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
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.
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.
Citations
More filters
TL;DR: In this paper, a retrospective phenomenological study investigates activities and actions identified by secondary statistics teachers who exhibit robust understandings of variation as deepening their understanding of statistical variation using phenomenological methods and a frame of Mezirow's transformation theory.
Abstract: This retrospective phenomenological study investigates activities and actions identified by secondary statistics teachers who exhibit robust understandings of variation as deepening their understandings of statistical variation. Using phenomenological methods and a frame of Mezirow’s transformation theory, analysis revealed learning factors that include their interests in statistics, motivation to encounter and resolve dilemmas, desires to have an overarching content framework, propensities for critical reflection, and actions on opportunities to engage in statistical learning activities and rationale discourse with more knowledgeable others. The extent to which these teachers embrace these opportunities distinguishes them from other teachers. Results from this study provide some basis for formulating hypotheses about secondary teachers’ statistics learning in general by contributing to understanding circumstances that may be conducive to developing deep understandings of statistical content. This study also advances the use of retrospective methods within a theoretical frame for adult learning to investigate teacher learning.
11 citations
TL;DR: A theoretical framework is provided to characterize how prior experience is used as a resource in data sense-making when the data are about students’ own physical experiences and centralizes and interrogates the work of “remembering” prior experiences and articulates how remembering is involved in interpreting quantified self data.
Abstract: Given growing interest in K-12 data and data science education, new approaches are needed to help students develop robust understandings of and familiarity with data. The model of the quantified se...
11 citations
Cites methods from "Exploring Students' Conceptions of ..."
...…education research, such as the computer mini-tools appearing in teaching experiments run by Cobb and colleagues (e.g., Cobb & Tzou, 2009), and homegrown visualization tools that can show distributions and variation have been developed for use in statistics education research (delMas & Liu, 2005)....
[...]
TL;DR: This article investigated the relationship between student achievement in statistics and factors at the student and teacher/classroom levels using the US 8th-grade Data and Chance content domain from the Trends in International Mathematics and Science Study, 2007 (TIMSS, 2007).
Abstract: This study investigated the relationship between student achievement in statistics and factors at the student and teacher/classroom levels using the US 8th-grade Data and Chance content domain from the Trends in International Mathematics and Science Study, 2007 (TIMSS, 2007). Using variables that have been linked to mathematics and statistics achievement in the literature, a hierarchical level modelling approach revealed significant achievement differences between boys and girls. Another important finding was related to a teacher's formal training. Although most of the TIMSS teachers reported participating regularly in professional development activities, almost half reported that they did not have a degree in either mathematics or mathematics education. Finally, TIMSS students' exposure to and learning of statistics-related concepts appeared to lag behind the expectations set forth in the Data Analysis and Probability Standard (National Council of Teachers of Mathematics [NCTM], 2000). Implications from ...
10 citations
Cites background from "Exploring Students' Conceptions of ..."
...…time understanding sampling distributions (delMas, Garfield, & Chance, 1999; Saldanha & Thompson, 2001), measures of variability (delMas & Liu, 2005), and probability and chance ideas and concepts (Garfield, 2003; Konold, 1995; Shaughnessy, 1992)....
[...]
Posted Content•
TL;DR: In this article, the authors developed and validated a scale to measure instructors' attitudes toward reform-oriented (or concept-based) teaching of introductory statistics in the health and behavioral sciences, at the tertiary level.
Abstract: Despite more than a decade of reform efforts, students continue to experience difficulty understanding and applying statistical concepts. The predominant focus of reform has been on content, pedagogy, technology and assessment, with little attention to instructor characteristics. However, there is strong theoretical and empirical evidence that instructors' attitudes impact the quality of teaching and learning. The objective of this study was to develop and initially validate a scale to measure instructors' attitudes toward reform-oriented (or concept-based) teaching of introductory statistics in the health and behavioral sciences, at the tertiary level. This scale will be referred to as FATS (Faculty Attitudes Toward Statistics). Data were obtained from 227 instructors (USA and international), and analyzed using factor analysis, multidimensional scaling and hierarchical cluster analysis. The overall scale consists of five sub-scales with a total of 25 items, and an overall alpha of 0.89. Construct validity was established. Specifically, the overall scale, and subscales (except perceived difficulty) plausibly differentiated between low-reform and high-reform practice instructors. Statistically significant differences in attitude were observed with respect to age, but not gender, employment status, membership status in professional organizations, ethnicity, highest academic qualification, and degree concentration. This scale can be considered a reliable and valid measure of instructors' attitudes toward reform-oriented (concept-based or constructivist) teaching of introductory statistics in the health and behavioral sciences at the tertiary level. These five dimensions influence instructors' attitudes. Additional studies are required to confirm these structural and psychometric properties.
10 citations
13 Jun 2016
TL;DR: This qualitative meta-analysis is aimed to explore the methods utilized in assessing statistical reasoning among students from all levels in descriptive statistics, and provides new information on statistical reasoning in descriptiveStatistics.
Abstract: To date, there are abundant studies on statistical reasoning in descriptive statistics and inferential statistics. Nevertheless, the types of statistical reasoning assessments used in those studies are different from each other. Hence, this qualitative meta-analysis is aimed to explore the methods utilized in assessing statistical reasoning among students from all levels in descriptive statistics. A total of 36 studies on reasoning about measures of central tendency, variability and distribution were found and reviewed in this paper. It was noticed that six major types of methods were employed to assess students’ statistical reasoning in descriptive statistics, namely interview, survey or questionnaire, tasks, tests, minute paper, and teaching. This study contributes considerably to the statistical reasoning area as it provides new information on statistical reasoning in descriptive statistics. For future studies, some recommendations are proposed to improve statistical reasoning assessments.
9 citations
Cites methods from "Exploring Students' Conceptions of ..."
...For example, delMas and Liu [40] used a technological tool in their interview while Reading [39] made use of a real-world task....
[...]
...Concept Method [39] Grades 7, 9, and 11 (aged 13 to 17) real world context delMas & Liu [40, 41] 12 university students Standard deviation Interview using conceptuall y enhanced software Sharma [42] 24 pre-service teacher education students Variability Questionnair e Watson, Callingha m & Kelly [43] 73 students (18 from Grade 3, 18 from Grade 5, 15 from Grade 7, 15 from Grade 9, 7 six-year-old children) Expectatio n and variation In-depth interview tasks Watson [44] 109 students aged from 6 to 15 Variation 3 interview protocol Peters [45] 16 secondary Variation Semi-...
[...]
...delMas & Liu [40, 41] 12 university students Standard deviation Interview using conceptuall y enhanced software Sharma [42] 24 pre-service teacher education students Variability Questionnair e...
[...]
References
More filters
TL;DR: In this paper, a general model of conceptual change is proposed, which is largely derived from current philosophy of science, but which they believe can illuminate * This model 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.
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.
5,052 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....
[...]
TL;DR: In this article, a detailed analysis of the ways in which scientists and science students respond to anomalous data is presented, giving special attention to the factors that make theory change more likely.
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.
1,434 citations
Journal Article•
230 citations