when elaborating on a content for teachers' training.
  • Author(s):
    Sharkey, C. K.
    Editors:
    Stallings, L.
    Year:
    2001
    Abstract:
    The purpose of this study was to investigate the conceptions secondary school students have when dealing with stochastic questions and the heuristics these students use to solve stochastic questions. The second purpose of this study was to determine if there were any effects of gender, grade level, mathematical placement, reading ability and prior stochastic experience on the students' stochastic achievement. The students' stochastic achievement was based on the percentage correct on a multiple-choice stochastic test and the students' conceptions and the heuristics they used were based on the answers students gave on a stochastic reasoning test. The analysis sample for the study consisted of 392 secondary school mathematics students in the Toms River, New Jersey, school district who took the multiple-choice stochastic test. Eighteen of the 392 students volunteered to take the reasoning test, where six students were from each group of students who scored in the top third, middle third and bottom third of the multiple-choice test. Statistical methods were used to test if there were any effects of the variables mentioned earlier on students' stochastic achievement, and whether there was a difference in the proportion of correctly answered questions on the multiple-choice test between probability and statistics questions. The results indicated that, at the 0.05 significance level, reading ability, grade level (Grade 9), the interaction between gender and mathematical placement (track 3), and the interaction between reading ability and stochastic experience had a significant effect on students' stochastic achievement. In addition, there was a significant difference in the proportion of correct answers between probability and statistics questions. Another question that was investigated in this study was if secondary school students use heuristics to solve stochastic questions. This question was qualitatively researched. From the results of the reasoning test, it was concluded that secondary school students use the following heuristics to solve stochastic problems: Belief Strategy, Equiprobable Bias, Bigger is Better, Prior Experience and Normative Reasoning. Belief strategy was used more often than the other heuristics. Also, it was determined that students do not always use the same heuristics to solve similar types of problems.
  • Author(s):
    Theodosia Prodromou
    Year:
    2016
    Abstract:
    In the Australian mathematics curriculum, Year 12 students (aged 16-17) are asked to solve conditional probability problems that involve the representation of the problem situation with two-way tables or three-dimensional diagrams and consider sampling procedures that result in different correct answers. In a small exploratory study, we investigate three Year 12 students’ conceptions and reasoning about conditional probability, samples, and sampling procedures. Through interviews with the students, supported by analysis of their work investigating probabilities using tabular representations, we investigate the ways in which these students perceive, express, and answer conditional probability questions from statistics, and also how they reason about the importance of taking into account what is being sampled and how it is being sampled. We report on insights gained about these students’ reasoning with different conditional probability problems, including how they interpret, analyse, solve, and communicate problems of conditional probability.
  • Author(s):
    Shaughnessy, J. M., & Zawojewski, J. S.
    Year:
    1999
    Abstract:
    Are you increasing your emphasis on probability and statistics with students? Are more of your students studying statistics or probability during secondary school? Are your students improving in their performance in data and chance? If you answered yes to any of these three questions, you are not alone, according to the most recent National Assessment of Educational Progress (NAEP). The NAEP is administered approximately every four years to students attending a representative sample of schools across the United States.
  • Author(s):
    Dierdorp, A., Bakker, A., Ben-Zvi, D., & Makar, K.
  • Author(s):
    Makar, K. & Confrey, J.
    Editors:
    Ben-Zvi, D. & Garfield, J.
    Year:
    2004
    Abstract:
    The importance of distributions in understanding statistics has been well articulated in this book by other researchers (for example, Bakker &amp; Gravemeijer, Chapter 7; Ben-Zvi, Chapter 6). The task of comparing two distributions provides further insight into this area of research, in particular that of variation, as well as to motivate other aspects of statistical reasoning. The research study described here was conducted at the end of a 6-month professional development sequence designed to assist secondary teachers in making sense of their students' results on a state-mandated academic test. In the United States, schools are currently under tremendous pressure to increase student test scores on state-developed academic tests.<br>This chapter focuses on the statistical reasoning of four secondary teachers during interviews conducted at the end of the professional development sequence. The teachers conducted investigations using the software Fathom&trade; in addressing the research question: "How do you decide whether two groups are different?" Qualitative analysis examines the responses during these interviews, in which the teachers were asked to describe the relative performance of two groups of students in a school on their statewide mathematics test. Pre- and posttest quantitative analysis of statistical content knowledge provides triangulation (Stake, 1994), giving further insight into the teachers' understanding.
  • Author(s):
    Mocko, Megan
    Year:
    2013
    Abstract:
    Online courses are becoming an increasingly more common option for college students and technology plays a critically important role. How can a course be taught in a way that engages the students so that they master the material as well as they would in a traditional classroom? In order to help accomplish these goals various technological packages must be chosen to bridge the gap between the traditional and online course. This paper will discuss the technological setup of an online Statistics course, and review the technology choices, implementations, and problems that arose. The paper will concentrate on the discussion of five areas: location of course, class conduct, communication, assessment and any additional hardware requirements.

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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

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