Students' Misconceptions in Interpreting Center and Variability of Data Represented via Histograms and Stem-and-Leaf Plots

Cooper, Linda L.; Shore, Felice S.

doi:10.1080/10691898.2008.11889559

Cited by 49 publications

(59 citation statements)

References 9 publications

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“…For instance, when student S8 was attempting to solve a question in Task 5 that involved finding the highest and lowest number of weeks needed to finish reading a storybook, she was not aware that the x-axis signified the number of weeks; she referred to the y-axis instead, as revealed in the following excerpt from her interview protocol. This error was also found in the study by Cooper and Shore [27]. …”

Section: Resultssupporting

confidence: 81%

“…For organizing and reducing data, earlier studies revealed that many students have misconceptions about measures of central tendency, including the mean [24–27], median [27], mode [28], and measures of variability [29–31]. Sharma [32] claimed that students may be bewildered when both measures are combined in one task.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…Representing data using different mathematical graphics, such as histograms [27,33,34], box plots [35], and bar graphs [36], can be a daunting task for many students. Consequently, we suggest three sub-processes of representing data in this study: (i) demonstrating data sets graphically using a computer, (ii) identifying different representations for the same data set, and (iii) judging the effectiveness of two different representations for the same data.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

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A Framework for Assessing High School Students' Statistical Reasoning

2016

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Based on a synthesis of literature, earlier studies, analyses and observations on high school students, this study developed an initial framework for assessing students’ statistical reasoning about descriptive statistics. Framework descriptors were established across five levels of statistical reasoning and four key constructs. The former consisted of idiosyncratic reasoning, verbal reasoning, transitional reasoning, procedural reasoning, and integrated process reasoning. The latter include describing data, organizing and reducing data, representing data, and analyzing and interpreting data. In contrast to earlier studies, this initial framework formulated a complete and coherent statistical reasoning framework. A statistical reasoning assessment tool was then constructed from this initial framework. The tool was administered to 10 tenth-grade students in a task-based interview. The initial framework was refined, and the statistical reasoning assessment tool was revised. The ten students then participated in the second task-based interview, and the data obtained were used to validate the framework. The findings showed that the students’ statistical reasoning levels were consistent across the four constructs, and this result confirmed the framework’s cohesion. Developed to contribute to statistics education, this newly developed statistical reasoning framework provides a guide for planning learning goals and designing instruction and assessments.

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Section: Resultssupporting

confidence: 81%

Section: Theoretical Considerationsmentioning

confidence: 99%

Section: Theoretical Considerationsmentioning

confidence: 99%

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A Framework for Assessing High School Students' Statistical Reasoning

2016

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“…The mean absolute deviation gives each deviation its proportionate place in the result, and is easier for new researchers and others to understand than SD is. New researchers struggle with the logic of statistics (Watts, 1991, Murtonen andLehtinen 2003), especially measures of variation (Cooper and Shore 2008), perhaps because it is made unnecessarily complicated by experts and practioners. Working with empirical astronomical data, Eddington (1914, p.147) found, and reported that the majority of astronomers also found, that the mean absolute deviation was a better measure of dispersion than SD.…”

Section: The Mean Absolute Deviationmentioning

confidence: 99%

Introducing the mean absolute deviation ‘effect’ size

Gorard

2014

International Journal of Research & Method in Education

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThis paper revisits the use of effect sizes in the analysis of experimental and similar results, and reminds readers of the relative advantages of the mean absolute deviation as a measure of variation, as opposed to the more complex standard deviation. The mean absolute deviation is is easier to use and understand, and more tolerant of extreme values. The paper then proposes the use of an easy to comprehend effect size based on the mean difference between treatment groups, divided by the mean absolute deviation of all scores. Using a simulation based on 1,656 randomised controlled trials each with 100 cases, and a before and after design, the paper shows that the substantive findings from any such trial would be the same whether rawscore differences, a traditional effect size like Cohen's d, or the mean absolute deviation effect size is used. The same would be true for any comparison, whether for a trial or a simpler cross-sectional design. It seems that there is a clear choice over which effect size to use. The main advantage in using raw scores as an outcome measure is that they are easy to comprehend. However, they might be misleading and so perhaps require more judgement to interpret than traditional 'effect' sizes. Among the advantages of using the mean absolute deviation effect size are its relative simplicity, everyday meaning, and the lack of distortion of extreme scores caused by the squaring involved in computing the standard deviation. Given that working with absolute values is no longer the barrier to computation that it apparently was before the advent of digital calculators, there is a clear place for the mean absolute deviation effect size (termed 'A'). Introduction and method

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“…Lately, Cooper and Shore (2008) studied students' misconceptions in interpreting center and variability of data represented via histograms and stem-and-leaf plots. Histograms and stem-and-leafs plots, beyond their value in interpreting center and variability, are strongly related to the foundational statistical concept of a distribution / cumulative distribution (which is further explored on the basis of Probability theory).…”

Section: Introductionmentioning

confidence: 99%

Difficulties Greek Senior High School Students Identify in Learning and the Teaching of Statistics: The Case of Experimental and Private High Schools

Ghinis

Korres

Bersimis

2009

Journal of Statistics Education

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The present paper examines the difficulties Greek senior high school students identify in learning Statistics and how these difficulties are related to the course's level of difficulty. Also it examines the difficulties students identify that teachers face while teaching Statistics, their suggestions for changes and how these difficulties and suggestions are related to the level of the students' satisfaction by the method of teaching. In the paper a case-study is presented, that was designed and realized at the Department of Statistics and Insurance Sciences of the University of Piraeus. In the study 163 students from Experimental and Private High Schools participated, all attending the 3 rd grade of Greek senior high school.

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Students' Misconceptions in Interpreting Center and Variability of Data Represented via Histograms and Stem-and-Leaf Plots

Cited by 49 publications

References 9 publications

A Framework for Assessing High School Students' Statistical Reasoning

A Framework for Assessing High School Students' Statistical Reasoning

Introducing the mean absolute deviation ‘effect’ size

Difficulties Greek Senior High School Students Identify in Learning and the Teaching of Statistics: The Case of Experimental and Private High Schools

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