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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01 Jan 2015
TL;DR: Shaughnessy et al. as discussed by the authors found that there was no statistically significant improvement in reasoning about variability when comparing distributions as students progressed through a college-level introductory statistics course.
Abstract: Current curricular documents including the Common Core State Standards (2010) and the Guidelines for Assessment and Instruction in Statistics Education (2005) have increased the need for students' understanding and reasoning about statistics at both the K-12 and college levels. In addition, an increasing number of students are taking the Advanced Placement Statistics Exam (College Board, 2011) or a college-level introductory statistics course (Scheaffer & Stasny, 2000). One of the main components for statistical thinking is consideration of variation (Wild & Pfannkuch, 1999). Previous studies have shown that students have misconceptions about variation (e.g. Reading, 2004; Torok & Watson, 1999) and students often lack the ability to give sophisticated answers (Shaughnessy, 2007). The goal of this study was to better understand how students' reasoning about variation in a distributional context changes as they progress through an introductory college-level statistics course. In order to better understand the longitudinal nature of this process during a semester-long introductory statistics course, both quantitative and qualitative data were collected at three different times (beginning, middle, and end of the course) in surveys and interviews. The Structure of Observed Learning Outcomes (SOLO) Taxonomy (Biggs & Collis, 1982) was used to understand and assess the quality of their reasoning. Qualitative data came from two sources: three interviews from each of the ten interviewees and three survey questions on each of three surveys from all participants. The interviews were transcribed and responses were sorted into appropriate locations in the SOLO Taxonomy. After coding responses to each question in each interview, themes of progress were then identified. These themes showed that students progressed through four different paths of reasoning including: improved, maintained, decreased, and inconsistent. Quantitative data showed that while students were good at reasoning about situations involving bar graphs and dot plots with regards to comparing variability in distributions, they struggled with reasoning about histograms. Overall, this study found that there was no statistically significant improvement in reasoning about variability when comparing distributions as students progressed through a college-level introductory statistics course. This lack of improvement suggested that perhaps college students needed to have direct intervention or cognitive conflict in order to make more progress in reasoning about variability when comparing distributions.
5 citations
Cites background or methods from "Exploring Students' Conceptions of ..."
...At the introductory college level, delMas and Liu (2005) conducted an exploratory study of students’ conceptions of standard deviation using an interactive computer environment and histograms....
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...Other students showed a developing sense of reasoning about standard deviation with the following explanations: contiguous, range, mean in the middle, and far away-values (delMas & Liu, 2005)....
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...In delMas & Liu (2005), students were led to believe that the data lay in the center of the bar instead of there being many possible data values for each data point within the bar....
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...…Bimodal and Uniform Basketball games scores Lifespan of pet in months Cell phone bill charge Histogram, Skewed and Uniform Money spent on groceries Quiz grades Money spent on groceries Histogram, Z and T Exam scores Price of Halloween costume Weekly minutes exercised and delMas and Liu (2005)....
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TL;DR: This article examined the knowledge structures and statistical reasoning of nine middle and secondary mathematics teachers as they responded to released items from the Level of Conceptual Understanding in Statistics (LOCUS) assessment during two 60-90 minute task-based clinical interviews.
Abstract: Recent standards reform documents across the globe have called for statistical literacy by the end of high school. Thus, it is important for teachers to develop a deep understanding of the content. Despite the relatively thick literature base connecting students’ content knowledge and reasoning, research on these connections among practicing teachers is in critical need. Our study contributes to this lack of research by examining the knowledge structures and statistical reasoning—and possible ways knowledge structures supported reasoning—of a stratified purposeful sample of nine middle and secondary mathematics teachers as they responded to released items from the Levels of Conceptual Understanding in Statistics (LOCUS) assessment during two 60–90 minute task-based clinical interviews. Knowledge structures were categorized as compatible-connected, incompatible-connected, and incompatible-disconnected. Teachers with less incompatible knowledge elements in their structures engaged more frequently in reasoning coded as sound. However, teachers frequently engaged in both sound and unsound forms of reasoning on the same task item. Implications are offered for teacher education and future research.
5 citations
Cites background from "Exploring Students' Conceptions of ..."
...One common misunderstanding students and teachers appear to have is that skewed distributions will be more variable than symmetric distributions (delMas & Liu, 2005; Doerr & Jacob, 2011)....
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TL;DR: In this article, the authors investigate the state of undergraduate business statistics education in the Middle East and North Africa (MENA) and assess its alignment with the best practices in equipping business graduates with the knowledge and skills demanded by the labor market.
Abstract: Purpose
The purpose of this study is to investigate the state of undergraduate business statistics education in the Middle East and North Africa (MENA) and assess its alignment with the best practices in equipping business graduates with the knowledge and skills demanded by the labor market.
Design/methodology/approach
A survey of 108 instructors from 80 business schools in 17 MENA countries was conducted to gauge information on the delivery of business statistics courses. The survey results were benchmarked to a proposed framework for best practices in business statistics education.
Findings
The gap analysis identified deficiencies in the delivery of business statistics education in the region as compared to international best practices. This study revealed a need to revise statistics education as part of a comprehensive reform of business education with the aim to meet international quality standards in business education.
Research limitations/implications
The study relied on the self-reported responses of business statistics instructors in MENA. One hundred eight questionnaires were completed, corresponding to a response rate of 40 per cent. Moreover, the study did not measure the effectiveness of teaching and learning in business statistics courses.
Practical implications
Recommendations from the study are intended to guide business statistics instructors in improving the quality of business statistics education through adopting more effective ways to enhance student learning experience and graduate employability.
Originality/value
This study is the first of its kind to investigate and assess the business statistics education in the MENA region.
4 citations
19 Dec 2016
TL;DR: Curriculum materials that promote teacher learning, as well as student learning, may be a critical element in supporting teachers’ enactment of the Common Core State Standards for Mathematics.
Abstract: The Common Core State Standards for Mathematics (CCSSSM) suggest many changes to secondary mathematics education including an increased focus on conceptual understanding and the inclusion of content and processes that are beyond what is currently taught to most high school students. To facilitate these changes, students will need opportunities to engage in tasks that are cognitively demanding in order to develop this conceptual understanding and to engage in such tasks over a breadth of content areas including probability and statistics. However, teachers may have a difficult time facilitating a change from traditional mathematics instruction to instruction that centers around the use of high-level tasks and a focus on conceptual understanding and that include content from the areas of probability and statistics that may go beyond their expertise and experience. Therefore, curriculum materials that promote teacher learning, as well as student learning, may be a critical element in supporting teachers’ enactment of the CCSSM. This study examines three secondary mathematics curriculum materials with the intention of determining both the opportunities they provide for students to engage in high-level tasks and the opportunities for teacher learning. Tasks in the written curriculum materials involving probability and statistics as defined by the CCSSM will be examined for evidence of these opportunities. The results of this examination suggest that one of the three secondary mathematics curriculum materials, Core-Plus Mathematics Project (CPMP), contains high-level tasks addressing many of the probability and statistics standards from the CCSSM. A second curriculum, Interactive Mathematics Program, also contains high-level tasks but has far fewer high-level tasks than CPMP. The third curriculum, Glencoe Mathematics (GM), addresses many of the probability and statistics standards from CCSSM but does so with low-level tasks. None of the three curricula provides ample opportunities for teacher learning in the areas of anticipating student thinking and providing transparency of the pedagogical decisions made by the authors when designing the materials.
4 citations
Cites background from "Exploring Students' Conceptions of ..."
...Delmas and Liu (2005) suggest that students will have difficulty with variability and as a result cannot make inferences or understand distributions....
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...Falk and Well (1997) suggest that correlation coefficient, specifically Pearson’s r, is used in education, psychology, the social sciences, and is central to many statistical methods, but current instructional practices lead to an impoverished understanding of conception of correlation....
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...Falk and Well (1997) suggest that correlation coefficient, specifically Pearson’s r, is used in education, psychology, the social sciences, and is central to many statistical methods, but current instructional practices lead to an impoverished understanding of conception of correlation. Rumsey (2002) suggests time focused on calculating correlation coefficients can inhibit understanding....
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01 Jan 2013
4 citations
Cites background from "Exploring Students' Conceptions of ..."
...Research has shown that the concept of distribution plays a major role in understanding how data behaves in graphical situations and is connected to the reasoning and understanding of variability (delMas & Liu, 2005; Makar & Confrey, 2003; Reading & Reid, 2004)....
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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•
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