Journal für Mathematik-Didaktik

, Volume 39, Issue 1, pp 97–125 | Cite as

Effects of Tables, Bar Charts, and Graphs on Solving Function Tasks

  • Tobias Rolfes
  • Jürgen Roth
  • Wolfgang Schnotz
Originalarbeit/Original Article


This paper presents an experiment that investigated the effect of forms of representation on students’ quantitative and qualitative reasoning on functions. The forms of representation we used were tables, augmented bar charts, and graphs. Research assumes that tables are more suitable for quantitative reasoning whereas graphs should be used for qualitative reasoning. The empirical results of the experiment indeed showed that tables and augmented bar charts were in general more suitable for quantitative reasoning than graphs. Concerning qualitative reasoning the results depended on how thoroughly the graph had to be inspected. If the task-relevant visual feature of the graph could be perceived with a glimpse, a graph was overall more suitable for qualitative reasoning than a table or an augmented bar chart. If the task-relevant visual feature could be identified solely after a thorough inspection of the graph’s shape, a table was generally more efficient for qualitative reasoning than an augmented bar chart or a graph.


Concept of function Covariation Qualitative reasoning Quantitative reasoning Forms of representation Integrated model of text and picture comprehension 

Die Wirkung von Tabellen, Säulendiagrammen und Graphen auf das Lösen von Aufgaben zu funktionalen Zusammenhängen


Der Artikel beschreibt ein Experiment, das die Auswirkung von Repräsentationsformen auf quantitative und qualitative Analysen von funktionalen Zusammenhängen durch Schülerinnen und Schülern untersucht. Als Repräsentationsformen wurden Tabellen, erweiterte Säulendiagramme und Graphen verwendet. Die Forschung nimmt an, dass Tabellen besser geeignet für quantitatives Denken sind, wohingegen für qualitatives Denken besser Graphen genutzt werden sollten. Die empirischen Ergebnisse des Experiments zeigten tatsächlich, dass Tabellen und erweiterte Säulendiagramme im Allgemeinen für quantitative Analysen besser geeignet waren als Graphen. Für qualitative Analysen hing das Ergebnis davon ab, wie gründlich der Graph zu inspizieren war. Wenn die aufgabenrelevante visuelle Eigenschaft des Graphen mit einem kurzen Blick wahrgenommen werden konnte, war ein Graph insgesamt besser geeignet für qualitative Analysen als eine Tabelle oder ein erweitertes Säulendiagramm. Wenn die aufgabenrelevante visuelle Eigenschaft nur nach einer gründlichen Analyse der Form des Graphen identifiziert werden konnte, war eine Tabelle im Allgemeinen effizienter für die qualitative Analyse als ein erweitertes Säulendiagramm oder ein Graph.


Funktionsbegriff Kovariation Qualitative Analysen Quantitative Analysen Repräsentationsformen Integriertes Modell des Text- und Bildverstehens 

Mathematics Education Subject Classification

C33 I23 



The project is funded by grants from Deutsche Forschungsgemeinschaft (DFG).

Supplementary material

13138_2017_124_MOESM1_ESM.pdf (297 kb)
Online material 1 Test items (German version)
13138_2017_124_MOESM2_ESM.pdf (148 kb)
Online material 2 Test items (English version)
13138_2017_124_MOESM3_ESM.pdf (117 kb)
Online material 3 Parameters of the three-dimensional Rasch model


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Copyright information

© GDM 2018

Authors and Affiliations

  1. 1.Institute for MathematicsUniversity of Koblenz-Landau, Campus LandauLandauGermany
  2. 2.General and Educational PsychologyUniversity of Koblenz-Landau, Campus LandauLandauGermany

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