Exploring Students' Conceptions of the Standard Deviation

Home
/
Papers
/
Exploring Students' Conceptions of the Standard Deviation

Journal Article•

Exploring Students' Conceptions of the Standard Deviation

Robert delMas, Yan Liu¹•Institutions (1)

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

TL;DR: This article investigated introductory statistics students' conceptual understanding of the standard deviation and found that students moved from simple, one-dimensional understandings of 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.

read less

Abstract: SUMMARY 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.

...read moreread less

Content maybe subject to copyright Report

Citations

PDF

Open Access

More filters

Development and Validation of A

[...]

Lao Juan, Kyu-Jin Yoon, Young-Bae Park, Young-Jae Park, Min-Yong Kim - Show less +1 more

01 Jan 2015

TL;DR: The results suggest that the LJQ is a reliable and valid instrument for evaluating LJ.

...read moreread less

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

...read moreread less

3,787 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 &…...
[...]

Journal Article•DOI•

How Students Learn Statistics Revisited: A Current Review of Research on Teaching and Learning Statistics

[...]

Joan Garfield¹, Dani Ben-Zvi²•Institutions (2)

University of Minnesota¹, University of Haifa²

01 Dec 2007-International Statistical Review

TL;DR: The authors provide 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, and suggest what can be learned from the results of each of these questions.

...read moreread less

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.

...read moreread less

418 citations

Journal Article•

Assessing Students' Conceptual Understanding after a First Course in Statistics.

[...]

Robert delMas, Joan Garfield, Ann Ooms, Beth Chance

01 Nov 2007-Statistics Education Research Journal

TL;DR: The CAOS test as discussed by the authors is designed to measure students' conceptual understanding of important statistical ideas across three years of revision and testing, content validation, and realiability analysis, and results 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.

...read moreread less

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.

...read moreread less

251 citations

Journal Article•DOI•

Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education

[...]

Ana Elisa Castro Sotos¹, Stijn Vanhoof¹, Wim Van Den Noortgate¹, Patrick Onghena¹•Institutions (1)

Katholieke Universiteit Leuven¹

01 Jan 2007-Educational Research Review

TL;DR: In this article, a systematic review of publications that provide empirical evidence of these misconceptions was presented. But, the methodology used in the empirical studies was very diverse and the sources and possible solutions for these misconceptions were not identified.

...read moreread less

190 citations

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)....
[...]
...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)....
[...]
...…(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…...
[...]
...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)....
[...]
...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)....
[...]

Journal Article•DOI•

What Does Research Suggest About the Teaching and Learning of Introductory Statistics at the College Level? A Review of the Literature

[...]

Andrew Zieffler¹, Joan Garfield¹, Shirley Alt¹, Danielle N. Dupuis¹, Kristine Holleque¹, Beng Chang¹ - Show less +2 more•Institutions (1)

University of Minnesota¹

01 Jul 2008-Journal of Statistics Education

TL;DR: In this article, the first studies on the teaching and learning of statistics appeared in the research literature, the scholarship in this area has grown dramatically, and given the diversity of disciplines, meth...

...read moreread less

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...

...read moreread less

134 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....
[...]
...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....
[...]
...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)....
[...]
...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)....
[...]

1
2
3
4
…
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24

Collapse

References

PDF

Open Access

More filters

Book Chapter•DOI•

Reasoning About Variation

[...]

Chris Reading¹, J. Michael Shaughnessy²•Institutions (2)

University of New England (United States)¹, Portland State University²

01 Jan 2004

TL;DR: Basically two main aspects of variation have come to light in these descriptions of variation: how spread out the numbers are and what is happening with the numbers contained within that range.

...read moreread less

Abstract: Basically two main aspects of variation have come to light in these descriptions. One aspect is how spread out the numbers are. Students give responses that suggest that some indication of variation is being considered when they are dealing with extreme values using the range. The other aspect is what is happening with the numbers contained within that range. Responses considering the behavior of the middle values may give specific information about the numbers; or they may just give attributes that are necessary for the numbers, such as wanting them to be different. When these two aspects of variation description are brought together, deviations begin to become an issue; and when these deviations are anchored to a specific value, usually a center of some description, it will eventually become the focus of the student’s description of a distribution.

...read moreread less

127 citations

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

...Very little research has been conducted on students’ understanding of variability (Reading & Shaughnessy, 2004; Shaughnessy, 1997), despite the central role the concept plays in statistics (Hoerl & Snee, 2001; Moore 1990; Snee, 1990) and an apparent conceptual gap in students’ understanding of...
[...]
...Shaughnessy (1997; Reading & Shaughnessy, 2004) noted that the standard deviation is both computationally complex and difficult to motivate as a measure of variability....
[...]
...Part of this difficulty may stem from a lack of accessible models and metaphors for students’ conceptions of the standard deviation ( Reading & Shaughnessy, 2004 )....
[...]
...Shaughnessy (1997; Reading & Shaughnessy, 2004 ) noted that the standard deviation is both computationally complex and difficult to motivate as a measure of variability....
[...]
...© International Association for Statistical Education (IASE/ISI), May, 2005 variability (Reading & Shaughnessy, 2004; Shaughnessy, 1997)....
[...]

Monograph•DOI•

Software Goes to School: Teaching for Understanding with New Technologies.

[...]

David N. Perkins

01 May 1997

TL;DR: This work brings together leading experts to offer an in-depth examination of how computer technology can play an invaluable part in educational efforts through its unique capacities to support the development of students in the understanding of difficult concepts.

...read moreread less

Abstract: This work brings together leading experts to offer an in-depth examination of how computer technology can play an invaluable part in educational efforts through its unique capacities to support the development of students in the understanding of difficult concepts. It is intended for students, researchers and professionals in educational psychology, developmental psychology, and software design.

...read moreread less

117 citations

Journal Article•DOI•

The Challenge of Developing Statistical Literacy, Reasoning and Thinking

[...]

Christine M. Anderson-Cook

01 Feb 2006-The American Statistician

96 citations

Journal Article•DOI•

Conceptually Enhanced Simulations: A Computer Tool for Science Teaching

[...]

Joseph Snir¹, Carol L. Smith², Lorraine Grosslight³•Institutions (3)

University of Haifa¹, University of Massachusetts Boston², Harvard University³

01 Jun 1993-Journal of Science Education and Technology

TL;DR: A way computer simulations can be used to address the problem of teaching for conceptual change and understanding by embedding the relevant physical laws directly into the program code and allowing for genuine discoveries.

...read moreread less

Abstract: In this paper, we consider a way computer simulations can be used to address the problem of teaching for conceptual change and understanding. After identifying three levels of understanding of a natural phenomenon (concrete, conceptual, and metaconceptual) that need to be addressed in school science, and classifying computer model systems and simulations more generally in terms of the design choices facing the programmer, we argue that there are ways to design computer simulations that can make them more powerful than laboratory models. In particular, computer simulations that provide an explicit representation for a set of interrelated concepts allow students to perceive what cannot be directly observed in laboratory experiments: representations for the concepts and ideas used for interpreting the experiment. Further, by embedding the relevant physical laws directly into the program code, these simulations allow for genuine discoveries. We describe how we applied these ideas in developing a computer simulation for a particular set of purposes: to help students grasp the distinction between mass and density and to understand the phenomenon of flotation in terms of these concepts. Finally, we reflect on the kinds of activities such conceptually enhanced simulations allow that may be important in bringing about the desired conceptual change.

...read moreread less

84 citations

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

...The program was based on design principles for creating conceptually enhanced software (delMas, 1997; Nickerson, 1995; Snir, Smith, & Grosslight, 1995)....
[...]
...The program was based on design principles for creating conceptually enhanced software (delMas, 1997; Nickerson, 1995; Snir, Smith, & Grosslight, 1995 )....
[...]

Journal Article•DOI•

Learning to Understand the Balance Beam

[...]

Pamela Thibodeau Hardiman, Alexander Pollatsek, Arnold D. Well

01 Mar 1986-Cognition and Instruction

TL;DR: In this paper, the authors used instance-based reasoning, qualitative estimation of distance, and the use of quantitative rules of limited generality to predict whether a configuration of weights placed on a balance beam would cause the beam to balance, tip left, or tip right.

...read moreread less

Abstract: Twenty-two university students who did not initially know the quantitative rule for predicting whether a configuration of weights placed on a balance beam would cause the beam to balance, tip left, or tip right were asked to induce the rule in a training procedure adapted from Siegler (1976). For each of a series of balance beam problems, subjects predicted the action of the beam and explained how they arrived at their prediction. Protocols revealed that although all subjects realized on early on that both weight and distance were relevant to their predictions, they used a variety of heuristics prior to inducing the correct quantitative rule. These heuristics included instance-based reasoning, qualitative estimation of distance, and the use of quantitative rules of limited generality. The common use of instance-based reasoning suggests that learning to understand the balance beam cannot be described completely in terms of a simple rule acquisition theory. Also, the variability in the use of heuristics acr...

...read moreread less

72 citations

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

...Conceptual change can be facilitated through a combination of discovery learning and direct instruction (e.g., Burbules & Linn, 1988) and by drawing students’ attention to relevant aspects that might be neglected (e.g., Hardiman, Pollatsek, & Well, 1986 )....
[...]