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Journal Article

Exploring Students' Conceptions of the Standard Deviation

01 May 2005-Statistics Education Research Journal (International Association for Statistical Education (IASE))-Vol. 4, Iss: 1, pp 55-82

AbstractSUMMARY This study investigated introductory statistics students’ conceptual understanding of the standard deviation. A computer environment was designed to promote students’ ability to coordinate characteristics of variation of values about the mean with the size of the standard deviation as a measure of that variation. Twelve students participated in an interview divided into two primary phases, an exploration phase where students rearranged histogram bars to produce the largest and smallest standard deviation, and a testing phase where students compared the sizes of the standard deviation of two distributions. Analysis of data revealed conceptions and strategies that students used to construct their arrangements and make comparisons. In general, students moved from simple, one-dimensional understandings of the standard deviation that did not consider variation about the mean to more mean-centered conceptualizations that coordinated the effects of frequency (density) and deviation from the mean. Discussions of the results and implications for instruction and further research are presented.

Topics: Standard deviation (61%)

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01 Jan 2015
TL;DR: The results suggest that the LJQ is a reliable and valid instrument for evaluating LJ.
Abstract: Objectives: Lao Juan (LJ, 劳倦) is a syndrome described in Chinese medicine (CM) that manifests with : Lao Juan (LJ, 劳倦) is a syndrome described in Chinese medicine (CM) that manifests with fatigue, fever, spontaneous sweating, indigestion, work-induced pain, weakness of the limbs, and shortness of breath. fatigue, fever, spontaneous sweating, indigestion, work-induced pain, weakness of the limbs, and shortness of breath. The present study was conducted to examine the reliability and validity of a Lao Juan Questionnaire (LJQ). The present study was conducted to examine the reliability and validity of a Lao Juan Questionnaire (LJQ). Methods: A total of 151 outpatients and 73 normal subjects were asked to complete the LJQ. Seventy-three normal subjects A total of 151 outpatients and 73 normal subjects were asked to complete the LJQ. Seventy-three normal subjects were additionally asked to complete the Chalder Fatigue Scale (CFS). Twelve clinicians determined whether the were additionally asked to complete the Chalder Fatigue Scale (CFS). Twelve clinicians determined whether the 151 outpatients exhibited LJ or not. The internal consistency and construct validity for the LJQ were estimated using 151 outpatients exhibited LJ or not. The internal consistency and construct validity for the LJQ were estimated using data from the outpatient subjects. The CFS data were used to examine the concurrent validity of the LJQ. Total LJQ data from the outpatient subjects. The CFS data were used to examine the concurrent validity of the LJQ. Total LJQ scores and the clinicians' diagnoses of the outpatients were used to perform receiver operating characteristics (ROC) scores and the clinicians' diagnoses of the outpatients were used to perform receiver operating characteristics (ROC) curve analyses and to defi ne an optimum cut-off score for the LJQ. curve analyses and to defi ne an optimum cut-off score for the LJQ. Results: The 19-item LJQ had satisfactory internal : The 19-item LJQ had satisfactory internal consistency (α=0.828) and concurrent validity, with signifi cant correlations between the LJQ and the CFS subscales. consistency (α=0.828) and concurrent validity, with signifi cant correlations between the LJQ and the CFS subscales. In the test of construct validity using principal component analysis, a total of six factors were extracted, and the overall In the test of construct validity using principal component analysis, a total of six factors were extracted, and the overall variance explained by all factors was 59.5%. In ROC curve analyses, the sensitivity, specifi city, and area under the variance explained by all factors was 59.5%. In ROC curve analyses, the sensitivity, specifi city, and area under the curve were 76.0%, 59.2%, and 0.709, respectively. The optimum cut-off score was defi ned as six points. curve were 76.0%, 59.2%, and 0.709, respectively. The optimum cut-off score was defi ned as six points. Conclusions: Our results suggest that the LJQ is a reliable and valid instrument for evaluating LJ. Our results suggest that the LJQ is a reliable and valid instrument for evaluating LJ. KEYWORDS Chinese medicine, chronic fatigue syndrome, Chinese medicine-pattern Chinese medicine, chronic fatigue syndrome, Chinese medicine-pattern

2,912 citations


Cites background from "Exploring Students' Conceptions of ..."

  • ...…are experiencing difficulties with introductory statistics, and emerge with a lack of understanding of core concepts, such as statistical variation (delMas & Liu, 2005), chance (Garfield, 2003), graphical representations of distributions (Bakker & Gravemeijer, 2004), sampling variation (Reading &…...

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Abstract: Summary This paper provides an overview of current research on teaching and learning statistics, summarizing studies that have been conducted by researchers from different disciplines and focused on students at all levels. The review is organized by general research questions addressed, and suggests what can be learned from the results of each of these questions. The implications of the research are described in terms of eight principles for learning statistics from Garfield (1995) which are revisited in the light of results from current studies.

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Abstract: This paper describes the development of the CAOS test, designed to measure students’ conceptual understanding of important statistical ideas, across three years of revision and testing, content validation, and realiability analysis. Results are reported from a large scale class testing and item responses are compared from pretest to posttest in order to learn more about areas in which students demonstrated improved performance from beginning to end of the course, as well as areas that showed no improvement or decreased performance. Items that showed an increase in students’ misconceptions about particular statistical concepts were also examined. The paper concludes with a discussion of implications for students’ understanding of different statistical topics, followed by suggestions for further research.

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Abstract: A solid understanding of inferential statistics is of major importance for designing and interpreting empirical results in any scientific discipline. However, students are prone to many misconceptions regarding this topic. This article structurally summarizes and describes these misconceptions by presenting a systematic review of publications that provide empirical evidence of them. This group of publications was found to be dispersed over a wide range of specialized journals and proceedings, and the methodology used in the empirical studies was very diverse. Three research needs rise from this review: (1) further empirical studies that identify the sources and possible solutions for misconceptions in order to complement the abundant theoretical and statistical discussion about them; (2) new insights into effective research designs and methodologies to perform this type of research; and (3) structured and systematic summaries of findings like the one presented here, concerning misconceptions in other areas of statistics, that might be of interest both for educational researchers and teachers of statistics.

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Cites background or methods or result from "Exploring Students' Conceptions of ..."

  • ...Third, with regard to the data gathering methodology, interviews (e.g., delMas & Liu, 2005), and mixture of multiple-choice and open-answer items can be found (e.g., Vallecillos, 1995, 1996, 2000, 2002)....

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  • ...Our search criteria identified five publications documenting empirical evidence about misconceptions regarding the idea behind the law of large numbers, more specifically: Well et al. (1990), Finch (1998), Sedlmeier (1998), Chance et al. (2004; see next section), and delMas and Liu (2005)....

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  • ...…(2004) More than 100 Variety None assumed 3 similar settings: activity with PC + assessment Software: simulation assessment: posttest and final exam delMas and Liu (2005) 12 – Pre-university 1 group: interview Interview while interaction with computer program Falk and Greenbaum (1995) 53…...

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  • ...Before being able to understand the concept and features of sampling distributions, students should be able to develop a good understanding of the idea of variability (delMas & Liu, 2005)....

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  • ...Another factor making it difficult to compare results of these studies is the differences in sample size, which range from very small (e.g., delMas & Liu, 2005; Vallecillos & Batanero, 1997) to large numbers of participants (e.g., Vallecillos, 1995, 1996, 2000)....

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Journal ArticleDOI
Abstract: Since the first studies on the teaching and learning of statistics appeared in the research literature, the scholarship in this area has grown dramatically. Given the diversity of disciplines, meth...

124 citations


Cites background or methods from "Exploring Students' Conceptions of ..."

  • ...In a related study, delMas and Liu (2005) studied students’ development of reasoning about standard deviation....

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  • ...The types of tasks used by delMas and Liu (2005) about what makes the standard deviation larger or smaller can be used to promote this type of discussion....

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  • ...Students have shown inconsistencies in their reasoning about the most "elementary" concepts of measures of central tendency and spread (e.g., Chance, delMas, and Garfield, 2004; delMas and Liu, 2005; Groth and Bergner, 2006; Noss, Pozzi, and Hoyles, 1999)....

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  • ...Researchers have found that use of specific technology tools can help illuminate difficulties in understanding particular concepts such as sampling distributions (Chance, delMas and Garfield, 2004) and standard deviation (delMas and Liu, 2005)....

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References
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Journal ArticleDOI
Abstract: It has become a commonplace belief that learning is the result of the interaction between what the student is taught and his current ideas or concepts.’ This is by no means a new view of learning. Its roots can be traced back to early Gestalt psychologists. However, Piaget’s (1929, 1930) early studies of children’s explanations of natural phenomena and his more recent studies of causality (Piaget, 1974) have perhaps had the greatest impact on the study of the interpretive frameworks students bring to learning situations. This research has led to the widespread study of students’ scientific misconceptions.2 From these studies and, particularly, from recent work by researchers such as Viennot ( 1979) and Driver (1 973), we have developed a more detailed understanding of some of these misconceptions and, more importantly, why they are so “highly robust” and typically outlive teaching which contradicts them (Viennot, 1979, p. 205). But identifying misconceptions or, more broadly speaking, “alternative frameworks” (Driver & Easley, 1978), and understanding some reasons for their persistence, falls short of developing a reasonable view of how a student’s current ideas interact with new, incompatible ideas. Although Piaget (1974) developed one such theory, there appears to be a need for work which focuses “more on the actual content of the pupil’s ideas and less on the supposed underlying logical structures” (Driver & Easley, 1978, p. 76). Several research studies have been performed (Nussbaum, 1979; Nussbaum & Novak, 1976; Driver, 1973; Erickson, 1979) which have investigated “the substance of the actual beliefs and concepts held by children” (Erickson, 1979, p. 221). However, there has been no well-articulated theory explaining or describing the substantive dimensions of the process by which people’s central, organizing concepts change from one set of concepts to another set, incompatible with the first. We believe that a major source of hypotheses concerning this issue is contemporary philosophy of science, since a central question of recent philosophy of science is how concepts change under the impact of new ideas or new information. In this article we first sketch a general model of conceptual change which is largely derived from current philosophy of science, but which we believe can illuminate * This article is partly based on a paper entitled “Learning Special Relativity: A Study of Intellectual Problems Faced by College Students,” presented at the International Conference Celebrating the 100th Anniversary of Albert Einstein, November 8-10, 1979 at Hofstra University.

4,862 citations


"Exploring Students' Conceptions of ..." refers background in this paper

  • ...Reading and Shaughnessy (2004) present evidence of different levels of sophistication in elementary and secondary students’ reasoning about sample variation....

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Abstract: Understanding how science students respond to anomalous data is essential to understanding knowledge acquisition in science classrooms. This article presents a detailed analysis of the ways in which scientists and science students respond to such data. We postulate that there are seven distinct forms of response to anomalous data, only one of which is to accept the data and change theories. The other six responses involve discounting the data in various ways in order to protect the preinstructional theory. We analyze the factors that influence which of these seven forms of response a scientist or student will choose, giving special attention to the factors that make theory change more likely. Finally, we discuss the implications of our framework for science instruction.

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