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.
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TL;DR: In this paper, the Horizon Content Knowledge (HCK) framework is proposed as a theoretical response to the knowledge needed for teaching mathematics in a continuous way, particularly relevant during transition to secondary school.
Abstract: Mathematics learning is a continuous process in which students face some abrupt episodes involving many changes of different natures. This work is focused on one of those episodes, transition from primary to secondary school, and targets teachers and their mathematical knowledge. By characterising the mathematical knowledge that teachers of mathematics need to smooth transition processes, we aim to highlight teachers’ impact in the continuity of mathematics education. The concept of Mathematical Knowledge for Teaching (MKT) developed by Ball among others (Ball, Thames & Phelps, 2008) and, within this framework, the construct Horizon Content Knowledge (HCK) emerge as our theoretical response to the knowledge needed for teaching mathematics in a continuous way, particularly relevant during transition to secondary school. The enrichment of the idea of HCK and the characterisation of its expression in the teaching practice intends to develop a theoretical tool to approach transition from teachers’ mathematical knowledge perspective.
14 citations
TL;DR: It is concluded that incorporating information technology in the statistics classroom is feasible due to its advantages although there could be some obstacles that need to be overcome.
14 citations
Cites background from "Exploring Students' Conceptions of ..."
...Besides, students also encounter difficulties in measures of variability (e.g. Garfield & Ben-Zvi, 2008d) which includes standard deviation (e.g. delMas & Liu, 2005)....
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TL;DR: Bar graphs and histograms are core statistical tools that are widely used in statistical practice and commonly taught in classrooms as mentioned in this paper, but despite their importance and the instructional time devoted to t...
Abstract: Bar graphs and histograms are core statistical tools that are widely used in statistical practice and commonly taught in classrooms. Despite their importance and the instructional time devoted to t...
13 citations
Cites background from "Exploring Students' Conceptions of ..."
...…by and can be used by students, studies of student understanding of histograms have revealed numerous misunderstandings and areas of confusion. delMas and Liu (2005) worked with 12 students enrolled in an introductory statistics course by having them manipulate data values displayed in…...
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01 Apr 2010
TL;DR: This article investigated students' conceptual knowledge and understanding of basic statistical concepts and compared it with statistical competence, which is associated with discrete statistical knowledge and basic interpretive skills. But they found that conceptual understanding of these concepts is more difficult to attain than statistical competence.
Abstract: This study investigates students' conceptual knowledge and understanding of basic statistical concepts and compares it against statistical competence, which is associated with discrete statistical knowledge and basic interpretive skills. It particularly examines the correspondence between students' perceived ability and their empirical understanding of the concepts. Two instruments were developed: a 20-item test to measure students' empirical understanding of the basic statistical concepts and a questionnaire with matching items to measure their perceived ability of these concepts. For a direct comparison of the two, students' responses to the test and questionnaire items were jointly analyzed using the Rasch measurement model. Results of the analysis show that conceptual understanding of basic statistical concepts is more difficult to attain than statistical competence. The results also suggest that students more often than not overestimated their understanding of basic statistical concepts, particularly those requiring conceptual understanding of the concepts.
12 citations
Dissertation•
01 Jun 2012
TL;DR: This dissertation aims to provide a history of educational psychology in the United States from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which major changes in educational methodology were made.
Abstract: University of Minnesota Ph.D. dissertation. June 2012. Major: Educational Psychology. Advisor: Robert delMas. 1 computer file (PDF); xiii, 281 pages, appendices A-J.
11 citations
Cites methods from "Exploring Students' Conceptions of ..."
...Third, researchers have used different methods for data collection—interviews (e.g., delMas & Liu, 2005; Kaplan, 2009; Konold et al., 1993) and a mixture of multiple-choice and open-ended questions (e.g., Haller & Krauss, 2002)....
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...Some researchers have used large-scale assessments (e.g., Carver, 2006; delMas & Liu, 2005, delMas, Garfield, Ooms, & Chance, 2006)....
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References
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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....
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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