Our purpose is to bring together perspectives concerning the processing and use of statistical graphs to identify critical factors that appear to influence graph comprehension and to suggest instructional implications. After providing a synthesis of information about the nature and structure of graphs, we define graph comprehension. We consider 4 critical factors that appear to affect graph comprehension: the purposes for using graphs, task characteristics, discipline characteristics, and reader characteristics. A construct called graph sense is defined. A sequence for ordering the introduction of graphs is proposed. We conclude with a discussion of issues involved in making sense of quantitative information using graphs and ways instruction may be modified to promote such sense making.

Making sense of graphs: Critical factors influencing comprehension and instructional implications.

Our research program is concerned with the trajectory of individuals from their initial participation in science-related activities to their full participation in scientific research. This study was designed to provide answers to questions about (a) the practices required for reading graphs in high school textbooks and scientific journals, and (b) the role of high school textbooks in the appropriation of authentic scientific graph-related practices. For our analyses, we selected five leading ecology-related journals and six representative high school biology textbooks. Although there were no differences in the total number of inscriptions used in journals and textbooks, there were significant differences in the frequency with which Cartesian graphs were used. To allow more detailed analyses, an ontology of graphs was developed. Our fine-grained analyses based on this ontology yielded qualitative differences between the uses of graphs and associated captions and main text as they appeared in high school textbooks and scientific journals. Scientific journals provided more resources to facilitate graph reading and more elaborate descriptions and interpretations of graphs than the high school textbooks. Implications of this study are outlined as they relate to (a) producing graphs, captions, and main text in high school textbooks; and (b) teaching and researching graph-related practices from anthropological perspectives. © 1999 John Wiley & Sons, Inc. J Res Sci Teach 36: 977–1019, 1999

Differences in graph-related practices between high school biology textbooks and scientific ecology journals

Graph-related practices are central to scientific endeavors and graphing has long been hailed as one of the core “general process skills” that set scientists apart. One research question that has not received much attention is, “Are scientists generally competent readers of graphs, or are graphs indissolubly tied to practices and understandings of their everyday workplace?” This study was designed to better understand the reading and interpretation of familiar and unfamiliar graphs by (mostly) scientists. From an extensive database on graphing involving university students to professionals, we selected two case studies and interpret them within a theoretical framework grounded in semiotics and hermeneutic phenomenology. The first case study provides a detailed analysis in which a scientist wrestles and in part inappropriately interprets an unfamiliar graph used in undergraduate ecology courses; the difficulties of the scientist include some of those identified among students in the graphing literature. The second case study provides an example of the transparent use of graphs in the work of a water technician who is not only familiar with her graphs, but who has an intimate, embodied knowledge of the world to which the graph refers. When it comes to reasoning, scientists are often taken as experts against which the performance of other individuals (“novices”) are judged (as inferior). If scientists’ own graphing practices are not general but tied to their embodied understanding, then the teaching of decontextualized graphing skills loses its legitimacy. Our results therefore have considerable implications to mathematics education. Professionals read graphs 2

Professionals Read Graphs: A Semiotic Analysis

The author is concerned about the methodology and instrumentation used to assess both graphing abilities and the impact of microcomputer-based laboratories (MBL) on students’ graphing abilities for four reasons: (1) the ability to construct and interpret graphs is critical for developing key ideas in science; (2) science educators need to have valid information for making teaching decisions; (3) educators and researchers are heralding the arrival of MBL as a tool for developing graphing abilities; and (4) some of the research which supports using MBL appears to have significant validity problems. In this article, the author will describe the research which challenges the validity of using multiple-choice instruments to assess graphing abilities. The evidence from this research will identify numerous disparities between the results of multiple-choice and free-response instruments. In the first study, 72 subjects in the seventh, ninth, and eleventh grades were administered individual clinical interviews to assess their ability to construct and interpret graphs. A wide variety of graphs and situations were assessed. In three instances during the interview, students drew a graph that would best represent a situation and then explained their drawings. The results of these clinical graphing interviews were very different from similar questions assessed through multiple-choice formats in other research studies. In addition, insights into students’ thinking about graphing reveal that some multiple-choice graphing questions from prior research studies and standardized tests do not discriminate between right answerslright reasons, right answers/wrong reasons, and answers scored “wrong” but correct for valid reasons. These results indicate that in some instances multiple-choice questions are not a valid measure of graphing abilities, In a second study, the researcher continued to pursue the questions raised about the validity of multiple-choice tests to assess graphing, researching the following questions: What can be learned about subjects’ graphing abilities when students draw their own graphs compared to assessing by means of a multiple-choice instrument? Does the methodology used to assess graphing abilities: (1) affect the percentage of subjects who answer correctly; (2) alter the percentage of subjects affected by the “picture of the event” phenomenon? Instruments were constructed consisting of

Assessing Students' Abilities to Construct and Interpret Line Graphs: Disparities between Multiple-Choice and Free-Response Instruments

Have sex differences in spatial ability evolved from male competition for mating and female concern for survival

This study investigates the relationship between logical thinking structures and the ability to construct and interpret line graphs. Seventy-two subjects in 7th, 9th, and 11th grades were administered individual Piagetian tasks to assess five specific mental structures: (Euclidean spatial structures) (a) Placement and Displacement of Objects (maintaining horizontal and vertical reference frames) and (b) One–One Multiplication of Placement and Displacement Relations (coordinate systems); (c) Multiplicative Measurement; (d) Multiplicative Seriation; and (e) Proportional Reasoning. Graphing abilities were assessed by having the subjects construct and interpret numerous graphs of varying content and difficulty. To minimize the researcher's guesses about interpretation, each subject's answers and reasons were subsequently explored during a clinical interview. The results indicate significant relationships of logical thinking to graphing ability. Multiplicative seriation, multiplicative measurement, and Euclidean spatial structures positively influenced graphing abilities. Subjects who showed evidence of proportional reasoning did significantly better on many graphing situations including choosing the part of the graph with the greatest “rate of change.” Locating points on a graph without a grid was significantly related to horizontal/vertical frames of reference. Students who did not possess the logical thinking structures were more likely to be dependent upon, and influenced by, perceptual cues and less able to interpret or construct graphs correctly.

An investigation of the relationship between logical thinking structures and the ability to construct and interpret line graphs

Piaget's Developmental Model: A Basis for Research in Science Education

Research was done to probe and extend Piaget's theory of the conception of speed. Specifically tested was the hypothesis that there is no hierarchical relationship in performance on the following Piaget-type tasks: conservation of distance, asymmetric series of speeds, one-to-many (circular) speeds, symmetric speeds, time, and proportional reasoning. The research also tested the gender-related performance on these six tasks. One hundred freshman and sophomore college students were shown demonstrations of equipment individually for each of the six tasks. A set of open-ended questions based on the demonstrations was administered to each subject in a 45-minute interview. Subjects were scored as “pass” on a given task if they manipulated objects in certain ways and gave specific types of explanations. A scalogram analysis of the data yielded a z-score of — 3.7 which indicated that subjects passed the task in a certain sequence. The tasks were found to form a unidimensional scale and to be increasingly difficult in the order listed above. A chi-square test for two independent samples showed a significant difference (alpha = 0.05) in performance between males and females on all speed tasks. No significant differences in performance between males and females were found for the distance and time tasks.

The performance of college students on piaget‐type tasks dealing with distance, time, and speed

https://onlinelibrary.wiley.com/doi/pdf/10.1002/tea.3660140416

Darrell G. Phillips

Papers

An investigation of the relationship between logical thinking structures and the ability to construct and interpret line graphs

Piaget's Developmental Model: A Basis for Research in Science Education

The performance of college students on piaget‐type tasks dealing with distance, time, and speed

The Karplus Islands Puzzle, Volume with Metal Cylinders, and Other Problems.