Understanding Graphs: Modeling Processes, Prerequisites and Influencing Factors of Graphicacy

reasoning abilities in a sample of 119 7th, 9th, and 11th graders. Furthermore, there is also evidence suggesting that there may be gender differences in graph literacy; boys were found to outperform girls (e.g., Lowrie & Diezmann, 2011; Åberg-Bengtsson, 1999; but see Curcio, 1987). Therefore, it is important to control for general cognitive abilities as well as gender when investigating the specific influence of basic numerical abilities on graph literacy. In sum, we suggest that students are facing different challenges when solving graph reading tasks. First, the respective graph reading problem needs to be mathematized to enable them to – second – locate the relevant information, either numerical information or patterns and trends. The third challenge may be to correctly perform the necessary arithmetic operations. In line with this idea, Curcio (1987) found that 7th graders’ comprehension of graphs and tables was associated positively with their prior knowledge about graphical language as well as about the mathematical content necessary to solve the tasks. This is first evidence suggesting that (basic) numerical abilities may specifically contribute to graph literacy. Understanding graphs  Influences of basic numerical abilities on graph reading performance 57 However, there are hitherto no empirical studies evaluating which specific basic numerical abilities influence graph reading performance. The current study pursued this question. Before describing the details of the present study, we will give a brief introduction to the idea of basic numerical abilities underlying numeric cognition. II.1. 2 Basic numerical abilities Research has revealed that numerical cognition is not a unitary construct (e.g., Dowker, 2005). This means that numerical and mathematical skills build upon several basic numerical representations (e.g., Dehaene, 2009) and abilities, which are assumed to be the building blocks of numerical cognition in general and children’s numerical development in particular (von Aster & Shalev, 2007). Basic numerical abilities include – but are not limited to – an understanding of nonsymbolic and symbolic number magnitudes (e.g., Dehaene, Piazza, Pinel, & Cohen, 2003; Siegler, 2016) and a spatial representation of the corresponding magnitude (aka the mental number line, e.g., Booth & Siegler, 2008; see Fischer & Shaki, 2014 for a review), a verbal representation of number words, but also arithmetical facts (such as multiplication tables, e.g., Dehaene et al., 2003), a visual Arabic representation for understanding number symbols (e.g., Dehaene & Cohen, 1997; De Smedt, Noël, Gilmore, & Ansari, 2013 for a review), an understanding of the place-value structure of the Arabic number system (e.g., Moeller, Pixner, Zuber, Kaufmann, & Nuerk 2011; see Nuerk, Moeller, Klein, Willmes, & Fischer, 2011), as well as abilities on procedural and conceptual numerical knowledge (e.g., carry operation, but also commutative law). A high level of mastery of these basic numerical abilities was repeatedly observed to be associated with actual numerical competencies but also predictive of future numerical competences as well as mathematical achievement in school (e.g., Moeller et al., 2011; Schneider, Grabner, & Paetsch, 2009). In the following, a few examples will be given to illustrate how basic numerical abilities were found to influence later mathematical achievement. For instance, Kolkman, Kroesbergen, & Leseman (2013) observed that, already in kindergarten, children’s early understanding of symbolic numbers as well as their skills in mapping these symbolic numbers to non-symbolic magnitudes, such as dot patterns, was an important predictor of their later numerical/mathematical development (see Schneider et al., 2017 for a meta-analysis). Furthermore, Booth and Siegler (2008) found that children’s performance on locating the position of a target number on an empty number line not only correlated positively with children’s actual basic numerical abilities (e.g., magnitude comparUnderstanding graphs  Influences of basic numerical abilities on graph reading performance 58 ison, see also Link, Nuerk, & Moeller, 2014) but also predicted their ability to acquire new arithmetical competences in the future. Related to this, Moeller et al. (2011) found that early placevalue understanding in first grade predicted later arithmetic performance as well as children’s math grades two years later. Moreover, recent evidence suggests that basic numerical abilities are predictive of understanding more complex mathematical concepts taught in secondary school such as fractions. For instance, Bailey, Siegler, and Geary (2014) found that basic arithmetic abilities assessed in first grade predicted arithmetic performance on fractions in secondary school (see also Vukovic et al., 2014). Interestingly, however, to the best of our knowledge, there is currently no study investigating the association of basic numerical abilities and graph reading performance. This comes somewhat as a surprise given the above-mentioned importance of graph literacy in everyday life as well as in math curricula. Therefore, the current study set out to evaluate the association of different basic numerical abilities with graph reading performance in a cross-sectional design. We hypothesized that basic numerical abilities implying the understanding of number magnitudes but also of basic arithmetic operations should be particularly relevant to graph reading. We expected such a pattern of results because graph reading tasks usually require a combination of the respective basic numerical abilities such as the identification and/or comparison of numerical magnitudes as well as (approximate)