Annotated Bibliography – Stephanie Gardner
Basic research question: Do student difficulties in selecting appropriate representations for their data
stems from their lack of understanding of what different representations of data imply and convey or if
these difficulties arise from a lack of understanding the data in the first place?
1. Grawemeyer B. & Cox R. (2004). The Effect of Knowledge-of-External-Representations Upon
Performance and Representational Choice in a Database Query Task. Diagrammatic Representation
and Inference: Third International Conference, Diagrams, Berlin, Springer.
In this paper the authors evaluated the relationship between study participants’ prior external
representation (ER) knowledge with their ability to choose an appropriate representation of data to
answer a simple query. The prior ER knowledge was characterized using a card sorting task prior to the
ER selection/query answering task. During the ER selection/query answering task the participants were
shown a total of 25 queries that were aimed to direct them to different tasks related to data sifting and
interpretation: associate, cluster, compare, correlate, distinguish, identify, locate, and rank. The
authors used in-house designed graphical representation generating software to instantiate the chosen
representations with the dataset once a participant chose which representation that they would use to
answer a given query. The results of this study suggest that participants with high prior ER knowledge
selected more varied representations to answer the queries than low prior ER knowledge participants.
In addition, high prior ER knowledge participants were more likely to choose the ‘correct’ representation
to answer the question and got the question right, than low prior ER knowledge participants. This is a
useful study for my proposed research project because it describes a strategy to help determine
students’ prior graphical knowledge which can be correlated with their graphical choices both in a task
like the ones described here and in their choices for representing their own data. In addition, they
describe some useful statistical and data analysis approaches that will be useful for me to consider.
2. Novick L.R. (2004). Mathematical Thinking and Learning Diagram Literacy in Preservice Math
Teachers, Computer Science Majors, and Typical Undergraduates: The Case of Matrices, Networks,
and Hierarchies. Mathematical Thinking and Learning, 6(3), 307-342.
In this paper, the author describes the results of a study done to examine the ability of three different
populations of undergraduate students to choose the most appropriate diagram/representation for data
described in a medically-based scenario. Students were provided with a description of the scenario and
then were asked to choose between two different representations for the scenario. After they made
their choice they were asked to describe why they chose the one they did and to give reasons why the
alternative was not the best choice. Student responses were coded according to their level of cognitive
complexity and articulation ranging from implicit (right choice, but unable to clearly articulate rationale
for choice) to translational (drawing analogies to other similar situations or ideas). This paper is
relevant to my research questions because it provides a model for a study instrument and study design
that will help answer my research question.
3. Schönborn K.J. & Anderson T.R. (2009). A Model of Factors Determining Students’ Ability to
Interpret External Representations in Biochemistry. International Journal of Science Education, 31:2,
193-232
In this article the authors report on experiments aimed at validating a model of the important
determinants of student challenges in interpreting external biochemical representations. The model
that the authors tested consists of three basic factors (conceptual, reasoning, and mode), and
combinations of them in pairs for the types of knowledge that students need when approaching
representations. The evaluation was carried out in a 3-phase, single interview technique (3P-SIT) where
students’ understanding, evaluation, and interpretation of a particular biochemical process first without
the representation and then with the representations. This is a semi-structured interview technique
that allows student understanding and reasoning to emerge organically. The model was validated their
model. This paper is relevant to my project because it provides a useful framework of student
knowledge that must be brought to bear when confronted with visualizing structures and data. It is also
possible that the 3P-SIT interview technique will be useful in my study.
4. Shah P, Mayer RE, & Hegarty M. (1999). Graphs as Aids to Knowledge Construction: Signaling
Techniques for Guiding the Process of Graph Comprehension. Journal of Educational Psychology, 91
(4), 690-702.
In this paper, the authors use an example graphical representation from a U.S. history book as a test
image to probe the salient features in graphical representations that are important for interpretation
and understanding by undergraduate students. Their findings demonstrate the importance of the type
of graphical representation of data (bar graph vs. line graph) for clear communication of data trends and
that by manipulating the representation, the interpretation is altered. They explore the effects of data
chunking and Gestalt principles on student responses. This paper is relevant to my research question
because it discusses and provides concrete examples about how the choice of data display can highlight
or obscure the major points of data collected. Important insights can be gained about biology student
understanding of graphical representation choice and its implications.
5. Zacks J. & Tversky B (1999). Bars and Lines: A Study of Graphic Communication. Memory and
Cognition, 27(6), 1073-1079.
In this study the authors wanted to examine the effects that the type of data representation (bars vs.
lines) and context has on undergraduate student description of them as discreet versus continuous
representations. In addition, they authors investigated whether the types of representations that
students produced was dependent on the type of verbal instruction that they received (using large and
small as descriptors versus rising and falling). As was hypothesized, students overwhelmingly described
bar graphs in discreet terms and line graphs as trends. When the authors presented students with
continous data plotted as discreet bars and discreet data plotted as lines, the students were somewhat
mixed in how they described the plots. Most of the time they described plots with categorical labels like
sex (male vs. female), as categorical regardless of whether a bar or line graph was used. The authors
conducted a very simple experiment to look into production of graphs by telling students to create a
graph using language that describes either a trend or categorical data set. As they predicted students
made bar graphs with categorical prompts and line graphs with tend prompts. This study is useful to me
because it illustrates the power of graph choice for extracting meaning and also touches on student
choice in which graph type to employ to illustrate data. My research question focuses more on student
choice of graph type for representation of data they gather without explicit leading by the instructor.