The Longitudinal Development of Understanding of Average

Watson, Jane; Moritz, Jonathan B.

doi:10.1207/s15327833mtl0202_2

Cited by 78 publications

(94 citation statements)

References 12 publications

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“…The incidence of LLN oriented reasoning in our study supports previous studies with middle school students (Watson & Moritz, 2000a). However, our students were not always consistent in reasoning this way.…”

Section: Lln Oriented Reasoningsupporting

confidence: 56%

“…We lack models that describe reasoning at this level. Presently, researchers are studying the development of children's statistical thinking within inquiry phases (Jones, Thornton, Langrall, & Mooney, 2000;Watson & Moritz, 2000a, 2000b. For instance, Watson and Moritz (2000a) have explored how children in grades 3-9 developed their understanding of average over a period of 3-4 years (i.e., data analysis phase).…”

Section: Introductionmentioning

confidence: 99%

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Statistical reasoning of middle school children engaged in survey inquiry

Lavigne

Lajoie

2007

Contemporary Educational Psychology

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The case study examined two groups of grade 7 students as they engaged in four inquiry phases: posing a question and collecting, analyzing, and representing data. Previous studies reported analyses of statistical reasoning on a single inquiry phase. Our goal was to identify the modes of statistical reasoning displayed during group discussions in all phases as children designed and conducted their own inquiry. A content analysis of audio and video recorded discussions yielded 10 statistical reasoning modes: six relate to Garfield and Gal's [Garfield, J., Gal, I. (1999). Teaching and assessing statistical reasoning. In L. V. Stiff, & F. R. Curcio (Eds.), Developing mathematical reasoning in grades K-12. 1999 Yearbook (pp. 207-219). Reston, VA: National Council of Teachers of Mathematics] statistical reasoning types involved in the collection, analysis, and representation of data and four modes deal with an aspect of inquiry not exclusively focused upon in the literature on statistical reasoning-i.e., the problem-posing phase. Although students' reasoning reflected an incomplete understanding of statistics they serve as building blocks for instruction.

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Section: Lln Oriented Reasoningsupporting

confidence: 56%

Section: Introductionmentioning

confidence: 99%

Statistical reasoning of middle school children engaged in survey inquiry

Lavigne

Lajoie

2007

Contemporary Educational Psychology

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“…Cai (1998) identified ways sixth grade students made sense of the algorithm for the mean, noting the limited ways in which they were able to use the underlying concept to solve various types of problems. Watson and Moritz (2000) looked at how elementary through high school students' understanding of average changes over time. Undergraduate college students have also been shown to have tenuous understanding of the mean: Pollatsek, Lima, and Well (1981) documented undergraduates' difficulties in determining weighted means, and Mevarech's (1983) study cited their dilemmas in identifying situations in which the mean algorithm had been incorrectly applied.…”

Section: Introductionmentioning

confidence: 99%

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

Cooper

Shore

2008

Journal of Statistics Education

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This paper identifies and discusses misconceptions that students have in making judgments of center and variability when data are presented graphically. An assessment addressing interpreting center and variability in histograms and stem-and-leaf plots was administered to, and follow-up interviews were conducted with, undergraduates enrolled in introductory statistics courses. Assessment items focused upon comparing the variability of two data sets of common range represented by bell-shaped histograms on a common scale, computing measures of center from data extracted from graphs, and in comparing the relative location of the mean and median on a histogram from skewed data. Students' misconceptions often stemmed from their difficulty in maintaining understanding of the data that are being represented graphically.

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“…However, research has investigated children's construction of graphs less frequently (diSessa, 2004;Nemirovsky, Tierney, & Wright, 1998;Watson & Fitzallen, 2010), and research devoted to bar graphs is even less common (Äberg-Bengtsson, 2006;Lehrer & Schauble, 2000Lehrer & Romberg, 1996;Watson & Moritz, 2000Wu & Krajcik, 2006). Kosslyn (1989Kosslyn ( , 2006 addressed the analysis of graphs from a cognitive perspective.…”

Section: Research On Graphing Difficultiesmentioning

confidence: 99%

Fifth Through Eighth Grade Students’ Difficulties in Constructing Bar Graphs: Data Organization, Data Aggregation, and Integration of a Second Variable

García-Milà

Martí

Gilabert

et al. 2014

Mathematical Thinking and Learning

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Abstract:Studies that consider the displays that students create to organize data are not common in the literature. This paper compares 5th through 8th graders' difficulties with the creation of bar graphs constructed using either raw data (Study 1, n=155) or a provided table (Study 2, n=152). Data in Study 1 showed statistical differences for the type of data organization but not for grade level. Students' primary problem was choosing a format that integrated a second variable and aggregating data. In contrast, when the table was provided (Study 2), we observed that 7th-8th graders outperformed 5th-6th graders. We interpret these results in terms of older students' better data interpretation competence. We conclude that students' difficulties in bar graphing can be traced to their tabulation processes. Data organization is an essential bridging tool for understanding the essence of the data and representing them graphically, and educators should devote to it the attention it deserves. . All of your comments and all of Reviewer 5's have been addressed in the revision. Reviewer 1's comment 1 and 2 are commented in the response table but did not generate any change in the manuscript. We interpreted them as additional comments rather than "must" suggestions. Please tell us if we need to make any additional changes. All changes are highlighted in the manuscript. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems CorporationThe Figures, Tables and Appendices are all the same excepte for Table 3 and Table 7 (there were small errors in the title). The paper contains 3 Appendices, 11 figures and 8 tables and its length is 35 pages long excluding cover page, letter, abstract, references, tables and figures. Aso, we have removed anonimity by adding two of our previous papers that are referred to in the manuscrit, and also, we have added the acknowledgments and proof read the text. We hope that the paper is close to publication. We again, are very grateful to the reviewers', as well as to your thorough revision of the manuscript. We hope that you will find that it is suitable for publication. With kind regards, Merce email: mgarciamila@ub.edu Cover LetterAll changes in the new manuscript are marked with the control of changes Reviewer 1 commentsAuthors' response 1. Given that the students come from multiple classrooms in multiple schools and each class is split among the two studies, it may help the readers if the authors create a graphic showing how the participant pool was created. This is just an idea but perhaps the authors could show 5 circles representing the 5 schools. Inside each school circle, a smaller circle or circles could be drawn to indicate the class or classes that came from that school. Each class circle could be labeled as a primary or secondary classroom. Each class circle could be further split with a line and the number of students that were assigned to study 1 and to study two could be labeled. I'm not sure if this is helpful but I thought I would suggest it as a way to help re...

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The Longitudinal Development of Understanding of Average

Cited by 78 publications

References 12 publications

Statistical reasoning of middle school children engaged in survey inquiry

Statistical reasoning of middle school children engaged in survey inquiry

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

Fifth Through Eighth Grade Students’ Difficulties in Constructing Bar Graphs: Data Organization, Data Aggregation, and Integration of a Second Variable

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