2011. Vol.2, No.5, 461-465
Copyright © 2011 SciRes. DOI:10.4236/ce.2011.25067
External Representations in the Teaching and Learning of
James R. Cox, Bethany W. Jones
Department of Chemistry, Murray State University, Murray, USA.
Received October 3rd, 2011; revised November 15th, 2011; accepted November 22nd, 2011.
This manuscript describes the role that external representations, such as diagrams and sketches, can play in or-
ganizing and learning concepts presented in a one-semester chemistry course (general, organic and biochemistry)
designed for nursing students. Although external representations are typically found in chemistry textbooks and
instructor-drawn notes, students are usually not taught or prompted to use various types of external representa-
tions to promote learning. Representations created by an instructor and a student are discussed to highlight ef-
fective ways to foster student participation in creating various diagrams. In addition, a student provides a per-
spective on the educational value of creating external representations and the roles of visual thinking and crea-
tivity in learning introductory chemistry. Although the model for this approach has been an introductory chemis-
try course, this approach can be widely applied across disciplines.
Keywords: Visual Thinking, External Diagrams, Active Learning
The availability and diversity of instructional methods in sci-
ence classrooms has increased tremendously in last decade. As
a result, the lecture format has been redesigned and more active
forms of teaching and learning have been developed (Derting &
Cox, 2008; Derting & Ebert-May, 2010; Deslauriers, Schelew,
& Wieman, 2011; Haak, HilleRisLambers, Pitre, & Freeman,
2011; Lee & Jabot, 2011; Mazur, 2009). This comes at a time
when the amount of content and information available in scien-
tific disc iplines is e ver expanding. At the same time, some ha ve
heralded the end of the information age and insist we are in an
interaction age (Milne, 2007) where student success depends on
meaningful interactions with instructors, each other and infor-
mation. Daniel Pink has suggested we have left the information
age and entered a conceptual age where right-brain aptitudes
such as creativity, design and pattern recognition will be indis-
pensible (Pink, 2005).
Another important issue in the current educational environ-
ment is the extent metacognitive and learning skills should be
incorporated into science courses, especially at the introductory
level. Metacognition is a complex area related to the manage-
ment of one’s own learning and is known to be an important
domain in student learning and success in chemistry (Cooper &
Sandi-Urena, 2009; Rickey & Stacy, 2000; Tsai, 2001). In ad-
dition, a recent report made a strong argument for teaching
introductory science students less content and more learning
skills in an effort to provide a richer learning experience and
promote science literacy (Coil, Wenderoth, Cunningham, &
Although robust and lively debates about content, course de-
sign and learning skills are important, the fact remains that
there are numerous students struggling to succeed in introduc-
tory science courses. In many ways, the solution to this prob-
lem boils down to what a recent report termed the Carnegie
Hall hypothesis, which relates intensive “practice” to the suc-
cess of underprepared students (Haak et al., 2011). The authors
of this recent report note that effective forms of practice require
students to challenge previous conceptions and explain their
thinking. For some students, practice only comes in the form of
working additional problems at the end of textbook chapters.
Although working problems is imperative, students can benefit
from having a wider array of options to practice concept mas-
tery and problem-solving strategies. One option is to introduce
students to the concept of visual thinking and the role that visu-
alization can play in tackling misconceptions and describing
thought processes (Gilbert, 2005; Mathewson, 1999; Schönborn
& Anderson, 2006; Stranger-Hall, Shockley, & Wilson, 2011).
The opportunity to use creativity and right-brain skills to tackle
more analytical and quantitative tasks may help a broad range
of students, even if some content has to be sacrificed.
This manuscript describes how a chemistry instructor pro-
mpted students in his introductory chemistry course to create
diagrams and sketches (external representations) to solve prob-
lems and learn concepts and how one particular student in the
course responded. External representations can be defined as
visual and spatial displays used to promote, discovery, memory,
inference and calculation and will be used as a broad term to
describe sketches, diagrams or illustrations generated by hand
or on a computer (Schönborn & Anderson, 2006; Suwa &
Tversky, 2002; Tversky, 2002). The literature describes the
educational and psychological value of external representations
in terms of memory, expressing ideas, making connections,
pattern construction and recognition and problem solving
(Gilbert, 2005; Gobert & Clement, 1999; Hall, Bailey, & Tillman,
1997; Larkin & Simon, 1987; Mathewson, 1999; Mayer &
Gallini, 1990; Ramadas, 2009). One of the most powerful as-
pects of creating external representations can be realized when
students see new ideas and concepts emerge after drawing a
sketch or diagram. These unintended discoveries provide a
greater context to the material and a scaffold in which to de-
velop new ideas or a greater understanding of a body of infor-
mation (Tversky, 2002).
J. R. COX ET AL.
There is also an expanding body of evidence that points to
the educational value of learner-centered pedagogies that have
students actively engaged in learning activities and deliberate
practice strategies (Derting & Ebert-May, 2010; Deslauriers et
al., 2011; Haak et al., 2011; Stranger-Hall et al., 2011; Weimer,
2002). Although this manuscript describes the use of external
representations in an introductory chemistry course, the meth-
ods discussed are just one way to promote deliberate and pro-
ductive practice sessions. As a result, the aim of this work was
not to assess the impact on student learning; rather it was to
develop a strategy to get students to construct external repre-
sentations and to obtain detailed information from a student that
found value in this approach. The next two sections are written
by an instructor (JRC) and a student (BWJ) in an introductory
chemistry course (general, organic and biochemistry) designed
for nursing students. Although the representations described in
the manuscript are for a chemistry course, the use of visual
thinking and student-generated diagrams should be of interest
to educators across disciplines. It should be noted that the type
and nature of the external representations described in this
manuscript are not typically found in traditional chemistry
textbooks. The goal of this approach was to show students how
to use their own creativity to generate representations that inte-
grate information and prompt them to see the interconnected-
ness of topics and ideas.
Role of Instructor (JRC)
As the instructor, I played two roles in introducing external
representations into this introductory chemistry course. The
first involves my use of sketches or diagrams during lecture and
discussion to provide new ways to present, analyze and inte-
grate information and concepts. An example of this type of
representation is shown in Figure 1 and is related to the strategy
used to perform unit conversions. This diagram, coupled with a
few practice problems, was used to introduce the mechanics of
solving these types of problems and the steps common to most
conversions (one unit is converted to another unit, usually with
one or more intermediate steps using conversion factors). Fig-
ure 2 shows another representation concerning the naming and
properties of carboxylic acids. A textbook typically presents the
rules of carboxylic acid nomenclature in text form and physical
property information (such as boiling point and water solubility)
in tabular form. The diagram in Figure 2 was constructed to
integrate these important areas and supplement the textbook
and course notes on nomenclature and properties. The purpose
of this diagram was to present some essential information on
carboxylic acids in a more visual form, although some text is
used to make key points.
It is likely that students will draw more educational value
from constructing their own diagrams compared to just using
ones supplied by an instructor (Gobert & Clement, 1999; Hall
et al., 1997; Stranger-Hall et al., 2011). Therefore, the second
role I played was mentoring students how to create their own
diagrams. Constructing useful diagrams is not easy for most
students and incorporating them in lecture or class discussions
may not be enough to prompt students to make their own. Class
time can be used for students to practice making various exter-
nal representations. One approach was to have a class art show
where student groups were tasked with making diagrams that
illustrate how to solve a particular problem, analyze concepts or
An instructor-generated diagram related to unit
An instructor-generated diagram that integrates various topics related
to carboxylic acids.
dissect molecules (Figure 3). Another approach I used was to
work one-on-one with students during office visits. These are
typically the students that need help and can benefit most from
a fresh approach to solving problems, organizing information
and learning concepts through representations.
Student External Representations (BWJ)
In courses outside the science s, I was alway s able to combine
my creativity and right-brain aptitudes with more traditional
methods (rewriting notes, listening to audio recordings of lec-
tures, etc.) to maximize my learning. However, when I started
in the Introductory Chemistry course, I was not sure how to use
my creative skills to further my learning. I took copious lecture
notes, read the textbook and worked the problems at the end of
the chapters; however, it was difficult to see how various parts
of the chapters fit together and the material seemed complex,
foreign and intimidating. This changed when the instructor
introduced the concept of creating diagrams to aid in integrat-
ing material and solving problems. This allowed me to tap into
my natural disposition of working though problems creatively
and visually and I was able to process and retain course infor-
mation much more readily and effectively. As a result, I now
think more visually when learning science and solving prob-
lems and utilize more creative learning methods in courses
within my nursing program.
The external representation in Figure 4 was created in order
to visualize and help retain the process of two fundamental
tasks in chemistry: 1) define and calculate the molecular weight
of a molecule from the periodic table and 2) calculate the mass
(in grams) of a molecule (from moles) using a conversion factor.
This external representation also helped me maintain the correct
J. R. COX ET AL. 463
A student-generated poster used in a chemistry art show. Posters of this
type were generated by student groups to highlight important aspects of
chemistry and to demonstrate the different types of diagrams that can
be created by students and student groups.
A student-generated diagram related to molecular weight and mole-to-
units (amu, grams, and moles) throughout the problem by using
color coding. When working problems related to molecular
weight and the conversion of moles to grams, I was able to
refer back to this picture in my mind, linking the periodic table,
molecular weight, and the conversion factor, like a map.
The external representation in Figure 5 was created in order
to visualize and retain the Gas Laws by providing the following:
1) a clear, visual picture of how the laws of Gay-Lussac, Boyle,
and Charles, are integrated to form the Combined Gas Law and
2) an understanding of how the Combined Gas Law, Avo-
gadro’s Law and the gas constant combine to form the Ideal
Gas Law. Prior to drawing this external representation, I did not
fully appreciate the interconnectedness of the gas laws. They
initially appeared to me as separate laws I would be required to
memorize from the textbook. It was not until creating this ex-
ternal representation that I was able to fully understand how
each law contributes to the overall behavior of gases under
External representations can also be used to analyze ques-
tions and problems missed on quizzes or examinations. Many
students do not spend enough time investigating the reasons
why they missed a particular problem. As a result, they do not
take advantage of excellent opportunities to identify weak-
A student-generated diagram that shows the relationship
between the various gas laws.
nesses in logic, content knowledge and problem-solving strate-
gies. Creating diagrams can be an effective way to reexamine
material and use assessments as a tool to promote learning and
not just for measuring learning.
Figure 6 shows a diagram created to analyze a problem
missed on an examination. I made this representation with text
and structures in order to construct a problem-solving process
that allowed me to reverse any inaccuracies or oversights by
crafting a detailed pathway to victory (correct answer) through
visualization. This simultaneously created a visual memory
with the capability to maintain a lasting impression of the fac-
tors associated with water solubility. The visual and integrative
nature of Figure 6 does not make the question any less complex,
just more discernable and accessible. Therefore, constructing
these types of diagrams allows me to learn from my mistakes
and provides a process to better analyze future questions. Ulti-
mately, it is less about getting questions correct on examina-
tions and more about learning the concepts associated with my
courses and developing habits of the mind that allow me to
think criticall y a n d cre atively.
Students are often presented information, concepts and prob-
lems in various forms, but are rarely taught how to organize and
integrate material in a way that supports learning (deliberate
practice). Students must be able to construct a conceptual
framework of ideas and facts and organize information in way
that it can be easily recalled and applied (NRC, 2000). This
manuscript has addressed many types of external representa-
tions and demonstrated how they can be used to organize and
integrate information. Also, the roles that instructors and stu-
dents can play in generating representations have been de-
scribed. Overall, the process of incorporating external repre-
sentations into a course can be summarized as Initiation-Op-
portunity-Visibility. Typi cally, students have to be prompted to
draw diagrams and instructors can initiate the proc ess by using
external representations during class and helping students make
their own diagrams. This can provide an opportunity for stu-
dents to use right-brain aptitudes to help them learn material
such as introductory chemistry. Also, it provides an opportunity
for some students to be introduced to design and symphony,
two of the senses described by Pink as important in the con-
ceptual age (Pink, 2005). Often, students who do not succeed in
courses such as introductory chemistry fail to grasp or visualize
J. R. COX ET AL.
A student-generated diagram used to analyze a question missed on an
the interconnectedness of complex ideas and problem variables.
External representations and visual thinking have the potential
to make complex ideas and problems more accessible and visi-
ble to a broad range of students who struggle in the areas of
information organization and synthesis, pattern recognition or
the ability to identify or focus on the hierarchical nature of
These concepts are related Dan Roam’s approach to solving
business problems and selling ideas with pictures (Roam, 2008).
Roam suggests that the real value of visual thinking is to make
complex issues understandable by making them visible, not
simpler. This has direct and significant consequences in teach-
ing at all levels. Instructors have to teach students to appreciate
and analyze the complexities of science, even in introductory
courses. Although simplification has its place in teaching and
learning, the principles of scientific disciplines can only be
broken down so far and the beauty and essence of many sys-
tems lies in their complexity.
We thank the Department of Chemistry and the College of
Science, Engineering and Technology at Murray State Univer-
sity for support of this project. The authors also acknowledge a
Hewlett-Packard Technology for Teaching Grant and a Micro-
soft Tablet PC Technology, Curriculum, and Higher Education
Grant for support of tablet-related instructional activities.
Coil, D., Wenderoth, M. P., Cunningham, M., & Dirks, C. (2010).
Teaching the process of science: Faculty perceptions and an effective
methodology. CBE-Life Sciences Education, 9, 524-535.
Cooper, M. M., & Sandi-Urena, S. (2009). Design and validation of an
instrument to assess metacognitive skillfulness in chemistry problem
solving. Journal of Chemical Education, 86, 240-245.
Derting, T. D., & Cox, J. R. (2008). Using a tablet PC to enhance stu-
dent engagement and learning in an introductory organic chemistry
course. Journal of Chem ic al Education, 85, 1638-1643.
Derting, T. L., & Ebert-May, D. (2010). Learner-centered inquiry in
undergraduate biology: Positive relationships with long-term student
achievement. CBE—Life Sciences Education, 9, 462-472.
Deslauriers, L., Schelew, E., & Wieman, C. (2011). Improved learning
in a large-enrollment physics class. Science, 332, 862-864.
Gilbert, J. K. (2005). Visualization: A metacognitive skill in science
and sience education. In J. K. Gilbert (Ed.), Visualization in Science
Education (Vol. 1, pp . 9-27). Dordrecht: Springer.
Gobert, J. D., & Clement, J. J. (1999). Effects of student-generated
diagrams versus student-generated summaries on conceptual under-
standing of casual and dynamic knowledge in plate tectonics. Jour-
nal of Research in Science T eaching, 36, 39-53.
Haak, D., HilleRisLambers, J., Pitre, E., & Freeman, S. (2011). In-
creased structure and active learning reduce the achievement gap in
introductory biology. Science, 332, 1213-1216.
Hall, V. C., Bailey, J., & Tillman, C. (1997). Can student-generated
illustrations be worth ten thousand words? Journal of Educational
Psychology, 89, 677-681. doi:10.1037/0022-06126.96.36.1997
Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes)
worth ten thousand words. Cognitive Science, 11, 65-99.
Lee, W. T., & Jabot, M. E. (2011). Incorporating active learning tech-
niques into a genetics class. Journal of College Science Teaching, 40,
Mathewson, J. H. (1999). Visual-spatial thinking: An aspect of science
overlooked by educato rs. Science Education, 83, 33-54.
Mayer, R. E., & Gallini, J. K. (1990). When is an illustration worth ten
thousand words? Journal of Educational Ps ych ol ogy , 82, 715-726.
Mazur, E. (2009). Farewell, lecture? Scienc e, 323, 50-51.
Milne, A. J. (2007). Entering the interaction age today: Implementing a
future vision for campus learning spaces. Educause Review, 42,
National Research Council (2000). How people learn: Brain, mind,
experience, and school. In Committee on Developments in the Sci-
ence of Learning, J. D. Bransford, A. L. Brown, & R. R. Cocking
(Eds.) with additional material from th e Committee on Learning Re-
search and Educational Practice, M. S. Donovan, J. D. Bransford, &
J. W. Pellegrino (Eds.), Commission on behavioral and social sci-
ences and education, National Research Council. Washington, DC:
The National Academy Press.
Pink, D. H. (2005). A whole new mind: Moving from the information
age to the conceptual age. New York: Riverhead.
Ramadas, J. (2009). Visual and spatial modes in science learning. In-
ternational Journal o f Science Education, 31, 301-318.
Rickey, D., & Stacy, A. M. (2000). The role of metacognition in learn-
ing chemistry. Journal of Chemical Education, 77, 915-920.
Roam, D. (2008). The back of the napkin: Solving problems and selling
ideas with pictures. New York: Penguin.
Schönborn, K. J., & Anderson, T. R. (2006). The importance of visual
literacy in the education of biochemists. Biochemistry and Molecular
Biology Education, 34, 94-102.
Stranger-Hall, K. F., Shockley, F. W., & Wilson, R. E. (2011). Teach-
ing students how to study: A workshop on information processing
and self-testing helps students learn. CBE-Life Sciences Education,
10, 187-198. doi:10.1187/cbe.10-11-0142
Suwa, M., & Tversky, B. (2002). External representations contribute to
the dynamic construction of ideas. Diagrammatic Representation
and Inference, 2317, 149-160. doi:10.1007/3-540-46037-3_33
Tsai, C.-C. (2001). A review and discussion of epistemological com-
mitments, metacognition, and critical thinking with suggestions on
their enhancements in internet-assisted classrooms. Journal of Chemi-
cal Education, 78, 970-974. doi:10.1021/ed078p970
J. R. COX ET AL. 465
Tversky, B. (2002). What do sketches say about thinking? AAAI Spring
Symposium on Sketch Un d e r s ta n d i ng, Menlo Park, CA. Weimer, M. E. (2002). Learner-centered teaching. Five key changes to
practice. San Francisco, CA: Jossey-Bass.