![]() ![]() ![]() Tairab and Al-Naqbi (2004) showed that students in 10th grade had difficulty understanding that the x- and y-axes illustrate the relationship between the independent and dependent variables. Extensive research has documented student difficulties with graph interpretation. The purpose of a graph is to communicate observational or numerical data in a visual format ( Tufte, 1983 Leinhardt et al., 1990), with the hope that the graph is interpreted in the same manner and with the same take-home message as the graph constructor intended. Furthermore, current studies in the field of biology education have shown that students who engage in research practices feel more inclusive in the learning process and gain better science process skills, such as data analysis and graphing ( Bangera and Brownell, 2014 Brownell et al., 2015 Linn et al., 2015).ĬONCEPTS AND SKILLS NEEDED FOR GRAPHING AND AREAS OF DIFFICULTY The increasing implementation of course-based undergraduate research experiences (CUREs) emphasizes the importance of understanding how students grapple with data and data presentation to facilitate their mastery of this skill (see Figure 1 in Auchincloss et al., 2014). Within the discipline of biology, there is an emphasis on the infusion of quantitative reasoning into the classroom, including creating and interpreting graphical representations (Association of American Medical Colleges, 2009 American Association for the Advancement of Science, 2011). ![]() Indeed, recent calls to reform the undergraduate curriculum include incorporating aspects of data literacy into the science, technology, engineering, and mathematics disciplines. The development of the skill to create appropriate and clear graphs is necessary for the scientifically literate individual ( Padilla et al., 1986). The result is a symbolic representation that displays experimental findings used by scientists for communication ( Beichner, 1994 Tairab and Al-Naqbi, 2004 Wainer, 2013). Graphs are the main components of the scientific language, because they can be used to condense and summarize large data sets. Differences in reasoning and approaches taken in graph choice and construction corroborate and extend previous findings and provide rich targets for undergraduate and graduate instruction. Most undergraduate students meticulously plotted all data with scaled axes, while professors and some graduate students transformed the data, aligned the graph with the research question, and reflected on statistics and sample size. When reflecting on their graphs, professors and graduate students focused on the function of graphs and experimental design, while most undergraduate students relied on intuition and data provided in the task. All professors planned and thought about data before graph construction. Operating under the metarepresentational competence framework, we conducted think-aloud interviews to reveal differences in reasoning and graph quality between undergraduate biology students, graduate students, and professors in a pen-and-paper graphing task. Past studies document student difficulties with graphing within the contexts of classroom or national assessments without evaluating student reasoning. Graphs are ubiquitous in the biological sciences, and creating effective graphical representations involves quantitative and disciplinary concepts and skills. A function presented in tabular form can also be reflected by multiplying the values in the input and output rows or columns accordingly.Undergraduate biology education reform aims to engage students in scientific practices such as experimental design, experimentation, and data analysis and communication.The order in which the reflections are applied does not affect the final graph. A graph can be reflected both vertically and horizontally.A graph can be reflected horizontally by multiplying the input by –1. We input a value that is 3 larger for g\left(x\right) because the function takes 3 away before evaluating the function f. To get the same output from the function g, we will need an input value that is 3 larger. For example, we know that f\left(2\right)=1. The formula f\left(x\right)=f\left(x - 3\right) tells us that the output values of g are the same as the output value of f when the input value is 3 less than the original value. ![]()
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