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

Abstract

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...

Video-worked examples to support the development of elementary students’ science process skills: a case study in an inquiry activity on electrical circuits

“…Regarding the collection and processing of data, it should be noted that this is not a common skill in literature and, therefore, has become a challenging issue for elementary students (Garcia-Mila, Marti, Gilabert, and Castells 2014). In the present work, this scientific skill was a statistically significant difference between the pre-and the post-test results (Table 2).…”

Longitudinal impact of interactive science activities: Developing, implementing, and validating a graphing integration inventory

“…Indeed, previous research in science education has explored science process skills related to experimentation (Padilla, Okey, & Garrard, 1984) and cognitive processing of graphs (Wang et al, 2012; Wavering, 1989). However, longitudinal analyses of graph comprehension growth among middle and high school students are situated primarily in mathematics education (cf., Curcio, 1987; Garcia‐Mila, Marti, Gilabert, & Castells, 2014; Hattikudur et al, 2012; Nathan & Kim, 2007; Padilla, McKenzie, & Shaw, 1986). Our work, thus, contributes to science education by building on the longitudinal work in mathematics education and the previous work in science education around experimentation and graph comprehension.…”

A Learning Progression for Constructing and Interpreting Data Display

“…1 In construction of statistical graphs, students continue to transit to an aggregate view of individual cases through quantification of aggregate properties (like ratios, portion, or percentage) of data values in statistical graphs (Wilson, n.d.) 2 Students are able to construct statistical graphs associated with a bivariate data set (Casey, 2015;Garcia-Mila et al, 2014) 3 With regard to the selection and usage of the appropriate graph form for the nature of a given data set, students develop additional statistical graphs to represent a (univariate or bivariate) numerical data set (Franklin et al, 2007;cf. Baker et al, 2001) Bar graph: In drawing a bar graph for a given bivariate data set (a list of 25 students who indicated gender and height), a student draws bars with frequencies of student height intervals on the y-axis (dependent variable) by student gender types on gender on the x-axis (two independent variables; Garcia-Mila et al, 2014) ↑ Transition from Level 4 to Level 5: Sufficient data aggregation (and data reduction) emerges and continues to mature into the upper levels of this progression 4…”

“…3 With regard to the selection and usage of the appropriate graph form for the nature of a given data set, students are able to identify appropriate types of statistical graphs to represent numerical or categorical data (e.g., drawing a bar graph for categorical data and a histogram for numerical data; Franklin et al, 2007) Bar graph: A student draws bar graphs for major divisions of the data unit scale, like 10s or 50s (Åberg-Bengtsson, 2006) Scatterplot: Students place the informal line of best fit through the most points, or through the first and last points among all the points on a scatterplot, revealing the transition from case-oriented view to aggregate view of data; they attend to a subset of collinear points on the scatterplot, while thinking of the points that were not collinear as outliers (Casey, 2015) 1 In drawing a given form of statistical graphs, students construct graphical components that are appropriate for the given graph form and use scaling and labeling correctly with proper data format (Baker et al, 2001;Garcia-Mila et al, 2014;Lehrer, 2011, as cited in National Research Council, 2014, but this depends on the complexity of given data. For example, in bar graphing, the x-and y-axes are appropriately constructed and labeled; individual cases of categorical variables are structured on the x-axis and quantitative values are structured on the y-axis; the magnitude of the quantitative values on the y-axis are represented by the heights of bars with a conventionally graded scale…”

“…2 Students draw statistical graphs associated with individual cases, thus their graphs show insufficient data reduction (Casey, 2015;Franklin et al, 2007;Garcia-Mila et al, 2014) 3 With regard to the selection and usage of the appropriate graph form for the nature of a given data set, students draw inappropriate statistical graphs for the types of data, like drawing a bar graph to display numerical data values (Franklin et al, 2007) Bar graph: In drawing a bar graph for a given bivariate data set (a list of 25 students who indicated gender and height), a student lists all the student names by gender on the x-axis and puts the student height intervals on the y-axis; however, the differentiated genders (the second independent variable) are not integrated with the student heights (the dependent variable; Garcia-Mila et al, 2014) ↑ Transition from Level 2 to Level 3: Sufficient data unit scale/scaling usage (i.e., the use of a conventionally graded scale) for a given data set and appropriate construction of graphical components in graphing (by different types of statistical graphs) emerge and continue to mature into the upper levels of this progression 2…”