Where do students get lost? The concept of variation (original) (raw)
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Development of the concept of statistical variation: An exploratory study
Mathematics Education Research Journal, 2000
An appreciation of variation is central to statistical thinking, but very little research has focused directly on students' understanding of variation. In this exploratory study, four students from each of grades 4, 6, 8, and 10 were interviewed individually on aspects of variation present in three settings. The first setting was an isolated random sampling situation, whereas the other two settings were real world sampling situations. Four levels of responding were identified and described in relation to developing concepts of variation. hnplicatioris for teaching and future research on variation are considered.
The Journal of Mathematical Behavior, 2002
This paper reports the analysis of performance assessment tasks administered in a seventh-grade classroom. The purpose of the assessments was to obtain data on students' current statistical understandings that would then inform future instructional design decisions in a classroom teaching experiment that focused on statistical data analysis. The tasks were designed to provide information about students' current understandings of creating data, organizing data, and assessing the center and "spreadoutness" of data. In considering the analysis, we found that the students typically viewed the mean as a procedure that was to be used to summarize a group of numbers regardless of the task situation. Data analysis for these students meant "doing something with the numbers." Based on this analysis, a goal that emerged as significant for the classroom teaching experiment was to support a shift in students' reasoning towards data analysis as inquiry rather than procedure. The influence of the students' prior experiences of doing mathematics in school was also apparent when they developed graphs. They were primarily concerned with school-taught graphical conventions rather than with what the graphs signified. In the course of the analysis we distinguished between additive and multiplicative reasoning about data. This distinction is significant given that the transition from additive to multiplicative reasoning constitutes the overriding goal of statistics instruction at the middle-school level.
Necessary Knowledge for Teaching Statistics: Example of the Concept of Variability
ICME-13 Monographs, 2018
This chapter explores teachers' statistical knowledge in relation to the concept of variability. Twelve high school mathematics teachers were asked to respond to scenarios describing students' strategies, solutions, and misconceptions when presented with a task based on the concept of variability. The teachers' responses primarily helped us analyze their comprehension and practices associated with the concept of variability and gain insight into how to teach this concept. Secondly, the study shows that students and high school teachers share the same conceptions on this subject. Keywords Professional knowledge • Statistics • Teacher's knowledge Teaching practices • Variability 10.1 Context The importance of statistics in our lives is such that data management has become a major key in the education of responsible citizens (Baillargeon 2005; Konold and Higgins 2003). The abundance of statistical data available on the internet, the studies reported on television news, or the studies and survey results published in newspapers and magazines all show that nowadays, citizens must have analytical skills to develop critical judgment and a personal assessment of the data they are confronted with daily. This role of statistics in our current society makes it necessary to consider teaching this discipline to train our students to be citizens of tomorrow. If the goal is to encourage statistical thinking in students as future citizens, then not only do we need to teach basic statistical data interpretation skills, but it is also essential to teach the
International Statistical Review / Revue Internationale de Statistique, 1995
Research in the areas of psychology, statistical education, and mathematics education is reviewed and the results applied to the teaching of college-level statistics courses. The argument is made that statistics educators need to determine what it is they really want students to learn, to modify their teaching according to suggestions from the research literature, and to use assessment to determine if their teaching is effective and if students are developing statistical understanding and competence.
Exploring variation in measurement as a foundation for statistical thinking in the elementary school
International Journal of STEM Education, 2015
Background: This study was based on the premise that variation is the foundation of statistics and statistical investigations. The study followed the development of fourth-grade students' understanding of variation through participation in a sequence of two lessons based on measurement. In the first lesson all students measured the arm span of one student, revealing pathways students follow in developing understanding of variation and linear measurement (related to research question 1). In the second lesson each student's arm span was measured once, introducing a different aspect of variation for students to observe and contrast. From this second lesson, students' development of the ability to compare their representations for the two scenarios and explain differences in terms of variation was explored (research question 2). Students' documentation, in both workbook and software formats, enabled us to monitor their engagement and identify their increasing appreciation of the need to observe, represent, and contrast the variation in the data. Following the lessons, a written student assessment was used for judging retention of understanding of variation developed through the lessons and the degree of transfer of understanding to a different scenario (research question 3). Results: The results were based either on the application of the hierarchical SOLO model or on non-hierarchical clustering of responses to individual questions in the student workbooks. Students' progress throughout the lessons displayed a wide range of explanations for the estimate of a single student's arm span, general surprise at the variation in measurements, and a large variety of hand-drawn representations based on the values or frequencies of measurements. Many different representations were also created in the software for the single student measurements and for the comparison of measurements for the two scenarios. Although the students' interpretations of their plots were generally more basic than sophisticated, the results of the assessment indicated that many students had developed the ability to transfer their appreciation of variation to another context and could clearly explain the meaning of variation. Conclusions: The findings highlight the importance of an early focus on variation and distribution, with meaningful activities that motivate students to conduct and observe measurements, together with creating both hand-drawn and software representations to relate their experiences.
International Journal of Computers for Mathematical Learning, 2007
New capabilities in TinkerPlots 2.0 supported the conceptual development of fifth-and sixth-grade students as they pursued several weeks of instruction that emphasized data modeling. The instruction highlighted links between data analysis, chance, and modeling in the context of describing and explaining the distributions of measures that result from repeatedly measuring multiple objects (i.e., the height of the school's flagpole, a teacher's head circumference, the arm-span of a peer). We describe the variety of data representations, statistics, and models that students invented and how these inscriptions were grounded both in their personal experience as measurers and in the affordances of TinkerPlots, which assisted them in quantifying what they could readily display with the computer tool. By inventing statistics, students explored the relation between qualities of distribution and methods for expressing these qualities as a quantity. Attention to different aspects of distribution resulted in the invention of different statistics. Variable invention invited attention to the qualities of ''good'' measures (statistics), thus meshing conceptual and procedural knowledge. Students used chance simulations, built into TinkerPlots, to generate models that explained variability in a sample of measurements as a composition of true value and chance error. Error was, in turn, decomposed into a variety of sources and associated magnitudes-a form of analysis of variance for children. The dynamic notations of TinkerPlots altered the conceptual landscape of modeling, placing simulation and world on more equal footing, as first suggested by Kaput (Journal of Mathematical Behavior, 17(2), 265-281, 1998). Keywords Statistics education Á Modeling Á Learning The discipline of statistics originated in problems of modeling variability (Stigler, 1986). History has not changed all that much: Professional practices of statisticians invariably include efforts to model variability (Wild and Pfannkuch 1999). It is through the contest among alternative models that statistical concepts become more widespread and stable
STATISTICS EDUCATION RESEARCH JOURNAL, 2012
Although statistics education research has focused on students’ learning and conceptual understanding of statistics, researchers have only recently begun investigating students’ perceptions of statistics. The term perception describes the overlap between cognitive and non-cognitive factors. In this mixed-methods study, undergraduate students provided their perceptions of statistics and completed the Survey of Students’ Attitudes Toward Statistics-36 (SATS-36). The qualitative data suggest students had basic knowledge of what the word statistics meant, but with varying depths of understanding and conceptualization of statistics. Quantitative analysis also examined the relationship between students’ perceptions of statistics and attitudes toward statistics. We found no significant difference in mean pre- or post-SATS scores across conceptualization and content knowledge categories. The implications of these findings for education and research are discussed. First published November 20...
Although statistics education research has focused on students' learning and conceptual understanding of statistics, researchers have only recently begun investigating students' perceptions of statistics. The term perception describes the overlap between cognitive and non-cognitive factors. In this mixed-methods study, undergraduate students provided their perceptions of statistics and completed the Survey of Students' Attitudes Toward Statistics-36 (SATS-36). The qualitative data suggest students had basic knowledge of what the word statistics meant, but with varying depths of understanding and conceptualization of statistics. Quantitative analysis also examined the relationship between students' perceptions of statistics and attitudes toward statistics. We found no significant difference in mean pre-or post-SATS scores across conceptualization and content knowledge categories. The implications of these findings for education and research are discussed.